## Complex Numbers

In my blog on numbers and operators we introduced complex numbers that involved i. I said i was an operator, not a number. As an operator it rotated a numerical scale through 90 degrees. We said that applying the operation twice as in i 2 was a rotation of the scale through 180 degrees thereby reversing the scale and equivalent to a minus (-) operation.

A complex number delivers a point on a flat 2 dimensional plane. It can also be regarded as a vector to that point from point 0, 0 in the coordinate system. Let’s say we have a point 6 + i 3 at which we construct an object. Out object points are relative to this point and we construct our object on what is a local copy of our global coordinate system but crossing at this point as shown in red.

Suppose we remove the constructed object from this location and rebuild it at say a point – 2 + i 7. It would be as if we had moved our local red coordinate system -8 horizontally and + i 4 vertically to that new point and constructed our object on that coordinate system there. We call this – 8 + i 4 a translation and it contains the elements we have to ad to the original point elements to to get the elements of our new point.

After translating the local coordinate system we use it rebuild our object at this new location. Alternatively, we might rebuild the object at points progressing along the blue line. By making the points close enough and the time intervals between constructions small enough our repeated rebuilding of the object we would see as its linear motion

If we multiply (6 + i 3) by (a + i 0) using the FOIL (first, outer, inner, last) method and then simplify we get a(6 + i 3i). We are effectively scaling the vector length from 0,0 to our point 6 + i 3 by whatever a is.

If, on the other hand, we multiply (6 + i 3) by (0 + i 1) we get 0 + i 6 + 0 + i2 3 = -3 + i 6 (as i2 = – (minus). It is as if the new point has been created by rotating its vector around the global 0,0 point some 90 degrees anti clockwise. In our above diagram we show this 90 degree rotation of 6 + i 3 in green. Multiplying any point, for example the points on our object or the points that make up the lines of its local coordinate system, by (0 + i 1) will do likewise. It is as if we have taken the local coordinate system at 6 + i 3, translated it to point -3 + i 6, rotated that system by 90 degrees anti clockwise and then rebuilt our object on that rotated system. If we multiply by (0 + i a) we still rotate by 90 degrees but scale all points multiplied by a.

If we multiply (6 + i 3) by (3 – i 2) as an example we get 18 ( a scaled up scalar), we get – i 12 ( a scaled up vertically down (- i) component), we get + i 9 ( a scaled up vertical (i) component) and finally we get – i2 6 (equal to a positive scalar 6). The whole simplifies to the vector or point 24 – i 3.

The complex conjugate of a complex number z = x + i y is defined as z* = x – i y. So the product of a complex number and its conjugate z z* which is also known as the quadrance of z Q(z)= (x + i y)(x – i y) = x2 + y2 which is the square of the vector’s length or the square of its conjugate’s length.

Here we show how the operation x i can act on other operators like plus and minus to change a linear direction. But such an operator only has effect when applied to numbers. So we also show how on a unit circle it can change + 1 through i1, -1 and -i 1 before returnng to +1. However it is essential to realise that x i does not just operate on these 4 select points on the unit circle. It can operate on any vector, including any unit length vector ending at a point on the circle as represented by a unit length complex number. It will rotate such vectors clockwise 90 degrees around an imaginary axis coming toward us out of the centre of the circle .

The Irish mathematician Sir William Rowan Hamilton spent much of his life truing to apply complex numbers to the triple numbers of 3 dimensions. In 1843 whist walking over what is now called the Broom Bridge in Dublin he had a flash of inspiration that involved basic rules for multiplication of quadruple numbers, later called quaternions. He carved into the stone of the bridge i2 = j2 = k2 = ijk = -1. I wonder would he have been better leaving out the 1 but retaining the minus ( a reverse operation).

## Matrices

A matrix is a rectangular array of numbers called elements. We can use matrices to solve linear algebra equations but more commonly they are used to store and manipulate changes made to objects in virtual space as in animated films and computer games graphics.

Matrix Addition and Subtraction can only be done when the number of rows in each matrix is the same and when the number of columns is the same. You simply add or subtract each like position value to get a third same shaped matrix .

Matrix Scalar Multiplication involves multiplying each matrix element by the scalar.

Matrix by Matrix Multiplication can only be done if the number of columns in Matrix A is the same as the number of rows in Matrix B. The resulting matrix has rows equal to the columns in A and columns equal to the columns in B.  It is important to realise that A x B is not the same as B x A, and may not be possible because of the rule. More on matrix multiplication later.

Transposition of a Matrix AT simply involves writing the column data in row format.

Types of Matrix
A vector matrix is usually a single row or column.
A null matrix is one having all elements equal to zero.
A diagonal matrix has numbers top left to bottom right and zero’s elsewhere.
A unit matrix is a diagonal matrix with 1 top left to bottom right.
A symmetric matrix is a square matrix with symmetry about the diagonal.
A skew symmetric matrixis also square. Its diagonal elements are zero and the symmetry about it involves opposite signs.
An orthogonal matrix  is square: multiplied by its transpose delivers a unit matrix.

The Inverse of a Square Matrix is written as A-1 When Matrix A is multiplied by its inverse A-1 a unit matrix is the result. We find the inverse of a matrix by dividing its adjoint    adj(A) by its determinant  |A|   (See below)

Matrix Determinant |A| is a single number. For a 2×2 matrix |A| is simply the difference in cross product that is the product of the lead diagonal numbers minus the product of the non leading diagonal numbers. For the 3 x 3 matrix shown the determinant is done either horizontally or vertically. Both give the same result.
a(ei-fh) –b(di-fg) + c(dh-eg)    or   a(ei –fh)-d(bi-ch) +c(dh-eg)

Note the second term in each of these calculations is negative. In reality the cross product difference associated with any element is that of the 2 x 2 elements below it and right of it and applied in cyclic fashion so that the top is below the bottom and the left side follows the right (see diagram). The second terms are then + b(fg-di)  and +d(hc –ib) which equate to the second terms shown above. The reason we make terms negative is so that we do the cross products in an as seen manner. Each element of a matrix has a cross product difference termed a Minor of that element. The minor for h is cd – af, that for i is ae – bd.

The Cofactor of a matrix element is produced by replacing each element in the matrix with the Minor product difference associated with it. The cofactor of the example 3×3 matrix on the right is shown below it on the right.

Applying the cross product differences cyclically as described above avoids minus terms otherwise if calculating minors as seen then minus terms apply at positions containing -3, -2, 1 and 5

Adjoint Matrix : Every square matrix A has an adjoint matrix adj(A). It is obtained by changing each element in the matrix to its cofactor as described above and then transposing that matrix.

Example Solving Linear Equations : Given the following three equations, solve for x, y and z   x + y + z = 6 ,  2x +3y +4z = 20 4x + 2y +3z = 17

The above equations iare shown in the three matrices left. Consider them as being A, U and R where U is the unknown matrix containing x, y and z and R the results matrix.  To solve this matrix equation  A x U = R we multiply both sides of it by the inverse of A  (A-1)  so that U = R x A-1.

The inverse of A (A-1) is its Adjunct adj(A) divided by its Determinant |A| whilst  adj(A) is the Transpose of the Cofactor of A. Left we have the cofactor and right we see adj(A) being multiplied by R to give us a 3, 6, 9 matrix.

However we are not done yet because we haven’t divided by the Determinant. We calculate the determinant as under
|A| = 1(3 x 3 – 4 x 2) + 1(4 x 4 – 2×3) + 1(2 x 2 –3×4) = 1 +10 -8 = 3.

We now divide the 3, 6, 9 matrix by 3 to get the matrix R = (1,2,3) and thereby solve our three equations with the three unknowns.  Our solution is   x = 1,  y = 2 and z = 3

Transformations in 3D. We may view any 3 dimensional object in virtual space as constructed from many joined up points. Each object or part object can have its own coordinate system and each object point is referenced by that coordinate system as linked perhaps to some parent coordinate system. Everything in view and the camera view directions and locations are part of a global coordinate system. The impression of motion is created by repetitively calculating the revised locations of points changed by transform changes and repetitively rebuilding the scene.

Transformations are changes made to an object. We may translate (relocate) an object, change its orientation relative to other objects, reflect it so as to make it appear as if viewed in a mirror, change its size or distort it. All can be done by matrices.

For example a simple two dimensional object like a triangle would be constructed from 3 points. We could then apply a colour to that shape giving it appearance.

In our diagram each triangle point in the triangle on the right is multiplied by the same matrix. The three new points that result are used to construct the triangle on the left.

In a graphics application the triangle would now appear as if rotated through 90 degrees counter clockwise about the coordinate origin. If we had wanted that rotation to appear as a motion we would have multiplied the points over time by many intermediate matrices and rebuilt the triangle many times on its way to that final location

How did we do this multiplication and how did we do the multiplication of the earlier 3 x 3 matrix with a 3 (row) x 1(column) matrix. The number we put in row n column m of the output matrix is obtained by multiplying each number in row n by its like position numbers in column m and summing the results . Our 6 in the 2nd row of the earlier output 3, 6, 9 column matrix was the result of multiplying 10 x 6 , -1 x 20 and -2 x 17 and adding them

In 3D scenes the matrices used are generally of the 4 row x 4 column type. As such they are capable of holding all transformation data. The elements m, n and o in the 4 x 4 matrix shown right are the x, y and z translations that any point, to which this matrix is applied, will undergo. Most matrixces are applied to objects that have no scale, shear or squashing and in such cases elements d, h, l and p will have values 0, 0, 0 and 1.

The rotation elements are there in the first 3 columns of the first 3 rows. Elements a,b, c describe how points in the x, y plane will change; e,f, g describe how points in the y,z plane change and i, j, k how points in the z,x plane change. It means, and ignoring any translations, the point 1, 0, 0 will move to a,b, c ; the point 0, 1, 0 will move to e, f, g. Apply the rotation and then add in the m, n, o value x, y, z translations to each point.

It is important to realise that

In computer graphics involving 3d scenes the programmer’s program determines the transform matrix that is to be used and the computer does all the hard work of determining all the new object points and thereby creating the changed or changing image. Action matrices are generally of the four by four type as illustrated.

## Dad’s War: Breakout to V.E. Day

Come 25th August 1944 and Paris had been liberated by French and US Forces and the British and Canadians were on the move again. The Canadians took Rouen on the Seine 29th August and the British took Amiens on the Somme 31st August. Some of the American troops landing in Normandy had moving South intent on joining French and other forces that had attacked the South East Coast and were moving inland. The Germans were evacuating from the Bay of Biscay and the Spanish border. Soon French and American forces would meet taking Bordeaux and not long after Montelimar.

On 1st September General Omar Bradley was put in command of a new 12th Army Group with plans to move East over the Moselle river pushing onto the German Western Front. Remember the Germans were also fighting the Russians on the Eastern Front. In the following two weeks they would cross the Meuse and the Moselle, take Liege in Belgium, occupy Luxembourg and cross the Belgium – German border at Aachen.

The British 21st Army now comprised the British 2nd Army and the 1st Canadian Army.
The Canadian Army were given the role of freeing the coastal ports and we learn more about that in a section below. Their armoured brigades (tanks) were not needed for these tasks and they crossed the Somme, took St. Omer, then crossed the Franco-Belgian border and overcame enemy forces at Ypres and Passchendaele before reaching Roulers in Belgium. The British 2nd Army were also on the move north into Belgium taking Brussels, Antwerp and Ghent. They crossed the Albert Canal and so moved closer to the borders of the Netherlands and Germany.

The map above shows lines of advances. In the month to the 14th of September the allies front line had moved from position 2 to position 3, close to the borders of the Netherlands and Germany. By comparison it had taken  over 8 weeks fom D-Day to get to position 2.

An Account of 4AGRA Involvement

This account concerns the 4AGRA 53rd medium regiment but gives us an insight into the role of the artillery. It says :-
“The Race To The Seine was on. The Regiment started its move early on the 17th under the command of 7th Armoured Division whose objective was the high ground east of Lisieux ( Due South of Le Havre and Due East of Falaise) This was a particularly exciting time for the Regiment as it exposed the troops to a new type of warfare supporting the fast-moving armoured units.
Although on the first day the guns were constantly moving forward to fire in support of the various armoured elements of 7th Armoured Division in reality they did not travel very far. It was another two days before they started to really get going – in fact on the 19th they liberated the village of Livarot on their way to the outskirts of Lisieux. The guns were held up by skilful rearguard action for another 48 hours before some fast moving on the 23rd and some lively shooting at the Seine crossing.
The battle ran away from them on the morning of 29 August. Positioned near Routot (South of the Seine West of Rouen) the Regiment paused while the armour raced across north-eastern France towards Brussels”

The 1st Canadian Army and Clearing the Coastal Ports.

The Canadian army had advanced over the Seine when on the 25th August it was assigned the task of clearing the coastal areas and opening the English Channel ports for supplies vital to the Allied advance. Taking control of the coastal defences would also stop the German rockets being fired at Southern England. It would be a difficult task because the Germans had been expecting an invasion, but not knowing where this would take place, they had prepared all the ports with fortifications and strong defences. With these new orders British 1 Corps peeled off for the port of Le Havre, whilst the Canadian 2nd Corps headed for the port of Dieppe.

Dieppe: Operation Fusilade 1/9/1944: The port was abandoned and the Canadian 2nd Division were welcomed into Dieppe. The first ship was able to deliver there on 6/9/44 after which a train departed for Brussels on the 9th of September.The last V-1 Rocket was fired from Dieppe on 1/9/44.
Dunkirk: 5/9/44 to May 45: The 2nd Canadian division were having trouble clearing out the approaches to Dunkirk and some units suffered very heavy casualties. Dunkirk was placed under Siege, during which on 14/10/1944 a truce was called to allow 18,000 Civilians and wounded belonging to both sides out. Surrender did not occur until the end of the war in the May of 1945.
Le Havre: 10/9/44 to 12/9/44: The British 1st Corps had arrived at the heavily defended Le Havre. It had a series of strong natural defences as bodies of water completely prevented access from the south, east and west. The north side of the port was heavily fortified, with a 7 metre deep by 3 metre wide anti-tank ditch. There were pillboxes with anti-tank and machine guns and 1,500 mines. Defenders were said to number about 8,000, of which 4,000 were artillery troops.
The port was captured with few military casualties. Artillery and air assaults had destroyed 350 ships and 18 kilometres of docks. They had made 80,000 people homeless and 15,000 buildings were in ruins. Le Havre was not operational until October 44
Boulogne 17/9/44 to 22/9/44 was defended by three Forts. The operation was delayed by supply difficulties and by the need to complete operations at Le Havre before necessary armour and artillery could become available. About 8,000 civilians were expelled from the Port by the Occupiers. They provided useful information for the Canadian attackers. Continued bombing and a creeping artillery barrages were used to dishearten the garrison and obtain the surrender of the 2nd of three forts. Because of sunken ships and mines the port was not open until late October.
Callais and Cap-Griz-Nez 25/9/44 to 30/9/44  Although it had now been decided that opening Antwerp for supplies would have priority heavy batteries at Cap-Griz-Nez were threatening the sea approach to Boulogne so both ports were to be taken. The pattern was to be the same, sealing off the, softening up the defenders using Artillery, Aerial and Naval attacks and then perform attacks with support from rolling Infantry Barrages.
Attacks started on 25th September at Callais. Some early attempts by groups of Germans to surrender resulted in them being shot down by their own side. On the 29th of September a truce was called so that 20,000 civilians could be released. Many of the German drivers who brought the civilians half way to Canadian transport surrendered. Callais surrendered 30/9/44 but because of damage the port was not open until late November.
Cap-Griz-Nez had two forts with very heavy guns defending them. It received heavy bombing, including that from two large guns at Dover named Winnie and Pooh. A number of infantry attacks were made. On the 29th September at 06.35 the Artillery started a 10 minute Creeping Barrage with the infantry following it. The defenders were under real pressure and by 10.30 they had surrendered.

4AGRA Accounts of the taking of the Ports

One says that at Le Havre 4AGRA were deployed in near full view of the enemy, putting the port under seige, with parleys, white flags and artillery duels before the port fell on the 13th September
Another account says that the 53rd regiment left the main battle front to support the 49th Division’s attack on the coastal town of Le Havre. It describes bombing by Lancasters from Bomber Command during daylight and eight batteries of medium guns firing to suppress the AA flak – each working with an Air O.P. (Observation Post) watching small sectors of the defences with an overprinted street map.
It continues by saying that on the 13th Septembe the guns moved back some 30 miles to Autretot for a week’s rest before heading towards staging near Dieppe and on to Deynze on the 22nd where their tractors were borrowed by the Royal Artillery Service Corps, who would normally be supplying food, water, fuel, and general domestic stores, but were helping to ferry ammunition across Belgium.”

The taking of Antwerp and Alternative Plans

On 4 September 1944, 30 Corps of the British 2nd Army reached Antwerp and, with the help of the Belgian resistance, the city was secured with its port facilities intact. However the port was useless because both sides of the 80km long Scheldt estuary, which connects the North Sea to Antwerp, were In German hands, Many of the German’s holding it were from the Falaise encounter,

General Guy Simmonds, Crerar’s 2nd in command wanted an attack on the Scheldt and had created a plan. However there was a rift between Crerar and Montgomery who had a plan for a thrust to the north using Paratroopers, including Americans and who had put this plan to Eisenhower. Because of American involvement Eisenhower was delaying his decision. In the circumstances, Crerar chose not to go against Monty and never put Simmonds plan to him. Delays gave the German forces the opportunity to build up their defence of the Scheldt. Montgomery’s plan was agreed and code named “market garden”.

Operation Market Garden

On 17th September operation “market garden” used US and British paratroopers in an attempt to secure a land route into the Netherlands. It was to involve advance taking of many bridges over canals and rivers allowing ground troops to move forward at speed.

The final crossings were to be over the two rivers that the Rhine becomes near the German border. The Waal, which takes 2/3rds of the Rhines waters was to be crossed at Nijmegen and the Lower Rhine, north of it was to be crossed at Arnhem.

The U. S. 101st division were to take and hold 2 river and 2 canal crossings  The U.S. 82nd were to take and hold  crossings over the Maas and Waal at Nijmegen and the British 1st  Airborne division the crossing over the Lower Rhine at Arnhem. The securing of the bridges was a success

The ground troops of British 30 Corps supported by 8th and 12 Corps passed quickly over the secured canals and Maas river crossings. However after advancing and securing the Waal bridge crossing at Nijmegen on 20th September they were held up. The result was that the British 1st Airborne paratroopers at  Arnhem on the Rhine were not reached in time. They were encircled and lost 7,000 of their 9,200 men. The film “A Bridge too Far” is about this action.

Canadian 1st Army Battle of the Scheldt

History suggests that the Scheldt Estuary and its German forces might have been easily taken had they been attacked early September after Antwerp was taken. With the partial failure of “Market Garden” and the need to alleviate the problem of supplies still coming from Normandy, Monty was now instructed to make the opening of the port of Antwerp a priority.

The Canadian Army, now under the temporary command of Guy Simmonds because Harry Crerar was ill and had been evacuated,  was given orders to cease activities at other ports and concentrate on opening this port.

On 3rd October RAF bomber command burst the Walcheren Island Dykes in three places at Westkapelle. The sea rushed in forcing the Germans to higher ground but at the cost of civilian life. The land battle could begin.

On 6th October attacks were made on the Breskens pocket, the area north of the Leopold Canal. Canadian Wasp Carrier Flame Throwers supported a move across the canal and at the same time amphibious craft made an attack across the inlet west of Temeuzen. Precarious footholds were established which, despite strong counter attacks were held. The positions were added to and soon Armoured Brigades could cross the inlet. The 3rd Canadian Division then fought actions to clear German troops from a number of towns and a coastal fort in the pocket.

Clearing the area to the north of Antwerp in readiness for an assault on South Beveland was put in hand. But progress over booby trapped, mined and flooded land in driving rain was difficult. The Canadians on 13th October, a day known to them as Black Friday lost nearly the whole of their Black Watch Brigade. A more successful 2nd attempt secured  entry to this South Beveland Peninsular on the 24th October but mines and mud slowed progress along it  and the canal across it was heavily defended. An amphibious attack across the Scheldt out flanked this defence, leading to its collapse and the clearing of South Beveland.

The Allies finally cleared all of the port areas by 8 November. It had been at a cost of 12,873 Allied casualties (killed, wounded, or missing), half of them Canadians. It was a further three weeks before the first ship carrying allied supplies could unload in Antwerp (29 November 1944), the delay being due to the necessity to de-mine the harbours.

British 2nd Army and the Drive to the Maas River

While the above battle was in progress Montgomery, recognising the need to protect the Allied gains against German Counter attacks had tasked the British 2nd Army to take the northern area up to the Maas river. 4AGRA were involved in these clearances.
4AGRA supported the early movements of the Canadian 1st Army  over the Turnhout Canal in preparation for their assault on the Sheldt. One report has the 233rd battery of dad’s 68th Medium Regiment positioned at Loon Op Zand, a short distance north of Tilburg and firing  in support of forward infantry and armour.

For a period of about 2 months 4AGRA were supporting attacks, by elements of both the Canadian 1st Army and British 2nd army on both sides of the Nijmengen corridor in wet and muddy conditions. If they were not supporting infantry divisions, as for example the 49th West Riding and 4th Canadian they were assisting the 1st Polish Armoured in their tank assaults.

One of the very few things I remember my dad telling me about the war was of the hold up at a river, named what to me sounded like “Mars” but which was clearly his reference to the Maas river. These established positions south of the Maas river were held and relatively stable for some time. Parts of the Southern bank of the Maas were indeed still the front line at the end of March 1945. I know not whether dad’s regiment was one of them but, at the end of the first week in December, some of the 4AGRA regiments, taking advantage of the hold up had a period of rest from the gunnery, withdrawing to the Brussels area for maintenance and refitting of their guns.

Battle of the Bulge : A Battle in the Ardennes

The Allied front line had still not reached Arnhem, when, on the 16th December the American lines to the south were broken by the German Panzers in what came to be known as the battle of the bulge. Hitler had massed numerous divisions for an attack through the thinly held Ardennes Forest area of southern Belgium and Luxembourg.

The plan was for the forces to cross the Meuse River and swing northwest some 60 miles to envelop the port of Antwerp. The plan was designed to sever the already stretched allied supply lines in the north and to encircle and destroy a third of the Allies’ ground forces. Hitler believed that the offensive could smash the Allied coalition, or at least greatly cripple its ground combat capabilities, leaving him free to focus on the Russians at his back door.

The map to the right shows allied positions, the front line, the German plan and the extent of the German success.

Eisenhower placed the American 1st Army and 9th Army, north of the bulge under the command of Montgomery, who already commanded the 21st Army Group comprising the British 2nd and Canadian 1st Armies The armies north and south of the bulge then attacked the flanks of the German breakthrough.

Some 15,000 air sorties were flown by the Allies in 4 days. These together with the German problem of supplying their tanks with fuel meant that by January of 1945 the “bulge” had failed. This battle of the bulge in the Ardennes area may have been an initial German success but its defeat led to the allies crossing the fortified Seigfied line after retreating Germans who were ordered by Hitler to destroy the Rhine Bridges.

Eisenhower now restored the American 1st Army putting it back under the control of the American Army Group commander Omar Bradley but leaving the American 9th army and its commander General William Simpson in the 21st Army Group under Montgomery’s control.

4AGRA Regiments involved in the Ardennes

Some 4AGRA regiments had retired to the Brussels area in December of 44 but their rest was cut short  when on the 20th / 21st  some, including the 53rd medium, got orders to move in support of British 30 Corps who were to take up positions along the Meuse from Namur to Givet.  29th Armoured Brigade would be there in support of  the line and the artillery regiments were to support them.

The 68th Medium Royal Artillery in common with others in 4 AGRA, with gun positions facing the German troops over the Maas River got urgent instructions to send half of their complement of guns down to the Bastogne area to assist in preventing further enemy penetration in Allied-held territory.

Enemy troops facing gun positions on the south of the River Maas had to be kept unaware of this movement and so missing guns were replaced by inflated true-to-size balloon rubber moulding of the original gun,with like colour and camouflage treatment. King-size thunderflash fireworks simulated their firing along with the remaining guns.

Whether dad’s gun was one of those removed in support of the Ardennes counter offensive I know not,. He certainly did speak of being held up at the Maas, so it may be that his gun was one of those that remained.

AGRA guns supporting the Ardennes fighting included their 52nd heavy regiment. They supported the allied counter attacks but always trying to to avoid the Americans advancing from the South West. The battles moved out of the range of the guns on the 12th January and after a few days they withdrew to their former battle stations in the Maas area and near Tilburg at  Loon-op-Zand.

Moving up to the Rhine – Action in the Reichwald Forest

Churchill, Roosevelt and Stalin met at Yalta on the Black Sea Coast on 4th February 45 to discuss and agree their plans for the offensive against and the subsequent occupation of Germany. Eisenhower  had asked his Generals to make plans to clear the area west of the Rhine River in Germany as far down as the German border with Austria and also South of the Maas and Waal rivers in the Netherlands. The armies involved would be the Canadian First Army, British Second Army, 4 American armies and a French army.

The northern borders of Germany with Holland were heavily defended with the best troops that were available to Germany, including a First Paratroop Army. The part of Gemany known as the Ruhr was the heart of its industry; any loss of Ruhr Plant and Equipment would be a serious loss to German Industry as a whole. Troops gaining access to the area between Roer river and Rhine river would pose a threat to this region and so be heavily opposed. Dams across the Roer river gave the German forces some advantage. Having control of the flow of its water meant they could flood the river and its surround area when Allied troop movements threatened.

Montgomery’s plan to push up toward the Rhine in this area was to employ a pincer movement. The British 2nd Army would continue fighting the Germans on the existing front line. The Canadian First Army, which at this stage had British 30 Corps under its command, would encircle the fighting Germans from the North. The American 9th Army, as part of 21st Army Group and under command of Montgomery, would similarly do so but from the South.

The action started with the bombing of the historic town of Kleve on the 7th February. Then on the 10th February the Canadian Army launched its troops  into the muddy flooded Reichwald Forest region near the Netherlands-German border. By the 23rd February they had only reached the position shown on the map. One reason for this was because the planned American 9th movement from the South had not been possible because the Roer had been flooded. Only after the 23rd Feb when conditions were improved could the pincer movements of operation “Veritable” from the North and operation “Grenade” from the South be effective.

The Battle of the Reichswald, near Kleve took place during late February, early March of 1945. It was between the Anglo-Canadian forces and 90,000 experienced and re-equipped German troops. Although the Anglo-Canadians’ had more equipment, armament, munitions and with nearly 200,000 men, more manpower, the ground conditions nullified many such advantages. The Anglo Canadians had about 23,000 casualties. About 50,000 German prisoners were taken.

American 9th Army troops had to manoeuvre through difficult conditions, caused by destructive Allied bombing and shelling. They often needed armoured bulldozers to clear the way for their armour to advance. Their army finally met up with the Canadian 2nd Army troops on 3 Mar, forcing the Germans to withdraw to positions around bridges on the Rhine and to the German Seigfried Line, a line of German Fortifications that was perhaps their best and heaviest defended line.

In an action slightly later than that shown on the above map and on the 8th of March the American First Army found the Ludendorf bridge at Remagen over the Rhine about to be blown. The bridge was blown and lifted but did not collapse due to the action of two Polish conscripts, who had tampered with fuses and the subsequent cutting of wires by Americans. A battle secured the bridge and allowed forces over it. However on the 14th March the bridge did collapse due to its continued use killing about 30 Engineers. This crossing of the Rhine had brought German forces to the area the area to restrict any further allied progress.

4AGRA in Support of this move up to the Rhine

4AGRA, usually attached to the British 1 Corps, were not the only artillery to be involved in the Northern moves toward the Rhine. The 2nd Canadian AGRA of the Canadian 2 Corps, the 5 AGRA usually attached to 30 Corps and the British 9AGRA, now also a part of the British 21st Army Group were involved. Some 184 guns were used, comprising a full range of artillery taken from each of those AGRA’s

4AGRA’s bombardment began at 05.00 am on the 8th of February and the guns fired their final rounds on the 10th February as the battle moved out of range. Each gun fired 229 rounds in the engagement. On the 11th some 4AGRA guns moved to St. Agatha to fire in support of the 51st Infantry who were having a difficult time in the Reichswald Forest. They then moved south east of Kleves to fire in support of the 3rd Canadian Division before further moves on the 28th Feb. to continue such support and in support of 11th Armoured. Finally they made moves on the 7th March to bombard the German bridge head at Wesel before taking some rest.

Preparing for the Rhine Crossing

The following map shows that by the 21st March some progress had been made from the position 5th March on the above map, partcularly to the South of Cologne. Allied forces were now in control over extensive distances on the West bank of the Rhine and the plans made for many coordinated Rhine crossings were now to be implemented on the 23rd and 24th of March.

Operation “Plunder” was the plan of the 21st Army Group and, like other plans that involved the American and French Armies to the South, it included the use of Paratroopers. The 21st Army code named its intended paratrooper operation “Varsity”. It would take place on the 24th and would be preceded in the late hours of the 23rd by the advance of ground forces over the Rhine, The use of paratroopers positioned beyond the German front lines would mean the Allies could attack the German Rhine defences on two fronts.

In preparation for the crossing allied forces bombed German airfields to reduce the capability of the Luftwaffe to interfere with the plans. The bombing had started on 21 Mar, and by 24 Mar the German air force were no longer able to put up much of a resistance against their Allied counterparts. Over 250,000 tons of supplies and 4000 artillery pieces were amassed on the west bank of the Rhine shielded by the largest smoke screen ever. Some 1 miillion soldiers were to participate in the actions.

The Allies Cross the Rhine

On the 22 Mar 1945, just before midnight, and contrary to orders from Omar Bradley,  the 5th Division of George Pattons 3rd Army crossed the Rhine, west of Mainz. Patton wanted an announcement that Americans had beaten the British in crossing the river. Opposition to the crossing was negligible and within 24 hours the entire US 5th Division had crossed the river.

It would not be so easy at other locations and to soften up the defending forces artillery bombing started on the 23rd of March in advance of the planned crossings.

British Second Army and Canadian First Army launched their assaults across the Rhine River north of the Ruhr River, late on the 23rd. They were attacking the north of the area known as the Ruhr. It was an area rich in the coal that supplied the German industies that backed their war effort and included the well known Krupp Steel Works at Essen. It was as a result heavily defended.

Throughout the night of 23 Mar and the next day, 80,000 British and Canadian troops crossed a 20-mile stretch of the river at 4 bridgeheads. One at Diersfordter, another at Wald and two over the road and rail bridges that crossed the River Issel at Hamminkeln. In the air 2,153 fighters supported these ground operations.

At the same time flying in tight formation, 540 American Dakota aircraft carried and dropped 12 parachute battalions, five British units from 6th Airborne Division, six US  units from 17th Airborne Division and one Canadian unit. The drops were closely followed by gliders packed with troops that also placed them beyond the German fromt line. This airborne operation was the largest of its kind during the entire war. It made use of 1,625 transports, 1,348 gliders, and 889 escort fighters to deliver over 22,000 airborne infantry into the intended target territory.  Weather for the drops and landings was perfect and almost everyone landed on their respective dropzones on higher ground overlooking the Rhine bridgeheads.

The Germans had been expecting an invasion of this area, and fighting in the drop zones was heavy. Some paratroopers who ended up in trees were cut down by German machine guns as they fought to free themselves. The 5th Parachute Brigade suffered particularly heavily from mortar fire exploding in the skies around them during the drop. There were also significant casualties from heavy anti-aircraft fire. By the end of the first day’s action 1,078 men of the British 6th Airborne Division had been either killed or wounded, with 50 aircraft and 11 gliders shot down. However the bulk of the airborne infantry had landed and were now participating in direct combat and attacking the German defenders from behind their lines.

On the 24th of March, Winston Churchill crossed the Rhine in an LCM (landing craft, mechanised), setting foot on the eastern bank of the Rhine. He later went as far as the railway bridge at Wesel in Montgomery’s staff car, a bridge that was still under enemy fire. It was a symbolic action to emphasise the crossing of the Rhine, something no foreign army had crossed in 140 years.
On this same day Hitler requested a counter attack against the American Rhine crossing at Oppenheim but was told no reserve forces were available for such an operation.

Meanwhile, the US Third Army captured Ludwigshafen and Speyer in Germany.  Not until the next day did the British army fully capture Wesel on the right bank of the Rhine
Eisenhower had been surprised, that the crossing of the Rhine north of the Ruhr had not been met with fiercer resistance and on the 25th in a face to face conversation Churchill had said to him “My dear General, the German is whipped. We’ve got him. He is all through.”

As US forces already occupied land east of the Rhine at Remagen, it provided an excellent place for Rhine crossings on the 25th. Further to the South, and on this same day, planned  drops of  American 13th Airborne troops were called off because the U.S. 7th Army having crossed the Rhine had met so little resistance.

The front line on the 28th March 1945 progress was as shown on the above map. Slightly later on the 1st April French First Army troops crossed the Rhine near Philippsburg .

4AGRA involvement in the Rhine Crossing Actions

Regiments began firing on the 23rd as part of the planned counter battery operations, continuing on the 24th with bombardments and various fire plans in support of the airborne assaults. Firing was constant day and night and with high accuracy, as directed in support of the assault troops by artillery command posts forward with the assault troops. On the 30th March the firing ceased

Rapid Advances after the Rhine Crossing

Montgomery, who was also Colonel Commandant of the Parachute Regiment, wanted 6th Airborne to head the advances on the other side of the Rhine and this they did on foot. In support of these airborne troops were the tanks of the Grenadier Guards and three regiments of artillery. In just seven days they marched and fought their way to the Baltic port of Wismar and joined up with the leading elements of Russian troops.

The Canadians and other British headed for Hamburg and the Baltic whist the American 9th performed a northern encircling of the German Army Group B in the Ruhr. With the defenses along the Rhine River falling apart, the heavily defended industrial Ruhr region was surrounded  depriving Germany of its war manufacturing capabilities. The allied armies were facing resistance that varied from none to fierce as they moved east.

Britain’s Prime Minister, Winston Churchill, urged Eisenhower to let the 21st Army Group leave the surrounded Ruhr and head for Berlin. In this he was supported by General George Patton who believed the 21st could reach Berlin in 3 days. However, Omar Bradley warned against the plan and Eisenhower ordered all armies to halt when they reached the Elbe and Mulde Rivers, perhaps for political reasons that would leave the Soviets to take Berlin.

Eisenhower’s requirements and instructions were for the 21st Army Group to move northeast toward Bremen and Hamburg. His instructions to the U.S. Ninth and First Armies were to hold the ground they had attained from Magdeburg through Leipzig to the western Czech border and his instructions to the 1st French, Seventh U.S. and Third U.S. armies were  to move into South Eastern Germany and Austria.

Meanwhile the British Eighth Army in Northern Italy were pushing the Germans back and against and over the borders of Yugoslavia, an action causing some friction with the Yugoslav forces there.

Death and Surrender

On the 15th of April British 11th Armoured liberated 60,000 at the Belsen Concentration Camp and on the 19th at Dachau US 42nd Infantry had SS Guards dig mass graves and bury high numbers of dead there.

On the 25th April all Germans left Finland. On the 27th of April Mussolini had been caught by Partisans trying to escape Italy and the following day he was killed. On the 30th, Hitler and Eva Braun committed suicide in his Fuhrer bunker in Berlin.

On the 1st of May German Forces in Italy surrendered making for about 1 million German and Austrian prisoners. Next day Berlin surrendered to the Soviets. On the 4th of May Montgomery took the unconditional surrender of about 1 million German forces in North West Germany, Denmark, Belgium and the Netherlands. He did this in his headquarters at Luneberg Heath, near Hamburg. On the 5th of May Bavarian forces surrendered and on the 6th Goering surrendered.

The German Armies were in disarray. Surrenders were being made on behalf of Army Groups, Corps, Divisions and by smaller groups. However German control and communications were such that many groups were fighting on which necessitated the Allies fighting on. Surrenders were accompanied by attempts to negotiate but each such attempt was accompanied by surrender unconditionally or else the Western allies would not take Germans across their lines leaving them to be dealt with by the Soviet forces.

On the 7th of May the German General Jodl unconditionally surrendered all German forces and that same day forces in Norway surrendered. On the 8th May Channel Island forces surrendered. All activities were set to cease at 23.01 Earopean Time and in the West that day 8th May, is celebrated as V.E. Day, Victory in Europe Day. The Soviets celebrate it 9th May. In reality fighting went on in isolated pockets for another fortnight.

The Final Gun Activities of 4AGRA

Whist some of 4AGRA regiments had retired to Brussels for a rest, others moved from the Tilburg Area to Till at the end of March, where they fired into woods north of Emmerich, on the Rhine and just North of Kleve and East of Nijmegen and the splitting of the Rhine into the Waal and Lower Rhine. After about 2 weeks at Till the artillery was able to cross the Rhine at Emmerich. From here some went to Duiven where they acted in support of 49th Divisions attack on Arnhem which was a success on the 17th of April, then on to Meppen where some stayed until the 28th moving to acted in support of 3rd Canadian Divisions attack on Leer and Detern to the North, that ended on the 4th May

The final gun positions for the 68th Mediums were in the German region of Meppen, a position they had moved to on about 17th April 1945. Though the battles and actions were now at an end and medium and heavy guns were no longer needed there was no question of troops leaving Germany as there was now much to be done

## Dad’s War D-Day to Breakout

D-Day was the planned day for the assault on the German forces in Normandy. The American Eisenhower was Supreme Commander whilst Montgomery would command all land forces as part of a 21st Army Group. The conditions needed to be right for the beach landings. They were an essential part of the sub operation “Neptune “. A window of opportunity arose and D-Day was set as the 6th of June 1944. Troops were aboard their ships as they put to sea on the 5th of June where the plans were revealed and put in motion.

Airborne Attacks

Starting before the beach landings and with drops from just after midnight and throughout the day airbourne troops both parachuted and glider landed at strategic locations on the assault area. The British 6th Airborne division landed about 8,500 in the area around Caen, whilst the American 82nd and 101st divisions landed about 17,000 men on the Cotentin peninsula, also known as Cherbourg Peninsula, to the west.

British objectives were to secure two Bridges, one over the Caen Canal known as Pegasus Bridge and one over the river Orne. They were to seize and destroy several other bridges that the enemy might use in a counter attack. A further objective was the German Melville Battery overlooking the Sword Beach area.

The specific missions of the two U.S. airborne divisions were to block approaches into the vicinity of the amphibious landing at Utah Beach, to capture causeway exits off the beaches, and to establish crossings over the Douve River at Carentan to assist U.S.troops in the merging of the two U.S. beachheads.

First to land were 6 British gliders towed by 6 Halifax Bombers carrying the airborne troops intent on securing the two bridges. After that pathfinder parachutists were dropped to radio mark three drop sites. The rest of the regiment followed in about air transporters including many towed gliders. Not all drops were as planned, which meant some troops did not rejoin their units until late in the day. In terms of the objectives set the drops were generally successful, with the bridges speedily captured and subsequently held. However the mission to take the Melville Battery failed as the attacking troops were hit by friendly fire.

Some 13,000 American paratroopers landed in the early hours of D-Day followed by nearly 4,000 daylight gliders. The parachute landings were not as well concentrated as the British landings. Because of the scattering, it was not until three days later that the German routes to the Utah Beach area were secured. Fortunately the scattered drops caused confusion and the Germans failed to exploit the situation. Over the following week the Germans in this area were defeated.

These advance drops were not the only air activities on D-Day. It is reported that over 11,500 aircraft flew over the Normandy beaches on D-Day, 3500 Gliders, 5000 fighters and 3000 Bombers.

The Sea Assault of Normandy Gets Underway

On board the ships sealed packages were broken open and it became clear to the British that Poland was Caen and Portugal was the Caen Canal.

At sea, flotillas of ships were moving via the area termed “Piccadilly Circus” to the south-east of the Isle of Wight. Some 6,939 vessels took part in the Normandy Landings, of which 1,213 were naval combat ships and 4,126 landing ships or craft. Also used were 736 ancillary craft and 864 merchant vessels. Playing an important role throughout June and July were the mine sweepers that cleared the routes so that few vessels suffered mine damage. The unnerving heave and rock of a high sea was causing many to doubt the effectiveness of the sea sickness tablets they had been given.

The D-Day Landings

U.S Troops
Utah Beach: U.S. 1st Army – 7th Corps from Dartmouth Area that included their 4th Infantry Division. The landings were in four waves of landing craft tanks (LCT’s) starting at 06.30 a.m : 23,250 troops landed 2,499 casualties, 338 killed.
Omaha Beach: U.S. 1st Army – 5th Corps from Portland and Falmouth that included the U.S 1st and 29th Infantry Divisions. Most problems were experienced here, both off shore and then on shore where defences were more than expected and pre invasion shelling had been ineffective. : 34,250 troops landed with between 2000 and 5000 casualties.

Gold Beach: British 2nd Army – athe 50th infantry division and an armoured division of British 30th Corps from Southampton area along with a Commando special unit and a specialist armoured division for mine clearing, recovery and other tasks in the British and Canadian sectors. Their landing area was between Courseulles and Arromanche: 25,000 troops landed about 1000 casualties.
Juno Beach: British 2nd Army – Canadian Forces as part of British 1 Corps from Portsmouth, comprising 3rd Canadian Infantry and 2nd Canadian Armoured Brigade. They landed between St. Aubin-sur-Mer and Courseulles–sur-mer along with a British Commando Unit: 21,400 troops landed less than 1000 casualties.
Sword Beach: British 2nd Army – British 1st Corps from Newhaven. The Corps landed between Ouistreham and Lion St. Mer with their 3rd Infantry Division and their 27th armoured Brigade. Either side of them landing on Sword and Commando special service units: 29,000 troops landed less than 1000 casualties

On D-Day the capture of Caen had been an objective for the British 3rd Infantry Division landed on the Sword beach. Although the beach was quickly under control the move inland had been met by the 21st Panzer Division who launched several counter attacks in the afternoon that effectively blocked the road to Caen. It was the only armoured resistance encountered that day. The failure to take Caen gave the Germans time to bring in more tanks and infantry.

The map shows the end of D-Day position and it is clear that the British were in command of areas over and to the east of the Caen Canal and Orne river.

Landing of 4AGRA‘s Regiments:

On the 4th June 53rd, 65th and 79th Medium regiments had embarked onto an LST (a Landing Ship Tank). This was a vessel similar to current RoRo Ferries where the Bow consists of two huge doors that open to reveal a ramp. On board this vessel, and on the 5th June came news that the invasion was to begin and real maps were issued. At 19:30 on the5th of June the LST weighed anchor.

The 53rd Medium, 65th Medium and 79th Medium regiments had been due to assemble on D Day on the left flank of the 5 mile Sword beach. However, at about 11:00 on that day they had encountered problems offloading 4AGRA’s Regiments and equipments to the ” Rhino” barges that would take them to the beach.

The photograph shows a U.S built LST (Landing Ship Tank) off loading British tanks and trucks to a “Rhino” barge. Often nicknamed a “Large Slow Target” although suffering very few losses, an LST, in suitable conditions, could open its bow doors on to a beach. Probably because it was an easy target on D Day many of them towed “Rhino” Barges whilst others carried on their deck the smaller Landing Craft Tank (LCT) which had a flat bottom and a “lower down” front.

The smaller Landing Craft Tanks were capable of carrying 18 tanks and 160 men and had their own engines. Some of the barges had their own outboard motors, others had to be towed by Rhino Tugs. Where an LCT or Rhino was used the equipment and men were offloaded to these barges or LCTs some miles out at sea.

The 53rd Medium, 65th Medium and 79th Medium regiments of 4AGRAs landed on the morning of 7th of June and were now able to support the assault divisions of the British 1 Corps and play an important part in repelling those early expected German counter attacks favoured by Rommel as it was he who commanded the German Forces opposing the Normandy invasion. On D-day the 6th of June he had been driving to a meeting with Hitler.

4AGRA arrivals were completed on Thursday June 8th 1944 when HQ 4 AGRA arrived and shortly after that on the same day the 68th Medium Royal Artillery landed on Juno Beach, Mike Sector. I believe the 150th Field Regiment and the 51st heavy also part of 4AGRA would land this day. It may well be they were landed by Landing Craft Tanks onto what would now be a quiter beach but with some overhead fire from naval forces and with many planes flying overhead to targets.

4AGRA were now there in full and able to support the British 2nd Army and specifically the infantry and armoured divisions of its 1 Corps.

Lack of Progress At Caen

The end of Day 1 position being as on the above map. The following operations followed.
Operation Perch started on 9/6/1944. It was to be a Pincer movement on Caen. Elements of British 1 Corps would be on the left over the Orne, British 30 Corps to the right and with the Americans on their right. There were some gains followed by some withdrawals until on the 19th of June, the combination of strong defences and bad weather brought to a halt further offensives
The Battle of Le Mesnil-Patry: This battle started on the 9th June. It was an operation by the Canadian 3rd and in particular their associated tank regiment the 1st Hussars. It is of note because by 12/6 it was a total failure. The Canadian party had been advancing with the Hussars leading and men of D company Queens Own Rifles riding on the tanks. An ambush, made possible by radio messages from the Hussars tanks resulted in the loss of 51 of its 53 Sherman tanks. All Hussar Officers were lost and all but two of its non commisioned officers similarly so. It was described as a modern charge of the light brigade.
Beach Supply problems:  Mulberry A had been in use for less than 10 days when, on June 19, it was severely damaged by the worst storms for 40 years. It was never used again and was scavenged to repair damage to Mulberry B. The Americans quickly reverted to the traditional methods of unloading from landing craft and DUKWs directly onto the beaches. Such was their success that on occasions they exceeded the impressive performance achieved at Mulberry B. However supply was still a problem and a harbour was needed. The American “lightning” Joe Collins attacked and took Cherbourg 22nd to 29th of June. The Germans, however, had done their best to wreck and mine the port and it only became available for limited use late July/ August.
Operation Epsom was proceeded by the one day Operation Martlet. It commenced on the 26th of June with the intent to capture high ground south of Caen. The operation would be supported by 736 artillery pieces, the Royal Navy and close air support. A planned preliminary bombardment by 250 bombers of the Royal Air Force did not happen because of bad weather. The attacks would involve elements of the newly arrived British 8 Corps supported by elements of 1 and 30 Corps. 8 Corps was able to advance nearly 6 miles but the Germans, throwing in their last available reserves, were able to achieve a defensive success, containing the British offensive. German counter attacks were repulsed and further advances by British forces were halted.
Operation Windsor was mounted in early July. The objective was to take the Village and Airfield at Carpiquet, both of which had been D-Day targets. The Operation was handed to the 3rd Canadian Division who took the village on the 5/7/1944. The airfield was not captured until 3 days later. The 3rd Canadian Infantry Division’s commander, Major General Rod Keller was severely criticised for not sending two brigades into Operation Windsor, and for delegating detailed planning. The poor performance of the 3rd Division was seen as additional evidence that Keller was unfit for his command.

Operation Charnwood: Montgomery now decided to capture Caen with a full frontal assault. Although Caen had now not the strategic importance it had on D-Day, it was the plan to drive the Germans south over the Orne river and possibly to secure and get over a bridgehead so as to lead to the higher grounds of the Verrières and Bourguébus ridges, paving the way for the British 2nd Army to advance toward Falaise. Three infantry division, including the newly arrived 59th and three armoured brigades of 1 Corps, were given the objective. Several waves of bombers would be used to facilitate the Anglo-Canadian advance and prevent German reinforcements from reaching the battle or retreating. Close support aircraft, the Royal Navy and 656 artillery guns would support the operation.

By noon on the 9th of July the Allied infantry had reached the Orne’s northern bank, virtually destroying the 16th Luftwaffe Field Division in the process. By late afternoon the northern half of Caen was firmly under Allied control. Some bridges were still intact, but these were either blocked by rubble or defended by German troops on the south side of the river. The debris that choked the streets made it almost impossible for British armour to manoeuvre, effectively preventing 1 Corps’, 2nd Army from exploiting the Corps success. Without possession of the terrain flanking the south of the city, no further gains could be made within Caen. A British troop note following the battle said “In the houses that were still standing there slowly came life, the French civilians realizing that we had taken the city came running out of their houses with glasses and bottles of wine.”
Operation Jupiter followed on the 10th July. It was an attempt by an infantry division to secure a bridge head in Caen. It failed due to extremely stiff resistance.

Accounts of 4AGRA Involvements

The following account is specific to the 53rd medium regiment but because they were, like Dad’s regiment, part of 4AGRA and in support of the assault troops of 1 Corps and specifically the 3rd Division Canadian forces it is worth including here.

“Early on the 7th, the Regiment began to reach the shore, with no casualties. The guns were immediately deployed between Hermanville and Colleville, and at 22.10 the guns fired blind, in support of the Norfolks of 185 Brigade, who had run into heavy opposition in Lebisey Wood.” (a few miles north of Caen)”
“Reverting to the command of 4th AGRA. the guns fired busily in support of 3rd Division, 6th Airborne across the Orne, and later the 51st Highland Division also across the Orne River.”

The report goes on to describe how the regiment took its first casualties with separate hits on an observation post officer, lance bombardier and gunner and woundings of a lietenant and driver. It then describes a move west of about 4000 yards and the firing of some 300 rounds in support of a successful bomber supported attack on high ground at Lebisey Wood. Another report of the time says.

“With guns deployed in a vast arc covering from Carpiquet aerodrome to the mouth of the Orne, 4 AGRA flung its whole weight into the slow slogging match which was to break the tightly packed elite of the German Army grouped around Caen. The Gunners sweated and toiled on a swift succession of counter-battery bombards, set-piece fire plans, harassing fire tasks, ‘Y targets’, air O.P. shoots and concentrations at call, as the infantry fought their slow way forward through the orchards of Normandy into a ruined factory at Colombelles and the splintered woods at Lebisey, down to the rubble of Caen.”

Operations Goodwood, Atlantic and Cobra

On July 10th Montgomery met with his Army Leaders, the American 1st Army leader Omar Bradley and the British 2nd Army leader Miles Dempsey. They drew up a plan that would require two main operations, Goodwood by the British / Canadians and Cobra by the Americans.

Goodwood would involve the British and Canadians circling round Caen from the North and attacking to the East of it. The British would head for and capture the Bourgébus Ridge, a heavily defended and strategic area. In the process it would draw the German armoured defences into the open where they could be weakened and held occupied and therefore unable to assist against an American attack that was to follow, to the west of Caen, as Operation Cobra .
The British 3rd and Canadian 3rd would need to pass over the Orne river, that passed through Caen on its way to the coast. There was also a canal to cross. There were three bridgeheads over which the troops and armoured brigades could pass. Artillery would be last crossing so they would only be able to give limited support from the British side of the river, in the attacks early stages. The inadequate artillery support would be made up for by massive air bombing.

Atlantic was the main Canadians part in this was operation It was to take the Eastern parts of Caen that had as yet not been liberated including a large steel works. Having done this they were to have another go at the heavily defended and strategically important Verrières Ridge, a few miles south of Caen.
Between 18th July and 20th July 1944 Goodwood and Atlantic took place. Argument still rages today as to whether it was a success or failure. The argument was fuelled in earlier years by those who were Monty’s supporters and by the many in high places who hated him. Goodwood achieved no breakout though Monty always insisted breakout was not part of the plan. The Bourgébus ridge was only partly taken and the attempt at the Verrières ridge resulted in over 2000 Canadian casualties. However Caen was taken and the Germans were drawn to the British and away from the Americans.

Cobra required the American armies to push South down the Cherbourg peninsula taking some coastal Ports; This they did with much success before moving east. The Germans had moved much of their heavy armour to defend against operation Goodwood and Bradley’s 2,251 tanks, 60% of which could, unlike the German Tanks, uproot hedges and therefore operate in open Country, faced only about 190 German Tank and bedded in Tank Busters. The Tank Busters were effective in resisting but when it was realised that they were located in “hot spots” and could be bypassed progress was good and German counter attacks were annihilated. The Americans had reached and liberated Avranches in the south by July 30th and by the 4th of August had reached Mortain and along with the British, Vire.

The combined army position as at 4th August was now as shown on the following map.

4AGRA became part of a New Canadian 1st Army

In July of 1944 the Canadian 1st Army Headquarters arrived with the intention of creating and introducing a Canadian 1st Army to the campaign. A Canadian Harry Crerar was to be its commander. Its Number 1 Corps were not available; they were fighting the Italians alongside the British and so a 2nd Corps would be created and become active.

By way of completing this Canadian 1st Army the British 1 Corps was transferred from the British 2nd Army and put under its control. 1 Corps comprised the 6th Airborne parachute regiment, the 51st Highland Infantry Division and the 49th West Riding Infantry Division. Its commander was a Joe Crocker and it had in support the artillery power of 4AGRA. Belgium and Dutch Troops were also for a while part of this army.
During its time in NW Europe the strength of this Canadian 1st Army would range from 200,000 to over 450,000 men of which between 105,000 and 175,000 were Canadian soldiers.
This new Canadian 1st Army became active 1/8/44 and as the 4th Army Group Royal Artillery was still in support of British 1 Corps, transferred to it we will continue to look at the general events of this campaign but with a specific interest in the activities of the Canadian 1st Army and particularly of its British 1 Corps.

Operations Totalise and Tractable

Operation Totalise: This operation followed failed late July attempts to capture the Verrières ridge. It was a night operation on August the 7/8th. It involved the 3rd Canadian Division and 33 Armoured Brigade, supported by heavy bombing of the flanks and by a barrage of Medium Artillery moving forward. It succeeded in moving nine miles forward, capturing the Verrières ridge but came to a halt on 11th August on approach to Fallaise. It was also in some ways a disaster with Canadian air support bombing and killing their own troops in conditions of poor visibility.

Operation Tractable followed between Aug 14th and 21st. The plan was that after some bombing of the enemy, the 4th Canadian Armoured division and the 1st Polish Armoured division would advance on the west whilst the 3rd Canadian Infantry Division and the 2nd Canadian Armoured Division would advance on the East. The objective was to Link up with the American 3rd Army at Chambois.

The armoured divisions took Fallaise on the 16th and Trun on the 18th. Meanwhile the Canadian 2nd and 3rd Divisions kept grinding away at the northern extremes of the Fallaise Pocket. On the 19th August the Fallaise gap was closed and the Canadian 4th Armoured drove into Chambois. American soldiers were already there.

By the end of August 21st, most German troops in the Falaise Pocket had surrendered. The area occupied by the Germans on 15th August had been 40 miles by 11 miles. On the 19th it was 7 miles by 6 miles andnow on the 21st the Germans were in flight, captured or killed. The fighting in and around Falaise had cost the Germans 70% of its military vehicles, 94% of its tanks and nearly all its artillery. Some Germans had escaped, mainly men from the 2nd and 12th SS Panzer Divisions but they had left behind nearly all of their vehicles. As a result of the chaos of war, no one is quite sure how many Germans were actually in the Falaise Pocket/Gap but a conservative figure has been put at 50,000 killed, wounded and taken prisoner with nearly all equipment destroyed or captured. However, figures as high as 200,000 have been put forward.

4AGRA Involvements

Two accounts; the first specific to the 53rd regiment, the second of a more general nature describe the events of this time, as applying to 4AGRA.
“On 17 July 1944 the Regiment found itself in Periers-sur-le-Dan in support of 3rd Division, who were taking part in operation Goodwood – the heavy armoured attack on Caen, designed to enlarge the beach- head southwestwards.
On the 19th the Regiment was able to move forward to Escoville, described by the Regimental history as a mosquito-ridden, flat, dusty plain, — It is from here that they fired hard in support of the final stages of Goodwood — in support of the Highland Division, who were pushing into Tilly-la-Campagne and Secqueville.
On 9th August the guns moved to Hubertfoile situated in the middle of the Caen Plain again described as a fly-ridden dust trap. The guns remained in action here for a total of six days moving on the 15th in drill order style and ending up at Estrees-la-Campagne which offered a dramatic view of the Polish tanks moving southwards towards the Falaise Gap. “

“Not till the first week in August did the Group deploy in the open country beyond Caen, but after that events, and the formation, moved quickly. First it supported a Canadian thrust on Falaise and then, swinging north-east, it leap-frogged its regiments forward in support of the advance through Lisieux and up to the crossings of the Seine. By this time 4 AGRA considered itself a complete master of the art of fire and movement”.

August 22nd 1944 and Break Out

At this stage German losses totalled 500,000 men, 1500 tanks, 3,500 guns and 20,000 vehicles. The allies had lost 209,672 men, two thirds of them British and Canadian.
Now the British and Canadians could join the Americans and French who had skirting the Falaise Pocket and were heading North to the Seine or into Southerm France. By the time British and Canadian forces were done at Fallaise, Patton and a French army were at the Seine North West of Paris and U. S. Forces had taken many places South East and North East of Paris.

The Cause and Outbreak of World War 2

Germany had been held fully accountable for WW 1 and the reparations required of it had left it economically poor and with extremely high inflation. In time a change in attitude toward it and new economic policies saw it borrow monies from America. It steadied inflation, provided jobs and Germans started having a better life. Then along came the Wall Street crash and America wanted its money back and Germans were suddenly poor again.

The Weimar government were blamed and Hitler’s party came to power with him as Chancellor. When its parliament was burned down Hitler was granted emergency powers. He became president on the death of Hindenburg, who had appointed him and so developed a dictatorship. His Nazi party had some opposition as they persecuted the supposed inferior groups but they were creating jobs for millions and so were accepted by the majority. They were particularly manufacturing war machines and on the 1st of September 1939 invaded Poland. As per a political agreement, that led Britain and France to declare war on Hitler’s Nazi Germany.

Dad is conscripted into the Royal Artillery

In early 1939 the Military Training Act was passed. It started a conscription process whereby all men between 20 and 21 would register in that year for military service. The first intake was in July. Dad would be 24 at that time and not included in this intake.

After war had been declared a National Service Act superseded the Military Training Act. It merged the regular army, TA, reserves and militia. It also made all men between 18 and 41 (later raised to limit to 51) liable for conscription. Conscripts were able to choose between the army, navy and air-force but allocation to regiment or corps was done by the Ministry for Labour. It was based on the individuals preference, a limited assessment of the individual and some inadequate guidance on the needs of the army services.

Prior to the outbreak of war Anti-Aircraft Artillery had being greatly expanded. Many experienced officers had been transferred there from field artillery regiments. The declaration of war meant air attacks were a real threat and dad who was fit and strong became a gunner in the Anti-Aircraft section of the Royal Artillery. His service record shows him as a Gunner in the R. A. for 6 years from 18th April 1940 to 13th April 1946. We know not what regiment he was in at the start of his war service.

Artillery Training would be needed but his war papers only have one entry saying that he passed DM 7/5/1941. DM is a gas that causes a burning sensation in nose and throat and
a heavy tight chest, accompanied by a nauseating feeling. The gas is used in some grenades that burn and emit smoke through holes in the grenade body. Dad would have used a gas mask and entered a chamber in which the gas was present.

I remember dad telling me he was at Spurn Head and Kilnsea featured in the conversation. I suspect he was a heavy anti-aircraft gunner there and possibly in 59 Regiment Eastern Command. The map is a modern map but illustrates the area. The inset shows how long the peninsular is (3.5 km). A lighthouse is located at its point though now cut off by high tides. There can still be seen at this location many of the concrete fortifications and gun positions that are relics of the war but much eroded by the sea.

In 1915 during WW1, an early warning station and a number of forts had been built there. One at Kilnsea, at the north end of the humber peninsular, a larger one called Spurn Fort at Spurn Head (point). A military railway had linked the Godwin Battery at the Kilnsea Fort with the Green Battery at the Spurn Head Fort. Two large fortifications had also been built on sand banks either side of the mouth of the estuary. These were Bull Sand Fort, with 12″ of seaward armour and positioned 1.5 miles off Spurn Head, and the smaller Haile Fort, on the low tide mark between Cleethorpes and Humbleton. The estuary forts are still standing to date. The battery forts used and much updated for WW2  are gone, the Kilnsey Fort area sold as a Caravan Park, the Spurn Head Fort area as a Nature Reserve.

The threat from air attack was as great as that from the sea in WW2 so in addition to having their  main “sea” guns updated to 6 inch and having other naval guns installed , the  Godwin and Green Batteries had new search lights and anti aircraft guns installed.

Heavy anti aircraft 3.7 inch quick fire guns would have been installed at each battery These were further supported by 4o mm Bofors Guns, 20 mm Oerlikon Canon and Lewis Automatic Machine Guns at locations throughout Spurn Head.

At Warren Head, between the Kilnsea and Spurn Head Forts about thirty huts were constructed to house men and women who manned a new anti-aircraft installation constructed there. Other buildings were added in this Warren Head area and another 20 huts were erected to house infantry close by. At its peak about 1,500 military personnel were located in accommodations on Spurn Head, an area closed to the general public.

At first the Warren Head area had 2 by 4.5 ” anti aircraft guns but these were soon replaced by the much quicker firing 3.7″ guns, by Bofors guns and by Bren guns that replaced the Lewis guns. The quick fire  3.7 inch guns were capable of firing 28lb 94mm shells to 30,000 feet at a rate of 20 rounds per minute. It was crewed by seven men but later by some women for Home Defence. At Spurn Head the guns worked with the searchlights, acoustic detectors and possible radar there. I am fairly confident dad was part of such a gun crew, and serving here at Warren Head or maybe at the Kilnsey Fort.

To supplement the existing WW1 standard gauge railway between the two batteries a road was constructed down the head via the Warren area to the point. A jetty was also built here so that heavy construction materials could be off loaded to the road and railway. There are still to be seen, in this area, massive concrete structures of pill boxes, anti tank blocks, weapons pits and gun emplacements. Many have been undermined by the sea.

The above photograph of dad, second from the left,with some army pals, I am confident, was taken whilst he was barracked in this area and I suspect taken looking toward the Warren Head anti aircraft installation from the seaward side of the peninsula. In the right background there are sandbag fortifications surrounding what appear to be 3 guns pointing skyward. The building is probably one of a number that includes their barracks, the tall structure an Observation Post. Most anti aircraft gun emplacements at this time  were sited on a circular arc, as was the case at the Godwin and Green Batteries. These guns are clearly in line, maybe because those Batteries covered the threats from the North and South.

The Humber area was bristling with military personnel because it was considered a likely area for invasion. Hull itself was hit by numerous High Explosive Bombs and Parachute Mines. Over three quarters of Hull housing was damaged, 152,000 people were made homeless, 1,200 people lost their lives there, and 3,000 were seriously injured. Hull often took bombing meant for more inland places, or from enemy aircraft that had failed to find Sheffield, or Leeds. No pilot would risk a potential heavy or crash landing with live and armed bombs aboard. Dumping of unused bombs was normal but whilst the RAF had strictly observed dump zones in the North Sea and English Channel the Luftwaffe, dumped bombs over Britain right from the start.

Stationed at Thorne

Dad was next stationed at Thorne, near Doncaster, where he lodged with a Betty and Tommy Nichol at 10, Tennyson Avenue. They came to be known by us as Uncle Tommy and Aunty Betty and in later years we would holiday there. I remember Tommy showing me, when I was a teen, how to set a car distributor contact points and another time going to Brimham Rocks with them.There was clearly not an army barracks at Thorne, so why was he at Thorne?

The map above shows us that Thorne was on the German bombing run across the Humber to the industrial centres of Yorkshire and Lancashire. I presume the army had numerous Anti – Aircraft guns inland so that if the guns located at the Humber Estuary missed their targets, the inland guns would have a second try. Thorne would be just one of many places where this would happen.

I must have gone to Thorne with mother at some time during the war, probably in 1943 when I was four. I do not remember what I presume must have been a stay with Betty and Tommy but I do have a vivid memory of going to an area near a street where a skyward pointing gun was sited. I remember the gun had two wheels and that a number of soldiers were there. We did not go near the gun. We stood on a pavement and a man (dad ) came across to talk to us.

At this time the gun shown right was very much in use by the Royal Artillery Heavy Anti-Aircraft Regiments. It satisfies my memory and is a QF 3.7″ Heavy anti-aircraft gun on mobile mount. It could be available within 15 minutes of arrival at a location. A similar gun was available on a fixed mount. Interestingly I picked out this gun from photographs before I knew that such guns were used to combat aircraft at Kilnsea. So dad would simply have moved from 3.7 inch guns on fixed mounts at Spurn Head to 3.7 inch guns on mobile mounts at Thorne.

There were three anti- aircraft and searchlight units in the Thorne area but only one in Thorne itself. This was at the end of Alexandra Street where it joined Brickyards Lane and I suspect where dad was based. It would I believe have been supplied with ammunition by the Barrow Haven Ammunition Dump on the South Bank of the Humber Estuary.

Dad is transferred to 68th Medium Regiment Royal Artillery

The Battle of Britain in the air and the Luftwaffe being diverted to the Russian Front had reduced air attacks on mainland Britain and so Dad, with his gunnery experience and in preparation for an assault on Germany, was moved from whichever regiment he was in to the re-formed 68th medium regiment Royal Artillery, a part of 4 Army Group Royal Artillery (4AGRA). He was now Gunner No 972810 in the R.A.

Dad’s assignment to the 68th would have been in the August of 1943 and I believe that his transfer was accompanied by a period of privilege leave.
Privilege leave was earned leave and it was clearly more possible to take such leave whilst UK based. His record shows that he was on leave in August and also in the November of 1943 and in late January / early February of 1944.

The photograph on the left shows him at Durham Station on his way back to the army after such a period of leave. I am the smartly dressed one in the middle, between mam (Ruby Gladys ) and dad. Since my grandchildren estimate my age in the photograph as nearer 4 than 5, I think the photograph was probably taken at the station after his August leave.

Whichever period of early leave it was, he would be heading for Perth in Scotland and for training in his changed artillery role.

The cap and collars of his uniform had badges that bore the mottos of the Royal Artillery. The Royal Artillery’s main motto and battle honour “Ubique”, meaning   “everywhere”, was granted by King William IV in 1833.

Everywhere was appropriate because Royal Artillery regiments were to be found with and under the command of assault land forces wherever they were. The cap badge also bears the subsidiary motto “Quo fas et gloria ducunt” which means “where right and glory lead”. Both mottoes are shared with the Royal Engineers, due to the shared Board of Ordnance history.

The Royat artilleries Field Regiments were to be found alongside and commanded by infantry divisions or armoured (tank) divisions. With their lighter 18/25 pound field guns they were highly mobile and moved with them. R.A. anti-tank regiments and anti- aircraft regiments were likewise to be found with infantry divisions.

Medium and heavy regiments with their longer range and greater power guns would be generally behind and in support of such divisional troops and controlled by Army Corps or divisional commanders. They were less mobile and would take up firing positions. But R.A. regiments were not just about supporting land forces. They might be on board merchant shipping as protection or used in coastal defences.

You might ask what all of this means. What are Corps, Divisions, Regiments, Brigades, Batteries, etc? What does Medium mean? What is a Battery? What guns and equipment do they have? How is an Artillery Regiment used in war? What is an AGRA? If at this stage you want answers to these questions follow this link

Training for War with 4 AGRA

After its formation in the March of 1943, 4AGRA started to assemble its regiments for pre war training, in the Tay river valley at Blairgowrie, Perthshire. The intention was to train its gunners and produce Artillery Regiments suitable for war. So as to be a part of 4AGRA the 68th medium regiment, originally formed in Lancashire was reformed. The 68th had become a “lost” regiment. Lost when Tobruk in Libya had fallen in the June of 42, after a long seige there and to the German Commander Rommel. Now, in 1943, it was being reformed taking from another Lancs regiment, 59 medium, and other Garrison Regiments.

The 51st Heavy Regiment had been first to arrive in April. The 53rd Medium, 65th Medium and 79th Medium Scottish Horse (an historical name) regiments arrived in May. The newly formed 68th Medium Regiment and 150th Field Notts Hussars (also a name) joined it later in August. 4AGRA were now a standard AGRA but with 4 x medium regiments instead of the usual 3. Its field regiment would operate 24 x 25 pdrs sometimes self propelled. Its medium regiments each had 16 x 5.5″ guns in two batteries of 8. Its heavy regiment would have 8 x 7.2″ Howitzers and 8 x 155 mm guns.

The artillery field guns had a max range of about 13,000 yards. They were manned by a crew of 6. The Howitzers had a 202 lb shell and a max range of nearly 17,000 yards. It was manned by a crew of 10. The 155 mm fired shells of about 100 lb in weight. It had a maximum range of about 25,000 yards and a gun crew of 14. The 5.5″ medium gun could send a standard 100 lb shell, carrying 10.5 lb of explosive up to 16,200 yards . Later 80 lb shells would carry 12 lbs of explosive up to 18,100 yards. Such guns were manned by a crew of 10.

Whilst here on training dad had 9 days of leave in the November of 43 and 9 days starting 31/1/44 when I suspect my brother Derrick was conceived. The leave is described as privilege but it is leave earned as a result of service. In each case of leave it can be seen that a free warrant was applied which meant you got a ticket to travel anywhere you wished. If no warrant was issued then you would take leave at your place of duty but resting from it.

Few in the regiments training at Blairgowrie had seen action. Most of them had gunnery experience but the actions in war were something different and intensive formation and unit training was required. This training was started under the command of Brigadier A. G. Matthew and continued in the May of 44 by a Brig. H. A. Hambleton, who then commanded the formation throughout the coming war operations. Training was strenuous with exercises like the fire and movement ‘Gallop’, the diggings of ‘Shovel’, the supply problems of ‘Sisyphus’ and the corps manoeuvres of ‘Eagle’ and ‘Blackcock’.

Training as recorded by a Gunner in 53 Medium Regiment

“My next move was to join a proper regiment at Blairgowrie, Perthshire, Scotland. 8 Troop 209 Battery 53 Med Regt RA. The regiment was stationed in a Smedley Raspberry Factory about quarter of a mile down the road from town near a big river. Every Sunday Morning Church Parade. We marched to church and then if not C.of E. could make own way to other churches. Some chaps soon found out that it was a good way to get out of Church Parade. Mum sends me a biscuit tin of cherries for my 20th birthday.

Training all the time on and off the moors for 2 and 3 weeks at a time. At first no tents and had to sleep fully dressed under tarpaulins in a line. 10 gun crew not good. One night raining hard have to pull over our heads to stop getting wet but have to get up in the middle of the night to do 2 hours guard duty. One time firing across Dundee water with all 16 guns. First time for us firing all 16 at once. Once, three weeks on the moors with snow and ice – have to go down to the stream and break the ice to wash and shave at 6.30am. At least we did have tents now.

One day after firing guns, we heard “Stand Easy”. I was on shells that day, putting on the fuses or airburst time fuses set in seconds. Anyway the order came, “Take Post” the Sergeant No 1 shouted loud to No 2 and No 3. But he forgot that there was already a shell in the gun and they rammed another shell up the breech. They soon realised what they had done. The officer ordered everybody back for 15 mins (which was the done thing). After that he ordered them to get it out and it was brought over to me. He said take the fuse off as quick as you can in case it goes off. The fuse nose was smashed in, they were made so as not to go off. But this did not always work as one gun crew later on in France got the next shell too close to the gun so that when the gun fired it recoiled and hit the shell killing several of them. Anyway everybody moved away while I unscrewed the fuse, There was me, leaning back on a pile of about 20 100lb shells. Anyway it came off otherwise I wouldn’t be here now.

Still going out one to three weeks at a time on moors, etc. up as far as Aberdeen and Inverness. After about six months, move again to Balero Camp, Carronbridge Dumfriesshire. About 1,000 men. Some Saturday nights go to Dumfries or to Carronbridge. “

Preparations for D-Day

All of the regiments assembling at Blairgowrie, had known they were earmarked for an assault on France as a part of 4AGRA, an R.A. group that would be in support of British 1 Corps, a part of the British 2nd Army. It was known there would be beach landings and so much thought was been given to getting the tractors and the guns they pulled from landing craft to the shore.

Waterproofing, including exhaust mods, had been carried out on the vehicles and the tractor drivers had all driven through 50 yards of 4 foot deep water in order to gain some experience of how their vehicles handled in water. Drivers had also gained experience driving on sand at Broughty Ferry, Dundee and later they all went in batches to Inveraray for landing simulations.

By February of 1944 draft instructions were starting to arrive and although these changed several times, it was clear that the 4AGRA regiments who were to land on D-Day would land at H + 5. The H represented the hour of the 1st landings and D the day of those landings and giving rise to D-Day. Neither of these were at this stage known ,or indeed where those landings would be.

On 6/4/44 (my birthday, I would be 5) dad’s papers show that dad made a will. A form of will is shown on pages 17 and and its reverse side 18 of his army booklet. But his will was completed on pages 15 and 16 of the booklet as these were used when leaving everything to one person. The vertical details on the left are what remain of page 15 after his will was cut out. It shows the date he made his will, the signature of the officer who received that will who added “fit”. It also shows that the extracted will was sent to the R.A. Paymaster.

It seems that 4AGRA troops all made wills before leaving Perthshire which happened on and around the 18th of April when 4AGRA regiments were on the move to Oxted in Surrey. They did so via Barracks at Carronbridge, near Thornhill north of Dumfries, then Catterick , Doncaster and Lutterworth. Four weeks of dress rehearsals took place at Oxted before 4AGRA left for camp A15 near Wickham in the Meon Valley, Hampshire, where three more days of preparatory training ensued.

Operation “Overload” with Eisenhower in charge had been much time in planning. It included operation “Neptune” better known as the Normandy Landings which would  involve the landing of some 150,000 men and 1500 tanks in a 48 hour period. It also planned the creation of two temporary harbours called Mulberry A and B that would be essential for supply purposes. Overlord also included a pipe line under the sea to supply fuel. Late on June 5th of 1944 the operation was underway because the planned landing were to take place on D-Day June the 6th 1944.

## Is the Covid 19 virus alive?

There is no consensus on what is and what isn’t alive. One definition describes a living thing as having an organised structure, requiring energy, adapting to environmental change and responding to stimuli. So far a rock will satisfy those criteria but the definition goes on to include reproduction, growth, movement, metabolism and death.

Single celled bacteria can reproduce and are regarded as living. Also classed as living are archaea; they have similarities to bacteria and like bacteria their cells are classified as of type prokaryote. Archaea have different cell walls, can live in extreme temperatures where bacteria would not survive, are unaffected by antibiotics and have three enzymes able to synthesise RNA molecules; bacteria has only one. The other major and larger cell type is that of eukaryotes and includes all animals and plant life and of course us humans.

So how should we see the Covid 19 virus. Is it alive or not?

In shape it is spherical and about 80 millionths of a millimetre in diameter. It has encased in its porous membrane the largest single RNA (ribonucleicacid) of any viruse being composed of over 26,000 nucleotides.

Viruses are much smaller than and not regarded as cells. They are thought of more as packages of proteins and nucleic acids. However, their genome of RNA contains the same bases of adenine, guanine, cytosine, but with uracil replacing thymine, as are present in all cell structures. Also like those cell structures there are genetic variations and the structure can evolve and change to better suit its environment. It is thought, for example, that covid 19 learnt to replicate itself faster in bats as bats built up strong antibodies.

Unlike prokaryote and eukaryote cells, viruses have no ribosomes and so cannot make their own proteins. In order to survive and replicate themselves they need to make proteins and this they do by first attaching their spike S protein to ACE 2 receptors of host cells and then opening up that host cell so that the viral RNA can utilise the replication machinery of the host cell. This it does so as to reproduce itself many times over before emerging from the host cell.

I am perhaps a little biased in that I regard all energy desiring atomic energy structures as living. I say that the gravity motion of earth toward the sun is a living desire of earth particles for sun energies and that we are held on the earth by our particle desires for earth energies. So, I do not hesitate to describe the Covid 19 virus structure that is using the energy of its environment to satisfy the energy needs of its particles as living. But what do you think. Do you think that a structure that can take control over our body cells is living?

The covid 19 virus carried on water droplets and gaining access to the Ace 2 receptors in our throats will cause the triggering of anti bodies. They are our structures way of defending themselves. If the viral load is high or the immune system weak the virus may gain access to the more numerous ace 2 receptors in the lungs damaging cells and causing congestion. Sometimes the immune system will respond by going into overdrive and as it does with arthritis start attacking healthy cells with disastrous results.

## Seeing colour

In reality there are no coloured objects, either natural or painted. All colours are brain interpretations of energy signals processed by them. “Seen” colours result from electrical energy pulses passing between the retinas of our eyes and the rear lobes of our brain, but particularly the thalamus and primary visual cortex. Such signals are tiny transfers of energy and all of a two way nature. The “seen” signals are processed and acted upon to deliver the energy display that we see as colour. We don’t always need our eyes open to “see” colour

Eye movements, both voluntary and involuntary, memories, visual images and spatial awareness all result from energy signals rapidly moving along nerve pathways in our brain. When the “seen” signals are at a minimum we see a restful blackness.

A major source of visual brain signals is the retinal cells in our eyes. They react to the energy levels of the photons of light received by them and therefore to their frequency and wavelength. In response to the received energies our retinal cells send electric energy not continuously, but as pulses along the optic nerve to the thalamus and primary visual cortex. To avoid image blurring energy signals received while our eyes move from one point of focus to another are discarded.

We also “see” coloured images when we dream and when we have unwanted brain nerve cell energy flows as with migraine or concussion. The thalamus is considered a major role player in sleep and wakefulness. It also acts as a nerve cell gateway both passing into storage and getting from storage memory fragments, thought to be held in the many synapses that each of the billions of nerve cells in the brain and in the central nervous system have. It would seem that the brain can assemble images from such energy fragments and may explain why our dreams can be colourful and vivid but also creations of what we call, in a conscious state, imagination.

When retiring to bed and closing my eyes I often see faint colours. They may be reds, blues, purples, etc. They are a sign that my brain is still active. When these colours subside and are replaced by black I know I am in a more restful state.

Science describes red, green and blue as being primary colours. It does so because when photons from light emitting sources that are “seen” separately as red, green and blue come to our eyes in equal parts we see white. It means that magenta, a mix of red and blue lights, when mixed with green light make for white. Yellow light when mixed with blue and cyan light mixed with red light similarly deliver white light. Understandably such light mixing is described as additive. Additive light “seen” in our brains is always brighter than its separate components.

Retinal cells are of two types called rods and cones. About 120 million rod shaped cells are present in an eye. They are mostly located around the boundary of the retina and are particularly useful at night when lower photon energy numbers are received. Cone cells number about 5 million and are mostly located near the retina’s centre.

There are three types of retinal cone cell. Each has a different energy structure and therefore each responds in its own way to a range of photon energies. As all of us humans have similar yet different structures and so colour perception isn’t truly the same for any of us. For some with colour blindness or blindness itself, what is “seen” is substantially different.

Retinal cone response curve diagrams most often colour the curves red, green and blue as shown and often accompanying descriptions describe the cones as responding to red, green and blue. They are wrong to do so. Each cone type responds to a range of colours, not to a specific colour. Their peak sensitivities are in some cases not even aligned with the visible spectrum colour assigned them. It is far better to regard the cones as responding to a range of short, medium and long wavelength energies in the visible spectrum.

You and I will obviously continue to describe objects as being of a certain colour. All I ask is that you be aware that in reality objects have no colour and that colour is our brain perception of the energy coming from such objects.

Contrary to the above view that has red, blue and green as the primary light colours, art teaches us that red, blue and yellow are the primary colours and that when a pair of them are mixed in equal proportions they deliver the secondary colours of purple, green and orange. Our colour wheel illustrates this but also shows marked with a T colours created by mixing primary colours in the proportions of 2 to 1.

Our sun emits a wide range of photon energies including all of those in the visible light spectrum which when added together deliver what our brain sees as white light. We on earth see the sun image as yellowish or even red. That is because some of its emitted visible energies are lost to our atmosphere. To astronauts in space the sun image is white.

The sun’s photon energies that land on earthly objects are absorbed by their atomic particle structures and processed by them. Those objects are all the while releasing most of that absorbed photon energy. If they didn’t they would get very hot. However the photons released are not those absorbed and they can be of much changed energies. All depends on the object particle structure and its energy environment.

Some structures emit a full range of visible photon energies and are seen as white, some emit no or few visible photon energies and are seen as black whilst some emit photon energies that our eyes see as a colour. It is as if the structure has subtracted from the sun light some of its visible light photon energies and reflected the others so as to deliver the colour we see.

I believe energy structures act on all received energies and released them at different energy levels. Some are released in the visible light range, some in non visible photon energy ranges. A black object like iron in full sun is releasing energy in the infra red range into the surround air. It will release such energies rapidly to contacting objects which is why such iron feels very hot when touched. Total energies gained by structures are never the same as the total energies released by them. It is why particle structures warm up or cool down and change in shape, as with expansion and contraction.

Paint mixed from pigments and applied to an object changes the atomic particle surface structure of that object. By selecting the pigments we apply to an object we can change the range of visible photon energies emitted by the surface of that object when a full range of visible light energies fall on it. This way we see the colour of our choosing. The more pigments we mix the duller the released and perceived colour is. We describe the process as subtractive.

Paints are mixtures, not chemical compounds. It means paints are composed of tiny, separated and different pigment structures. Each pigment “subtracts” some of the incoming visible light. Each pigment structure has a desire to seek out and draw to it from the incoming photon energies those that are useful and desired by it.

The role of electrons in structures is to seek out and collect energies that are of benefit to other particles in their structure and to avoid or collect and release the energies that are not wanted. The particles in most solid structures have restricted movements and their electrons have little choice but to absorb and subsequently emit energies that are not so much wanted. The more mobile particles in liquid and gas structures can better use their internal energies to avoid the energies they don’t want. The visible energies we see are those emitted by a structure.

Those of you who have printers will probably know that print cartridges are usually of cyan, magenta and yellow. Some articles will tell you that these three colours are more appropriate primary colours. When applied to paper or other structures these cartridge colours are the colours our brain sees in daylight.

We see cyan because its structure is drawing in and using light wavelengths that we would see as red, we see yellow because its structure similarly acts on and uses blue light wavelengths and we see magenta because its structure has a desire for and uses green wavelengths.

If we mix cyan, magenta and yellow together in equal parts the cyan structure draws in and uses red, the magenta and yellow structures do likewise with green and blue related photon wavelengths. No red, green or blue light is released and so we see black because all three primary colours in the daylight are made use of by the mixed structures. It would be very wasteful to mix the cyan, magenta and yellow cartridges to make a commonly used black so most printers have ready mixed black cartridges.

The arguments about which colour primary system is right are a little misleading. Whilst red, green and blue are perhaps an optimal 3 colour primary system for delivering colours in light adding systems like those in television, phones and cameras, it is by no means the only one. In no way can those three colours alone produce all of the colours the human brain can see.

Similarly the cyan, magenta, yellow primary system that subtracts red, green and blue from the light falling on them may be an optimal system for material colouring but it is not the only one and again cannot replicate all the colours our brains can perceive.

It is the case that all primary colouring systems approximate perceived colours. Additive systems as in televisions, etc have difficulty replicating deep greens, deep blues and violets. We must also understand that the colours of the visible part of the electro magnetic spectrum as seen in a rainbow or through a prism are just a tiny fraction of the colours that our brain can conjour up. There are millions of colours that the brain can perceive that are not in the spectrum including main colours white, black and magenta.

We do not fully understand the brain processes that see colour and I certainly don’t. What I can say is that they are about energy structures changing in response to energy inputs. Perhaps someone out there can explain what is happening in the brain that causes us to see magenta when looking at white after staring at green and why it is that a migraine aura will move the position of its “seen” image when we move our eyes behind closed lids.

Essentially, don’t let any of the above stop you enjoying the gift of sight and in particular the colours we see.

## Rubik Patterns

In the pattern sequences below F, T, K , B, R  and L are all clockwise turns of the Front, Top, bacK, Bottom, Right and Left faces. The lower case letters are anti clockwise turns of those same faces.

To make the two colours per face checkerboard pattern shown on the right do 180 degree turns of 3 x opposite faces (say 180 degree turns of Front, Back, Left, Right, Top and then Bottom) Repeat the pattern to correct the cube.

The sequence of turns F2 K2  T b  L2 R2  T b
will make for the 4 hole cube shown left. Top and bottom will be left untouched. Reverse the process to return the cube to its former state.

The sequence of turns T b   K f   R l   T b
makes for a 6 hole cube. It, as always leaves the centre colours as they were moving the top, right and back face colours clockwise around the top right back corner and the bottom front and left colours anticlockwise round the bottom left front corner.

Reverse the process to return the cube to its former state but remember to have the same top and front centre face colours. Alternatively just seek and suitably position the three face colours that need rotating clockwise and repeat the same sequence.

If you perform the sequence that produced the two colour checkerboard pattern and then follow that with the sequence that produced the 6 hole pattern you will get a checkerboard pattern as shown left with three colours per face.

You can reverse the two sequences but alternatively as for the 6 hole pattern you can repeat both patterns if you first identify the three corner block colours that need clockwise rotation.

The sequence R L K F performed 3 times will make for a zig zag pattern around the cube sides as shown left. Repeat the sequence to restore the cube to its completed state.

The sequence of moves
F2 R2 T2  f  K  B2 L2  F K  will make for a pattern of T’s on each of the 6 cube faces as shown in the illustration right. The reverse of the sequence k f  L2 B2 k F T2 R2 F2  will reverse the process and restore the cube.

The sequence of moves
F T F R L2 K b R B2 L b K R2 L F T F
will make for a pattern of stripes around the sides of the cubes as shown. The reverse sequence f t f l R2 k B l B2 r B k L2 r f t f
will undo the stripes

The sequence of moves
F k T F T F T L K L2 k T f  L T l  K will make for the arrow head pattern illustrated right.  The reverse of the sequence
k L t l F t K L2 k l t f  t f t K f  will restore the cube. Alternatively position the cube so that the 3 L shaped colours at the top right front corner need a clockwise turn and then do the same move sequence that made the arrow pattern again.

Sequence F L F t R T F2 L2 t l K b k L2 T  makes for an 8 cube block with a 27 cube block. Note that the sequence rotates the L shape colours around the top right corner cube clockwise so to correct the cube simply position the other diagonally opposite corner of the cube at the top right hand and repeat the sequence.

The cube in a cube in a cube pattern shown right is the result of sequence F B f B2 l k T L B R T l f T L T2
It is one block within an 8 block cube within a 27 block cube.

To reset the cube reverse the sequence .

## Visible Light Energy

Visible light energy radiations are just a tiny part of the electromagnetic radiation spectrum. We are able to see this small band of radiations and so it has been the most studied. Whilst this blog is about visible light much of what is said is applicable to the rest of the spectrum.

If you have not red my blog on radiation I there explained that photon energies are energy pulses and that they, like particles, are composed of energy fragments and that they proactively interact by exchanging energies. Photons energies come together in coherence but they are also influenced by particle energies. So let us consider cohered light passing an edge or through a slit. It diffracts but why?

Diffraction is most evident with monochromatic light that is cohered with plain wavefronts. These are shown in blue in the diagram, which also shows and identifies just 6 of the millions of photon energies in the light beam.

What appears to us as a sharp material edge is in reality a photon exchanging particle structure and it bears influence on and attracts the passing photons, highly attracting those closest to it, less so those furthest from it. The structure attractions are why the photons follow a curving path.

The photons want to maintain both their independence and spatial coherence but to achieve that for the whole light beam bundle the photons represented by a would have to slow substantially whilst the bundle represented by f, would need to speed up substantially. They cannot do that and what happens is that photon bundles break up. Bundles a and b do succeed in staying cohered by exchanging energy, They are most influenced by the edge particles and turn the most. Bundles c and d cohere and turn less whilst e and f cohere and turn least. If we observe the output light on a screen it displays a pattern of light and dark bands.

When we observe light that has passed through a glass or water, the observed object is seen to be displaced from where we know it to be. This is due to a similar bending of light called refraction. The cohered photons from each and every tiny point on the viewed object follow their own unique and bent path to our eye retina rods and cones as shown for just one such object point.

Being cohered means the photons want to stay together but, because they approach the glass at an angle, some are nearer to the glass than others and they are attracted to the glass energies and turn toward it. The light photons want to remain cohered and by exchanging energies they succeed in doing that. Our wavefronts now travel through the glass at that changed angle.

Glass has a very rigid particle structure. Its electrons are held quite firmly in place and are limited in their ability to move toward and collect photons. It is why light passes through glass. But that does not mean to say that they do not attract photons. They do so and more so than the more sparse particles of atmospheric gases. Photons that had a slight wiggling motion through the atmosphere have a more pronounced wiggling motion through the glass. It is why photon speed appears slowed in glass.

When the wiggling and cohered photons reach the glass to air structure, they again do so at an angle and those arriving their first are first freed from the higher attractions of the glass particles and so they speed up. But their still slower colleagues want to stay with them and remain cohered. Exchanges of energy occur that result in the light bundle moving off into the air in a changed direction and as cohered photon wavefronts to our eyes. Our eyes see the point location on the object, and all other point locations on the object, as in the direction of the incoming photons and displaced from the real position of the object.

White light we see is actually a combination of spectrum frequencies. Watch a piece of iron being heated. Its surface particles are interacting with environmental energies in excess of their needs, processing them and dispersing them to other particles and back to the atmosphere. At first we see lower energy photons as red and then as higher energy photon are released we see the mixture that is orange before the yellows dominate . We don’t see the hotter blue photons because unlike those emitted when we burn natural gas they are mixed with all of the other photon energies coming to our eyes so we see white.

It may puzzle you as to why white light refracted through a glass block as above does not break up into colours, yet when passed through a prism it does just that as shown in the illustration. My blogs on gravity and on particles explained how attractions and repulsions at the macro and particle levels were about particle desires and repulsions of photon energies. Larger bodies of energy (larger masses) were more attracting of photon energies than smaller bodies of energy.

What we perceive to be white light is the result of a number of photon energies acting on our eye retinas. Light we see as violet has the highest visible photon energy whilst light we see as red has the lowest visible energy. After being refracted at the first prism surface the photon energies that constitute white light have to pass between the more energy attracting base of the prism with its higher energy and mass content.

All photon energies are attracted to the base energies but they cannot all move toward the base as photons of light, like particles, use their distance apart to control their energy exchanges. The more dense violet and blue energies get priority in moving toward the prism base displacing the yellow and red frequencies upward and encouraging their attraction to the prism top. The displacement is not unlike that experienced by less dense atmosphere molecules that in competing with others for earth’s “gravitational attraction” energy find themselves pushed to higher levels.

On being refracted at the second surface the colours become more deviated. The mix of yellow and blue photon mix we see as green whilst the red and yellow junction mixes to orange and the violet blue to indigo.

## Algebra

The secret to maintaining an equality, or for that matter an inequality, is to treat both parts of the equality the same. Whatever you do to one side of an equation do the same to the other and equality will always be maintained.

Algebra involves unknown numerical values that are represented by letters. Being unknown means you cannot combine them with known values. But you can combine or deduct them from multiple values of themselves. The process of solving algebraic equations involves manipulating unknowns to one side of the equation and knowns to the other.

When learning about quadratic equations we will be told that the solution to an equation of general form ax2 + bx + c = 0 is x = [ -b ± √(b2 -4ac)] /2a
Let’s have a go at proving that

Start by dividing throughout by a so that x2 + bx/a + c/a = 0 and then try to factorise it in the form (x + ?)(x + ?) + some constant = 0.
Clearly to get the term bx/a the ? bit has to be b/2a

The expansion of (x + b/2a)(x + b/2a) = x2 + bx/a + b2/4a2
and if we deduct from both sides of this equation b2/4a2 and add c/a we get
(x + b/2a)(x + b/2a) b2/4a2 + c/a = x2 + bx/a + c/a = 0

So (x + b/2a)2 = b2/4a2 – c/a and x + b/2a = ± √ ( b2/4a2 – c/a )
which when simplified leads to x = [ -b ± √(b2 -4ac)] /2a