Trooping the Colour

Looking good at age 94 and 99 respectively

We are at great-great-grandma's where the TV rules the day, and have just finished watching the Queen's official birthday Trooping the Colour at Windsor Castle. It brought back memories of school days. Once a certain age all pupils, unless with good reason, had to choose to be an Army, RAF or Navy cadet and play soldiers every Friday afternoon thereafter. I choose the RAF. Most of the time we were square bashing but there was some desk work - I remember learning about the Bernoulli principle and lift. I still have a certificate from an exam we took - I'll dig it out when we get home. On one occasion the NCO giving the lecture asked the class if we knew what "info" was. Bloody information he shouted, as if that was a peculiar revelation.

Every term there would be an outing. We came to school in our cadet regalia and bearing a packed lunch and were whisked off in a hired coach to our mystery destination, often a military base with real soldiers. On one such occasion I got to fly in a chipmunk. On another we went up in a cargo plane with no windows so one wonders what the point was. We had our own firing range using .22 rifles where I seem to remember I did better than average: on one outing got to fire a .303 and experienced its considerable kick-back.

Once a year there would be a General Parade over which a visiting top-notch would preside. It meant standing for hours on end waiting for things to happen. Usually one or two cadets would faint during this ordeal and this added a bit of interest to the otherwise dullness.

John Ashurst with Duke of Edinburgh 1965

One year the top-notch was the Duke of Edinburgh. He arrived by helicopter, landing in the playing field, and that was sufficient novelty to mark the event in our memories. So we did the general salute and march past thing, like in the Trooping the Colour, in which you marched forward whilst facing to the right and saluting. And then back to standing at attention in our ranks whilst the Duke did his rounds, stopping every so often to ask some boy an inane question. And I fervently hoped that he would not stop in front of myself. The same sort of feeling as in pass-the-parcel with forfeits, or that ridiculous party game where you have to dress up and eat a bar of chocolate with knife and fork, chocolate the previous folk have slobbered over...

Clive Sinclair, slide rules and log tables

Clive Sinclair, entrepreneur par excellence

Long, long ago, when I was in the sixth form at PSS, calculators of the add / subtract / multiply / divide type were starting to become commonly available but were not allowed in school... Calculators, it seemed, were for the weak.

Instead we were taught long multiplication and division, and to use log tables in maths although in science we were allowed to use a slide rule. A slide rule works like log tables but is a whole lot easier to use.

If you know all about logs and slide rules, or if you are already bored out of your mind, then this is the place to stop reading.


If...

then, by definition,

Thus the exponent (aka index) x in the first equation is the logarithm to base n of y.  The clever bit comes as a result of the rules of indices, thus

Here I have changed the variable names (otherwise I would have run out at 'z'), and shown that when two numbers r and s are multiplied, their logarithms are added.

The same applies whatever the base n is.

So, back then, long, long ago, we had 4-figure log tables, or 5-figure if you were lucky (or had a lot of time on your hands). These were look-up tables for finding the logarithm of a number to 4 or 5 decimal places. The book would also contain tables for the inverse operation "anti-log" (which is one and the same as exponentiation) together with tables for finding the sine, tangent or cosine of an angle and their inverse operations, square and cube roots, and such-like.  A mathematician's ready reckoner. To multiply two numbers you first look up their logs, then add these together and look up the anti-log of the answer.

You show a book of log tables to today's youth and they won't believe that this is how we did multiplications and divisions.

The slide rule has logarithmic scales so that the logarithm of a number is translated into physical length - to multiple two number you simply move the sliding part (which also has a logarithmic scale for the second number) thus adding the distances and effectively adding the logarithms. The final value is read off using the first scale which thus takes the anti-log and gives the product.  Other scales are included for finding trigonometrical functions and squares or square roots.

You can get 3 figure accuracy from a slide rule if you are careful which was good enough for most undergraduate experimental work.

At college a friend purchased a Sinclair Scientific calculator - the first scientific calculator within reach of students. Although it only had 5 digit accuracy this machine was a wonder to behold. I bow to Clive Sinclair whose inventions have been truly prophetic even if they were not always wholly reliable.

Talking about Clive, the same friend owned a Micromatic - a matchbox sized radio - on which, during school lunch break, we used to listen to I'm sorry I'll read that again, a radio show which was a precursor to Monty Python.

When I started work at Kingswood Warren I was introduced to the HP35 which, apparently, was introduced in 1972 as the first ever scientific calculator but too expensive for the average student. It boasted a splendid bug in that it reckoned that exp(ln (2.02))=2.  This was corrected in the next model HP45.

These calculators had power-hungry red LED displays - liquid crystal had not been invented. Talking of LED's I remember a boy bringing an LED to school - it was the first I had ever seen and blew my mind: at last a source of light without (much) heat just like a glow-worm!

And talking about inventions - an interesting coincidence, for someone that works in electronics, is that the transistor was invented around the time or just before I was born.

So much has changed since then - the rest is history...