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...