CASH, SOLO
and TOAD.

24th January 2014. We needed to make a tapering bush for our
phonograph cylinder player project. (Two, actually; one for each end of the
cylinder, but that’s not important right now.) Above you see the first. It’s a
piece of 2" diameter aluminium bar, about
1.125" long. But we had to a machine a taper on it, so that it would go
inside the cylinder record and support it. After measuring a number of
cylinders, we decided that the taper should go from 2" to 1.6" over
about 0.75 of an inch. Fine, we thought, and set up the compound slide on our
little lathe. But then arose a problem – what angle did we need to set to
achieve our desired taper? I suppose we could just have tried the ‘suck it and
see’ approach, but this was uninviting. Then I remembered, yet again, dear old
Dr. Kober. He was our third-year form master, which
would have been in the academic year 1957-58, at Camp Hill Grammar School,
Birmingham. He taught maths, at which I was always
dreadful. However, when we started on Trigonometry, he wrote on the blackboard
three mnemonics, acronyms: CASH, SOLO and TOAD, which have stayed with me ever
since. Of course, Trigonometry is all to do with right-angled triangles, so
let’s look at one:

For
any of the three angles in the triangle, the word TOAD meant: Tangent = length
of the Opposite side divided by length of the ADjacent
side. Hence TOAD. (The adjacent side could not be the
Hypotenuse, because that was the special, exalted side of the triangle.)

Similarly,
SOLO meant Sine = length of the Opposite side divided by length of the LOng side (i.e. the Hypotenuse). Hence SOLO.

Likewise,
CASH meant Cosine = length of the Adjacent Side divided by the length of the Hypotenuse.
Hence CASH.

This
was clearly the way forward! We rapidly drew our triangle…

0.75"
was the length of our taper; 0.4" was the desired reduction in diameter –
but this is shared equally on both sides of the workpiece, so we need to lose
half that by machining away 0.2". It was easy to calculate the Hypotenuse,
*h*, as *h*^{2} = 0.75^{2} + 0.2^{2}
. So we knew all the sides, & hence could use CASH, SOLO or TOAD
just as we liked. Let us use CASH:

Cosine
= Adjacent Side divided by Hypotenuse; and angles, as I dimly recall, are often
called *θ, *so:

*cosθ* =
0.75 / 0.7762

*cosθ** *= .9662

From
online tables, *θ* = 15°, almost
exactly. Bingo. Hence the lump of metal in the image above.

It
is indeed a tribute to the teaching abilities of Dr. Kober, that I still remember CASH, SOLO and TOAD to this day,
and better still, have been able to use that information to solve a problem. He
had a wonderful way of ‘putting things over’ to his sometimes rather
indifferent, or in my case opaque, pupils. He still did this, when it was
widely discussed & believed, that he had been in a Concentration Camp in
during WW2, and had come to the U.K. afterwards; though this can only be
conjecture on my part. It was so long ago. Yet I still remember quite clearly,
after he had been absent for some time through illness, he returned,
ebulliently, to our class, and proclaimed: ‘Hello boys! Good to see you. I hope
you haven’t missed me?’ At that point, the Form Captain should have told us to
stand up and applaud this valiant man. But those were conventional days, when
such displays of enthusiasm were not really acceptable. Still, the foregoing
may stand as a small but sincere tribute to an excellent teacher who imparted
many useful things to a large number of pupils, the best part of 60 years ago.

*Page written
24th January 2014.*

*Re-formatted 19th December
2015..*