FC 52/80

Ever thought about slide rule used to add two numbers with it?

Well, in this post you will find some tricks to use your slide rule in very different ways.Written in 2005, I repost the entire article here to prevent it to dissapear, as many things before, in the Net.

Original from AntiQuark site, here.

The main purpose of slide rules is to do multiplication. Slide rules were never designed for addition… OR WERE THEY? If you ignore the fact that addition is trivial with a pencil and paper, and is possible to do mentally without being a superhuman, you might find the addition tricks useful (assuming you still use a slide rule.)

Another trick is that you can multiply with a slide rule. Yeah I know, slide rules were designed for multiplying. But the cool thing is, you can multiply WITH THE WRONG SCALES!

So, next time someone at a party starts with the lighter tricks, just whip out your slipstick and wow the crowd with the following maneuvers…

Adding with the C and D scales.

The C and D scales are logarithmic scales designed for multiplication. Since we want the result of x + y, we need to find a multiplier (let’s call it m) such that x * m = x + y. Solving for m:

x * m = x + y
m = x/x + x/y
m = x/y + 1

Following the steps below will multiply x by x/y+1, resulting in x + y.

Example: calculate 2.3 + 4.5

- Move the leftmost ’1′ of the C scale to 2.3 on the D scale.
- Move the cursor to 4.5 on the D scale.
- Notice that the cursor is at 1.956 on the C scale.
- Mentally add 1 to 1.956 to get 2.956. Move the cursor to 2.956 on the
C scale.
- The cursor will now be at the sum of 2.3 + 4.5 on the D scale, or 6.8.

Adding with the L scale

There isn’t really anything special about this trick. L (or Log) scales
on a slide rule are unusual in that they are evenly spaced like a
regular measuring scale. As a result, simple addition of the distances
on the L scale is equivalent to numeric addition. Any ruler with an L scale won’t do though; the L scale has to be on the slider for this trick to work. It seems that this layout was more common on Picketts than on any other brand.

Example: calculate 0.23 + 0.45

- “Reset” the rule so that all the scales are lined up.
- Move the cursor to 0.23 on the L scale.
- Move the leftmost 0 on the L scale to the hairline.
- Move the cursor to 0.45 on the L scale.
- Reset the rule again so that all the scales are lined up.
- The cursor should now be at 0.68 on the L scale, which is the sum of
0.23 + 0.45.

Multiplying with Log-Log scales

The LL (or Log Log) scales are for exponentiation, or calculating x^p. To do multiplication on these scales, we have to find a power p such that x^p is equal to x * y.
Solving for p:

x^p = x * y
p log(x) = log(x * y)
p = log(x)/log(x) + log(y)/log(x)
p = log(y)/log(x) + 1

Notice the similarity to the addition trick above. The steps below will calculate x^{log(y)/log(x) + 1} which is equal to x * y.

Example: calculate 4.5 * 6.7 on the LL3 scale.

- Move the cursor to 4.5 on the LL3 scale.
- Move the leftmost 1 (the index) of the C scale to the cursor.
- Move the cursor to 6.7 on the LL3 scale.
- Notice that the cursor is at 1.264 on the C scale.
- Mentally add 1 to 1.264 to get 2.264. Move the cursor to 2.264 on the
C scale.
- The cursor should now be at 30.15 on the LL3 scale, which is the
product of 4.5 x 6.7

Dividing with Log-Log scales

Similarly to the multiplication trick above, we want to find a power that produces the same result as a division.

x^p = x / y
p log(x) = log(x / y)
p = log(x)/log(x) – log(y)/log(x)
p = 1 – log(y)/log(x)

The mental calculation here, 1-N, is a little more difficult than 1+N. I find it’s easier if you don’t try any mental calculations, and instead measure ticks symmetrically around 0.5.

Example: calculate 95 / 20.

- Move the cursor to 95 on the LL3 scale.
- Move the rightmost 1 on the C scale to the cursor.
- Move the cursor to 20.
- Notice that the cursor is at 6.57 on the C scale. (Actually it’s at 0.657, but this explanation is infinitesmally easier if I say it’s at 6.57.)
- Mentally calculate 5 – 6.57. It’s easy if you think of reflecting the
value 6.67 to the other side of 5. Instead of a point 1.57 to the right
of 5, go 1.57 to the left of 5. Move the cursor to 3.43.
- The cursor should now be at 4.75 on LL3, which is the result of 95/20.

Trucos con la regla de cálculo

¿Alguna vez has pensado por qué no se pueden hacer sumas (y restas) con una regla de cálculo?

En el artículo trascrito íntegramente, en inglés, se demuestra que (al menos la suma) la regla de cálculo puede ser usada en formas que quizás no estaban previstas ni documentadas en los manuales de uso. He copiado íntegramente el artículo de AntiQuark para preservarlo para la posteridad y evitar que se pierda en la red ( ).