OK, so what the devil is an old-fashioned slide rule doing in a collection supposedly dedicated to programmable calculators, you ask?

The answer is simple: slide rules are not merely the oldest practical scientific calculators in existence, but they also happen to offer, in the hands of the expert user, capabilities that can only be replicated by electronic calculators if they have at least some rudimentary keystroke programming capability.

Slide rules are, of course, based on an important property of logarithms: when you multiply two numbers, the logarithm of the result is just the sum of the logarithms of the multiplicands. Adding numbers with a ruler is easy: you measure one distance next to another, and the combined distance will be the sum of the two. Slide rules are merely rules that are marked not with ordinary numbers, but their exponents; this way, the distances you add are really the logarithms of the numbers on the markings, and the result that you read off will be the product.

In other words, slide rules are very effective for multiplying and dividing numbers. But slide rules with multiple scales offer a lot more: their scales let you easily read off logarithms and exponents, trigonometric and other functions. And, when you combine this capability with the use of the sliding scale, what you in fact get is a programmable device, that can perform a variety of predetermined operations easily and repetitively.

Here is a concrete example. Let's say you wish to compute the volume of a sphere: $V=4\pi r^3/3$. You can, of course, perform this computation as a number of separate steps: take the logarithm of $r$, multiply it by 3, take the exponent of the result, multiply that by 4 and then by $\pi$, and then divide by 3. Kind of boring, especially if you need to repeat the computation several times for different $r$'s.

Or, how about this: make sure that the C, D, and K scales are visible. Slide the 1 on the C scale over 1.612 on the D scale. This completes the "programming" of the device. Now to actually compute the volume for a given $r$, move the marker over r on the C scale. Read the result off the K scale. Presto.

For instance, if you move the marker over 2, the result on the K scale will be approximately 33.5. A quick check with an electronic calculator shows that indeed, the correct result is 33.51.

How is this possible? Well, the K scale is just the cube of the numbers on the C and D scales. By setting the C scale properly, we "preprogrammed" a multiplication of $r$ by 1.612, which is just the cube root of $4\pi/3$. The result is then raised to the third power when we read off the corresponding number from the K scale.

The same computation would take approximately 10 or so program steps on your typical keystroke-programmable calculator. How is that for a device that was invented some two centuries ago?