 Thacher's Cylindrical Slide Rule  © Museum of the History of Science, Oxford This instrument is a very clever design of slide rule. It is 50 centimetres in length and is therefore already quite big, but to do calculations to the same accuracy on a straight slide rule, the straight slide rule would have to be over 20 metres long.

The main purpose of a slide rule is for doing complicated multiplication and division. Before the invention of electronic calculators, slide rules were the only way of doing big calculations without looking answers up in heavy books of printed tables. Until about twenty years ago most school children learnt how to use a slide rule. Slide rules depend on the theory of logarithms. This theory was discovered by the Scottish mathematician John Napier in 1614 and is very important. The theory of logarithms (logs) states that one number multiplied by another is equal to the log of the first number added to the log of the second number. If you know the logs of the two numbers, by looking them up in a table, it is simple to perform the multiplication. Rather than use a table to look up the logs of the numbers you are multiplying, it is also possible to use a ruler with a logarithmic scale of numbers drawn on it. On this scale, as the numbers increase, the distance between them starts to decrease, at a rate that follows a precise mathematical law. If you put two logarithmic scales side by side so that they can slide against one another, it is simple to add the logarithms of two numbers together: place the start of the second scale at the log of the first number you are multiplying, then find the log of the second number you are multiplying on the second scale and see what number it is next to on the first scale. Think about it. This is the answer to the multiplication and is all you need to know to use a slide rule. If you want to do division, just do the same thing in reverse. © Museum of the History of Science, Oxford
This cylindrical slide rule is just a clever way of allowing two very long logarithmic scales to slide past one another. One of the logarithmic scales is printed on paper glued to the cylinder. The other logarithmic scale is cut up and glued to the outer framework of bars. The cylinder can be rotated and the outer framework of bars can be moved from side to side. This allows any number on the first scale to be lined up with any number on the second scale. With it, multiplication and division of numbers with up to four digits can be done. This slide rule was patented by Edwin Thacher in 1881 and was made by the Keuffel and Esser Company of New York, in about 1890. Interestingly, a very similar slide rule appears on the windowsill of Woody Allen's office in his famous film about New York, Manhattan, made in 1979.  