3.3 Gauge Marks

Many slide rules have additional markings on their scales called “Gauge Marks” (sometimes called gauge points). A gauge mark indicates a commonly used numerical value that can be found quickly for use in certain computations. The most common mark is usually for the value of \(\pi\) = 3.14159… On the rule used in the examples above, we see a \(\pi\) symbol on the A and B scales. Consider its use for the following (which is similar in technique to our last example): Set the 1 on the B scale to the \(\pi\) gauge mark on the A scale. On the D scale directly below the \(\pi\) will be \(\sqrt{\pi} \approx 1.77\). Now look at numbers along the C scale; take 4, for instance. The number below it on the D scale will be \(\sqrt{\pi} \times 4 \approx\) 7.09. Looking directly up on the A scale we see the “square” of this result, which will be \(\pi \times 4^2 = 7.09^2 \approx\) 50.3. That is, with the B scale gauged to \(\pi\) on the A scale, the A scale will give the area of a circle for any radius read off from the C scale. Check: Suppose the radius is 2; then without moving the slide at all one can find the value of 2 on the C scale and directly read off the area \(\pi\times 2^2\) = 12.5 on the A scale right above. A great time saver when repeating many similar calculations!

Using a \pi Gauge Mark.
Using a \(\pi\) Gauge Mark.

Other gauge marks might be for \(\pi/4\) = 0.785, \(\sqrt{\pi}\) = 1.772, and \(\sqrt{\pi/4}\) = 0.886, which are often used for calculating cross sections and volumes, etc.; \(e\) = 2.718, for exponentials; Watts/Horsepower = 746 (or, 7.46 on the rule), for power conversion calculations; degrees/radian = 57.30 (or, 5.73 on the rule) for trigonometry calculations, and many others.

Some slide rules have very few if any gauge marks, while some slide rules have many. And while there was a bit of consistency in the labeling of certain special numbers (\(\pi\) was most always marked as \(\pi\)), there certainly was no set standard and so many variations are seen. In fact some slide rules might have a “mark” on the rule, but the mark does not have a label at all. The definitive guide to the values and labels of Gauge Marks on slide rules can be found in the Pocketbook of the Gauge Marks, by Panagiotis Venetsianos, published by the Oughtred Society and available on its web site. Another nice table can be found at the ISRM web site.