# Spherometer

Built by David Smithers in September 2007 for the Three Supports Secretary’s Challenge

As its name suggests, this is a device for measuring the diameter of a sphere.

## Theory

The instrument enables you to measure the height *h* shown in figure 1. *d* is the distance between a leg and the central screw.

Mathematics shows that:

*diameter* = (*h*^{2} + *d*^{2}) / *h*

## Practice

*d* can be measured or calculated. For this model, *d*^{2} is exactly 4/3, or 1.333.

To measure *h*, rest the legs of the instrument on the sphere and gently turn the screw until it just touches the sphere. Note the dial reading. Now place the instrument on a flat surface and gently turn the screw until it touches the surface, counting the number of revolutions as you do so. Note the dial reading and calculate the fraction of a revolution from the difference between the two readings. Call the total number of revolutions *n*.

Since Meccano screwed rods have 32 threads to the inch, *h* = *n* / 32. Knowing *d*, we can now work out the diameter using the above formula.