The Theory of the Polar Planimeter,

Transactions and Proceedings of the Royal Society of New Zealand, Volume 34, 1901, Page 569

Papers.—1. “The Theory of the Polar Planimeter,” by C. E. Adams, B.Sc. Sir James Hector said that a most ingenious form of a planimeter had been devised by Mr. Beverley, an inventive gentleman of Dunedin, still among us, and was shown at the, New Zealand Exhibition nearly forty years ago. The following was an abstract of the account of Mr. Beverley's instrument which was given in the Report on the New Zealand Exhibition, 1865, page 188. This was now a very rare book. “Two Plato-meters (not named ‘Planimeters’), invented and made by A. Beverley, Dunedin, are interesting and valuable instruments. An instrument to effect the same purpose was first exhibited by the famous inventor and mathematician Mr. E. Sang, of Kirkcaldy, in Scotland, at the exhibition of 1851. Other similar instruments have been invented, especially by Professor Clerk Maxwell, to overcome the mechanical difficulties by the introduction of contact spheres. This is a beautiful idea, but mechanically impossible. Mr. Beverley's platometer, which rejects sliding motion, and is very simple and inexpensive, should come into general use in all survey offices.” At the same time he showed a clock which had been going ever since it was made without the aid of weights or springs—which, in fact, as far as motive-power was concerned, had been untouched since its construction. A glass cylinder filled with air resting on a surface of cantor-oil supplied the power, every change in temperature affecting the pressure. The force thus generated was taken up by an ingenious mechanical contrivance and conveyed to the works. For forty years the timepiece had kept time without stopping, and it bade fair to go as long as the works held together and the day and night temperatures continued to vary. A member who objected that the pinions would clog and wear out was reminded that the problem of perpetual motion was apart from wear-and-tear of mechanism. Mr. Martin Chapman remarked that he had known the clock, which was still going, for many years past.