Graham, in the year 1715, made several experiments to ascertain the relative expansions of various metals, with a view of availing himself of the difference of the expansions of two or more of them when opposed to each other, to construct a compensating pendulum. But the difference he found was so small, that he gave up all hope of being able to accomplish his object in that way. Knowing, however, that mercury was much more affected by a given change of temperature than any other substance, he saw that if the mercury could be made to ascend while the rod of the pendulum became longer, and _vice versâ_, the centre of oscillation might always be kept at the same distance from the point of suspension. This idea happily gave birth to the mercurial pendulum, which is now in very general use. [Illustration: _Captn. Kater, del._ _H. Adlard, sc._ _London, Pubd. by Longman & Co._] In the mean time, Graham’s suggestion excited the ingenuity of Harrison, originally a carpenter at Barton in Lincolnshire, who, in 1726, produced a pendulum formed of parallel brass and steel rods, known by the name of the gridiron pendulum. In the mercurial pendulum, the bob or weight is the material affording the compensation; but in the gridiron pendulum the object is attained by the greater expansion of the brass rods, which raise the bob upwards towards the point of suspension as much as the steel rods elongate downwards. In the present article, we shall describe such compensation pendulums as appear to us likely to answer best in practice; and we trust we shall be able to simplify the subject so as to render a knowledge of mathematics in the construction of this important instrument unnecessary. The following table contains the linear expansion of various substances in parts of their length, occasioned by a change of temperature amounting to one degree. We have taken the liberty of extracting it from a very valuable paper by F. Bailey, Esq., on the mercurial compensation pendulum, published in the Memoirs of the Astronomical Society of London for 1824. TABLE I. _Linear Expansion of various Substances for One Degree of Fahrenheit’s Thermometer._