The dilatation of substances by heat, and their contraction by cold, occasion such irregularities in the rate of clocks and watches as would render them unfit for astronomical or nautical purposes, were it not for a very beautiful application of the laws of unequal expansion. The oscillations of a pendulum are the same as if its whole mass were united in one dense particle, in a certain point of its length, called the centre of oscillation. If the distance of this point from the point by which the pendulum is suspended were invariable, the rate of the clock would be invariable also. The difficulty is to neutralize the effects of temperature, which is perpetually increasing or diminishing its length. Among many contrivances, Graham’s compensation pendulum is the most simple. He employed a glass tube containing mercury. When the tube expands from the effects of heat, the mercury expands much more; so that its surface rises a little more than the end of the pendulum is depressed, and the centre of oscillation remains stationary. Harrison invented a pendulum which consists of seven bars of steel and of brass, joined in the shape of a gridiron, in such a manner that, if by change of temperature the bars of brass raise the weight at the end of the pendulum, the bars of steel depress it as much. In general, only five bars are used; three being of steel, and two a mixture of silver and zinc. The effects of temperature are neutralized in chronometers upon the same principle; and to such perfection are they brought, that the loss or gain of one second in twenty-four hours for two days running would render one unfit for use. Accuracy in surveying depends upon the compensation rods employed in measuring bases. Thus, the laws of the unequal expansion of matter judiciously applied have an immediate influence upon our estimation of time; of the motions of bodies in the heavens, and of their fall upon the earth; on our determination of the figure of the globe, and on our system of weights and measures; on our commerce abroad, and the mensuration of our lands at home.
The expansion of the crystalline substances takes place under very different circumstances from the dilatation of such as are not crystallized. The latter become both longer and thicker by an accession of heat, whereas M. Mitscherlich has found that the former expand differently in different directions; and, in a particular instance, extension in one direction is accompanied by contraction in another: for example, Iceland spar is dilated in the direction of its axis of double refraction (N. 205), but at right angles to that axis it is contracted, which brings the crystal nearer to the form of the cube and diminishes its double refractive power. When heat is applied to crystals of sulphate of lime, the two optical axes (N. 207) gradually approach, and at last coincide; when the heat is increased, the axes open again, but in a direction at right angles to their former position. By experiment M. Senarmont has concluded, that in media constituted like crystals of the rhomboidal (N. 169) system the conducting power varies in such a manner, that, supposing a centre of heat to exist within them, and the medium to be indefinitely extended in all directions, the isothermal surfaces are concentric ellipsoids of revolution round the axes of symmetry, or at least surfaces differing but little from them. The internal structure of crystallized matter must be very peculiar thus to modify the expansive power of heat.