EXPANSION OF SOLIDS WITH RISE OF TEMPERATURE. 27 



if A is kept fixed, B will be lowered a distance, 3i. If after this 

 we allow the brass to expand, B will be now raised a distance 2b, and 

 since 2& = 3i, B resumes its original position. 



The pendulum as actually made is merely a double 

 arrangement of this kind as in Fig. 19, where two 

 metals, of expansion in the ratio 2:1, are taken for 

 simplicity of construction. 



A mercurial compensating pendulum is frequently 

 employed. In this the bob consists of a glass cylindrical 

 vessel containing mercury. As the temperature rises, 

 the vessel is lowered through the increase in length 

 of the pendulum rod. But at the same time the 

 mercury expands more than the glass, and its centre of 

 gravity rises in the vessel. The depth of the mercury 

 is so adjusted that the effective length of the pendulum 

 is invariable. 



M. Guillaume has discovered a nickel-steel, which 

 he terms " Invar," which has a negligible co-efficient 

 of expansion at ordinary temperatures. This is very 

 suitable for pendulum rods, and will probably super- 

 sede compensating pendulums. It has already super- 

 seded compensating measuring rods for survey purposes. 



In compensating chronometers, the difference of 

 expansion is made use of in another way. The rate of 

 the chronometer depends on the resistance of the hair- 

 spring to coiling, and on the disposition of the mass 

 of the balance-wheel. As the temperature rises, the 

 resistance of the hair-spring decreases, and if the 

 wheel were of one metal it would expand and throw 

 its mass farther from the centre, On both accounts 



IG. 19. Gridiron 

 Pendulum of 2 

 metals, with ex- 

 pansion : : 1 : 2. 



the time of vibration would be longer and the chronometer would lose. 

 But the rim of the balance is made of two metals, say brass and steel, of 

 unequal expansion, that with the less expansion being inside, and the 



wheel is discontinuous as shown in Fig. 20. 

 The outer rim expands more than the inner, 

 and the two loaded ends therefore curl in- 

 wards with rise of temperature. The loads 

 are so adjusted that the mass is thrown 

 inwards by a sufficient amount to compensate 

 for the weakening of the hair-spring and the 

 expansion of the spokes. It may be noted 

 that the effect of the weakening of the spring 

 is far greater than that of the expansion. 



Metallic thermometers are made in which 

 FIG. 20.-Compensating Bal- the Une 1 ual expansion of the two parts of a 

 ance for Chronometers, compound curved bar, formed by two strips of 

 Outer rim brass, inner rim different metals brazed together, results in a 

 steel. change of curvature. But the strains to 



which the metals are subjected on being 



raised to a higher temperature are usually so great in these instru- 

 ments that the metals on being brought back to the original lower 



