ON TIMEKEEPERS. 153 



may from this cause be interrupted. To prevent this accident, a small bar 

 or pin is usually fixed on the balance spring, which is carried outwards 

 when the vibration begins to be extended too far, and stops the further 

 progress of the balance by intercepting a pin which projects from it. This 

 arrangement is called banking the balance. 



We have already seen that the squares of the times of vibration of two 

 pendulums are proportional to their lengths ; so that if we add to a pen- 

 dulum one hundredth part of its length, we increase the time of its vibration 

 very nearly one two hundredth. But since all bodies are expanded by heat, 

 the variable temperature of the atmosphere must necessarily produce 

 changes of this kind in the motions of pendulums, and it may be observed 

 that a clock goes somewhat more slowly in summer than in winter. The 

 same expansion has a similar effect in the motion of a balance, and the 

 increase of temperature produces also a diminution of the elastic force of 

 the spring itself. There is, however, a great difference in the expansibilities 

 of various substances ; dry deal is one of the least expansible, and is there- 

 fore often used for the rods of pendulums. Brass expands one part in a 

 hundred thousand for every degree of Fahrenheit, or a little more or less 

 than this, accordingly as it contains more or less zinc. Glass and platina 

 are less than half as expansible as brass, iron about two thirds, and 

 mercury three times as much. A pendulum of brass would therefore 

 make one vibration in ten thousand less at 70 than at 50, and would lose 

 8^ seconds in a day : a balance regulated by a spring would lose much 

 more ; for I have observed that vibrations governed by the elasticity of 

 steel have lost in frequency as much as one ten thousandth part for a 

 single degree of Fahrenheit ; and Berthoud informs us, that where a clock, 

 probably with a pendulum of steel, loses 20 seconds by heat, a watert loses 

 eight minutes. 



Mr. Graham appears to have been the first that attempted to compen- 

 sate for the effects of temperature by the different expansibilities of various 

 substances. He employed for a pendulum, a tube partly filled with mer- 

 cury ; when the tube expanded by the effect of heat, the mercury expanded 

 much more ; so that its surface rose a little more than the end of the pen- 

 dulum was depressed, and the centre of oscillation remained stationary.* 

 This mode of compensation is still practised with success; but the 

 gridiron pendulum is more commonly used ; it was the invention, of 

 Harrison, t who combined seven bars, of iron or steel, and of brass, in such 

 a manner, that the bars of brass raised the weight as much as the bars of 

 iron depressed it. At present five bars only are usually employed, two of 

 them being of a mixture of zinc and silver, and three of steel. Mr. Ellicott$ 

 suspended a pendulum at the extremity of a lever, which was supported* 

 by a pillar of brass much nearer to the fulcrum ; as the pendulum ex- 

 panded, the end of the lever was raised in the same degree, and the weight 



* A Contrivance to avoid the Irregularities of a Clock's Motion, Ph. Tf. 1726. 

 xxxiv. 40. 



t In 1726. An account is to be found in the Minutes of the Roy. Soc. for 1749, 

 and in Ph. Tr. xlvii. 521. See also Harrison's work, with preface by Maskelyne, 

 4to, Lond. 1767. 



J Ph. Tr. 1752, xlvii. 479. 



