ON TIMEKEEPERS. 199 



the cause of the error. The strength of the spring is found to be less im- 

 paired by use when it is hardened than when the steel is softer. It some- 

 times happens, that from a sudden motion, or from some other accidental 

 circumstance, the balance of a timekeeper may be thrown beyond the point 

 at which the pallets are impelled by the scape wheels, and the whole motion 

 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 pro- 

 gress of the balance, by intercepting a pin which projects from it. This ar- 

 rangement is called banking the balance. 



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

 dulums are proportional to their lengths ; so that if we add to a pendulum 

 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 ex- 

 pansion has a similar elFcct in the motion of a balance, and the increase of 

 temperature produces also a diminution of the elastic force of the spring it- 

 self. There is, however, a great ditt'erencc in the expansibilities of various 

 substances; dry deal is one of the least expansible, and is therefne often 

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

 thousand for every degxee of Fahrenheit, or a little more or less tloan 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 84- seconds in a day; a ba- 

 lance 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 Bertlioud 

 informs us, that where a clock, probably with a pendulum of steel, loses 20 

 seconds by heat, a watch loses eight minutes. 



Mr. Graham appears to have been the first tliat attempted to compensate 

 for the effects of temperature by the different expansibilities of various sub^ 



