ON THE BALANCE OF THE CHRONO- 

 METER*. 



IT is well known that a common watch goes more slowly 

 when its temperature is raised, and versa vice. The reason of 

 this is that the elasticity of the balance-spring decreases with 

 the increment of temperature and increases with its decrement. 

 Neglecting the mass of the spring and the connection of the 

 balance *fith the other parts of the watch, we may take as the 

 equation for determining the oscillations of the balance, 



eO_ 



dt* + 1~ 



where e depends on the form and elasticity of the spring, and 

 / is the moment of inertia of the balance. The time of oscilla- 



tion depends, of course, on the ratio y, e being, as we have 



said, a function of t the temperature. In order, therefore, 

 to the equable rate of the watch,- it would be necessary that 



/ should be such a function of t, that -j may be constant. In 



the balance of a common watch I is sensibly constant. Hence 

 the inequality of which we have spoken. 



In the chronometer the balance is so constructed that its 

 figure alters when the temperature varies. The figure repre- 



Cambridge MathematicalJournal, No. XXI. Vol. iv. p. 133, May, 1844. 



