450 Prof. Potter on the Definition of the Temperature of Bodies, 



and if — 67°= 1°, we have 



l°=Ma t \8r 



and the time St becomes longer as t° is less. 



The full discussion of these formulae was not carried out by 

 MM. Dulong and Petit ; but, remembering the principle of the 

 homogeneity of algebraic expressions applied to physics, we may 

 easily put them into an intelligible form. 



Taking the formula v = Ma e> , let v be the value of v when 

 /° = 0, and then 



V=M 



and since a and t are numbers, the equation is homogeneous, 

 and may be put into a form more intelligible, since v would be 

 unknown. 



Let t°=0 + t! , and v' the value of v when the temperature 



was 6, 



or 







then 

 and 





v r =v . aQ 



v v .a^ +t ' os > 

 v 1 v Q . a 6 



v = v' . a* 



= a tl0 



and the law holds good for any assumed zero of temperature ; 

 also if we put * ,0 = 1°, 



-j— = [a — 1) = constant 



v— v 



for any temperature, and the change in the rate of cooling is 

 uniform. 



Taking the logarithms, we have 



<*log>)=log € (J) 



and 



t fo = 



**6) 



log e (a) 



which expresses the temperature t'° for any assumed zero in 

 terms of the velocities of cooling by radiation only ; and the de- 

 grees above zero equal the logarithm of the ratio of the velocity 

 of cooling at that temperature to the velocity of cooling at the 

 zero of the scale divided by a constant quantity. This is the 

 dynamical measure of the temperature t'° on the scale ; and v, the 



