and on its Measurement by Thermometers, 449 



very small, we have 7 very small also. When we recognize that 

 c is a function of the temperature, say c=f(t°), the correct 

 differential expression becomes 



40-? 



cr 



dy =f{t°)dt° 



and 7 is now the quantity requisite to raise the unit of mass 

 through 1°, and therefore 



= J f(t°)dt° 



With respect to the dynamical definition of the measure of 

 temperatures, we have the formula of MM. Dulong and Petit as 

 follows. Let v be the velocity or rate of cooling of a body in a 

 vacuum, {0+t) the temperature of the body, 6 the temperature 

 of the substance surrounding the vacuum, a and m constants, and 



then 



i;=M(«'-l) 



They say*, "We may conclude, then, that if it were possible to 

 observe the absolute cooling of a body in a vacuum, that is to 

 say the loss of heat of a body, without any restoration on the 

 part of the surrounding bodies, this cooling would follow a law 

 in which the velocities would increase in a geometrical progres- 

 sion, while the temperatures increase in an arithmetical progres- 

 sion ; and, further, that the ratio of this geometrical progression 

 would be the same for all bodies, whatever the state of their 

 surface may be." In their experiments the ratio was 1*0077 

 for all bodies, and M = m . a 6 is the return radiation of the sur- 

 rounding body ; and in order that this may be zero, we must 

 have 6=. —• 00, or the absolute zero of temperature must be at an 

 infinite number of degrees below the freezing-point of water; 

 and yet, as they argue, M may not be zero, since the capacities 

 of bodies diminish as their temperatures dimmish.* 



The expression for the rate of cooling becomes, if t is the time, 



dt° 

 dr 



or, taking finite differences for differentials, 



-8t°=v.ST=Ma i0 .ST 



* Herschel 'On Heat,' p. 280. 



