238 THE POPULAR SCIENCE MONTHLY 



in equation (2), temperature T x being higher 6 than temperature T 2 . 

 Therefore, since m 1 and ra 2 depend only upon T x and T 2 , respectively, 

 it is permissible to adopt the equation 



TJT 2 = mjm 1 (4) 



as the definition of the ratio T 1 /T 2 . This definition of temperature 

 ratios is originally due to Lord Kelvin. 



Another way to express the definition which is involved in equation 

 (4) is to consider that the factor m 1 is the smaller the higher the 

 temperature T 1} so that we may adopt k/m t as the measure of the 

 temperature T 1 and Jc/m 2 as the measure of the temperature T 2 , giving 



m 1 = fc/T 1 (5) 



and 



m , 2 = Je/T 2 (6) 



where h is an indeterminate constant. Therefore equations (2) and 

 (3) may be written in the general form 



$ = lcW/T (7) 



where </> is the thermodynamic degeneration involved in the conversion 

 of an amount of work W into heat at temperature T, and h is an 

 indeterminate constant. 



The ratio of two temperatures as defined by equation (4) is very 

 nearly the same as the ratio of two temperatures as measured by the 

 gas thermometer, and therefore gas thermometer temperatures may be 

 used throughout this discussion without appreciable error. 7 



Since the factor Jc in equation (7) is indeterminate, we may use 

 as our unit of thermodynamic degeneration the amount which is 

 involved in the conversion of one unit of work into heat at a tem- 

 perature of one degree on the " absolute " scale ; then the value of 

 h is unity and equation (7) becomes 



c)> = W/T (8) 



6 The idea of higher and lower temperature is not dependent upon any 

 method of measuring temperature. When a substance receives heat definite 

 observable effects are produced, and when these effects are produced by placing 

 one substance in contact with another substance, the other substance is known 

 to give heat to the given sixbstance and its temperature is known to be higher 

 than the temperature of the given substance. Does not one know that a stove 

 is hotter than the floor, for example, when one spills water partly on the stove 

 and partly on the floor? 



7 One of the most important discussions in elementary thermodynamics is 

 that which establishes this fact. See Art. 58 of Franklin and MacNutt's 

 " Elementary Theory of Heat " for a very simple discussion of this matter. 



