Dimensions of Physical Quantities. 105 



Thus the satisfactory expressions of the dimensions of the 

 various thermal units is not possible so long as there is any 

 doubt as to the mechanical definition of temperature. 



The equation 



[ML2T-2] = [JMc6'] 



leads, if we regard c as a number, to the result 



The quantity 6 can hardly be taken as an abstract number, 

 because the scale on which it is measured affects the numerical 

 value of J, but, on the other hand, temperature as measured 

 on the ordinary thermometer-scales has no relation to the 

 units of length, mass, or time. No change in these units 

 would aflFect the magnitude of the degree Centigrade or 

 Fahrenheit. So long, therefore, as we adhere to the system 

 of measuring heat in terms of caloi'ies instead of in ergs, tem- 

 perature must be regarded as a fundamental quantity in the 

 sense that the unit of temperature, though necessary for the 

 expression of other thermal units, is itself independent of the 

 units of length, mass, and time. 



If it were sufficiently certain that the analogy offered by 

 the theory of gases might be extended to all cases, it would 

 follow that temperature depended only on mean energy of a 

 particular kind (in gases the mean energy of translation) 

 possessed by the molecules. The mean value of a quantity 

 is of the same dimensions as the quantity itself, and thus 

 temperature might be regarded not only as being measured 

 by, but as being the mean energy of translation of a mole- 

 cule, or of a standard number of molecules. The dimensions 

 of temperature would thus be [ML^T~^]. The number 

 which expressed a given temperature would depend on the 

 fundamental units, because they determine the magnitude of 

 the unit of energy. It would be independent of the concrete 

 mass or velocity of the molecules of any particular gas. 



In the case of air at 0° C. and at atmospheric pressure 

 V = 48,500 centim. per second. If then, exempli gratia, 

 the unit of temperature were that necessary to produce an 

 increase of 1 erg in the mean total energy of translation of 

 the number of molecules contained in 1 cub. centimetre of gas 

 at 0° C. and at atmospheric pressure, the absolute tempera- 

 ture of melting ice on this scale would be 



1 X -001293 X 485002=1-5207 x 10^ 



Absolute temperatures Centigrade could be converted into 

 this scale with considerable accuracy bv the multipher 10^18 ; 

 for, dividing 1-5207 x 10' by this number, we get 273-7, 



