Temperature in Length, Mass, and Time. 97 



which has that temperature ; and that t is proportional to E. 

 Thus temperature is a quantity of the same kind as energy, 

 and its dimensions are therefore 



ML 2 T~ 2 . 



Again, we have seen that k depends only on the size of the 

 degrees on our scale of temperature ; and these degrees have 

 hitherto been chosen of an arbitrary size. 



If we were intimately acquainted with the constitution of 

 bodies, the mass of their separate molecules, and so on, we 

 should be able (without requiring any experiments on that 

 hypothetical condition of matter called " perfect gas ") to find 

 the value of k corresponding to degrees of any given size on 

 the absolute scale. Or, again, a given value of k will deter- 

 mine the size of the degrees on our scale. If we assume k=l, 

 we get an absolute unit of temperature, derived from those of 

 length, mass, and time, and independent of any other quan- 

 tities. The relation (2) then becomes £ = E ; i. e. any tempe- 

 rature is measured by the mean-kinetic-energy-per-molecule 

 of a perfect gas having that temperature. With the C.G.S. 

 system of units, the unit temperature would he that of a perfect 

 gas whose mean kinetic energy per molecule ivas one erg. 



From our present knowledge of the mass of molecules, and 

 of the properties of imperfect gases, we may form a very 

 rough idea of the relation between the Centigrade and the 

 C.G.S. scales of temperature. For a perfect gas we have the 

 relation 



PV = §x kinetic energy of gas, 



where n = number of molecules in the volume V, and E, as 

 before, is the mean-kinetic-energy-per-molecule. Now let 

 P = one atmosphere = (roughly) 10 6 dynes per square centi- 

 metre, let V = 1 cubic centim., and let the temperature be 

 0° C. Then, according to Sir W. Thomson's measurements, 

 n — about 6 x 10'- 1 ; 



3 10 6 xl 



~2 6xl0 21 ' 

 = 2-5xlCT 16 . 



This number is then a very rough estimation of the value 

 of the temperature 0° C. in absolute C.G.S. measure. Thus 

 273 Centigrade degrees are equivalent to 2*5 x 10 -16 absolute 



Phil Mag. S. 5. Yol. 24. No. 146. July 1887. H 



