24 MOLECULAE MOTION AND ITS ENERGY 13 



in which form its agreement with Boyle's law, viz. that 

 the pressure of a gas is proportional to its density, is more 

 directly seen. 



In this new form, however, it teaches us much more ; 

 it empowers us to draw a remarkable and very important 

 conclusion. Since two of the magnitudes occurring in the 

 formula, viz. the pressure p and the density p, are directly 

 amenable to observation and measurement, the formula 

 allows us to deduce from them the third, viz. the value of 

 G, the mean speed of the molecules, in absolute measure. It 

 was Joule T who by this conception opened up to investiga- 

 tion a field which one would have been tempted to think 

 was closed to human knowledge; and Clausius 2 followed 

 him along the path thus trodden to explore an unseen 

 world. 



Though measured by the height h of a column of mercury, 

 the pressure p is not identical with this height, but with the 

 action of gravity on the column when taken of unit area. 

 If, then, q denotes the density of mercury and g the accelera- 

 tion of gravity, we have 



P = 



and therefore G is given by 



G 2 = Sgqh/p. 



Let us make this calculation for the temperature C. 

 and the pressure of one atmosphere, i.e. of a column of 

 mercury O76 metre high. We will take K&gnault's 3 

 value, q = 13-596, and his values for the density of the 

 various gases ; we must therefore take the value of gravity 

 for Paris, where Begnault made his observations, and put 

 g = 9*80896 metres per sec. per sec. The density p of the 

 gas is, like the density q of mercury, to be referred to water 

 as unity ; but if instead it is referred to air, which under the 



1 Mem. of the Manch. Lit. and Phil Soc. [2] ix. 1851, p. 107 ; Phil Mag. 

 [4] xiv. 1857, p. 211. 



2 Pogg. Ann. c. 1857, p. 375 ; Abhandl. iiber d. Warmetheorie, pt. ii. 1867, 

 p. 254 ; transl. Phil Mag. [4] xiv. 1857, p. 108. 



3 M4m. de VAcad. de Paris, xxi. 1847, p. 162. 



