THE FORMS OF ENERGY. 119 



for each 1 rise at constant pressure. Let this volume be at and 

 760 mm. pressure in a vertical cylinder 1 sq. cm. section, and let the 

 atmospheric pressure be represented by a piston loaded with a column 

 of mercury 76 cm. high and 1 sq. cm. in section, and so weighing 



76x13-596 = 1033 grammes weight. 



When the air is heated from to 1 the volume expands 1 cc. and the 

 piston is pushed out 1 cm., so that work is done equal to 1033 cm. 

 gms. 



Now let us turn to the heat measurements. The density of air at 

 and 76 cm. is, according to Regnault, '001 293, so that the mass of air 

 heated is 



272-5 x 0-001293 = 0-3523 gm. 



At constant pressure the specific heat of air C.,, is, according to Regnault, 

 0'2375, and according to E. Wiedemann, whose value we shall take, 

 0'2389, and this is the heat put in per gramme of air in raising its 

 temperature from to 1. 



But it is only the excess of this over specific heat at constant volume 

 O r , which is the equivalent of the work done. Now C fl may be found 

 from Op from the relation (chap, xviii.) 



G p Adiabatic Elasticity. 

 C v Isothermal Elasticity. 



This ratio has been determined in various ways, and we may take its 

 value as very near 1-405,* whence 



0-2389 

 ^"TioT 



Then O p -0, = 0-2389 - 0'1700 = -0689. 



Multiplying by the mass heated, we find 



0-0689 x 0-3523 = 0-02427 calory 



as the heat equivalent of the 1033 cm. gms. of work done. Then the 

 mechanical equivalent of the calory is 1033 -r 0*02427 = 42560 cm. gms., 

 and this is the mechanical equivalent in centimetres and grammes 

 weight. Mayer, using the data available in 1842, found 36500 cm. gins. 

 The calculation depends entirely on the assumption that no work is 

 done in the mere separation of the particles of air. In a second paper 

 published in 1845 j Mayer supported the assumption by quoting an 

 experiment by Gay-Lussac (Memoires d'Arcueil, 1807 : Gilbert's Annalen, 

 xxx., 1808, p. 249), which went to show that if a gas expands from one 

 vessel into another equal vessel previously empty, the first loses just as 

 much heat as the other gains. Mayer saw that the cooling in the first 

 vessel is due to the work done by the remaining gas in pushing out that 

 which passes into the second vessel, and the heating in this vessel is due 



* Meyer, Kinetic Theory of Gases, p. 123. 



+ This is slightly less than Joly's direct determination (p. 85), which gives C = 

 0-17154. The uncertainty in the Specific Heat of Air at constant pressure also 

 makes I he result uncertain. 



t Helm, Die Energetik, p. 24. 



