283 



cular vortices, wliile the second is a consequence of the law of the 

 conservation of vis viva. 



First, As every portion of an atomic atmosphere is urged towards 

 the nucleus or atomic centre by a centripetal force equal to the cen- 

 trifugal force arising from the oscillation which constitutes heat, it 

 follows that, when by compression, each portion of such an atmo- 

 sphere is made to approach the centre by a certain distance, the vis 

 viva of its oscillation will be increased by the amount corresponding 

 to that centrifugal force, acting through that distance ; and conversely, 

 that, when, by expansion, each portion of the atmosphere is made to 

 retreat from the centre, the vis viva of its motion will be diminished 

 by a similar amount. 



Secondly, Let a portion of any substance undergo any changes of 

 temperature, volume, and figure, awd at length return to its primi- 

 tive volume, figure, and temperature. Then, the absolute quantity 

 of heat in the substance, the arrangement of the atoms, and the dis- 

 tribution of their atmospheres, being the same as at first, it follows 

 that the algebraical sum of the vires vivse cojisumed and produced 

 during the changes, whether in the shape of expansion and compres- 

 sion, or in that of heat, must be equal to zero ; that is to say, if on 

 the whole, a certain amount of mechanical power has appeared, and 

 been given out from the body in the form of expansion, an equal 

 amount must have been communicated to the body, and must have 

 disappeared in the form of heat ; and if a certain amount of 

 mechanical power has appeared and been given out from the body in 

 the form of heat, an equal amount must have been communicated to 

 the body, and must have disappeared in the form of expansion. 



From those principles the author deduces an algebraical expres- 

 sion of three terms. The first term represents the variation of heat 

 arising from mere change of volume ; the second, the variation of 

 heat produced by change of the distribution of the density of the 

 atomic atmospheres dependent on change of volume ; and the third, 

 the variation of heat due to change of the distribution of the density of 

 the atomic atmospheres, dependent on change of temperature. In all 

 those terms there is a common factor, bearing a constant ratio to the 

 absolute quantity of heat in the body. In the first term, that factor 

 is multiplied by the variation of the logarithm of the density of tlie 

 body, and in the second and third by certain functions of the density 



