Mr. W. J, M. Rankine on the Mechanical Action of Heat. 17 



spherical layer undergoes, the portion of atmosphere between it 

 and the nucleus is invariable. This condition is expressed by 

 the equation 



from which it follows that 



and consequently that 



— 3 / du .u8u'\lr{u,I>,T) = 



Hence, making 



9 f' — f^du.u^Mu,D,T) = V, . . (5) 



the second integral in equation (2) is transformed into 



By means of those substitutions we obtain, for the mechanical 

 value of the heat consumed in unity of weight of a fluid by any 

 indefinitely small change of volume or of molecular distribution — 



or taking V = -pr to denote the volume of unity 

 of weight of the substance, 



,^„ , . . , ^. T — K BJ) T — « SV 



Of this expression, the portion — jT-yi • "tT ~ r,y,M ' "V" 

 represents the variation of heat arising from mere change of 

 volume. 



(6.) 



T — K^..d\] T — K^^dV 



_ gv -TTT = — TT-TT? BD -m, denotes the variation of heat 



CfiM dV C?tM dl) 



produced by change of molecular distribution dependent on 



change of volume. 



Phil. May, S. 4. Vol. 7. No. 12. Jan. 185 t. C 



