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pound of air ; the first bracketed term of the second member is the 

 excess of work done in pushing it forward, above the work spent by 

 it in pushing forward the fluid immediately in advance of it in the 

 narrow passage ; and the second bracketed term is the amount of 

 intrinsic energy given up by the fluid in passing from one situation 

 to the other. 



Now, to the degree of accuracy to which air follows Boyle's and 

 Gay-Lussac's laws, we have 



if t and T denote the temperatures of the air in the two positions 

 reckoned from the absolute zero of the air-thermometer. Also, to 

 about the same degree of accuracy, our experiments on the tempera- 

 ture of air escaping from a state of high pressure through a porous 

 plug, establish Mayer's hypothesis as the thermo-dynamic law of 

 expansion ; and to this degree of accuracy we may assume the in- 

 trinsic energy of a mass of air to be independent of its density when 

 its temperature remains unaltered. Lastly, Carnot's principle, as 

 modified in the dynamical theory, shows that a fluid which fulfils 

 those three laws must have its capacity for heat in constant volume 

 constant for all temperatures and pressures, a result confirmed by 

 Regnault's direct experiments to a corresponding degree of accuracy. 

 Hence the variation of intrinsic energy in a mass of air is, according 

 to those laws, simply the difference of temperatures multiplied by a 

 constant, irrespectively of any expansion or condensation that may 

 have been experienced. Hence, if N denote the capacity for heat of 

 a pound of air in constant volume, and J the mechanical value of the 

 thermal unit, we have 



Thus the preceding equation of mechanical effect becomes 



Now (see "Notes on the Air-Engine," Phil. Trans. March 1852, 

 p. 81, or "Thermal Effects of Fluids in Motion," Part 2, Phil. Trans. 

 June 1854, p. 361) we have 



