Prof. Thomson on the Thermal Effects of Fluids in Motion. 287 



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 rnay 

 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 



E-e = JN(T-0. 

 Thus the preceding equation of mechanical effect becomes 



| = PvO-^) + JN(T-0. 



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

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

 June 1854, p. 361) we have 



,^ _ _1_ H 1_ PV 



•' ~ k-\ t, - k-l T' 

 where k denotes the ratio of the specific heat of air under constant 

 pressure to the specific heat of air in constant volume ; H, the pro- 

 duct of the pressure into the volume of a pound, or the " height of 

 the homogeneous atmosphere" for air at the freezing-point (26,215 

 feet, according to Regnault's observations on the density of air), and 

 tg the absolute temperature of freezing (about 274° Cent.). Hence 

 we have 



^ = Pvfi+JLVi_£.) = ^ZZfi_i\ 



2ff \ k-U\ T/ k-l \ Tj 



Now the velocity of sound in air at any temperature is equal to 

 the product of \//c into the velocity a body would acquire in falling 

 under the action of a constant force of gravity through half the 

 height of the homogeneous atmosphere ; and therefore if we denote 

 by a the velocity of sound in air at the temperature T, we have 



a" = kffVY. 

 Hence we derive from the preceding equation, 

 T- 1 _ k-l fqV 

 T ~ 2 [ccj ' 

 which expresses the lowering of temperature, in any part of the 

 narrow channel, in terms of the ratio of the actual velocity of the 

 air in that place to the velocity of sound in air at the temperature 

 of the stream where it moves slowly up towards the rapids. It is to 

 be observed, that the only hypothesis which has been made is, that 

 in all the states of temperature and pressure through which it passes 

 the air fulfils the three gaseous laws mentioned above ; and that 

 whatever frictional resistance, or irregular action from irregularities 

 in the channel, the air may ha^e experienced before coming to the 

 part considered, provided only it has not been allowed either to give 



