180 



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 

 t n the absolute temperature of freezing (about 274 Cent.).' Hence 

 we have 



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

 the product of \/7c 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 



Hence we derive from the preceding equation, 



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 irregxilarities 

 in the channel, the air may have experienced before coming to the 

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

 out heat or to take in heat from the matter round it, nor to lose 

 any mechanical energy in sound, or in other motions not among its 

 own particles, the preceding formulae will give the lowering of tem- 

 perature it experiences in acquiring the velocity q. It is to be 

 observed that this is not the velocity the air would have in issuing in 

 the same quantity at the density which it has in the slow stream 

 approaching the narrow passage. Were no fluid friction operative 

 in the circumstances, the density and pressure would be the same in 



