288 Royal Society : — 



out heat or to take in lieat 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 

 the slow stream flowing away from, and in the slow stream approach- 

 ing towards the narrow passage ; and each would be got by con- 

 sidering the lowering of temperature from T to t as simply due to 

 expansion, so that Ave should have 



T \v) 



by Poisson's formula. Hence if Q denote what we may call the 

 "reduced velocity" in any part of the narrow chaimel, as distin- 

 guished from q, the actual or true velocity in the same locality, we 

 have 





and the rate of flow of the air will be, in pounds per second, wQA, 

 if IV denote the weight of the unit of volume, under pressure P, and 

 A the area of the section in the part of the channel considered. 

 The preceding equation, expressed in terms of the " reduced velo- 

 city," then becomes 



and therefore we have 



The second member, which vanishes when ^ = 0, and when t=T, 

 attains a maximum when 



t = -83 T, 

 the maximum value being 



Q 



- = -578. 

 a 



Hence, if there were no fluid friction, the " reduced velocity" could 

 never, in any part of a narrow channel, exceed '578 of the velocity 

 of sound, in air of the temperature which the air has in the wide 

 parts of the cbannel, where it is moving slowly. If this temperature 

 be 13° Cent, above the freezing-point, or 287° absolute temperature 

 (being 55° Fahr., an ordinary atmospheric condition), the velocity 

 of sound would be 1115 feet per second, and the maximum reduced 

 velocity of the stream wotJd be 644 feet per second. The cooling 

 effect that air must, in such circumstauces, experience in acquiring 



