181 



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 we should have 



_ /yy-i 



T~ W 



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

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

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

 have 



V 



and the rate of flow of the air will be, in pounds per second, w?QA, 

 if w 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 



t *-l/T\i* 

 -f = (t) 



and therefore we have 



a V l_^ 1 \1/ \ 1 



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

 attains a maximum when 



t = -83 T, 

 the maximum value being 



?=-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 channel, where it is moving slowly. If this temperature 

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

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

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

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



