590 Dr. W. J. Walker on the Effect of 



where p ± is the pressure in the reservoir in lb. per sq. ft. abs. 

 v 1 is the specific volume of the gas in the reservoir in 

 cubic feet per ]b., 



_ P _ pressure at discharge 

 p 1 pressure in reservoir * 



The suffix c in u c and Q e refers to the constancy, of specific 

 heat as assumed in the derivation of these formulae. 



In applying the foregoing equations (1) and (2) to experi- 

 mental results it is customary to account, by one means at 

 least, for departures from theoretical discharges by a suitable 

 variation of 7. Such a procedure can scarcely be called a 

 satisfactory one, and it is proposed in what follows to deduce 

 a rational formula (assuming, at first, linear variable specific 

 heat conditions) which will require no such adjustment. 

 This can then be extended to include quadratic variable 

 specific heat conditions and so on for any variation of specific 

 heat with temperature of the form K = a + bT + cT 2 + dT 3 + . . . 

 which may be specified. 



In the adiabatic expansion of a gas, the velocity at any 

 cross-section of the stream is given by 



i a = 2gK\ dT feet per sec, 



(3) 



■assuming a reservoir of infinite capacity, K p being the specific 

 heat at constant pressure, in ft. lb. per lb. per degree centi- 

 grade, T being temperature in degrees centigrade absolute 



Let K P = A + ST, 



K„ = B + ST, 

 .K« being the specific heat at constant volume. 



Also, let m= ^, 



A ■, S 



and x= — . 



..-. » 2 = 2</[A{T 1 -T}+|{T^-T^}] 



= 2 9 ^zr x ipi v i -pv] \ 1 + ^r Got +P2V2) J . (4) 



INow, during adiabatic changes of state 

 p V m e \T — constant. 



