THERMAL EFFECTS OF FLUIDS IN MOTION. 
359 
tory principles. From (22) and its equation of condition (19) we derive only a single 
equation among the constants, which is as follows : — 
A/q + B 
(A ^-75 + B ) 2 
(c+^-+jr-) =-008163. 
\ M -75 ‘475/ 
(31) 
Another equation besides the three, (27), (29), and (31), is required to determine 
the four remaining unknown constants, A, C, D, G ; and is afforded by a determina- 
tion of the density of air, which has been most accurately given by Regnault, who 
finds that the weight of 26224 cubic feet of air at constant temperature 0° Cent, and 
constant atmospheric pressure, in lat. 45°, amounts to the same as the pressure per 
square foot, a result which is expressed by the equation 
nO = 26224. 
Here II denotes the value of p in the empirical formula (17), which corresponds to 
t=t 0 , (the absolute temperature of the freezing-point,) and Hence we have 
the equation 
A«„+B+C+2+!=26224 (32) 
l 0 l o 
Calling 26224, H, (the “ height of the homogeneous atmosphere”) for brevity, and 
denoting the true value of A t 0 by which must be very nearly equal to H, we may 
simplify the treatment of the four equations by taking the approximate value H for 
At 0 , in three of them, (27), (29), (31), without losing accuracy, and we may after- 
wards use (32) to determine the exact value of $|. Accordingly (and to avoid subse- 
quent confusion of algebraic signs in the numerical results) it is convenient to 
assume 
C=-?JK D=^j3, G=-Hy. ...... (33) 
Then, taking everywhere B=0 as we have found it, we have, instead of (32), (27), 
(29), (31) respectively, 
1 -a +fri) =H 
(34) 
JK 5+ n 
1 0 +17 + «0+17) S_ H t 0 x 
100 “-(T + 1 -w)^+(T + l-(^o?W ) y=1004x ' 000011575 • 
and 
^ 0 + 4‘75 (£ + 4 
' _(t 0 + 4-7$ 
■7or~\ t 0 
X *008163. 
(35) 
(36) 
(37) 
Reducing to numbers the coefficients of a, (3, y, and the other terms, by using the 
value 273'72 found above (30) for f 0 ; 1390 for J ; and ’238 for K according to the 
observations and theoretical conclusion regarding the absolute value of the specific 
heat of air under constant pressure, published in Notes to Mr. Joule’s paper on the 
