350 
MR. C. GODFREY ON THE APPLICATION OF FOURIER’S 
In the present case S = 0, and 
C = 
V 
cos 2i tux dx. e~ hv '. v dv dpi 
(Wo 
, + j i)\(sL\; 
- XV J \2ttYJ 
Now 
+ CO 
5 
COS 27 TUX- 
(J.r 
- JL)\ [XL 
XV j \2irV 
— CO 
+ 00 
27 rvp (* cos 2-ttux dx 2iruv 2 r irY 
= cos ——+ \ - , , X2 - = cos . —— 
\ a! , + ¥_\‘ « vf 
2ttYJ 
W e may omit certain constant factors, and write 
2 7 TV.p 1 vfu , * 7 7 
. — . e v e M . v dv dp 
v f 
. ^. «-K)- 
_rfu 
C W' 
c=n 
Jo J i 
AY [ 
= a— 
27T?( Jo 
COS . 
0 J o NV 
. 2ttVjV chi 
0 sm ^v ‘ 7 
We may still further simplify this by introducing the notation of page 347. 
Omitting unnecessary factors, 
If- vkY dV 
C = - sm — . — 
n Jn Yh- ./(P 
= - ( sin 2b aP . 
U Jo 
/(P) 
dV 
e-W-Wf-“ F/(P) 
. e 
—P 2 — a 2 v,P/(P) 
(vii.), 
when 
26 = 
0 
a* = 
V/b 
7 r-ns 2 
Yh 4 
P = r/d 
- p2 / 1 
/(?) = p + ( fh + 2 
\ rP 
e *VR 
To deduce V (the visibility function) from C, all we have to do is to put u = 0 in 
C, and divide C by the quantity thus formed. 
Limiting Case of Zero Pressure. 
§ 44. If the pressure is very small, n, the number of molecules in unit volume 
becomes small, and with it a~. We are thus reduced to 
»- p2 dP 
- o f(ef 
Tait, ‘Edinb. Trans.,’ a t o1. 33, p. 95. 
