62 J. H. Lane on the Theoretical Temperature of the Sun. 
—3) w—ax k(k—2)(2k—83) — 
k(2k 
A= (A- 1)(2k—1) ge’ @ 12(k—1)2(8k—2) x2 ++ &e. 
Pa lth 0—-Fal 
~ 3k(@k—1) 
With the values of a’ and v’ determined, using 7’ and m’ to 
express in like manner the corresponding values of r and m at 
the upper limit of the theoretical atmosphere, we find from 
equations (4) and (5) 
eS = 
(a’ —a) + &e. 
in mig! 3 
i eed PE (14) 
ne 2yl2 wk 
ee ee 2, 
4n(k —1)R?r!?9, (9 ee. 
and by equation (1), %=— F473 See , (15) 
_k-1 m' Rta! / 9@\3 
= ey *) ee) 
A ee at equation (7) will show that c — equation 
(13), or = ee may be taken equal to e me throughout the 
: Saddeestie upper part of the volume of the hypothetic gas- 
eous body in which 1-5, or 1—-=,, i is sufficiently small to be 
neglected. This substitution in the last equation gives 
k-1 a= 
iemmae "es = —r), nearly, (17) 
— ack 
uw’ k—1 y —r k-1 
and also om (2) Qo (=) nearly, 
Co 
1 cas Ae = r, k-i m —r k-1i 
mee Pe x 73 a (= 5" AB) 
Now the mechanical equivalent of the heat in the mass ¢ of a 
cubic unit in yarns of any perfect gas whose atmospheric 
subtangent is %, is ri ; ¢°ot, and the mechanical equivalent of 
‘the heat that it would give out, in being cooled down under 
constant pressure to absolute zero, is mai? If the density 
¢ is taken in units of the density of water, and the unit of 
ie. sae 
een sa eB act 
TSS Rest: saree GE! 
ES 9 See 
