60 oJ. H. Lane on the Theoretical Temperature of the Sun. 
is to be kept up by the oe due to the mutual approach 
of the parts of the sun’s mass consequent on the loss of heat 
by oy come in when we perins a material departure 
from these laws of Mariotte and of Poisson at the extreme 
Spiiipecratnres and pressures in the sun’s body, or how far such 
difficulties intervene, will be considered further on. 
means of the constant value of o,and the value of ¢ 
given in (1), the above differential equation is transformed into 
hokey =~ bss 
the integral of which gives 
Q ie k—1 RR? = ade 
day Wow aay ae oMt, Oyo re yet (2) 
in which @o I is the value of ¢ at the sun’s center. 
We have 
r ts 
aif or? dr= 470, ve Sot dp, (3) 
0 0 2% 
If now we a 
ko Mt, 4 
aa pee ri) * (4) 
we shall have ' 
ko Mt 8 
mate NR) . ©) 
in which ft —0? dz, (6) 
and equation (2) becomes 
Q ee ude 
es a ys ae (7) 
In equations 6) and (7) it is plain that upon the value of & 
alone depends: first the form of the curve that expresses the 
value of > for each value of x; secondly, the value of the 
0 
upper limit of « corresponding to ar? ; and thirdly, the cor- 
+ 
responding value of «. These limiting, or terminal, values of 
x and “, cannot be found except by calculating the curve, for 
equations (6) and (7) seem incapable of being reduced to a com- 
plete general integral. But when these values have been found 
any proposed value of &, they may be introduced once for 
all into equations (4) and. 5), from which the values of 2; and 
of ¢ fy 8 are at once deduc 
made these calculations for two different’ assumed 
valine: of k, viz., k=1-4, which is near the experimental ele 
