J. H. Lane on the Theoretical Temperature of the Sun. 68 
length be the foot, this expression is multiplied by 62} to give 
for the mechanical equivalent in foot pounds 
—14+Kx-1 a FA yy! SPF fel 22 te 1 
nek Q° ota? hb = (” r\ 
k—1 Mr'*\ r |} 
(19) 
ms i o-at, of ts heat in the mass 
eac 
makes in a aga path through free eg till it impinges 
upon another compound molecule. If we wish to find the 
mechanical pote ON oe which would be vie to this aati of 
translation alone, we must put =1% in the factor 7-5 ; 5 OF 
which 9-ot¢ is multiplied, and this gives 39°ct. To find ‘Sah 
this the mean of the squares . he. ——— of translation of ° 
the compound molecules, we y the mass g, and, if the 
foot be the unit of length, ie ie = 64:3, whence we have 
for the bia found by taking the square root of this mean 
of the squares 
k—1 
3 k—1 m' R2x'\2/0\ = 
8024/30; i= 8-02(5 : a) (2 £) (20) 
Determination of the curve of density for k= i ‘4.—Beginnin 
with «= 1, in equations (8) and (9), we find «= 2626 an 
0 to 
(2) ='8520. Developing the values of u and a ) for 2= 
iy ‘L, x=1-2, &c., by means of differences we arrive at the values 
#=2°145 and ({) ='1378 whenx=4'0. Putting these values 
into equations (12) and (13) we find 
x’ = 5355, #2’ = 2°188. 
If we now allow 74d of the radius “<i the 7 este evade — 
c Uy 
mean ic gravi earth’s mass at 54, and the mean 
specific eae of ‘he 4 sun within the photosphere at + that of 
the earth, as it is known to be, these values of x’ and u’ give 
us in equation (14) 
“ ¢, = 28°16, 
so that the density of the sun’s mass at the center would be 
nearly one-third greater than that of the metal platinum. 
Curve of densi ty for k=14.—For this value Pe a SR 
coefficients in equations (8) and (9) are placed by those in (10) 
