224 Journal of the Asiatic Society of Bengal. [June, 1912. 
is the first integral of (1); and for = 400, a foot anda year being 
the units (assuming the average value of & to be equal to that 
bv, 
found by Thomson for certain specimens of rocks), = will be 
negligible if t= 10°, except for a comparatively small thickness 
(about 568 miles). Thus, the variation is confined to a thin 
crust and therefore the solution will be applicable to the earth 
for 10° years. Moreover the heat gradient given by (3) appears 
The discovery of radium with its peculiar properties funda- 
mentally alters the problem. e have to conceive nucleii of 
highly concentrated energy disseminated through the mass of 
the earth and giving out heat very slo y. 
From this point of view the following problem is of interest, 
(1) Conceive a sphere (centre, origin) in an infinite 
homogeneous solid at every point of whose sur- 
solid harmonio of degree n, at t=0, to find the 
subsequent temperature at every point (7, 6) of the 
solid. 
(2) Let the temperature at the surface at time ft be 
1 
2 {(t) to find the temperature at any point at ¢. 
(1) The solutior. 
ooo). Oo 
ee 2 Wage a 
y k Vv, where ¥ at aye 3 
with the specified condition is 
- 1 ff _@=2'P+y-y'P+@-2) 
A4ntor/ k= —— . ae 
l ' 
yn(zl y! 2!)d8. 

ee re xa! + yy! + 22! 
~ 2h at e Akt ‘ae Qkt 

1 r’+a* rf racos 6 
2h he ee S Be Yet yhz')ds. 
1 r +a” 
os 2k i . Zz : Ae (cos 6)* y,(x%!y!z!) dS. 
(say) (where 9=the angle between z, y, zand z!, y!, z', and 
. 
P,,, a surface harmonic) 

1 r? + q? A 4r 
2k/nt @ 4kb °° O"* Om gy: Yn(%Y %)- 



