( 175 ) 
The potential of a spherical shell in point P becomes therefore: 
sing R A, sin(qr + @) 
qh r 
A, sin (gr + @) 
Ns 
Though the function is of no importance for the 
theory of the molecular forces, it has nevertheless another remarkable 
physical signification. 
By twice differentiating with respect to x, we shall easily find: 
ap ey A, sin(qr + @) ne 3 A, sin(qr+ a@)a® 3A, ¢ cos (qrtea)x? 4 
ee Na eS 5 a7 4 
du? rè r? r 
A, geos(gr +e) A, q* sin (qr + a) 2? 
ole r2 = a . 
dp dp 
a an 9 
dy” dz* 
sions. By adding these equations, we get: 
Aq sin(gr + @) __ 
7 
In the same way we find for corresponding expres- 
a ik eR Lt) 
VP 
As is well known this differential equation is of great importance 
in the theory of the conduction of heat. The function found is an 
extension of the calorie potential of MaTHiegu. 
; ‚ 3 Ae-v + Bew 
If we had deduced for the first found function p (7) = gd ddr 
the second differential coefficient according to 2, we should have 
found : 
dp Ae-ar 4 Bear  394(Ae—v—Ber)a2?  3(Aear Begr)a? 
Sa Se ins eal eR 
da” rö r r° 
q (Aer — Bear) 4 q? (Ae—ar + Bes) x? 
ns r? 
If we calculate in the same way the corresponding expressions for 
d? ac 
Die ed. 
a aa) We find by putting the three quantities together : 
y z 
!) In putting g=0 we retind the potential which we should have found according 
to the law of attraction of Newton. 
15 
Proceedings Royal Acad. Amsterdam, Vol, LI. 
