520 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
On developing r=a{\-\-^y), and substituting the value otp, we obtain 
+ 27r^ ^da^-\-A^‘7r\^J^ ^ddY^-\-^J^ ^c^Yad- etc.J 
d-S-ry^ ^da^-\-A^'7r\^J^ ^daYV^-^-^J^ ^daW^-\-^J^ ^f/Wad- etc.J 
sin" ^-^/a"(^cos" -\-\fa\ 
But 
z/=Yo+Y,+Ya+....Y,. 
Hence if this value be substituted in the above equation, and if after substitution, 
similar functions of 6 and oj, the coordinates of the point in the nucleus be equated to 
zero, we shall find 
— 2‘r^^y^ ^da^-\- J* ^.d.a^Y J* ^^dd^'W^=.0. 
But (art. 5) as Wo=0, and /*— is constant, this expression shows that Yo may receive 
an arbitrary value. Yi = 0 by the property of the centre of gravity, which is the 
origin of the coordinates. When i=2, 
-5-y__ s.dY,+ —J^^ e-da+-^J^ g.da^Y, 
+|(/— /)«' cos* d— i/a*(cos* 0— i) = 0. 
But we have already found 
(3W,= -m/(o')(cos*d-i), 
hence the above becomes 
4/3j7ra^ 
-^4(0,0') (cos*d-i), 
where a') is a function depending on the attraction of the shell, or in other 
words, depending on the arrangement of the shell’s strata. 
When i is any number greater than 2, we have 
4'!ra’ 
2i-\- 
‘ Vo Z'”' I Z*“' dWi-\ /*“ 7 1 ^TT Z'® j 
But as Wi=0, and as the surface of the nucleus is a spheroid of revolution, Yi= 0. At 
