470] 
NOTE ON THE ATTRACTION OF ELLIPSOIDS. 
383 
Hence, calculating the approximate values, and restoring in each case the omitted 
factor, 27r, we have 
Attraction 
A = 2ttu — 2 V2 7tgC, 
33 
B — % V2 ira-, 
53 
C — lira — 1 V2 ttcA, 
33 
D = ^ V2 7rcC, 
E — 1 V2 7TOL-, 
33 
or, if we please, 
Attraction 
F = jç V2 7ra- ; 
A 4- B — 27ra — ^ V2 7TCC, 
33 
(7 = 27ra — 1 V2 7toD, 
„ D + E + F = §V2 ?ra* ; 
so that ultimately the attraction of the portion D + E + F vanishes in comparison with 
those of the portions A + B and G; and the attraction of these last, that is, of the 
whole shell, is = 47ra, twice the attraction of an infinite plate of the thickness a.