LF. H. Bigelow—The Harth a Magnetie Shell. 89 
Compare Maxwell’s Electricity and Magnetism, vol. ii, 434, 436; Sir W. 
Thomson’s Electrostatics and Magnetism, p. 486; Sir W. Thomson’s Mathemat- 
ical and Physical Papers, vol. i, p. 35; Watson and Burberry’s Electricity and 
Magnetism, vol. ii, pp. 18-43; Paul Drude’s Physik des Aethers, pp. 36-51. 
Inflected. Ezxflected. 
: Ji 1 
External Potential, Ve=+R°—- HX —Ha vet ORs eS H— Ha 
e+2 7 +2 
—1R DR 32° 
External Force, Xe=—H Bae! =e <a) +H ea ey ak (1-F)+ 
+2 73 w+273 2 
3 TR 
Res Bed | Wes he = (1-3! 
een rs w+2 7° r? 
= ai aes 3 
al teen 1") Tecate BR quire 
e+2 7? r w+? 72 iy 
F 3 w—-LH 
M i | ange ae ee 
agnetization, rote n 
R = radius of sphere; r=radius vector to point &. y.z.; “ = magnetization 
constant; H=magnetic force of field. 
From these can be found expressions for the potential and 
force at the surface or inside the sphere. 
Bors =r cos 0, 47 = 7 sin 
The normal and tangential components are, 
F,= Xcos0+Y sin @ =K—+y¥% 
F,=—Xsin0+Y¥ cos=—X 4 +Y=. 
From the values of Xe, Ye given above, 
M—1 ___, F,sin 0+F cos 6 Inflected System. 
a ~~ (F,+F,)sind—(F,+2F,)cos6 Exflected System. 
_ (Fr +2F,)cos 6—(F,, + F,)sin 0 
1—8sin 6 cos 6 i 
provided the paths inside the surface are known. 
Both systems. 
Stream Lines. 
: ; ; dV dV 
Differential Equation, ae dla — i Pp =)03 
where p is perpendicular to the axis of symmetry «. 
N — dae Sites Const. 
Inflected. 
(a? + p a 2 +3H p° EyAected. 
a ao 2 § 
2R ao a i va Inflected. 
y 
2N Exflected. 
hes 7 a xflecte 
