A Treatise On Electricity And Magnetism volume 1

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4- 15 /[144-84/4-&c.
V 2 212 SPHERICAL HARMONICS. [146.
+ afiy*[ 16 + 72/ + 209/+488/ + &C. + # 10 /[ 60+ 342/+1222/ + &C. + a? 12 / [150+1050/ + &C.
64 + &C. (21) It will be more convenient in subsequent operations to write these coefficients in terms of a, b, and c, and to arrange the terms according to their dimensions in c. This will make it easier to differentiate with respect to c. We thus find 19 . (22) (23) (24) -f 40 6 7 k- 13 (25) 146. ] TWO SPHERICAL CONDUCTORS. 213 ( 26 ) -f 5250 9
...9 + 336a 7 n )c- 18 . (27) 14 (28) :i7 . (29) (30) (31) (32) 15 . (33) (34) (35) (36) (37) The values of the r's and ^'s may be written down by exchanging 1 a and b in the ^'s and jo's respectively.
If we now calculate the potentials of the two spheres in terms of these coefficients in the form (38) (39) then, m, n are the coefficients of potential (Art. 87), and of these m = c~ l +jt?i ac~ z +p 2 a? c~* + &c. , (40) n = b-i-frac-t-qzatc-* &c. , (41) 214 SPHERICAL HARMONICS.
or, expanding in terms of a, d, c, (42) c- 22 .


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