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XIII. On Electrical Motions in a Spherical Conductor. 
By Horace Lamb, M.A., formerly Fellow of Trinity College, Cambridge, Professor 
of Mathematics in the University of Adelaide. 
Communicated by J. W. L. Glaisher, M.A., F.R.S. 
Received March 14,—Read April 5, 1883. 
This paper treats of the motions of electricity produced in a spherical conductor by 
any electric or magnetic operations outside it. The investigation was undertaken 
some time ago in illustration of Maxwell’s theory of Electricity. This theory is 
so remarkable, more especially in the part which it assigns to dielectric media in the 
propagation of electromagnetic effects, that it seemed worth while to attack some 
problem in which all the details of the electrical processes could be submitted to 
calculation, although it was evident beforehand, from the researches of Helmholtz 4 ' 
and others, that the results (so far as they are peculiar to the theory) would be of far 
too subtle a character to admit of comparison with experiment. In studying the 
mathematical character of the problem above stated I was led to a certain system 
of formulae which I have since utilised in two communications to the London 
Mathematical Society,! and which seem likely to be of use in a great variety of 
physical questions. 
§ 1 consists mainly of a recital of the fundamental equations and of the conditions 
to be satisfied at the surface of a conductor. It is assumed, in the first instance, that 
the magnetic susceptibility of the conductor is zero. 
In §2 is introduced the assumption that all our functions vary as e kt , where t is the 
time, and X a constant. It is pointed out that this assumption is sufficiently general. 
The fundamental equations are then put into a mathematically convenient form. 
Before, however, proceeding to apply these equations as they stand, I examine the 
effect of assuming that the velocity (v) of propagation of electromagnetic effects in 
the medium surrounding the conductor is practically infinite. This assumption, 
which has been made by all writers (including Maxwell himself) who have applied 
Maxwell’s theory to ordinary electromagnetic phenomena, greatly simplifies the 
calculations without sensibly impairing the practical value of the results. If L 
* Crelle, t, 72 (1870). 
t “ On the Oscillations of a Viscous Spheroid,” Proc. L. M. S., Nov. 10, 1881 ; and “ On the 
Vibrations of an Elastic Sphere,” May 11, 1882. 
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