6 PREFACE. 



developed in copper, wood, glass, etc., by rotation, might be 

 explained. On this hypothesis M. PoisSON has founded his 

 third memoir, and thence deduced formulae applicable to mag- 

 netism in a state of motion. Whether the preceding hypothesis 

 will serve to explain the singular phenomena observed by 

 M. ARAGO or not, it would ill become me to decide; but it is 

 probably quite adequate to account for those produced by the 

 rapid rotation of iron bodies. 



We have just taken a cursory view of what has hitherto been 

 written, to the best of my knowledge, on subjects connected 

 with the mathematical theory of electricity; and although many 

 of the artifices employed in the works before mentioned are 

 remarkable for their elegance, it is easy to see they are adapted 

 only to particular objects, and that some general method, capable 

 of being employed in every case, is still wanting. Indeed 

 M. PoiSSON, in the commencement of his first memoir (Mem. 

 de V Institute 1811), has incidentally given a method for deter- 

 mining the distribution of electricity on the surface of a spheroid 

 of any form, which would naturally present itself to a person 

 occupied in these researches, being in fact nothing more than the 

 ordinary one noticed in our introductory observations, as re- 

 quiring the resolution of the equation (a). Instead however 

 of supposing, as we have done, that the point p must be upon the 

 surface, in order that the equation may subsist, M. POISSON 

 availing himself of a general fact, which was then supported by 

 experiment only, has conceived the equation to hold good 

 wherever this point may be situated, provided it is within the 

 spheroid, but even with this extension the method is liable to 

 the same objection as before. 



Considering how desirable it was that a power of universal 

 agency, like electricity, should, as far as possible, be submitted 

 to calculation, and reflecting on the advantages that arise in the 

 solution of many difficult problems, from dispensing altogether 

 with a particular examination of each of the forces which actuate 

 the various bodies in any system, by confining the attention 

 solely to that peculiar function on whose differentials they all 

 depend, I was induced to try whether it would be possible to 

 discover any general relations, existing between this function 



