I. Mathematical Investigations concerning the Laws of the Equilibrium 

 of Fluids analagous to the Electric Fluid, with other similar Researches. 

 By George Green, Esq. Communicated hy Sir Edward Ffrench 

 Bromhead, Bart. M.A. F.K.S.L. and E. 



[Read Nov. 12, 1832.] 



Amongst the various subjects which have at different times occupied 

 the attention of Mathematicians, there are probably few more interesting 

 in themselves, or which offer greater difficulties in their investigation, 

 than those in which it is required to determine mathematically the 

 laws of the equilibrium or motion of a system composed of an infinite 

 number of free particles all acting upon each other mutually, and ac- 

 cording to some given law. When we conceive, moreover, the law of 

 the mutual action of the particles to be such that the forces which 

 emanate from them may become insensible at sensible distances, the 

 researches to which the consideration of these forces lead will be greatly 

 simplified by the limitation thus introduced, and may be regarded as 

 forming a class distinct from the rest. Indeed they then for the most 

 part terminate in the resolution of equations between the values of 

 certain functions at any point taken at will in the interior of the sys- 

 tem, and the values of the partial differentials of these functions at the 

 same point. When on the contrary the forces in question continue 

 sensible at every finite distance, the researches dependent upon them 

 become far more complicated, and often require all the resources of 

 the modern analysis for their successful prosecution. It would be easy 

 so to exhibit the theories of the equilibrium and motion of ordinary 

 fluids, as to offer instances of researches appertaining to the former 

 class, whilst the mathematical investigations to which the theories of 

 Electricity and Magnetism have given rise may be considered as in- 

 teresting examples of such as belong to the latter class. 



Vol. V. Pakt I. A 



