66 Electric and Magnetic Science. 



represents the sum of all the electric or magnetic charges in the 

 field, divided by their respective distances from some given point : 

 to this function Green gave the name potential, by which it has 

 always since been known.* 



Near the beginning of the memoir is established the 

 celebrated formula connecting surface and volume integrals, 

 which is now generally called G-reeris Theorem, and of which 

 Poisson's result on the equivalent surface- and volume-distribu- 

 tions of magnetization is a particular application. By using 

 this theorem to investigate the properties of the potential, 

 Green arrived at many results of remarkable beauty and 

 interest. We need only mention, as an example of the power 

 of his method, the following : Suppose that there is a hollow 

 conducting shell, bounded by two closed surfaces, and that a 

 number of electrified bodies are placed, some within and some 

 without it ; and let the inner surface and interior bodies be 

 called the interior system, and the outer surface and exterior 

 botlies be called the exterior system. Then all the electrical 

 phenomena of the interior system, relative to attractions, 

 repulsions, and densities, will be the same as if there were no 

 exterior system, and the inner surface were a perfect conductor, 

 put in communication with the earth ; and all those of the 

 exterior system will be the same as if the interior system did not 

 exist, and the outer surface were a perfect conductor, containing 

 a quantity of electricity equal to the whole of that originally 

 contained in the shell itself and in all the interior bodies. 



It will be evident that electrostatics had by this time 

 attained a state of development in which further progress could 

 be hoped for only in the mathematical superstructure, unless 

 experiment should unexpectedly bring to light phenomena of 

 an entirely new character. This will therefore be a convenient 

 place to pause and consider the rise of another branch of 

 electrical philosophy. 



* Euler in 1744 (De melhodis inveniendi . . .) had spoken of the vis potentialis 

 what would now be called the potential energy possessed by an elastic body 

 when bent. 



