46 APPLICATION OF THE PEECEDING RESULTS 



value before found, / 3 = ~/ l~~0~D + 7pf> an ^- neglecting 



&*pj we obtain 



- pda, 



the same quantity as on the element da- of the first surface. If, 

 therefore, we conceive any portion of the surface A, bounded by 

 a closed curve, and a corresponding portion of the surface B, 

 which would be cut off by a normal to A, passing completely 

 round this curve ; the sum of the two quantities of electric fluid, 

 on these corresponding portions, will be equal to zero ; and con- 

 sequently, in an electrical jar any how charged, the total quantity 

 of electricity in the jar may be found, by calculating the quan- 

 tity, on the two exterior surfaces of the metallic coatings farthest 

 from the glass, as the portions of electricity, on the two surfaces 

 adjacent to the glass, exactly neutralise each other. This result 

 will appear singular, when we consider the immense quantity of 

 fluid collected on these last surfaces, and moreover, it would not 

 be difficult to verify it by experiment. 



As a particular example of the use of this general theory : 

 suppose a spherical conductor whose radius a, to communicate 

 with the inside of an electrical jar, by means of a long slender 

 wire, the outside being in communication with the common 

 reservoir ; and let the whole be charged : then P representing 

 the density of the electricity on the surface of the conductor, 

 which will be very nearly constant, the value of the potential 

 function within the sphere, and, in consequence of the communi- 

 cation established, at the inner coating A also, will be 4-TraP 

 very nearly, since we may, without sensible error, neglect the 

 action of the wire and jar itself in calculating it. Hence 



/3 = 4?raP and f = 0, 



and the equations (8), by neglecting quantities of the order 6, 

 give 



We thus obtain, by the most simple calculation, the values of 



