180 ON THE LAWS OF 



Having thus the value of / (x, y) we thence deduce 

 . n-1 



sm 



The value of p here given being expressed in quantities 

 perfectly independent of the situation of the axis from which 

 the angle & is measured, is evidently applicable when the point 

 P is not situated upon this axis, and in order to have the com- 

 plete value of p, it will now only be requisite to add the term 

 due to the arbitrary constant quantity on the left side of the 

 equation (26), and as it is clear from what has preceded, that 

 the term in question is of the form 



--3 



const, x (1 r z ) * , 



we shall therefore have generally, wherever Pmay be placed, 



. n 1 



-* ( 8 



p = (1 - r'V . const. 



The transition from this particular case to the more general 

 one, originally proposed is almost immediate : for if p represents 

 the density of the inducing fluid on any element dcr^ of the plane 

 coinciding with that of the plate, p l d(r i will be the quantity of 

 fluid contained in this element, and the density induced thereby 

 will be had from the last formula, by changing q into p^cr^. 

 If then we integrate the expression thus obtained, and extend 

 the integral over all the fluid acting on the plate, we shall have 

 for the required value of p 



7T 



ft being the distance of the element dv^ from the point to which 

 p belongs, and a the distance between da^ and the center of the 

 conducting plate. 



Hitherto the radius of the circular plate has been taken as 

 the unit of distance, but if we employ any other unit, and sup- 



