60 Mr green, on THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



The value of p here given being expressed in quantities perfectly 

 independent of the situation of the axis from which the angle 6' is 

 measured, is evidently applicable when the point P is not situated upon 

 this axis, and in order to have the complete value oi 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 pre- 

 ceded, that the term in question is of the form 



n-3 



const. X (1 - /') 2 , 

 we shall therefore have generally, wherever P may be placed. 



P = (l-r-) 



1-3 



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 dai of the plane coinciding with 

 that of the plate, p^da-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 pidai. 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 



p=(l-0^ .jconst. \f ^ fp^da ^" J^ }; 



B being the distance of the element dai 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 suppose that b is 



the measure of the same radius, in this case we shall only have to 



.^ a r' d(Tx , R . ,, , „ , , 



write ^ > ^ ' -^ and -g- m the place of a, r, da, and R respectively, 



recollecting that -^ is a quantity of the dimension with regard to space, 

 by so doing the resulting value of jo is 



