432 Rev. H. Moseley on the Theory of Resistances in Statics, 

 Also, by the principle of least pressure, 

 2P = minimum 





(2) 



The first of these equations is satisfied by the condition 

 J5*P = a minimum. Multiplying the two last equations by 

 the indeterminate quantities A and B respectively, and adding 

 them to 8£P, we obtain 



SZT = X^ 



f{g(l+A*+B^)+Ap}8* 



[{^(l + Ajr + Bjtf+BpJay 



Let the indeterminate quantities A and B be taken, subject 

 to the condition that for any given values of a x y x% x^y 29 x 3 y 3 , 

 &c, the values of P 15 P 2 , &c, shall be such as will satisfy the 

 equations (1). 



x l y l , x^ycp &c, may then be considered independent vari- 

 ables, and SF a minimum function of these variables. Hence, 

 therefore, 



Adding the above equations, having multiplied the first by 

 dx, and the second by dy, we obtain 



{^dx+ ^T d y) (1 + A^+By)+ F{kdx+Bdy) = O 

 .-. d{P(l+Ax+By)} = 



.. P= 9 



l+Ajr + B^ 



Let there be taken a line at a perpendicular distance from 



the origin, equal to —======— ; also let it be inclined to the 



s/ A" + B 2 



axis of x at an angle a, such that 



