CHAP. VII.] OF ELIMINATION. 107 



be if the element r, referring to prevention of pain, were elimi- 

 nated. Now bringing the terms of the equation to the first side, 



we get 



w st (/? + r rp) - 0. 



Making r = 1, the first member becomes w st, and making 

 r - it becomes w - stp ; whence we have by the Rule, 



(w - si) (w - stp) = 0, (7) 



or w - wstp - wst + stp = ; (8) 



whence stp 



= st + stp - 1 ' 



the development of the second member of which equation gives 

 w = stp + Q$t(l -p). (9) 



Whence we have the conclusion, Wealth consists of all things 

 limited in supply, transferable, and productive of pleasure, and an 

 indefinite remainder of things limited in supply, transferable, and 

 not productive of pleasure. This is sufficiently obvious. 



Let it be remarked that it is not necessary to perform the 

 multiplication indicated in (7), and reduce that equation to the 

 form (8), in order to determine the expression of w in terms of 

 the other symbols. The process of development may in all cases 

 be made to supersede that of multiplication. Thus if we de- 

 velop (7) in terms of w, we find 



(1 - st) (1 - stp) w + stp (l-w) = 0, 



whence _ stp 



= stp -(I -st) (I -stp)' 9 



and this equation developed will give, as before, 

 w = stp + - st(l - p). 



13. Suppose next that we seek a description of things limited 

 in supply, as dependent upon their relation to wealth, transferable- 

 ness, and tendency to produce pleasure, omitting all reference to 

 the prevention of pain. 



