108 OF ELIMINATION. [CHAP. VII. 



From equation (8), which is the result of the elimination of 

 r from the original equation, we have 



w - s (wt + wtp - tp) - ; 



whence w 



s - 

 wt + wtp - tp 



= wtp + wt(l-p)+-w(l-t)p + -w(l- t) (1 - p) 



We will first give the direct interpretation of the above solution, 

 term by term ; afterwards we shall offer some general remarks 

 which it suggests ; and, finally, show how the expression of the 

 conclusion may be somewhat abbreviated. 



First, then, the direct interpretation is, Things limited in 

 supply consist of All wealth transferable and productive of pleasure 

 all wealth transferable, and not productive of pleasure, an indefi- 

 nite amount of what is not wealth, but is either transferable, and not 

 productive of pleasure, or intransferable and productive of pleasure, 

 or neither transferable nor productive of pleasure. 



To which the terms whose coefficients are - permit us to add 

 the following independent relations, viz. : 



1st. Wealth that is intransferable, and productive of pleasure, 

 does not exist. 



2ndly. Wealth that is intransferable, and not productive of plea- 

 sure, does not exist. 



14. Respecting this solution I suppose the following remarks 

 are likely to be made. 



First, it may be said, that in the expression above obtained 

 for " things limited in supply," the term " All wealth transfer- 

 able," &c., is in part redundant ; since all wealth is (as implied 

 in the original proposition, and directly asserted in the indepen- 

 dent relations) necessarily transferable. 



I answer, that although in ordinary speech we should not 



