110 OF ELIMINATION. [CHAP. VII. 



coefficient, give, on addition, wt; the terms w (1 - t) p and 

 w(\ ~t) (1 - p) 9 which have - for their coefficient give w ( 1 - 1) ; 

 and the terms (1 - w) (1 - t)p and (1 - w) (1 -t) (1 -p), which 

 have -ft for then* coefficient, give (1 - w) (1 - t). Whence the 

 complete solution is 



_ _ - - , 



with the independent relation, 



w (1 - Z) = 0, or w = - 1. 



The interpretation would now stand thus : 



1st. Things limited in supply consist of all wealth transferable, 

 with an indefinite remainder of what is not wealth and not transfer- 

 able, and of transferable articles which are not wealth, and are not 

 productive of pleasure. 



2nd. All wealth is transferable. 



This is the simplest form under which the general conclusion, 

 with its attendant condition, can be put. 



16. When it is required to eliminate two or more symbols 

 from a proposed equation we can either employ (6) Prop. I., or 

 eliminate them in succession, the order of the process being in- 

 different. From the equation 



w = st (p + r pr), 



we have eliminated r, and found the result, 



w - wst - wstp + stp = 0. 



Suppose that it had been required to eliminate both r and t, then 

 taking the above as the first step of the process, it remains to 

 eliminate from the last equation t. Now when t = 1 the first 

 member of that equation becomes 



w - ws - wsp -f sp, 

 and when t = the same member becomes iv. Whence we have 



w (w - ws - wsp + sp) = 0, 

 or w - ws = 0, 



for the required result of elimination. 



