510 Mr TOZER, on THE EFFECT OF MACHINERY 



The total loss to the labour-fund while the machinery is in pro- 

 gress is 



a; ' a — 1 



X "■ q- 



And in the 1 '*' year of its employment the whole capital C is abstracted. 



Let the machinery be made to last rf, years by the expenditure 



of «i, fh, «3 ftd, in the 1^', a'"", f/' years respectively and be worth 



a when rejected : also let the expenditure and profit be equivalent 

 when the machine continues d years unimpaired, and then becomes 

 useless. 



This condition gives 



w,?"' + (kq"'-' + +a,,q-a = C{q'^-q% 



or 2(«,9"'-')-a = C(9^. -«?";; 

 and d = log. {(^^0 - ^(Sa,?".-' -a)} ^ 



log. q ■ 



Let V^ be the exchangeable value of the machinery, 



A the annuity necessary to pay the profit on C and provide 

 new machinery at the end of f/' years, paying also for the 

 necessary repairs during this interval, 



ri, the produce due to the use of the machinery, 



r to the labour it displaces, 



p, p^, prices of produce before and after its employment, 



G the whole annual gain to the community occasioned by its 

 uses. 



