174 Professor Whewell on the 



this machine : 7 the rate of profit. The machine at the end of 

 last year was worth the wages expended on it, together with 

 profits, that is (i + y)Fw. It must produce, this year, the profit 

 on what it is worth, and the wages of those who work it, with 

 profits: that is, it must produce y{l + y)l'w + (l + y)lw. 



In the same manner let a machine have been produced by 

 the labour of I' labourers last year, V in the preceding year, I" 

 in the year before that, and so on. And let / men be employed 

 in working the machine,- then its produce must be worth 



(1 + 7) Iw + (1 + yfl'w + (1+ yfU'w + &c. 



Let L be the number of men requisite to obtain the same 

 produce without the machine. Then Lw is their wages, and (1+7) 

 Lw the value of the produce. Therefore, if the machine can be 

 employed without loss 



{l + y)lw + (l+yy-l'w + (l+yyi"w + &c.= or < (1 + 7) Lw, 



and l + (l + y)l' + (\+ yfl" + &c. = or < L. 



Hence l + l' + l" + &c.<L; 



or, when machinery is employed, it has always cost less labour 

 than would obtain the same produce without machinery, Ric. 



p. 44. 



Let b be the sum expended upon an average, every year for 

 k years, in the construction of the machine, a the value of the 

 machine when constructed. Then 



c =5{(l +7 ) + (l+7) ; ... + (l+7)^=5 v 2> . 



12. When a machine, or stock of any kind, is employed in 

 production, a certain sum is annually requisite to replace the 

 wear and tear of the capital so existing. Mr. Ricardo supposes 

 these annual sums to accumulate at interest, so as to become suf- 



