ON THE WEALTH OF A COMMUNITY, &c. 509 



If C be engaged in paying wages, it will yield annually a profit 

 = C{q-\); this, while the machinery is in progress, must be partly 

 taken from capital. 



Suppose the machinery to take b years to complete, and a part 

 of C = - to be expended every year in its construction till it is com- 

 pleted, then the productive capital will be diminished, 

 at the beginning of 1"' year by — , 



2" f(l+?). 



^"^ J (1+9 + 9'). 



b'' -(1 + 9+ «'->) = ^?^ 



^ ^ ^ ' X q-l ' 



S + 1- ^.qt^, 



X ^ q-\ ' 



and at this time the whole capital will have been expended on the 

 machine ; 



Let a fractional part, the m''' of the expenditure for machinery, 



go to the labour, and B„ B, ^^ be the sums by which the fund 



for paying wages is diminished during the 1^', 2"" ...!.. p'" years of the 

 progress of the machinery. 



Thus 



B,=-{l-m), B, = ^(l+q-m); 



B, = ^{l+q + q'-m), 



' X \q-l j q q'-\ \q - \ '") 



3t 2 



