514 Mr TOZER, ON THE EFFECT OF MACHINERY 



And the community would gain or lose as 



r, 1-0--' 1, 



- > or < , — ^ + - /. 

 r 1—qq 



The common mode of calculating the annuity A has been used, 

 but it does not appear to be strictly applicable; it makes no provision 

 For paying machine makers in the first year after the machinery comes 

 Jnto use, and does provide for their payment in the (rf + 1) year; 

 that is, after the machinery is finished. 



To commence the manufacture of new machinery immediately an 

 additional capital must be employed, to advance the wages of its 

 makers; and if the same sum is paid every year in this way, the ad- 

 ditional capital must equal that part of the annuity A which is avail- 

 able for a similar purpose. 



Let Cy be the additional capital. 



Cy is the annuity, commencing at the beginning of 1'' year and 

 ending at the beginning of rf'" year, which pays for the machine. 



Hence, since at the beginning of «?"" year this amounts to 

 Cy(l+9 + .... 9^-) = Cy.?^, 



and at the end of rf* year this is worth Cy .q. '—-— , which must = C, 



Again, the produce must supply an annuity A, which pays the 

 profits on C{\+y), and accumulates by the end of r/"' year to C{\+y). 



Tlie accumulation is therefore worth 



at end of V year A-C{l^-y){q-l), 



2"^ year {A- C{\ + ij){q-\)\ {\+q). 



which must = C(l +y). 



rf'-year \A-C{l^y){q-\)\^^, 



