152 ^^' GREGORY ON HORSE POWERS, 



Staeaton's mea- A (ingle inrtance may be adduced, to which the meafure 

 p^Sbk^to an' °^ ^'"- Smeaton is inapplicable, and in which we muft have 

 horfe fuftaining recourfe to fome fuch meafure as that mentioned by Profeflbr 

 i^weightr'^"'^^ Robifon. Suppofe that a horfe while (landing ftill fuftains by 

 means of a rope and firaple fixed pulley, a mafs of a hundred- 

 weight, and thus keeps it fufpended at the top of a well, for 

 the fpace of a minute. Neither the animal nor the weight 

 moves, but (hall we therefore fay, in conformity, as it would 

 feem, with Mr. Smeaton*s meafure, that there is no power 

 expended, and no etfed produced ? On the contrary we know 

 there is a power expended, and that the effort if fufficiently 

 Jong continued would completely tire the horfe. The effedl 

 which is produced is the annihilation of the fimultaneous a6lion 

 of gravity upon the fufpended mafs ; confequently, the effe6l 

 produced is equal, and contrary to the momentum that would 

 be generated by, gravity in the fpace of a minute. So that 

 50 X 32 J X 1 12=s216160, is the proper reprefentative of the 

 ■^, power expended, as well as of the work done. Were the 

 rope to be cut and the weight fuffered to fall for a minute, 

 the fame number would likewife denote (he labour of the 

 horfe in reftoring it to its original place, provided that could 

 be accompliftied in an equal fpace of time, without the horfe 

 changing his fituation. 

 general ftate- ^^ "^^J "°^' perhaps, be entirely ufelefs to, (late this matter 

 ment. rather more univerfally. To thi^ end, let M reprefent any 



mafs or body, gzz32 -^ ket, the velocity communicated to a 

 body falling freely in the firft fecond of .^me, and t' an inde- 

 finitely fmall portion of any time whatever /. Then will g T 

 ^ be the velocity generated in the inftant t', and M g t' the cor- 



refponding quantity of motion ; this, therefore, meafures the 

 eflfbrt which muft be exerted at each inftant to fuftain the 

 weighti whether that etFort be applied immediately, or through 

 the intervention of a (ingle fixed pulley. Hence it follows, 

 that during the whole time t, the force will have confumed a 

 « quantity of motion equal to /'M g t' z=M g t: that is to fay, 

 if ^ denote the time af^lhe end of which the agent is no longer 

 able to fuftain the mafs M, we may regard M g t as being an 

 adequate meafure of the force <p of that agent. If the agent 

 not only prevent -ihe mafs from'iiiJih'ng, but actually raife it 

 \vith a given uniform velocity V during the whole time t, 

 then we muft add the quantity of motion MV to the formerj> 



; which 



