148 MR. GREGORY ON HORSE POWERS^ 



n 



wlieii tli€ |»erformance will be denoted by ^ . x W t? 



And if the value of V thus exhibited be once afcertained esei 

 perimentally, we need never be apprehenfive of a material lofs 

 by a fmall, variation from it; for by a well known property of 

 thofe quantities which admit of a proper maximum and mini- 

 mum, a value affumed at a moderate diftance from either of 

 *hefe extremes will produce no fcnfible change in the effecl. 

 Ixampie* In fome of the aflions of men, fuch as dragging a boat along 



a canal, &c. the value of n in the preceding theorems has 

 been found tp be nearly t= 2» And the draught of horfes is 

 conformable to a law not widely different. Thte beft experi- 

 ments which have yet been made on this point with regard to 

 horfes drawing in nearly redilinear paths, lead us to conclude 



Ihaf wis then very nearly =^, in the expreflion M cc (U — V) 

 AtTuming therefore for the utmoft walking velocity of a horfe, 

 the value U = 9 feet per fecond, a value which is quite high 

 enough, any propofed etlimates of the flrength of this animal 

 may be compared with facility. Thus, for example, let us 

 enquire which is greater, the eftimate of Mr. More (men- 

 tioned by Mr. Hornblower) of 80lbs. three miles per hour, or 

 4-| feet per fecond; or that of ISOlbs. moved at the rate of 

 three feet per fecond ? Here we fliall have 



(9-3)^ : (9-4-4)* ;; 130 : 7 l|lbs. nearly. 

 The operation may eafily be performed by means of a table of 

 logarithms, and fliews that the mean eftimate I have laid down, 

 when reduced to the fame velocity as that by Mr. Moore, fur- 

 nifiies a refult lefs than his by 8flbs. Which of thefe is the 

 moll accurate can only be determined by future experiments. 

 On the power If, however, either of thefe eflimates fliould be adopted, 

 of horfes walk- jj- maybe proper to remark that they would not hold with re- 

 pj^hs- gard to the power of horfes working in circular paths ; y^t, if 



^ it be at all proper to ufe harfe poivers in eftimating the energy 

 of machines, it feemy^oft naturaf*to take thefe powers as ex- 

 erted by the animal in a round walk ; fo that it is Hill necelTary" 

 to have a feries of experiments to determine the values of n, 

 and the relation of M and V whep horfes draw in circular 

 —of different walks ofdifferent radii. I fay, ^dfferent radii, becaufe it is 

 xadu. certain tl»t aixttri^ lyaribust the greater the radius of the circle 



in 



