MR. GREGOkV ON MORSE POWERS. 147 



tjuenily omitted in confequenc^ of an implicit reliance upon a 

 riiaxim, which, though highly ufeful under proper reftriaions, 

 is far from univerfal in its application. In the cafe before us, 

 if we admit the maxim now alluded to, namely, that what is 

 gained in poiver is loji in time, with regard to the machine 

 through whofe intervention the velocity of the weight is ren- 

 dered different from that of the horfe, it would be unfafe to 

 adopt it in the appreciation of the varied energy of the ani* 

 nial when moving with different velocities. The reafon of 

 this is obvious. The energy of the horfe is obliged to be em- An We, hav- 

 ployed not only in overcoming the weight or refiftance which ca?ry,*Toes not 

 oppofes his progrefs, but in part in moving him/elf ; for the exert his force 

 particles which conftitute his frame poffefs weight and inertia, J^J'^^ ^^* '^^'^^ 

 and therefore cannot be put into motion without effort. Hence 

 it follows that there is a certain velocity, which may be de- 

 noted by U, with which, when the animal moves, his whole 

 power will be employed in producing his own motion folely, 

 without being able to move any other body. If a body whofe 

 mafs is M be attached to the horfe, fo that he cannot move ' 

 without giving an equal velocity to the extraneous body, i\\6 

 fame effort being employed both in moving the animal and the 

 mafs attached; the velocity V, with which they move muff 

 neceffarily be lefs. And if M be farther increafed while the 

 weight and energy of the horfe continue the fame, the velo- 

 city V will be ftill farther diminilhed ; and thus as M in- 

 creafes V will diminifli, until when M arrives at a certain 

 magnitude, W, the, animal is unable to make any progretfive 

 motion, and exerts his force at what is called a dead pull. If 

 M exceeds W, then will V become negative, and inflead oF 

 the animal advancing with the load, the load will compel him 

 to move backwardsj and no ufeful work can be accompliflied. 



Now thefp circumftanccs may be expreffed algebraically, Method of corn- 

 by the general formula M oc (U — V) , in which the exponent of horfes. 

 n can only be determined by means of judicious and numerous 

 experiments, where the magnitude of JVJ (hould be afcertained 

 for many variable values of V betweeff the terms V=U, and 

 V=Q. From this theorem, following the common rules for 

 t!ie maxima and minima of quantities, it may readily be found 

 that in order to have the ufuful work done the greateff poflible, 



'U . u 

 we muft increafe or df^cre^fetne weight till V becomes =: > 



L 2 when 



