VOL. LXVI.] PHILOSOPHICAL TRANSACTIONS. 73 



by whatever cause, the impression it will make on a uniformly resisting medium, 

 or on uniformly yielding substances, will be as the mass of matter of the moving 

 body, multiplied by the square of its velocity : the question, therefore, properly 

 is, whether those terms, the quantity of motion, the momenta of bodies in motion, 

 or forces of bodies in motion, which have generally been esteemed synonymous, are 

 with the most propriety of language to be esteemed equal, double, or triple, when 

 they have been generated by an equable impulse, acting for an equal, double, 

 or triple time ; or that it should be measured by the effects being equal, double, or 

 triple, in overcoming resistances before a body in motion can be stopped ? For, 

 according as those terms are understood in this or that way, it will necessarily 

 follow, that the momenta of equal bodies will be as the velocities, or as the 

 squares of the velocities respectively ; it being certain, that, which ever we take 

 for the proper definition of the term quantity of motion, by paying a proper 

 regard to the collateral circumstances that attend the application of it, the same 

 conclusion, in point of computation, will result. I should not therefore have 

 thought it worth while to trouble the society on this subject, had I not found, 

 that not only myself and other practical artists, but also some of the most 

 approved writers, had been liable to fall into errors, in applying these doctrines 

 to practical mechanics, by sometimes forgetting or neglecting the due regard 

 which ought to be had to these collateral circumstances. Some of these errors 

 are not only very considerable in themselves, but also of great consequence to 

 the public, as they tend greatly to mislead the practical artist in works that daily 

 occur, and which often require very great sums of money in their execution. 

 I shall mention the following instances. 



Desaguliers, in his 2d volume of Experimental Philosophy, treating on the 

 question concerning the forces of bodies in motion, after taking much pains to 

 show that the dispute, which had then subsisted 50 years, was a dispute about 

 the meaning of words ; and that the same conclusion will be brought out, when 

 things are rightly understood, either on the old or new opinion, as he distin- 

 guishes them ; among other things, tells us, that the old and new opinion may 

 be easily reconciled in this instance : that the wheel of an undershot water-mill 

 is capable of doing quadruple work when the velocity of the water is doubled, 

 instead of double work only ; " because (the adjutage being the same), says he, 

 we find, that as the water's velocity is double, there are twice the number of 

 particles of water that issue out, and therefore the ladle-board is struck by twice 

 the matter, which matter moving with twice the velocity that it had in the first 

 case, the whole effect must be quadruple, though the instantaneous stroke of 

 each particle is increased only in a simple proportion of the velocity." See vol. 2, 

 Annotations on lecture 6th, p. 92. 



Again, in the same volume, lecture 12th, p. 424, referring to what went 



VOL. XIV. L 



