376 " PHILOSOPHICAL TRANSACTIONS. [ANNO 1778. 



stances that are usually brought on both sides are to be treated in a similar way. 

 The meaning of the terms must first be defined; then the principles assumed 

 explained ; and if we cannot tell at first sight, whether they are agreeable to 

 experience or not, as is frequently the case, we must examine into their conse- 

 quences by the assistance of geometry, and we shall at last arrive at some simple 

 principle, the existence of which is necessarily implied in the original hypothesis. 

 The collision of spherical bodies is the most simple ^vay of communicating 

 motion from one to another ; and therefore such examples are better adapted to 

 throw light on a disputable question, than where the suppositions are moie per- 

 plexed with mechanical contrivances. Besides, when the theory of mechanics is 

 well understood, and the foundations of error discovered, the same reasonings 

 are easily transferred to other cases, and similar precautions applied. Indeed 

 practical artists have little to do with the sudden communication of motion by 

 impact. The collisions of bodies are too violent operations to enter into the 

 composition of useful machines, in which motions are rather to be preserved by 

 the gradual effects of weights and pressures. An accurate knowledge therefore 

 of these effects is more essential to the interests of society; and the only way of 

 arriving at such a knowledge, is always to distinguish those principles which 

 nobody denies, from those others which are found to take place only in some 

 particular circumstances. The following problem was proposed, and a solution 

 given to it long ago, by D. Bernoulli, in the Comment. Petrop. torn. 2. 



" Sit grave aliquod cujuscunquefigurae cba, fig. 10, cujus centrum gravitatis 

 sit D ; ex quo et radio dm descriptus intelligatur circulus mnp, cui filum circum- 

 volutum est pmn, cujus fili extremitati appensum sit pondus q, quod descensu 

 suo grave cba in gyrum agit circum centrum gravitatis d ; dico velocitatem cor- 

 poris Q sequentem in modum determinari posse. Sit md = « , consideretur 

 corpus suspensum ex puncto m oscillari, esseque centrum osciilationis in o, 

 sitque do = b, pondus gravis totius cba = p, pondus corporis iippensi=/j; 

 altitudo ex qua corpus q delapsum est =: r ; altitudo quaesita per quam grave ali- 

 quod cadendo acquirere possit velocitatem corporis q = z ; dico fore z = 



, et si tempus quo corpus naturaliter cadit, per altitudinem i; dicatur /, 



erit tempus insumptum a corpore a = ts/— , id quod experientiae conforme 



esse plurimis institutis experimentis semper inveni." 



Both these conclusions are derived by this author from the principle, which 

 they call the conservatio virium vivarum ; but as he has not given the several 

 steps of his reasoning, it may be useful to supply them here, before we proceed 

 to make any remarks on his solution. And first, suppose the axis at d to be 

 perpendicular to the plane of the figure, and conceive the whole body to be re- 

 solved into iiu indefinite number of prismatic particles, each of which is perpen- 



