VOL. LXVIir.] PHILOSOPHICAL TRANSACTIONS. 37y 



levers, before it will be equal to the motion communicated. The properties of 

 the lever are well understood and easily applied, and because their evidence de- 

 pends on experience, and is as firmly established as the 3d law of motion itself, 

 it is always best to make use of those two universal principles, instead of others 

 which are more liable to deceive us.* 



In all cases concerning the motion of a single body, or system of bodies, 

 where there is any rotatory motion, the consideration of the lever becomes requi- 

 site, and that, with a just application of the laws of motion, is sufficient for the 

 resolution of the most arduous problems. It is now pretty well agreed on, that 

 the neglect of this circumstance is one cause of that material error, which Sir 

 Isaac Newton himself is supposed to have fallen into in the SQth prop, of the 3d 

 book of his Principia. 



I had several reasons for insisting so particularly on the demonstration of this 

 3d case. It is in itself one of the most neat and elegant problems we have; and, 

 what is of more consequence, it admits of an experimental proof and illustra- 

 tion. It is obvious, that the motion of the body amb may be made so slow, 

 that the time of q's descent through any assignable space may be measured to 

 the greatest exactness. The velocity of q may also be inferred with the same 

 ease by observing the velocity of any particular point in the body to which the 

 velocity of a always bears an invariable ratio. Such experiments, it must be 

 owned, seem very unfit for the first discovery of the laws of nature; though, as 

 I have shown, it is not impossible to collect them that way; but after they are 

 discovered, the application of them to the solution of such intricate problems is 

 both entertaining and instructive, and then the agreement of the experiments 

 themselves with the theory becomes a solid argument for the certainty of our 

 principles. 



We have shown, that in this case at least Bernoulli's hypothesis is founded on, 

 and coincides with, the commonly received doctrine of motion, and therefore we 

 can hardly entertain a doubt of the success of the experiment, supposing it had 

 never been tried. The author himself, in the passage above quoted, tells us, 

 that he found it so; but we need not rest on his authority: a similar experiment 



* It is acknowledged, that the experiments which have been made to determine the effects of wind 

 and water-mills do not agree with the computations of matliematicians ; but this is no objection to the 

 principles here maintained. Writers generally propose such examples witli a view ratlier of illustrating 

 tlie methods of calculation by algebra and fluxions, tlian of making any usefiil improvements in prac- 

 tice. They suppose the particles of the fluid to move in straight lines, and to strike the machine with 

 a certain velocity, and after that, to have no more effect. As such suppositions are evidently incon- 

 sistent with the known properties of a fluid, we are not at a loss to account for a difference between 

 experiment and theory ; and therefore it should seem unreasonable to assert, that certain authors of 

 reputation have neglected the collateral circumstances of time, space, or velocity, in the resolution of 

 these problems, unless we were able to point out such omissions. — Orig. 



3 C 2 



