5 ^1 Demttif.r.i.l^ns of the Fundamental Property of the Lever. 



therefore the principle, as applied by the author, is certainly not applicable. If in this de-' 

 monftratiou we fuppofe a plane body, in which the three forces ai5, inllcad of fimply a 

 lever, then the three forces being actually dircdcd to the fame point of the body, the body 

 would be at reft. But in rcafoning from this to the cafe of the lever, the fame difficulties 

 would arife as in the proof of Sir I. Newton. But admitting that all other objcdlions 

 could be removed, the dcmonftration fails when any two of the forces are parallel. 

 Anotlicr demonllration is founifed upon this principle, that if two non-claftic bodies meet 

 with equal quantities of motion, they will, after impa£l, continue at reft ; and hence it ic 

 concluded, that if a lever which is in cquilibrio be put in motion, the motiorw of the two 

 bodies muft be equal ; and therefore the prefluresof thefe bodies upon the lever at reft to 

 put it in motion, muft be as their motions. Now in the firft place, tliis is comparing the 

 cfFetls of prcfTurc and motion, the relation of the meafures of which, or whether they ad- 

 mit of any relation, we are totally unacquainted with. Moreover, they afl under very 

 different circumftances ; for in the foriner cafe the bodies a£led immediately on each other, 

 and in the latter, they adl by means of a lever, the properties of which we are fuppofed to 

 be ignorant. of. When forces aiEl on a body confidcred as a point, or direftly againft the 

 fame point of any body, we only eftimate the effeiSl of thefe forces to move the body out 

 of its place, and no rotatory motion is either generated, or any caufes to produce it confi- 

 dered in the inveftigation. AVhen we therefore apply the fame propofition to inveftigatc 

 the efteft of forces to generate a rotatory motion, we manifeftly apply it to a cafe which 

 is not contained in it, nor to which there is a fingle principle in the propofition applicable. 

 The dcmonftration given by Mr. Landcn, in his Memoirs, is founded upon felf-evident 

 principles •, nor do 1 fee any objeftions to his rcafoning upon them. But as his inveftiga- 

 tion confifts of feveral cafes, and is befidcs very long and tedious, fomcthing more fimple 

 is ftill much to be wiflied for, proper to be introduced in an elementary treatife of me- • 

 chanics, fo as not to perplex the young ftudent, either by the length of the dcmonftration 

 or want of evidence in its principles. What I here propofe to offer will, I hope, render 

 the whole bufinefs not only very fimple, but alfo perfedly fatisfaftory. 



The dcmonftration given by Archimedes would be very fatisfaflory and elegant, pro- 

 vided the principle on which it is founded could be clearly proved, viz. that two equal 

 pcwers at the extremities, cr their fiim ni the middle, of a levir, tuould have equal effeBs to move 

 about any point. Now, that the effefts will be the fame, fo far as refpefts any progreffive 

 motion being communicated to the lever when at liberty to move freely, is fufficiently 

 dear -, but there is no evidence whatever that the effe£ls will be the fame to give the lever 

 a rotatory motion about any point, becaufe a very different motion is there produced, and 

 we are fuppofed to know nothing about the efficacy of a force at different diftances from 

 the fulcrum to produce fuch a ngrotion. Befides, the two motions are not only different, 

 but \hejame forces are known to produce diffirent effciSls in the two cafes ; fo that in the 

 former cafe the two equal powers, as the extremities of the arms, produce equal effects in 

 generating a progreffive motion ; but in the latter cafe, they do mt produce equal effe£ls in 

 .generating a rotatory motion. We cannot, therefore, reafon from one to the other. The 

 ^principle, however, may be thus proved : 



Let 



