Fundamental Property of the Lever. — Add of Tin^ 54 3 : 



Let A C, PI. XXII. Fig. i . be two equal bodies on a (Iraight lever, A P moveable about P. 

 Bifea A C in B : produce P A to Qjind take B Q^B P, and fuppofe the end Q_to be fuf- 

 tained by a prop. Then as A and C are fimilarly fuuated in refped to each end of the lever, 

 that is, AP = C Q^ and A Q_=C P, the prop and fulcrum muft bear equal parts of the 

 vhole weight ; and therefore the prop at Q_will be prefied with a weight equal to A. Now 

 take away the weights A and C, and put a weight at B equal to their fum ; and then the 

 weight at B being equally diftant from Q_3nd P, the prop and fulcrum muft fuftain «qual 

 parts of the whole weight, and therefore the prop will now alfo fuftain a weight equal to A. 

 Hence, if the prop QJ)e taken away, the moving force to turn the lever about P in both 

 cafes muft evidently be the fame ; therefore the efFe£ls of A and C upon the lever to turn 

 it about any point, are tiie fame as when they are both placed in the middle point between 

 them. And the fame is manifeftly true if A and C be placed without the fulcrum and 

 prop. If therefore A C be a cylindrical lever of uniform denCty,^ its effedl to turn itfelf 

 about any point will be the fame as if the whole .were colleded into the middle point B • 

 which follows from what l<as been already proved, by conceiving the whole cylinder to be 

 divided into an infinite number oflarains perpendicular to its axis of equal thicknelTes. 



The principle therefore aftumed by Archimedes is thus eftabliflied upon the moft felf- 

 evident principles, that is, that equal bodies at equal diftances muft produce equal efteds ; 

 which is manifeft from this confideration, that when all the circumftanccs in the caufe are 

 equal, the eftedts muft be equal. Thus the whole decronftration of Archimedes is rendered 

 perfe£lly complete, and at the fame time it is very fliort and fimple. The other part of the 

 demonftration wefhallhere infert for the ufe of thofe who may not be acquainted with it. 



Let XY, Fig. 2. be a cylinder, which bifeft in A, on which point it would 

 manifeftly reft. Take any point Z, and bife£l Z X in B, and Z Y in C ; then, from 

 what has been proved, the efFeSs of the two parts Z X, Z Y, to turn the lever about 

 A, are the fame as if the weight of each part were coUedled into B and C refpeftively, 

 which weights are manifeftly as Z X, Z Y, and which therefore conceive to be placed at 

 B and C. Now A B = A X-X B=i X Y— ^ X Z = | Y Z ; and A C=A Y— Y C 

 ={-XY— ^ZY=^XZ; confequentlyAB: AC : : i Y Z : i^ XZ : : Y Z : XZ : : the 

 weight at C : the weight at B. 



The property of the ftraight lever being thus eftabliflied, every thing relative to the bent 

 lever immediately follows. 



Obftrvations on the Acid ^of Tin, and the Analyfu of its Orej. Read at the Sitting of the Clafe 

 of Mathematical and P hilojophical Sciences of the National Infiitute of France, the firjl of 

 MeJJidor, in. the Tear 5. By Citizen GUYTON *. 



At has long been obferved that the nitric acid calcines tin inftcad of dilTolving it, and 

 the phloglftic liypothcfis was incapable of explaining this phenomenon. It remained among 



'' InfcrtcJ in the XXIVlli vulumc uf the Annalts dc Chimio. 



the 



