B A L 



Ocular'! let fall from C upon the directions will be always 

 equal to each otiicr. B\it w la-n C is above or bclr>\v WP, 

 an equilibrium of equal weights does not occur, unlefs WP 

 coincide witii tlic horizontal line AR. In this cafe, the 

 perpendiculars let fall from C upon the directions of W and 

 P, are tqnal to GB and GA, CO btin^ perpendicular to 

 AB ; but when the balance ia in any othtr pofition WP, the 

 perpendicular CI is greater than CH, becaufe ^ L, which 

 is lefs than CI, is equal to ,fM,i which is greater than CH. 

 W will thcixlore dclctnd and continue to vibrate till it« mo- 

 tion be deilrovcd by fridion. (See Lever.) If P and Vv be 

 unequal, and C be in the right line WP, the heavier of them 

 will dtfcend till WP be perpend'cular to the horizon, or, 

 if the center of motion be not in WP, till PxCH=WxCI. 

 It is evidrnt from what has been fald, that the nearer the 

 centre of i/iavity of the beam is to tlie centre of motion, 

 the nicer will be the balance, and the (lower its vibrations : 

 thus, if aCbc (fi^. ll.) be the beam, and C the center of 

 motion, the difference between the elTefts of having the 

 centre of gravity at K, or c, will be the fame as if we 

 compared tlie velocities of two pendulums, of the length 

 CK and Cr, which are in a fubduplieate ratio of their 

 lengths. The tendency to an horizontal polition is, there- 

 fore, increalcd by lowering the center of gravity, in which 

 cafe it will alfo require a greater additional weight to caufe 

 it to turn or incline to any given angle, and it is confequently 

 lefs fenfible with a greater load. The fixing of the centre 

 of motion in a balance is, therefore, of peculiar importance, 

 for on this depends the eaie with which it will be afftdtcd by 

 a fmaller weight ; and the rtadinefs with which rt will return 

 to its horizontal pofition : and it is evident, that the belt 

 pofition is that in which the centre of motion is a little above 

 the centre of gravity ; and even in this it lliould be propor- 

 tioned to the diltance of the weights from the fulcrum, and 

 the quantity of matter to be weighed, which, in diflerent 

 beams, can only be attained by the practice and experience 

 of the maker. 



It has already appeared, that if the arms of a balance be 

 unequal, the weights in cquipoife will be unequal in the fame 

 proportion. But it fhould be obferved, that though the 

 equality of the amis of a balance is ufeful in the making of 

 weights by bifeiftion, a balance with unequal arms will 

 weigh as accurately as another with equal arms, provided 

 the llandard weight itfelf be firlt counterpoifed. then taken 

 out of the fcale, and the thing to be weighed be put into 

 the fcale, and adjulttd agalnll the counterpoife : or, when 

 proportional quantities only are confid-.red, the bodies under 

 examination may be weighed againlt tlic weights, taking 

 care always to put the weights in the fame fcale; for then, 

 though the bodies may not be re:dly equal to the weights, 

 yet their proportions to one another will be the fame as if 

 they had been accurately equal to them. However, it is 

 iiidifpenfably neceiTary that their relative lengths (hould con- 

 tinue invariable. For this purpdfe it is neceffary either that 

 the three edges be all truly parallel, or that the points of 

 fufpenfion and fupport fliould be always in the fame part of 

 the edge, which lalt rtquifite is mo(t eafily obtained. 



If a beam be adjuftcd fo as to have no tendency to any 

 one pofition, as in cafe I. above ftated, and the fcales be 

 e^qually loaded ; then, if a fnidll weight be added in one of 

 the leaks, that balance will turn, and the points of fufpen- 

 fion will move with an accelerated motion, fim.ilar to that of 

 falling bodies, but as much flower in proportion, very near- 

 ly, as the added we'ght is lefs than the whole weight borne 

 by the fulcrum. The ftronger the teudency to an liorizontal 

 pofition in any balance, or the quicker its vibrations (iee 

 cafes 3. and 5.), the greater additional weii^ht will be re- 

 flLiired.to caufc it to turn or incline to ai>y given angle. If 



8 



B A L 



a b-^Iance were to turn with the ten thoufandth part of the 

 Weight, it would move at the quickeft I0,0CX3 times flower 

 than a falling body ; that is, tie di<h containing the weight, 

 iuftead of falling through fi/Ctcen feet in a fecond of time, 

 would fall through only two hundrcith part of an inch, and 

 it would require four feconds to move tlirough one third 

 part of an inch ; confequently, all accurate weighing muft 

 be (low. 



Long beams have been generally recommended ; becaufe 

 the quantity of motion in a given body varies as its didance 

 from the fulcrum; and, therefore, the greater the dhlance, 

 the more diltinguilhable will be the motion arifin^ from any 

 fniall difference between, e. g. P and W. Long beams are 

 alfo thought to have lefs friction ; but this has been doubted. 

 And it has been remarked, that the quicker angular motion, 

 greater Itrength, and lefs weight of a (hort balance, arc cer- 

 tain advantages. 



The index that is placed perpendicularly to tlie beam of a 

 balance, in order to afceitain its pofition, afftfts its equili- 

 brium, except it be in an horizontal fituation ; the momen- 

 tum of the index being nicafiired by its weight multiplied 

 into the dlilance of its centre of gravity, from a line per- 

 pendicular to the horizon. But the error that would arifc 

 from hence is corrcftcd by continuing the index, or placing 

 a weight on the oppofite fide of the beam. The fcaics of 

 a balance (lijuld be fufpcnded in fuch a manner, that in all 

 pofitions the Itiings of the fcales may be parallel to one an. 

 other; otherwife the weights, though equal, willnot.be in 

 equilibrio. 



Very delicate balances are not only ufeful in nice experi- 

 ment?, but they are much m.ore expeditious than others in 

 common weighing. If a pair of fcales, with a certain load, 

 be barely fenfible to -^th of a grain, it will require a confi- 

 derable time to afcertain the weight to that degree of accu- 

 racv, becaufe the turn muft be obferved feveral tiiBES, and. 

 it is very fmall. But if no greater accuracy were required, 

 and fcales were ufed which would turn wiih the hundredth, 

 of a grain, a tenth of a grain, more or lefs, would make 

 fo great a difference in the turn, that it would be feen im- 

 mediately. A degree of fenfibility may be given to a ba- 

 lance, that turns with a certain addition, but is not m.oved 

 by any fmaller weight, by producing a tremulous motion in 

 its parts. Thus, if the edge of a blunt faw, a lile, orother 

 iimilar inftrument, be drawn along any part of the cafe or 

 fupport of a balance, it will produce a jarring, which will 

 diminilli the frittion in the moving parts fo much, tl.at the 

 turn will be evident with one third or one fourth of the ad- 

 dition ihat would elfe have been required. In this way a 

 beam which would only turn by the addition of a tenth of a 

 grain, will turn with the thirtieth or fortieth of a grain. 

 In order to regulate the horizontal tendency in fomc beams, 

 the fulcrum is placed below the points of fufpenfion, and a 

 (liding-weight is put upon the (ty'.e or ir.dex, by means of 

 which the centre of gravity may be raifed or lowered. 



Mr. Nicholfon, of vvhofe oLl'ervations on the properties 

 of the balance we have availed ourfelves in the preceeding 

 part of this article, has recommended the following fet of 

 weights, as proper to accommpany it, when it is applied 

 to chemicjl and fimilar purpofes : viz. lOOO grains, 

 900 g. 800 g. 7COg. 600 g. 500 g. 4007. 300 g. 200g. 

 !oog. 90 g. 80 g. 705. Cog. 50 g. 40 g. 30 g. 20 g. 

 'o g- 9 g- 8 g 7 g. 6 g. 5 g. 4 g. 3 g. 2 g. 1 g. T^ff g- 



■Atj:- tsS- As- -feg- Tusr- Ag- Ag- Ag- tI-cZ- 



-r?3.(C- Ao-g- rl^g- T*^g- A^g- tStt g- tIti g- tJt g- 

 W'llh thcle tiie philolopher will always have the fame 

 number of weights in his fcales as there are figures in the 

 number cxprefling the weights in grains. Mr. Nicholfon 

 fubioins an account of fotne balances, which have been con- 

 •• Itrufted 



