B A L 



ftruiTled by differer.t petfoiis for nice experiments. The 

 firft he mentions is that of Mufchenbrock, winch turned 



with -^ of a grain, and which weighed to -s-rWu P^'*- °^ 

 the whole ; afcertaining fuch weights truly to four places 

 of figures. In the Philof. Tranf. vol. Ixvi. p. 50. we 

 have mention of two accurate balances of Mr. Bolton ; one 

 of which would weigh a pound, and turn with ^V of a 

 grain, and give the yn-ijrs °^ ^^'^^ weight ; and the other 

 weighed | an ounce, and turned with tl.c -j-J^ of a grain, 

 or the -ilo s of the weight. Mr. Read's balance men- 

 ticined in p. 511. of the fame volume, turned with lefs than 

 a pennv-weight, and even with four grains, when loaded 

 with fifty-five pounds, i. e. about -^gl-uT! of the weight, and 

 which might be relied on to five places of figures. Mr. 

 Whitehurlt's balance (Ibid. p. 576.) weighs one penny 

 weight, and is fenfibly affeiled with -^^^ of a grain, i. e. 

 jTT^. part of the weight. Mr. Nieholfon's balance, with 

 1200 giains in each fcale, turns with j\j of a j^rain, or 

 ryJois of '^'"-" whole. This balance, he lays, will ferve to 

 determine nil weights between 100 grains, and 4000 grains 

 to four places of figures. Mr. Alcliorne's (mentioi^td 

 Ibid. vol. Ixxvii. p. 205) is true to three grains with ijjb 

 an end ; and hence the weight is known to ^ iuaa P^rt, or 

 to four, or barely five places of figures. The balance of 

 Dr. George Fordyce, made by Mr. Ranifdtn, mentioned in 

 Ixxvth volume of the Phil. Tranf. when leaded with four or 

 five ounces, fhevvcd a dilference of -ra'-j^ of a grain, or 

 1 84'^ag ps'"'^ of the weight. Mr. Magellan's would bear 

 leveral pounds, and (hew -rV of a grain, with one pound an 

 end. This is the -j-^'^st; of the weight and anfwers to five 

 ■figures. The Royal Society's balance, lately made by Mr. 

 Ramfden, turns on fteel edges upon planes of pulifhed 

 cryftal, and afcertains a weight to the fcven millioath part, 

 and may be ufed in, general practice to determine weights 

 to five places and better. To which we may add, that the 

 balance ufed by count Rumford, in his experiments for al- 

 oertaining the weight afcribed to heat (Phil. Tranf. for 

 1799. partii.), ferved, as he informs us (p. 187.), to mea- 

 lurc ; a 00 c g of the weight which he examined. Nichol- 

 fon's Chemiftry, c. vi. Parkinfon's Syllem of Mechanics, 

 &c. p. 134, &c. Defaguliers's Exp. Phil. vol. i. p. 140, ^c. 



Mr. Ludlam has contrived a balance of a new conftruc- 

 ticn for the woollen manufaftures. Their thread is made 

 into fliains of the fame length ; and the fincncfs of it is de- 

 nominated from the number of (l<ains which go to a pound ; 

 the coarfed being about twelve to the pound, and the fined 

 near fixty. This machine is defigned for weighing the 

 . fkains, in order to determine their relpcftive finenefs. It 

 refembles the beam of a common pair of fcales ; at one end 

 of it is fixed a weight, called a counterpoife, and at the other 

 end a hook ; in forting, the Ikain to be examined is put 

 upon the hook, and finlfs down more or lefs, according to 

 its weight, till the counterpoife, by rifing, balances it : then 

 the index or cock of the beam, points out on a graduated 

 arch the number of ikains of that fort which goesto ihepound. 

 A fcale, inftead of the hook, might be ufed for weighing 

 money, if the arch were properly divided for that purpofe. 

 See a drawing of this machine and the explanation of the 

 theory of it, in Phil. Tranf. vol. Ix. N"'25, p. 205. 



The ienl-Zcver balance, is a balance (Ji^. 12.) which afts 

 by a fixed weight C, increafing in power as it afcends along 

 the arc FG of a circle, and pointing by an index to the 

 number or divifion of the arc which denotes the weight of 

 any body put into the fcale E. With this inftrument, one 

 conftant weight lerves to weigh all others, by only varying 

 the pofition of the arms of the balance, inftead of varying 

 the places or points of fufpenfion in the arms themfelves. 

 The following property of the balance was firil fug- 



B A L 



gelled by Dr. HelHiam (fee his Courfe of Le(£tures in Na- 

 tural Philofophy, publilhed by Dr. Robinfon, p. 91), com- 

 municated by him to Dr. Defagulicrs (fee his Courfe of 

 Experimental Philofophy, vol.i. p. 152.), and pubhlhed in 

 the Phil. Tranf. for 1729. The property is this, that if 

 a man Handing in one fcale and counterpoifed by a weight 

 in the other, lays his hand to any part of the beam, and 

 predes it upwards, he will deftroy the equilibrium and caufe 

 the fcale in which he ftands to preponderate. Thus, if a 

 man, whofc weight is equal to JV, itandinR in one feale and 

 in equilibrio with P placed in the other (fig. 8.), prcfs the- 

 beam upwards in D with a force equal to .^, the dimiiution 

 of /^'s momentum is equal to Qx FD ; and becaufe the 

 re-af\ion at the fcale is equal to (>, the increafe of IV's mo- 

 mentum is equal to i^X Fyl, and confequently IF will de- 

 fcend with a force equal to ^X y!D. If the ijreifure be 

 upwards at F, IV will defcend with a force refulting 

 from this prefTure, equal to .^.X EF, and from thi rc-ailion 

 with a force equal to ^X F/l ; and, therefore, the whole 

 force of defcent is equal to Qx EJ. Thus, alfo, if the 

 prelTure be downwards at D, the increafe of /;'"s momentum 

 is equal to Qx FD, and the diminution of its momentum 

 =.QXjP-^; and, confequently, /-K will afcend with a force 

 equal to IVx DA. If the preffure be downwards at E, the 

 diminution of IV's momentum, or the increafe of P'i mo- 

 mentum, is equal to QY EF, and a part, Q, of IV'i weiglit 

 being transferred to E, the diminution of its momentum, on 

 that account, is equal to Qx FA, and confequently the 

 whole diminution of JV's momentum, or force of P'i afceiit, 

 is equal to Q - EA. 



Balance of the Air, is ufed to denote the weight of that 

 fluid, vi'hereby, according to its known property, it preffes 

 where it is leaft refilled, till it l)e equally adjufled in all parts. 



Balance, AJfay, is a nice balance ufed in determining the 

 exaft weight of minute bodies. Its (Irufture is very little 

 different from tliat of the common fort ; except that it is 

 made of the bell fteel, and fitted for moving with the fmall- 

 eft weight. 



The beam of this balance is fnfpended in a fork, the two 

 legs of which are fteel fprings joined at the top, but kept 

 together below with a brafs pliant clafp, parallel to one ano- 

 ther, and at the diftance of 2 J lines. When this clafp is 

 taken off, and the legs of the fork ftretched out, the axis of 

 the beam may be put into two holes at the ends of the legs, 

 or removed from them. A (harp needle is fixed in the head 

 of the fork, which ftands perpendicularly, when the fork is 

 fufpended, and is fo long, as almoft to touch the top of the 

 tongue of the beam put into the fork when in equilibrio. 

 This needle is the telt or mark of the equilibrium ; and for 

 the convenience of obferving it, the legs of the fork are 

 broader in that place, and have an opening two or three lines 

 wide. Two fcales made of a thin plate offilver, i-J inch in 

 diameter, fufpended on three fmall filken ftrings, almoft as 

 long as the beam, and tied together at the top with a filver 

 hook in the form of an S, are hung to the extremities of the 

 beam ; and to each of thefe fcales belongs a fmall difh of 

 filver or blued fteel, fomewhat lefs than one inch in diameter, 

 and both of equal weight ; the bodies to be weighed are put 

 into thefe difties, with a pair of pincers, or with a fpoon, or 

 fmall fhovel, when they are pounded ; and then the 

 difties are put into the fcales. The balance is fufpenikd on 

 a moveable brafs or copper fupport, confifting of a pcdeftal, 

 and a pillar fet upon it about twenty inches high, at the top 

 of which projefts at right angles, an arm one inch in length: 

 at the extremity of this arm is a fmall pulley three lines in 

 diameter, another at the top of the pillar, and a third near 

 the bottom of it ; all which pullies move with eafe on the-ir 

 refpedive axes. At the diftance of jf inch below the 



upper 



