BALA 
falling bodies; that is, the difli containing the weight, in¬ 
stead of falling- through fixteen feet in a fecond of time, 
would fall through only two hundred parts of an inch, and 
it would require four feconds to move through one-third 
part of an inch :^confequently, all accurate weighing muft 
be flow. If the indexes of two balances be of equal 
lengths, that index which is connected with the fliorter 
balance will move proportionally quicker than the other. 
Long beams are the molt in requeft, becaufe they are 
thought to have lefs fridtion; this is doubtful: but the 
quicker angular motion, greater flrength, and lefs weight, 
of a (hort balance, are certainly advantages. 
“ ii. Very delicate balances are not only ufeful in nice 
experiments, but are likewife much more expeditious than 
others in common weighing. If a pair ot fcales with a 
certain load be barely fenfible to one-tenth of a grain, it 
will require a confiderable time to alcertain the weight to 
t>h'at degree of accuracy, becaufe the turn muft be o'bl'erv- 
ed feveral times over,.and is very fmall. But if no great¬ 
er accuracy were required, and fcales were ufed which 
would turn with 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 immediately. 
“ 12. If a balance be found to turn with a certain addi¬ 
tion, and is not moved by any fmaller weight, a greater 
fenlibility may be given to that balance, by producing a 
tremulous motion in its parts. Thus, it the edge of a 
blunt favv, a file, or other limilar inftrument, be drawn 
along any part of the cafe or fupport of a balance, it will 
produce a jarring, which will diminifli the fridlion on the 
moving parts fo much, that the turn will be evident with 
one-third or one-fourth of the addition that would elfe have 
been required, fn this way, a beam, which would barely 
turn by the addition of one-tenth of a grain, will turn 
with the one thirtieth or fortieth of a grain. 
“ 13-. A balance, whole horizontal tendency depends on¬ 
ly on its own weight, as in rule 3, will turn with the fame 
addition, whatever may be the load ; except fo far as a 
greater load will produce a greater friftion. 
“ 14. But a balance whole horizontal tendency depends 
only on the elevation of the fulcrum, as in rule 5, will be 
lei's fenfible the greater the load ; and the addition requi- 
j’ite to produce an equal turn will be in proportion to the 
load it felt. 
“ 13. In cider to regulate the horizontal tendency in 
fonie beams, the fulcrum is placed below the points of 
fvrlpenlion, as in rule 4, and a Aiding weight is put upon 
the cock or index, by means of which the centre of gravi¬ 
ty may be railed or depreffed. This is a ufeful contrivance. 
“ 16. Weights are made by a fubdivifion of a ftandard 
weight. If the weight be continually halved, it will pro¬ 
duce the common pile, which is the fmalleff number for 
weighing between its extremes, without placing any weight 
.in the fcale with the body under examination. Granula¬ 
ted lead is a very convenient fubftance to be ufed in this 
operation of halving, which however is very tedious. The 
leadielt way to fubdivide fmall weights, confifts in weigh¬ 
ing a certain quantity of fmall wire, and afterwards cut¬ 
ting it into fuch parts, by meafure, as are defiled ; or the 
wire may be wrapped clofe round two pins, and then cut 
a funder with a knife. By this means it will be divided 
into a great number of equal lengths, or fmall rings. The 
wire ought to be fo thin, as that one of thefe rings may 
barely produce a fenfible effeft on the beam. If any quan¬ 
tity (as, for example, a grain) of thefe rings be weighed, 
and the number then reckoned, the grain may be fubdivi- 
ded in any proportion, by dividing that number, and ma¬ 
king the weights equal to as many of the rings as the quo¬ 
tient of the divifion denotes. Then, if 730 of the rings 
amounted to a grain, and it were required to divide the 
grain decimally, downwards, would be equal to 675 
rings, would be equal to 600 rings, ^ to 525 rings, &c. 
Small weights may be made of thin leaf-brafs. Jewellers 
foil is a good material for weights below the -Jg of a grain, 
as low as to T J> 5 grain, and all lower quantities may be ei- 
1 
N C E. 
ther eftimated by the pofition of the index, or fliewn by 
actually counting the rings of wire, whofe value has been 
determined. 
“ 17. In philofophical experiments, it will be found ve¬ 
ry convenient to admit no more than one dimenficn of 
weight. The grain is of that magnitude as to deferve the 
preference. With regard to the number of'weights we 
ought to be provided with, for nice experiments, writers 
have differed according to their habits and views. Ma¬ 
thematicians have computed the leaft poflible number with 
which all weight's within certain limits might beafeertain- 
ed; but their determination is of little ufe, Becaufe, 
with fo fmall a number, it muft often happen that the fcales 
will be heavily loaded with weights, on one tide, put in 
with a view only to determine the difference between them. 
It is not the leaft poflible number of weights which it is 
necelfary an operator fliould buy to effect his purpofe, that 
we ought to enquire after, but the rnoft convenient num¬ 
ber for ascertaining his enquiries with accuracy and expe¬ 
dition. The error of adjuftment is the leaft poflible, when 
only one weight is in the l'cale; that is, a Angle weight of 
five grains is twice as likely to be true, as two weights, 
one of three and the other of two grains, put into the dilh 
to fupply the place of the Angle five; becaufe each of 
thefe laft has its own probability of error in adjuftment. 
But, fince it is as inconliftent w ith convenience to provide 
a fingle weight, as it would be to have a Angle charafter 
for every number ; and as we have nine characters, which" 
we ufe in rotation, to exprefs higher values according to 
their poiition ; it will be found very ferviceable to make 
the fet of weights correfpond with our numerical fyftem. 
This directs us to the fet of weights as follows: 1000 
grains, cjoog. 8oog. 7O0g. 6oog. scog. 400g. 30og. 2005. 
loog. 90g. Bog. 70g. 6og. 5 og. 4og. 3 og. 20g. jog. gg. 
8g- 7 S* 6 S■ 5 S- 4 g- 3 g- 2g. ig. T^g". -^g. Yog. T 5 5 g. 
_^Lcr _3-.gr. or _J_<r _5 —cr _?_cr — 2 —or _§—cr _5_ <t _4_ 0 - 
lOo* ion* 10 O lOO* lOOO* lOOO' iOOO 1 O OO lOOO* lOOO* 
TooS- T§oo- T5og- With thele the philofopher will al¬ 
ways have the fame number of weights in his fcales as 
there are figures in the number expretffng the weights in 
grains. Thus 742.5 grains will be weighed by the weights• 
700, 40, 2, and- 4 ,-.” 
With relpeCt to accurate balances, Mufchenbroek, in 
his Cours de Phyfique, tom.ii. p.247, fays, he ufed an- 
ocular balance of great accuracy, winch turned with 
a grain. The fubftances he weighed were between 200 
and 300 grains. His balance therefore weighed to the 
1 ' 2~o o o P art °f the whole; and would afeertain fuch weights 
truly to four places of figures. In the Phil. Tranf. vol. 
Ixvi. p. 509, mention is made of two accurate balances off 
Mr. Bolton; and it is faid that one would weigh a pound, 
and turn with the -^g of a grain. This, if the pound be - 
avoirdupois, is yg-ggg of the weight; and fhews that the 
balance could be well depended on to four places of fi¬ 
gures, and probably to five. The other weighed half an 
ounce, and turned with the -jJ-g of a grain. This is the’ 
■ 2 00 of the weight. In the fame volume, p. 511, a ba¬ 
lance of Mr. Read’s is mentioned, which readily turned 
with lefs than one pennyweight, when loaded with 551b. 
before the Royal Society; but very diftinftly turned with 
four grains, when tried more patiently. This is about the 
YY060 P art °f the weight; and therefore this balance may 
be depended on to five places of figures. Alfo, p. 576, a 
balance of Mr. Wliitehurft’s weighs one pennyweight, 
and is fenfibly afteffled with the 20 \y 0 of a grain. This 
is the Y iioo o P art of the weight. Mr. Nicholfon’s fcales 
of the common conftruClion, made by a (kilful workman 
in London from rule 8, with 12Q0 grains in each fcale. 
turns with the -J= of a grain. This is the 
84000 
of the 
whole; and therefore about this weight may be known to 
five places of figures. The proportional delicacy is lefs 
in greater weights. The beam wili be near a pound troy ; 
and, when the fcales are empty, it is affedlcd by the yJgg 
of a grain. On the whole, it may be ufefully applied to 
determine all weights between 100 grains and 4000 grains 
to-four places of figures.. 
A 
