554 
‘ motion in a balance is consequently of peculiar import- 
‘ad ance, for on this depends the ease with which it will be 
. affected by a smaller weight, and the readiness with which 
the beam will return to a horizontal position. And it will 
be seen that the best position of all is that in which the 
centre of motion is a little above the centre of gravity. 
Even in this, it should be proportioned to the distance of 
the weights from the fulcrum, and the amount of the load, 
which can only be attained in different beams by practice 
and experience. In order to regulate the centre of gravity 
in balances of precision, they are made to carry a small 
weight either over or under the centre of motion, which is 
moveable by means of a screw. 
From what has been said it would appear that if the 
arms of a balance be unequal, weights which form an 
equipoise will be unequal in the same proportion, But 
although for many purposes the equality of the arms of a 
balance is advantageous, yet a balance with unequal arms 
will weigh just as accurately as one with equal arms, pro- 
. vided the standard weight itself be first counterpoised, 
; then taken out of the pan, and the weight to be compared 
be substituted and adjusted against the counterpoise. Or 
when proportional quantities only are required, they may 
be weighed against standard weights, taking care always 
to put these weights in the same pan. But in this case it 
is indispensable that the relative lengths of the two arms 
of the beam continue invariable. For this purpose, either 
the three knife-edges should be truly parallel, or the points 
of suspension and support be always in the same part of 
the knife-edge. 
If the beam of an equal armed balance be adjusted so as 
to have no tendency to any one position, as in(@), and the 
pans be equally loaded, then if a small weight be added to 
one of the pans, the balance will turn, and the point of 
suspension move with an accelerated motion, similar to 
that of falling bodies, but very nearly as much slower in 
proportion as the added weight is less than the whole 
weight borne by thefulcrum. The stronger the tendency 
to a horizontal position in a balance, or the quicker its 
vibrations—see (c) and (2)—the greater additional weight 
will be required to cause it to turn or increase to any 
given angle. Ifa balance were to turn with zpt00 part of 
the weight, it would move at the quickest, 10,000 times 
slower than a falling body ; that is to say, the pan con- 
taining the weight, instead of falling through 16 ft. in a 
second of time, would fall only through jy part of an 
inch ; consequently all accurate weighing must be slow. 
Long beams have been generally recommended because 
the quantity of motion in a given body varies as its 
distance from the fulcrum ; and therefore the greater the 
distance, the most distinguishable will be the motion 
arising trom any small difference between the weights 
compared, On the other hand, there are certain advan- 
tages in the quicker angular motion, greater strength, 
and less weight of a short beam. 
The pans of a balance should be suspended in such 
‘a manner that in all positions the corresponding cords or 
rods may be parallel to one another; else the weights, 
though equal, will not be in equilibrium. 
In ordinary commercial balances, the preponderance of 
‘either pan is indicated by a slender rod attached to the 
beam immediately over its centre of motion in a line 
perpendicular to the axis of the beam, and moveable 
freely between the two forks of the handle. It is called 
the tongue of the balance, and the degree of preponder- 
ance of either pan is shown by the greater or less devia- 
tion of the tongue from its normal vertical position, In 
balances of precision, the index is’ a longer needle-rod, 
- fixed either in a line perpendicular to the axis of the 
beam, and below its centre of motion, or in a line in 
continuation of its axis. In both cases the pointer moves 
along a graduated index. But an index placed perpendi- 
cular to the beam affects its equilibrium when turning 
from its horizontal position ; the momentum of the index 
NATURE 
being measured by its weight multiplied with the distance — 
of its centre of gravity from a line perpendicular to the 
horizon. The error thence arising may, however, be 
corrected by continuing the index-rod or counterpoising 
it, on the opposite side of the beam. : 
The finest balances of the*® Standards Departments 
have the index pointer in the line of the axis of the 
beam, as shown in Fig. 16, which represents the left-— 
hand side of the balance, the right-hand side being 
similarly furnished with a pointer and index scale. 7 
This is the medium size of six of the finest balances of 
the Standards Department, constructed by Mr. Oertling, 
For all weighings of standards requiring special accuracy, 
the highest and lowest points reached by the needle in 
each oscillation of the balance are read on the index scale 
through a telescope fixed at about 5 ft. distance, by which — 
means each reading can be satisfactorily taken by esti- 
mation to one-tenth of a division of the scale. ¥ 
Another balance of the Standards Department is one 
constructed by Barrow, and used by Prof. Miller for all 
his weighings during the construction of the new Stan- 
dard pound. The knife-edges work upon quartz planes, 
Index scales marked ona thin and nearly transparent 
slip of ivory are fixed immediately above each end of 
the beam and oscillate with it. They are of the following 
form and size. These scales are illuminated by a candle 
Fic. 17.—Index Scale of Barrow’s Balance. 
placed at a little distance either in front of or behind the 
balance case, a lens being interposed; and they are 
viewed through compound microscopes having a single 
horizontal wire fixed in the focus of the eye-piece. The 
microscopes are fixed to the front of the balance-case, — 
and as the observer must necessarily be close to the micro- 
scopes during weighings, a second glass screen is inter- 
posed between him and the front of the balance-case, 
having openings opposite the eye-pieces of the micro- 
scopes. 
The weight intended to be carried by each of these 
balances, and the mean value of one division of the index 
scale, or the weight represented by it, when the balance is 
fully loaded, may be seen in the following table :— ; 
ee —— ee 
Tenetuad ; Mean value of — 
Balance, | eee To carry in each pan. 1 div. of Index 
Scale. 
In. ~~ Avoir. Troy. Grains. 
No.1 36 56 to 14 lbs., or 500 to 200 oz. |o'r5 
No.2 2 7to 21bs,, or 200to 2002, lo’oz 
No.3 | 16 rb. to20z. or 29to20z. |o'oors 
No. ay th 10 1 oz, and under, x oz. and underjo‘0008 
ay? 5 10 aoe and under. o"0002 : 
No. | 20 1 kilo. and under, 0°0015,0ro'r m, 
Barrow’s ade 1 kilo. and under. i mt 
0°005, Or 0°34, 
‘ 
There is another much larger balance which was origi- 
nally constructed for weighing the contents of water of - 
the Imperial Standard bushel, the total weight in each pan 
being nearly 300lbs, The beam of this balance is of — 
mahogany, 67fin. inlength. With a full load, the mean 
value of 1 div. of the index-scale iso'4 grain, This balance, 
like the other, is enclosed in a large plate-glass case. : 
_ In all these balances, the value of a division varies from — 
time to time according to the weight in the pans, the 
condition of the balance, the state of the atmosphere, — 
&c., and in all very accurate weighings it is desirable to 
determine the value for each comparison, by an additiona 
weighing, after a very small weight, accurately verified and — 
equal to a few divisions only of the balance, has been” 
added to one of the pans, so that its effect on the read 
of the index scale may be noted. The above stated value 
