METHODS OF WEIGHING. 
765 
it near the end, which is inserted through a hole in the middle of the right-hand end 
of the balance-case. By sliding the rod in the opposite direction, the loop with the 
pan and weight suspended from it, is brought near to the left-hand end of the beam, 
to which the pan is transferred by a brass rod passing through a hole in the left-hand 
end of the balance-case. Pins inserted in holes at each end of the tube at right angles 
to it, prevent it from being pushed too far. A similar tube half-way between the 
balance and the back of the case, serves to transfer the other pan and weight from 
one end of the beam to the other. In this manner any number of comparisons may 
be made without opening the balance-case, except in the middle of the series, for the 
purpose of changing the pans. The transfer of the pans and weights from one end 
of the beam to the other, might be effected still more conveniently by means of two 
coarse screws of the same length as the balance-case, turned by small winches at 
each end, and provided with loosely-fitting nuts with wire loops from which to 
suspend the pans and weights. 
In the course of making the preliminary observations some peculiarities of the 
instrument were discovered, which, though they probably exist in other balances, do 
not appear to have been hitherto noticed. One of these is, that the expansion of one 
arm by heat, the left in the present case, is a little greater than that of the other arm. 
Hence, when the weights in the two pans are nearly equal and of equal volume, the 
reading of the scale in the position of equilibrium diminishes as the temperature of 
the beam increases. Another is, that the sensibility of the balance, as measured by 
the number of parts of the scale equivalent to a given weight, was found to diminish 
with an increase of temperature. The cause of this is obvious. The beam being of 
bronze and the knife-edges of steel, the balance-beam becomes an over-compensated 
pendulum, and an increase of temperature increases the distance between the middle 
knife-edge and the centre of gravity of the beam and weights, supposing the latter 
concentrated in the extreme knife-edges. Possibly also, the flexure of the beam may 
increase with the temperature, or the mean expansion of the upper bar of the beam 
may be greater than that of the under bar. The variation of the sensibility of the 
balance is so large, that it is necessary to determine the weight equivalent to a given 
number of parts of the scale for each set of observations, except in cases where the 
temperature is very nearly the same. 
For the comparison of the smaller weights two excellent balances by Robinson 
were used, one having a beam 10‘5, the other a beam 5‘5 inches long. The reading 
of the scale of these balances increases on the addition of a small weight to the weight 
in the left-hand pan. 
Comparisons q/Sp, RS, Sb, K, Ex, L, Ed, R. 
T is a platinum troy pound left a little in excess ; P the sum of five weights of 
platinum making together a troy pound ; h is the height of the mercury in the 
5 H 2 
