166 An Inquiry concerning the 
motion were firmly fixed in their places in a right line, and 
the beam being afterwards finifhed, and its two arms brought 
to be in equilibrio, the balance was proved by fufpending 
weights, which before were known to be exactly els to 
the ends of its arms._ 
If with thefe weights the balance remained in equilibrio, it 
was confidered as a proof that the beam was juft ; but, if oné 
arm was found to preponderate, the other was gradually 
lengthened, by beating it upon an anvil, until the difference 
ef the lengths of the arms was reduced to nothing, or until 
equal weights, fufpended to the two arms, remained in equi- 
Kbrio; care being taken, before each trial, to bring the two 
ends of the beam to be in equilibrio, by reducing, with the 
file, the arm which had been lengthened. 
Though in this, method of conftruéting balances the moft 
perfect equality in the lengths of the arms may be obtained, 
and confequently the greateft poffible accuracy, when ufed at 
' atime when the temperature of the air is the fame as when 
the balance was made; yet, as it may happen that, in order 
to bring the arms of the balance to be of the fame length, 
ene of them may be much more hammered than the other, 
I fufpected it might be poffible that the texture of the metal 
forming the two arms might be rendered fo far different by 
this operation as to occafion a difference in their expanfions 
with heat ; and that this difference might occafion a fenfible 
error in the balance, when, being charged with a great 
weight, it fhould be expofed to a confiderable change of 
temperature. 
o determine whether the apparent augmentation of 
weight, in the experiments above related, arofe in any de- 
gree from this caufe, I had only to repeat the experiment, 
caufing the two bottles A and B to change places upon the 
arms of the balance; but, as I had already found a fenfible 
difference in the refults of different repetitions of the fame 
experiment, made as nearly as poffible under the fame cir- 
eumftances, and as it was above all things of importance to 
afcertain the accuracy-of my balance, I preferred making a 
particular experiment for that purpofe. 
My firft idea was, to lufpend to the arms of the balance, by 
very 
