ig6 Mr. Atwood's Investigations for determining 
be still less possible to measure the said differences of weights 
with the exactness required for the determination of the law 
observed by the spring s forces. Experiments of this kind 
should not therefore be absolutely relied on for ascertaining 
practically the isochronal property of spiral springs, although 
this property must be allowed to exist in theory, whenever the 
forces of elasticity at the several angular distances from the qui- 
escent position are in the precise ratio of those distances. The 
isochronal law of variation, here mentioned, may be conveni- 
ently assumed in theoretical investigations, and proper correc- 
tions or equations, when necessary, may be applied to compen- 
sate for the deviation from this law, which may subsist in any 
particular spiral spring, whenever it can be satisfactorily ascer- 
tained, or reduced within known limits, by such mode of infe- 
rence as the nature of the case may admit of. This assumption 
will appear the less exceptionable from considering, that the 
elastic forces of spiral springs which are not isochronal deviate 
from the law of variation in question, in some cases by exceed- 
ing, and in others, by falling short of it ; and no other law is 
suggested either by theory or experiment, which more gene- 
rally corresponds with the action of balance springs. 
The vibration of a balance impelled by a single spiral spring 
only, has been the subject of the preceding investigations ; 
but cases occur in which two or more springs are employed 
in giving vibratory motion to the balances of watches. Not 
to mention preceding instances, Mr. Mudge, an eminent 
watch-maker of the present times, has invented a method of 
combining the action of spiral springs, to impel the balance in 
each semiarc of vibration, on a principle not more remarkable 
for the novelty than it is for the ingenuity of the contrivance. 
The consideration of this additional case will therefore not be 
