409 
on the rate of chronometers. 
The true measure of time is derived from the balance, and 
its vibrations will be isochronous, when the adjustments of 
the spiral spring are such as to admit of its elastic force va- 
rying directly with the arcs of vibration. As a necessary 
consequenee of this principle, the application of any disturb- 
ing force will occasion no derangement in the rate, since the 
arcs of vibration, whether increased or diminished, must all 
be performed in the same absolute time. 
It may however be questioned, whether a chronometer 
ever existed, in which the elastic force of the spring varied 
precisely with the arcs of vibration ; for it has been shown 
by Mr. Atwood,* that though the weights employed to 
counterpoise the elastic force of a spring, at different angular 
distances from its quiescent position, may appear to be in the 
exact ratio of those distances, discrepancies too small to be 
detected by the nicest experimenter may exist, but yet be 
considerable enough, from the delicate nature of the ma- 
chine, to create a sensible alteration of rate. 
Any change in the arc of vibration of the balance of a 
chronometer thus constituted, must therefore be attended 
with some alteration of rate ; and that it is extremely pro- 
bable such a change must take place when a time-keeper is 
placed in air of different densities, the arcs increasing when 
the density is diminished , and diminishing when it is in- 
creased , may be inferred, from the extreme delicacy of the 
balance, and its spring, and their consequent susceptibility 
of change. 
The daily aberration of a chronometer, arising from a 
* Philosophical Transactions for 1 794. 
MDCCCCXXIV. sG 
