200 Mr. Harvey on the influence of 
It maybe questioned, if ever a chronometer existed, in which 
the vibrations of the balance were perfectly isochronous; or 
in other words, in which the adjustments of the spiral spring 
were such as to admit of its elastic force, varying precisely 
with the arcs of vibration. Mr. Atwood has shewn in the Philoso- 
phical Transactions for 1794, that although the relation between 
the elastic force of the spring, and the magnitudes of the arcs of 
vibration, may appear to be in a perfect ratio of equality, there may 
nevertheless exist such exceedingly minute deviations from this 
state, as to render it impossible to be detected, by the most delicate 
experimenter; and yet these minute inequalities may be consider- 
able enough to produce in the interval of twenty-four hours, a sen- 
sible alteration of rate. Hence it is, that the application of a mag- 
netic force to a chronometer, having a balance in any degree mag- 
netic, in almost every case, produces a visible alteration of rate. 
In an example furnished by the able mathematician before quoted 
he demonstrates, that a variation of a thousandth part from a per- 
fect state of equality, in the relation between the elastic force of 
the spring, and the arcs of vibration, is capable of producing an 
acceleration of + 2”.62 in the daily rate, when the semi-are of 
vibration is diminished 8°; and he even states, that an increase 
of rate amounting to 20 or 30 seconds may exist, and yet the 
differences arising from the deviation of the elastic force of 
the spring, from the law of isochronism, be too minute to be ren- 
dered sensible by any statical counterpoise of the force of the 
spring. 
Assuming therefore a perfect isochronism in the vibrations of a 
balance, as a condition scarcely to be obtained, the deviations from 
it, may be contemplated under two points of view; since the elastic 
force of the spring may vary either in a ess ratio than the angular 
distances from the point of quiescence, or in a greater; and which 
suppositions will account for the apparent anomalies presented by 
different chronometers, when subject to the action of a magnetic 
force. 
This will appear evident, by referring to the function, which ac- 
cording to Mr. Atwood, represents the daily abberration of a time- 
