of measuring Time ai Sea. 65 
nism of the vibrations proceeds,in a great measure, from the 
curve of the escapement; that thus, by what precedes, this 
isochronism does not appear founded on fixed and inyariabie 
principles. : 
A still more powerful motive to determine us in favour 
of the isochronism and freedom of the vibrations, as far as 
it is possible to obtain them, is, that the same obstacles, of 
whatever nature they may be, arising from the air, or from 
some slight friction, which oppose themselves to the motion 
of the regulator, will have so much the less influence on the 
time of its vibrations as they are more free: this is what it 
is so important to clear up, and which I shall demonstrate 
by the following propositions. 
Definition. 
It is necessary to distinguish two times in the vibrations 
of a body: that which it employs to overcome the accele- 
rating force, aud that where this force restores to it the mo- 
tion which it has lost. I call that where the accelerating 
force is surmounted, retarded semi-vibration, and that where 
the body returns to its point of rest, accelerated semi-vilra- 
tion. 
Proposition. 
In every body that would make isochronous vibrations 
when disengaged from foreign obstacles and aided by an 
accelerated force, the resistance of the air, friction, &c. 
shortens the time of the retarded semi-vibration. 
Suppose that at the instant w hen it begins to be retarded, 
a body A has, for example, the requisite velocity to describe 
a space of thirty, but that it only describes one of twenty, 
because the friction which it experiences consumes a part of 
its motion; it is required to show, that A will describe the 
space twenty, with its initial velocity thirty, in less time than, 
if having experienced no resistance foreign to the accelerating 
force, it had described this same space twenty by means of 
an initial velocity of twenty. The following is the way I 
prove it: 
It is only in the last point of the space twenty, that A 
moves with the same velocity which it would have bad in 
Vol. 26..No, 101. Or/. 1806. this 
