of measuring. Time at Sea. . 51 
balance are isochronous, or whether they differ in time ac- 
cording as they are more or less extended. 
We know, by the theory of forces, that the different ex- 
cursions of a moveable body are isochronous, when those 
which push them are in the ratio of the distance of the term 
to which they make it bend. The true method of clearing 
up the present question appears therefore to be, to examine, 
by experiment, whether the force of spiral springs augments 
according to the proportion of the spaces described in their 
different contractions or their different openings. 
To know what we are to think on this capital point, I 
took the main spring of a common wateh and attached its 
interior extremity to an arbor, sustained by very fine pivots, 
which carried a large pulley: I then fixed the extericr end of 
this spring to a fixed point, so that it might rest in its na- 
tural state. This done, I fixed a wire to the pulley and 
wound it round; then I fixed to the other end of this wire a 
small hook, on which | placed successively different weights, 
these weights bending the spring in opening and shutting 
it, more than if it had caused a balance to vibrate: I ob- 
served the ratio in which the book descended, and | found 
it always as the weight with which it was charged*. If, for 
example, half an ounce made it descend a certain quantity, 
an ounce made it descend a double quantity, and so on. 
Indeed it was not the same when the arbor had made se- 
veral turns ; the spaces described then, no longer augmented 
in proportion to the weights: this difference, very sensible 
on the side where the spring shut, became almost nothing 
on the side where it opened: this is why J attribute it, in 
a great measure, to the change of the lever by which it 
acted. 
However it may be, as the ratio of the weights takes place 
in our experiment for arcs much greater than those which 
the balances of watches describe, it appears that we should 
be in the right to conclude that its vibrations are exactly 
isochronous ; that, consequently, the inequalities of the mo- 
tive force, those which arise from losses of freedom in the 
* Dr. Hook discovered this many years before, and made it the subject of 
am anagram, which Dr. Wallis found to be Ut tensio sic vis. —T.S. E, 
D2 wheel- 
