of measuring Time at Sea. 49 
Besides, when we bend an elastic plate much, it begins to 
break in its convex part: does not this show that the pores 
of this part widen, whilst those of the cavity close? 
We therefore cannot bend a spring without part of the 
fluid which causes the elasticity being Jost on one side of 
its Strength by a small compression, ae that of the op- 
posite side gains by it. This evidently procures the effect of 
M. Bernoulli’s two springs. The idle equilibrium, which 
this geometiician conceived, is therefore a chimerical being. 
THis error, I may remark by the way, comes from the 
same source which occasioned that of the vis viva (forces 
vives*). Those who have admitted them have not suffi 
ciently discriminated the apparent from the real obstacles 
which a body in motion has to surmount. In-+he spring, 
for example, the first are always as the square of the velo- 
city of the body that surmounts them, but the second are 
only as the simple velocity. ‘ 
We may conclude that the vibrating force ae a spring is 
a constant force, the effect of heat ekcepted! provided i it is 
in a free and unconstrained state; that, et ery spring being 
in the case of the constrained equilibrium, what M. John 
Bernoulli says of this equilibrium is absolutely as applicable 
to one only as to two opposite springs, such as he requires. 
We may consequently infer from these principles, that the 
vibrations of the spiral spring are exactly isochronous ; that 
being therefore applied to the watch by a good dead escape- 
ment, abstracting from friction, it would compensate the 
inequalities of the mover and of the wheel-work :. this 1s 
what I shall examine in the following article. 
Article IT. 
Second source of inequalities in watches : the non-tsochronism 
of the vibrations of their regulator, arising as well from the 
spiral spring itself, as from the nature of the escapement. 
Nothing is more important for the theory of watches in 
general, and to ditect the’ artist who executes them, thun to 
* See Saverien, Dict. de Mathématiques, art. Forces; and vol, iii, p- $5, of 
John Bernoulli’s Works. Geneva, 1742.—T.S. E. 
Vol, 26. No. 101. Oct.1806. D know 
