\ 
of measuring Time at Sea. 53 
gulating or spiral spring. If with the same kind of dead 
escapement certain watches go badly, whilst others are 
very regular, we here see the cause of it; and moreover 
the new observation may be of great help in the disposition 
of pendulums, whether small or second, where the pendulum 
is suspended by a spring: in effect, we know by what pre- 
cedes that it must have such a Jength in the spring of sus- 
pension, that all the vibrations of these pendulums may be 
isochronous. 
Though we should suppose, even in the regulating spring 
of a watch, the length requisite to render all the vibrations 
of the balance isochronous, if it was applied there by the 
common methods, this isochronism would be presently de- 
stroyed by the friction of the pivots of the balance, which, 
according to the remark made by Daniel Bernoulli*, would 
become always less considerable in great arcs than in smal] ; 
for, by theory, the obstacles of friction, the tenacity of oil, 
&c., as those of gravity, of springs, of cohesion, &c. are 
proportional to the times during which they are surmounted. 
Now, the vibrations independent of these frictions being 
supposed isochronous, these frictions must become neh 
less considerable with regard to the force which surmounts, 
them, when, for example, these arcs are doubled; since 
this force, being as the arcs, is then doubled, and the time 
not sensibly different. 
M. Sully has made experiments on this subject as decisive 
as they are curious, which may be consulted f. 
The. inverse of what precedes takes place for the friction 
occasioned by the balance wheel on the parts of the escape- 
ment, viz. the cylinder in those of Graham, and on the 
plates or planes in those of Debautre, Sully, Le Roy, Gour- 
dain, &e, These frictions, instead of rendering the Jong vi- 
brations quicker than the short ones, on the contrary aug- 
ment the duration of the former :' the follawing is the cause; 
»—The balance “being supposed to have the necessary free- 
* Recherches Méchaniques et Astronomiques, &c. p. 41, 
+ Suite de la Description @un Horloge, &e. p. 168: Dissert. sur une Montre 
Marine, Se, 
D3 dom, 
