54 Le Roy’s Memoir on the lest Method 
dom, it is impossible to augment the arc without aug- 
menting the force which supports the vibrations, and con- 
sequently the pressure of the balance wheel on the cylinders 
or planes, &c.; and as, by theory, a quadruple force is ne- 
cessary (abstraction being made from a great number of 
causes, both physical if, mechanical, sacks concur here 
to destroy a part of the motion of the balance); as it is ne- 
cessary, I say, to have a quadruple force to impress on the 
balance as well as on the balance wheel a double velocity, 
it follows, that the pressure on the cylinders, the planes, 
&c. (always in proportion to the motive force) augments 
here in a much greater ratio than the force of the regulator 
1o overcome them, which ts only as the velocity. We know, 
also, that when the wheel-work is impeded, whether by 
friction, the coagulation of the oil, &c., there must arise 
considerable variations in watches with a dead escapement, 
for then the force communicated to the balance 1s necessarily 
much less. But the friction on the cylinders or planes is 
not dinrinished by this, because the pressure of the wheel 
on these cylinders or planes is a dead force, and the resist- 
ances and friction of the wheel-work have no sensible effect, 
except when the moveable parts are in motion. 
We can hardly determine any thing respecting those 
causes which affect the isochronism of the vibrations in 
watches with a dead escapement, and which, withort any 
thing regular, make them advance or retard. All that we 
can say is, that they augment or diminish according to the 
quantity of friction on the cylindric portions, according to 
the form of the balance, the size of its pivots, the quality of 
the oil, the length of the spiral spring, the number of vi- 
bidtions 7 ina given time, the length of the arc, the points of 
that arc where the wheel ceases to act on the balance, the 
number of teeth in the balance wheel, its mass, the quan- 
tity of motive force, &c. 
There are, without doubt,’a number and a magnitude of 
vibrations where the effect of these different causes is least 
sensible; hut what precedes has already proved to us, that 
the best way, without any comparisgn, will be always (as 
I shall 
