52 Le Roy’s Membir on the best Method 
wheel-work, &c.,-become nearly compensated in watches 
having a dead escapement: but this is what does not take 
place. In all the experiments that I have made on the dura- 
tion of the vibrations of their regulators, making oscillations 
either by the action of the wheel-work, or freely and inde- 
pendently of this action, I have almost always found, as 
well as the most celebrated artists and men of science*, 
that the long vibrations were always slower than the short: 
T haye even remarked that in a double arc the difference was 
most frequently -45. This effect arises, I believe, from the 
mass of the spring, or perhaps from the obstacles which it 
experiences internally + to display its strength. 
It is only lately that I have at last found, as I shall ex- 
plain more particularly, what is very important, and which 
besides must serve as a base to the theory of watches, and a 
guide to workmen who construct them; viz. that there is 
in every spring of sufficient extent a certain length where 
all the vibrations, long or short, are isochronous ; that this 
length being found, if you shorten the spring, the long vibra- 
tions are quicker than the short ones; if, on the contrary, 
vou lengihen it, the small arcs are described in‘less time than 
the large ones}. It is on this important property of the 
spring, hitherto unknown, | that the regularity of my marine 
watch particularly depends, as we shall see in the end. From 
what precedes we are sensible that the accuracy of watches 
depends, in a great measure, on the length given to the re- 
* This is shown in the writings hitherto given on clock-work. See M. Sule 
ly’s Dissertation on his Marine Watch, (4to. 1726, Paris.) Les Etrennes chrono= 
metisqyes of M. Le Roy, p. 69, &c. The attempts made by several artists to ’ 
correct this retardation prove it also; witness the compensation curb of 
M.-Gourdain, adapted to the spiral spring. The Report made to the Bourd of 
Longitude who examined Mr. Harrison's time-keeper, shows that the English art- 
ists are of the same opinion. See the Gazette du Commerce for the year 1765, 
Tuesday, October 8; and the Report, signed Ludlam, sent to the Academy. 
The principles, says this Report, on which Mr. Harrison forms the third change 
as, that the long vibrations of a balance, whose motion is caused by the same spring, 
are made in less time. This principle is contrary to all the opinions received among 
men. of science, workmen, ke. 
+ See vol. iii. p. 97, of John Bernoulli’s Works.—T. S. E. 
} ‘The way in which he made this important discovery 15 related in the be- 
ginning of Article VIIi, Part IIL—T, S.E, 
gulating 
