56 Le Roy’s Memoir.on the best Method © 
force of the spiral, the greater or less freedom of the ba- 
lance, &c. In general, watches with dead escapements 
advance about ie Minutes in twenty-four hours, when, 
from the heat of the fob, which is nearly equal to that felt 
under the tropic, it passes to that degree of cold. which pro- 
duces ice. 
If we wish to know how much influence the balancé and 
the spiral spring have separately on these errors, the calcu- 
lation is easily made. 
Experience shows that a steel bar of three feet increases 
1-60th of an inch nearly, or = ,,th part, when from freez- 
ing cold it passes to a heat which raises Reaumur’s thermo-— 
-meter* to 30°, about equal to the heat of the fob of a middle~ 
aged man. 
Now the weight of a balance being known, the resistance ° 
which it gives to the spiral is in the direct ratio of the square, 
of the distance of its circumference of percussion, if we may. 
so express it, from the centre of its motion ; and by theory, 
the number of vibrations is in the inverse proportion of this 
distance: therefore a watch taken from the fob to a place 
where it freezes, when it is arrived.at the cold of the place, 
each of its vibrations, by the contraction of the balance’ 
alone, ‘is accelerated the 7,,th; that is to say, the watch 
by this cause advances about 11” per hour; the remainder 
of the gain being produced by the increase of elasticity in 
the spiral spring, and other causes. 
* The degrees of Reaumur’s thermometer may be converted to Fahren- 
R -x* 9 
dad i 2 = Fahren. Therefore 30° 
heit’s by the following equation: 
of Reaumur’s is = 99% of Fahrenheit’s. 
Smeaton, in the Phil. Trans. for 1758, has given the expansion of one foot 
of blistered steel = 3454; qdths of a foot for 180° of Fahrenheit, which for 
three feet at 100° amounts to z77'ygdths of a foot. Now the English foot’is 
to the French foot as 4000 to 4263; therefore the foregoing expansion in 
French measure is =¢°5¢°'3;qdths of a foot for 30° of Reaumur, which is 
nearly 4% times greater than Le Roy statesit. If we had taken hard steel it 
would have been greater still, in the proportion of 138 to 147,—T,S, E. 
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