of measuring Time at Sea. 139 
required compensation. The thermometers making part of 
the regulator, when the spirit of wine, by its dilatation, 
pushes a part of the mercury contained in the outer branch tt 
(fig. 7.) towards that to, which is near the axis of motion, a 
portion of the mercury, forming part of the mass of the regu- 
Jator, passes then from its circumference towards its centre. 
At temperate, for example, the mercury occupies the parts 
tkkt ofthe tube; whilst, in extreme cold, when Reau- 
mur’s thermometer is at 15 degrees below freezing*, the 
branch ¢o is empty, and that corresponding, ¢f, is full of 
mercury. Now as the mass of a balance resists in the ratio 
of the square of its distance from the centre, there arises 
evidently from this a compensation ; the retardation arising 
from losses of elasticity in springs, and from the dilatation 
of the balance by great heat, being compensated by the loss 
of mass in the circumference of the regulator, and vice versa 
in the passage to cold: this effect is so much the more cer- 
tain, as there is no play to fear here; besides, the dilatation 
of spirit of wine by heat, and its condensation by cold, are 
constant effects, as we have found by the thermometers of 
this liquor, which at the end of thirty years had Jost nothing 
of their exactness. 
The following is the computation of these thermometers, 
to whichI have given the fourm we see them of, in order that 
the balls might be turned towards the centre of the balance, 
and also to diminish the resistance that the air gives to the 
motion if it was near the circumference. 
Calculation for the Thermometers. 
Suppose the weight of the balance to be three ounces, or 
1728 grains, experience proves that for 30 degrees of heat a 
marine watch where this effect is not compensated loses 157 
per hour, or z},th part. Tt is therefore necessary, that by 
the diminution of its mass the balance should produce an 
equivalent acceleration: now 1729, the number of grains of 
which three ounces are composed, divided by 240, is equal 
to seven grains; and as the accelerations are only as the 
_ square roots of the diminutions of the mass, it is necessary 
to take away about 14 grains of the mercury, placed towards 
* Or 14 below: zero of Fahrenheit’s. 
the 
