Dent’s new Compensation Balance for Chronometers. 85 
Thermometer. __{ Tension of balance-spring. 
0000 
66 , 0.9958 
100 0.9911 
Thus the experimental tension at the mean temperature of 66° 
Fahrenheit is 0.9958; and the tension computed upon the sup- 
position that it varies as the temperature, is 0.9956; differing 
only by the quantity .0002th part of the whole force, correspond- 
ing to about 2° of the thermometer, which, considering the diffi- 
culty experienced in maintaining an equality of temperature, in 
the individual experiments, is not a greater difference than might 
be reasonably expected, in all probability therefore the tension 
varies nearly as the temperature, within ordinary limits ; but with 
regard to the variation in the inertia, we know that the effect 
produced by the compensating weights, by their approach and 
recession from the centre of the balance, varies as the square of 
the central distance; and therefore it is not to be wondered at, 
that the required ratio betwen the tension and inertia should 
occur only at two temperatures: nor is it surprising that when 
chronometers are regulated for mean temperatures only, they 
should lose at the extreme ones; since in the case of an increase 
of temperature, the approach of the weights to the centre is not 
sufficiently great to effect the compensation, and in the case ofa 
decrease of temperature their recession from the centre is too great 
to compensate for the increased rigidity of the balance-spring. 
It is true, that this law of variation in the inertia applies only to 
each particle of the balance in reference to its distance from the 
centre of motion, and not to a mass, unless referred to the centre 
of gyration ; and as the whole inertia of the balance is made up 
of the inertia of the fixed arms, as well as the movable compen- 
sating weights and rim, it is plain that any attempt to exhibit 
by computation the variation of the whole inertia due toa change 
of temperature, would involve not only a consideration of the 
figure of the balance, but also a knowledge of the law of varia- 
tion in the central distance (as depending upon temperature) of 
the weights and rim, of which we are at present more in igno- 
rance than of the Jaw that exists between the temperature and 
the tension of the balance-spring. The inertia of the balance is 
a more complicated function of the temperature than the tension 
of the balance-spring, and involves a higher power of it: and this 
is still a source of difficulty. 
