88 Dent's new Compensation Balance for Chronometers. 
ter may go mean time at the mean temperature, as in the extreme _ 
temperatures, the tensions of the balance-spring, which are here 
represented by the lines BG, B’G’, and B’ G”, should be in pro- 
portion to the ordinates B D, B’ D’, and B” D”, which cannot be 
the case unless B’ D’ is equal to B’ m, or unless the point D/ coin- 
cide with the point m, or the curve D D/ D” coincide with the 
straight line Dm D’—which is impossible. The quantity m D‘ 
or difference between the inertia of the balance and what tf ought 
to be, for the chronometer to go mean time, is seen in the diagram 
to be the greatest at the intermediate temperatures, which in the 
actual performance of the chronometer is the case—and as they 
are found to gain at these temperatures, it is clear that BY D’ is less 
than Bm, or the curve is convex towards the axis BB’. If 
the chronometer, instead of being adjusted to the extreme tem- 
peratures, be adjusted to the mean, and one of the extreme tem- 
peratures, (as the highest for instance,) join DD’ and produce it 
until it meets D” B” in the point x ; then since D” B” is greater 
than n B” by the difference D’ n ; the inertia will be greater than 
it ought to be, to an increased amount, corresponding to a dimin- 
ished gaining, or an increased losing rate of the chronometer, 
which is also found to be the case. I shall now proceed to show 
the mode of construction of the balance which I have adopted in 
order to obviate the error; and I have accomplished this, not by 
supplementary weights, but by effecting a more perfect conform- 
ity with the proper law of approach in the compensating weights 
themselves ; the correction being, thereby, both continuous and 
simultaneous. 
Before entering on a description 
of my improvements, I will ex- 
plain, ftom the following diagram, 
the defects in the construction of 
the ordinary compensation-balance, 
and show its inadequacy to accom- 
plish the required correction for the 
varying tension of the balance- 
y * * ’ . 
1 being on the outside of the Segments, and steel on the inside ; ¢, compen- 
sating weights. 
