Dent's new Compensation Balance for Chronometers. 87 
destroy all confidence in the performance of such chronometers 
at mean temperatures, (the very temperatures at which their ser- 
vices are most required, ) but it is also a gross violation of the law 
of continuity, upon the maintainance of which, the correct per- 
formance of chronometers must depend. 
Tn order that what I have stated with respect to chronometers 
of the usual construction may be the more apparent, we will, for 
the sake of illustration, suppose the tension of the balance-spring 
to be in proportion to the temperature ; then in the accompanying 
figure, let BB’ B” be a scale of equal parts, and representing the 
scale of a thermometer. 
Fig. 1. 
B B B’ 
100° 66° 32° 
At the extreme temperatures, B and B”, suppose a chronometer 
to be regulated to mean time; then since at these temperatures, 
the tension of the balance-spring must have the same ratio to the 
inertia of the balance, take BD and B” D” at right angles to B 
B”, in proportion to the inertia at these temperatures ; and also the 
parts BG and B’ G”, in proportion to the corresponding tensions 
of the balance-spring. Join DD” and GG”. Since the tension 
is proportional to the temperature, the locus of G will be the 
straight line GG", and from the relation which exists between 
the inertia and the temperature, the locus of D will be a curve 
line, as DD’ D”. Let B’ D’ be another ordinate to the curve, at 
an intermediate temperature, which produced meets D D” in the 
point m, and cuts GG” in G’. Now in order that the chronome- 
