84 Dent's new Compensation Balance for Chronometers. 
with the historical details of the subject, that the road to perfec- 
tion in the art of chronometer-making is, as in most other arts, a 
wearisome one, more frequently leading to profitless trouble, than 
contributing either to the interest of the contriver or the benefit 
of the public. Nevertheless, by such investigations has been 
obtained the knowledge of a curious fact, which has lately exci- 
ted the attention and ingenuity of various persons engaged in the 
manufacture of chronometers. 
The fact alluded to is this—that if chronometers, as generally 
constructed, be regulated to mean time at mean temperature, the 
chronometer will Jose at the extremes of heat and cold; or, if ad- 
justed to keep mean time at the extremes, they will have a ten- 
dency to gain at the intermediate temperatures. 
This fact, although in all probability known to others, was 
_ first pointed out by myself in No. 14 of the Nautical Magazine, 
in the year 1833, but I am not aware that the slightest hint has 
ever yet been given as toits ¢rue cause. In order to explain it, 
we must bear in mind, that no chronometer can keep a uniform 
rate, unless the tension, or moving force of the balance-spring, 
has an invariable ratio to the resistance of the inertia. Now in 
chronometers, as usually constructed, this ratio cannot, from the 
nature of the construction of the balance, be maintained at differ- 
ent temperatures; since the tension of the balance-spring, when 
influenced by a change of temperature, varies according toa law 
different from that observed in the simultaneous variation of the 
inertia. We cannot, indeed, assign with any great precision the 
law which connects the tension of the balance-spring with the 
temperature. ‘That the force of tension, however, varies very 
nearly as the temperature, within ordinary limits, may be seen 
from the following experiments made with a chronometer having 
a glass disc for the balance, and a balance-spring of hardened and 
tempered steel. 
Thermometer. | Hourly rate. Number of vibrations in one hour. 
32 + 5.74 3605.74 
66 — 1.80 3598.20 
100 — 10.30 3589.70 
Now since the force of tension of the balance-spring (the inertia 
and friction remaining the same) varies as the square of the num- 
ber of vibrations made in the same period, we have the following 
results from the above, taking the force of tension at 32° to be 
unity. 
