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iECTUJIE XVJI.

The elasticity of this spring adds a minute force to the power of gravitation,which acts on the pendulum, and this force* must he considered when thelength of a simple pendulum is compared with the frequency of its vibra-tions. It does not, however, interfere with the equality of the vibrationsamong each other; for in all springs, Dr. Hooke’s general law, that the forceincreases as the degree of flexure, is found for moderate oscillations to he per-fectly accurate; such a force, therefore, accelerates the larger and the smallervibrations precisely in the same degree. But in balances, it is desirable tohave the velocity, and the extent of the vibration, as great as possible, inorder that the motion may be the less influenced by the inequalities of thesustaining power, and in large excursions, Dr. Ilooke’s law is not so pre-cisely true; there must also necessarily he some inaccuracy from the loss of acertain portion of the force in generating the momentum of the spring itself,which, when the form is spiral, introduces great, intricacy into the calcula-tion of the properties of the vibration. Yet it has been found by experimentthat a certain length may be determined for almost every spring, which willafford vibrations either perfectly or very nearly isochronous. In order thatthe weight or inertia of the spring may interfere the less with the regularityof its motion, it is sometimes tapered, and made thinner at the extremity:it is now also usual in the best watches to employ a spring coiled into acylindrical form, like that of the spring of a bell, of which the motion ap-pears to be somewhat more regular than that of a Hat spiral. This was in-deed the original construction, but was probably laid aside on account of thespace which it required. The balance springs are made of the finest steel,and the best are manufactured in this country, although the French arc saidto have the tart of making their main springs of a better temper than ours.Sometimes the balance spring is made of an alloy of gold and copper; thesesprings are very elastic, but they are too liable to break. Mr. Earnshaw ob-serves, that the strength of a spring always diminishes a little as it wears; andendeavours to derive a compensation for this diminution of strength, by em-ploying a spring of such a form, that the vibrations in small arcs may be alittle more frequent than in larger ones, in order that when the presence ofdust and the tenacity of the oil contract the extent of the vibrations, thiscontraction may tend to produce an acceleration which compensates for thediminished force of the spring. But it is perhaps more eligible to make everycompensation, as far as possible, independent of circumstances foreign to