198 LECTURE xvir. 



The elasticity of this spring adds a minute force to the power of gravitation, 

 which acts o*\ the pendulum, and this force mxist be considered when the 

 length of a simple pendulum is compared with the frequency of its vibra- 

 tions. It does not, however, interfere with the equality of the vibrations 

 among each other ; for in all springs, Dr. Hooke's general law, that the force 

 increases as the degree of flexure, is found for moderate oscillations to be per- 

 fectly accurate; such a force, therefore, accelerates the larger and the smaller 

 vibrations precisely in the same degree. But in balances, it is desirable to 

 have the velocity, and the extent of the Vibration, as great as possible, in 

 order that the motion may be the less influenced by the inequalities of the 

 sustaining power; and in large excursions. Dr. Hooke's law is not so pre- 

 cisely true; there must also necessarily be some inaccuracy from the loss of a 

 certain 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 experiment 

 that a certain length may be determined for almost every spring, which will 

 afford vibrations cither perfectly or very nearly isochronous. In orcler that 

 the weight or inertia of the spring may interfere the less with the regularity 

 of its motion, it is sometimes tapered, and made thinner at the extremity : 

 it is now also usual in th.e best watches to employ a spring coiled into a 

 cylindrical form, like that of the spring of a bell, of which the motion ap- 

 pears to be somewhat more regular than that of a flat spiral. This was in- 

 deed the original construction, but was probably laid aside on account of the 

 space which it required. The balance springs are made of the finest steel, 

 . and the best are manufactured in this country, although the French are said 

 to have the art of making their main springs of .a better temper than ours. 

 Sometimes the balance spring is made of an alloy of gold and copper; these 

 springs 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; and 

 endeavours 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 a 

 little more frequent than in larger ones, in order that when the presence of 

 dust and the tenacity of the oil contract the extent of the vibrations, this 

 contraction may tend to produce an acceleration which compensates for the 

 diminished force of the spring. But it is perhaps more eligible to make every 

 compensation, as far as possible, independent of circumstances foreign to 



