VOL. LXXXIV.] PHILOSOPHICAL TRANSACTIONS. 381 



similar to that of gravity on a pendulum : each kind of force has the effect of cor- 

 recting the irregularities of impulse and resistance, which otherwise disturb the 

 isochronism of the vibrations. 



Daring the present century, various improvements have been made in the con- 

 struction of watches, chiefly by the artists of this country, to whose ingenuity 

 and skill, aided and encouraged by public rewards, we must attribute the excel- 

 lence of the modern watches and time-keepers, so highly valuable for their uses 

 in geography, navigation, and astronomy. The principles on which time-keepers 

 are constructed, considered in a theoretical view, attbrd an interesting subject of 

 investigation. It is always satisfactory to compare the motion of machines with 

 the general laws of mechanics, whenever friction and other irregular forces are so 

 far diminished as to allow of a reference to theory ; especially if inferences likely 

 to be of practical use may be derived from such comparison. In time-keepers, 

 the irregular forces, both of impulse and resistance, are much diminished by the 

 exactness of form and dimension which is given to each part of the work ; and 

 they are further corrected by the maintaining power derived from the main 

 spring : for whatever motion is lost by the balance from resistance of any kind, 

 almost the same motion is communicated by the maintaining power, so as to 

 continue the arc of vibration, as nearly as possible, of the same length. 



In these machines, the real measure of time is the balance, all the other work 

 serving only to continue the motion of the balance, and to indicate the time as 

 measured by its vibrations. The regularity of a time-keeper will therefore de- 

 pend on that of the time in which the balance vibrates : to investigate this time 

 of vibration, from the several data or conditions on which it depends, is the ob- 

 ject of the ensuing pages. 



Let PMNS (pi. 4, fig. 13), represent the circumference of a watch balance, 

 which vibrates by the action of a spiral * spring, on an axis passing through the 

 centre c. Let odbe be the circumference of a concentric circle, considered as 

 fixed, to which the motion of the balance may be referred. In the circumference 

 of this circle let any point o be assumed, and when the balance is in its quiescent 

 position, suppose a line to be drawn through c and o, intersecting the circum- 

 ference of the balance in the point a ; the radius ca will be an index, by which 

 the position of the balance, and its motion through any different arcs of vibra- 

 tion, will be truly defined. In the ensuing pages, the motion of the balance, and 

 the motion of the index ca, will be used indifferently, as terms conveying the 

 same meaning. Since the b dance is in its quiescent position when the index ca 

 is directed to the fixed point o, on this account o is called the point of quiescence 

 of the balance, or balance spring, indicating the position when the balance is not 



• In these investigations it is indifferent whetlier tlie balance is supposed to vibrate by the action 

 of a spiral or hehcal spring. — Urig. 



