210 



HISTORY OF SCIENCE. 



to the curved surfaces at each oscillation. This problem was the origin 

 of the notion of evolutes and involutes. The curve F H A, formed as 

 the manner stated above, is called the involute of c A, while the latter 

 is the evolute of F H A. Elegant as is the idea of the cycloidal pen- 

 dulum, it was found that the circular pendulum fulfilled more con- 

 veniently all the conditions required in practice. 



Huyghens was the author of another invention of the greatest utility 

 in the construction of timekeepers, namely, the application of the spiral 

 spring which regulates the movements of the balance-wheel. This 



FIG. 96. 



spring performs the same part for the balance that gravity does for a 

 body oscillating in a cycloidal arc ; for, as the wheel is moved from 

 its position of rest, the spring tends to bring it back with a force pro- 

 portional to the amount of displacement, and this is the condition 

 necessary in order that the oscillations should be isochronous i.e., 

 performed in equal times whatever their extent. Fig. 95 shows the 

 balance-wheel of a chronometer, with the spiral spring A attached to 

 the axis on which it turns. Fig. 96 shows the position of the balance- 

 wheel in the chronometer, and its connection with the escapement by 

 which the oscillations are made to control the motion of the train of 

 wheels. Since the invention of the mechanism, many refinements have 

 successively been introduced into timekeepers. The last two figures 

 show an arrangement of the balance-wheel by which alterations in its 

 rate of vibration, which would otherwise be occasioned by changes 



