OF DEFLECTIVE FOKCES. 



136 



body, and PM the 

 force, which may be di- 

 vided or resolved into 

 two parts, PQ and 

 QM. But PQ is to 

 LK, or HD, as PC to 

 LC, or HC; conse- 

 quently this part of the 

 force will always be 

 employed in generating 

 the regular velocity; 

 and QM is equal to 

 KR, which is the sine 

 of the angle KNR or BCL to the radius KN=:DI=AC, 

 each of these lines being equal to the sine of BI ; the line QM 

 therefore varies as the velocity, and will always be equiva- 

 lent to the friction, provided that it be once equivalent to 

 it, as it is supposed to be at A ; the ratio of the forces con- 

 cerned, in any two succeeding instants, being always such 

 as to maintain a regular vibration. 



If the pendulum be initially in any other situation than 

 that which is here supposed, its subsequent motion may be 

 determined by comparison with that of a point so vibrating, 

 and its progress may be estimated, with tolerable accuracy, 

 while this deviation exists, by supposing it to perform 

 small vibrations with respect to its mean place, in which 

 the immediate effect of resistance may be neglected : but 

 since these vibrations are not supported by any new sus- 

 taining force, they will evidently be rendered by degrees 

 smaller and smaller, so that the pendulum will ultimately 

 approach infinitely near to the regular state of vibration 

 here described, which may, therefore, be considered a^ 

 affording a stable equilibrium cf motion. 



M 2 



