and on the Theortf of Escapements. Hi 



But ft sin' nt + b from nt + b = o to w< + i = tt is - - • 



8 ■ w ' 



therefore the proportionate increase of the time of vibration 



Ex. 2. The friction at the point of suspension is constant. 

 Here/= -c: and it will be convenient to take the intetirals 

 during that time in which the friction acts in the same dire<-tio)i, 

 that is, from the beginning of a vibration to its end, or from 



nt + b = - '^ , ton< + 6=- 

 '2 2 



Hence the increase of the arc of semi-vibration 



t' /■ r 



— - ■- It COS ntJrb: 



which from n< + i = - J to nt^b=1 gives the increase = - ^^ 

 The proportionate increase of the time of vibration 



/( sin nt-v b 



■Kiia 

 which between the same limits is o. 



Ex. 3. The resistance varies as the nf jjower of the velocity , 

 or = kvi"\ tn being any whole number. 



Here /= - kn"'a'" . cos'", nt + b. 



Hence the increase of the arc of semi-vibration 



= - /.•«"'-' . or ./t cos""^ ' . nt + b, 



to be taken between the same limits as in the last example. 



