134 



Mr Sans; on the Manner 'in tvhich 



tional to' the difference between the angles D/E and DME, or 

 what is the same thing, to MEy — MD/T 



Having obtained this simple method for determining the in- 

 fluence of the maintaining pressure on the rate of the chronome- 

 ter, T proceed to solve the interesting problem, 



To place the arc of impulsion so that the time of the oscilla- 

 tion may not be altefed by the stroke of the escapement. 



The question at once reduces itself to this ; the points A, M, 

 /and A, being given, to find the length of the radius MD, in 

 order that the angle ME/may be equal to MD/ Now, if 

 these angles be equal to each other, their cosines will also be so, 

 whence 



' ME^ -f E/— M/2 : MD^ + U/^— M/2 : : 2ME-E/ : 2MD-jy Or 

 MD* + Ap—Mf^ : MD^ + A,/*— M/: : A/: A,/ From which 

 bj division MD* + A,/*_M/* : Ap-AJ^ • • A,/: A/-A,/ Or 

 MD^_M/« = Af-fA, . 



Hence the following very simple construction : 



A it 



On A A, describe the semicircle, and erect the perpendicular 

 fQ so as to obtainyG* = AjyA, : and from M with the radius 

 MG describe the arc EGD ; the perpendiculars EC, DB, will 

 define the position of the ai-c of impulsion. 



From this construction, it is clear that the pointy is inva- 

 riably within the arc of impulse corresponding to no accelera- 

 tion ; and that when, as in actual practice, the friction is small, 

 the proper position for that arc is just a little before the. centre 

 of the oscillation. When the arc BC is removed nearer A, the 



