134 



Mr Sang on the Manner in which 



tional to the difference between the angles D fE and DME, or 

 what is the same thing, to ME/ — MD/ 



Having obtained this simple method for determining the in- 

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

 ter, I proceed to solve the interesting problem, 



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

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



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

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

 order that the angle MEjfmay be equal to MD/? Now, if 

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

 whence 



ME 2 -f E /— M/ 2 : MD 2 4- D/ 2 ~M/ 2 : : 2ME-E/ : 2MD\D/ Or 

 MD 2 4- A/ 2 — M/ 2 : MD 2 + A,/ 2 _M/: : A/: A,/ From which 

 by division MD 2 + A,/ 9 — M f 2 : A/ 2 — A,/ 2 : : A,f : A/- A,/ Or 

 MD 2 , — M/ 2 = A/-/ A, . 



Hence the following very simple construction : 





ST 



























1 , 





1 





JL M 



On AA, describe the semicircle, and erect the perpendicular 

 fQ so as to obtain /G 2 1= AffA y : and from M with the radius 

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

 define the position of the arc of impulsion. 



From this construction, it is clear that the point f 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 



