330 Mr. L. C. Jackson on 



that we can now obtain simultaneous traces of the motion of 

 each bob on the same photographic plate. 



As the traces showed that the damping for the present 

 arrangement was not negligible, it was thought desirable to 

 take this into account in the theory. 



The paper includes twenty-four photographic repro- 

 ductions of the double traces obtained for the motions 

 of the bobs under various conditions of starting and 

 coupling. 



II. Theory. 

 Equations of Motion and Coupling. 



Using the notation of the previous paper, the equations of 

 motion may be written : 



M§+M«^ = Mm^ 3 (1) 



N^ + (Nn 2 + Mm 2 a 2 J^=Mm 2 ^. ... (2) 



M m 2 



Putting =— • r=p —j r =7j and inserting the frictional term 



dv N n " 



2 k -~ in the first, we have 

 az 



d 2 ii „ 7 du „ 

 (Pz (m 2 , A 



;^ + U +p mx ) z = m «py- 



in 

 If m 2 u is put equal to a and [-pm 2 u 2 equal to 1> 3 we 



have : ^ 



3k»£+*v-«* • • • • (3) 



d 2 z 



^- + bz = apy (4) 



From (3) and (4) we may write for the coefficient of 

 coupling 7, 



v>=T^- • • (5) 



V 



To solve (3) and (4), try in (4) 



