Mechanical Analogy to Coupled Circuits. 567 



taken on the horizontal line A^. (A 1 and S x coincide since 

 the velocity in the first belt is zero.) The points AiA 2 &c, 

 form with A x y the velocity diagram. The semicircles are 

 described with the A points as centre?. The first T point 

 being found, a horizontal line through T gives all the other 

 corresponding T points, thus avoiding the necessity for a 

 second measuring of the v's. The points a, /3, y, S on the 

 circles are the points of contact of the tangents correspond- 

 ing to the four paths. The dotted lines with arrows drawn 

 across the belts are the steering directions for those belts,, 

 the heavy lines being the true paths, 



In this diagram the breadths of the belts are all equal, also 

 the velocities in belts 1 & 9, 2 & 8, 3 & 7, 4 & 6 are equal, 

 that is things are symmetrical about belt 5. When the path 

 crosses belt 5 it changes the direction of its curvature, other- 

 wise the second half is a repetition of the first half. This 

 arises of course from the fact that the directions in two belts 

 having the same velocity must be the same. 



N.B. — There is an error in fig. 8. Instead of S 1 B 1 being 

 produced, A 1 G 1 should have been drawn parallel to ^> 1 B 1 . 



LIX. On an Exact Mechanical Analogy to the Coupled 

 Circuits used in Wireless Telegraphy, and on a Geometrical 

 Method of Interpreting the Equations of such Circuits. Eij 

 Professor Thomas K Lyle, M.A., Sc.D., F.R.S.* 



1. "TF a periodic E.M.F. = E acts on a circuit having 

 A resistance = R, inductance = L, and capacity = K, 

 it is well known that the current C produced will satisfy the 

 differential equation 



L(D. + ?D + J I )0. DE , 



where D stands for d/dt. 

 If 



this equation can be written in the form of Ohm's law as 



rC=E, (I.) 



where r represents the differential operator 



L D 



* Communicated bv the Author. 



