PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 553 



r^ 



urged towards the bottom of the diagram by forces of intensity E, Ei, Et. 

 The lines drawn across the masses indicate wings of such shapes as to 

 make the resistances due to the air r, ri, r^. dynes respectively, when 

 the corresponding velocities are one centimeter per second. It is evi- 

 dent from the geometry of the figure that the velocity of L downward 

 is equal to the sum of the ve- 

 locities of Lx and L2 upward. 

 The tension of the string at- 

 tached to L and passing over 

 the massless pulley A is at 

 every instant half that of the 

 cord which is attached to the 

 massless pulley B, and equal to 

 the tension of the cord which 

 connects Zi and L^. The 

 equations of motion of the 

 masses are of the form (17). 

 If, as a consequence of applied 

 forces or impulses, the string 

 should become slack, the anal- 

 ogy between the mechanical 

 and the electromagnetic prob- 

 lems would disappear, and it 

 is sometimes convenient to 

 imagine the masses attached 

 to taut endless strings in some 

 such manner as is shown in 

 Figure 11. It is very easy to 

 construct a model of this kind 

 which will work fairly well if 

 one uses for masses properly 



loaded roller skates which move about on the level top of a table. The 

 masses may be connected by fine catgut passing around small, cheap 

 pulleys with vertical axes mounted on the table. 



A special case of some practical interest is that indicated in Fig- 

 ure 9b, where the terminals of a battery without sensible self-induc- 

 tance are connected by two inductive branches in parallel. The 

 currents are given by the equations 



L.L,'^ + {{r -f n) L,+ {r + r,) A] ^' 



+ (nrg + rri + rr^) Ci = r.E (20) 



Figure 10. 



Figure 



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