552 PROCEEDINGS OF THE AMERICAN ACADEMY. 



get a differential equation of the second order for Ci in which the 

 inductances and their derivatives are known functions of t, and the 

 initial values of (7^ and C\ are also known. This new equation may 

 be found by equating to zero the determinant 



{L+LO C'\+(2L'+2L\+r+r{) C\+{L"+L'\) C^ 



LC'\+(2L'+r)C\+L"Ci 



(L+Li)C"i+(iv'+L'i+r+ri)Ci-fi-Ej 



LC\+{L'+r)Ci-E-E2 



(19) 



and, although it may be somewhat simplified, it generally proves rather 

 intractable. If, however, the interval T is so short that the changes 

 in the inductances may be regarded as impulsive, the corresponding 

 changes in the currents may be found immediately, for if the equations 

 be integrated with respect to the time from ^ = to t = T, and if T 

 be made to approach zero, while the currents remain finite, it appears 

 that LC + LiCi and LC + L^C^ have the same values just after the 

 impulsive change in the inductances as they had just before the change. 

 The induction flux through each circuit chosen for the equations re- 

 mains unchanged by the sudden change of inductances. 



It is easy to find a number of different problems in mechanics each 

 of which yields equations of motion of the form (17), and is, therefore, 

 analogous in a sense to the electromagnetic problem under considera- 

 tion. Such an analogy, even though it be difficult to embody it in a 

 working model, sometimes makes clearer to a person already familiar 

 with mechanical principles the nature of the phenomena which he is to 

 look for in interpreting his electrical equations. It will do no harm if, 

 in imagining a mechanical system which is to serve this purpose, we 

 postulate the existence Oi flexible, inextensible, massless strings, or 

 even, at a pinch, the existence of stiff, nearly massless rods, or of pulley 

 wheels so light that their moments of inertia shall be negligible. It is 

 often desirable to imagine the motions of the masses which in the me- 

 chanical system represent the inductances in the electrical problem, to 

 be hindered by retarding forces proportional to the velocities, to repre- 

 sent the electrical resistances. The resistance which the air offers to 

 a body moving through it with a constant velocity not greater than 50 

 cms. per second is very nearly proportional to that velocity ; and since 

 the velocities which in the mechanical case correspond to the currents 

 are usually much smaller than that, the resistance may be sufficiently 

 well indicated by thin wings or vanes of proper size attached to the 

 masses. 



In the arrangement shown in Figure 10 the masses L, Li, L-z, are 



