242 Mr. B. Hopkinsou. [June 16, 



their surrounding coils (whether damping coils or field coils)* is equiva- 

 lent to that of a circuit of a certain resistance E supposed to surround 

 completely laminated magnets of the same size and shape magnetised 

 by a constant field current. The induction linked with this circuit 

 will be, taking the notation already used, v I or v (A + a), where 

 v is a constant. The current round the circuit, produced by the 



v dl v da mi . 



oscillation, is, therefore, - p ^- or - ^ -T-. This current tends to 



slightly demagnetise the magnets if a be increasing, and its effect on 

 the induction linked with the field coils and armature may be repre- 



da 

 sen ted by a term - /* 77* where /x is a positive constant. The quantity 



/A is a time, it is the time in which the induction in the magnets falls 

 to l/e of its initial value if the field coils be suddenly short-circuited. 

 If the armature be forced to make small oscillations, given by = 

 sin 6Y, about the state of steady motion, the induction will be as before 

 (p. 240). 



I = ( A + a) sin 6 + b cos 0, 



where now, however, 



while, as before 



The E.M.F. at the terminals of the motor is 



~ 



= P l( a o + a ) tin-pi + (A> + ft) cos pt] 

 + Lp {(a + a) cos pt - (/3 + ft) sin pt} 



|La sin pt + L/3 cos pt + A cospt 



We drop the terms in square brackets, and investigate the damping 

 effect of the " Amortisseur " coil separately as a small effect of the 



* It is worth noting here that the result, so far as damping is concerned, ia the 

 same whether the additional copper is put into a separate short-circuited winding 

 or into the field coils. In the latter form it assists in reducing the ordinary losses 

 in those coils. 



