178 PROCEEDINGS OP THE AMERICAN ACADEMY 



coil. The coil could therefore be moved through all positions, from 

 perfect parallelism to its. neighboring coil in the interrupted circuit to 

 a position at right angles to this coil. The horizontal axis was pro- 

 vided wiih an index arm which moved over a graduated circle. Call- 

 ino- 6 the anjrle of inclination of the axis of the movable coil with the 

 axis of the fixed coil in the interrupted circuit, and N the strength of 

 the induction current in the movable coil, we have evidently, on the 

 supposition that the strength of the alternating current remains constant, 



N = constant X cosine 6. 



When the axes of the coils are at right angles, cosine 6 = 0, and we 

 should have silence in the telephone. Since adopting this arrange- 

 ment we have discovered that Dr. Bowditch, of the Harvard Medical 

 School,* has employed this arrangement of a movable coil placed in 

 front of a fixed coil as a modification of Du Bois Reymond's appa- 

 ratus for controlling induction currents so that they may be admin- 

 istered by known amounts for physiological purposes. In Du Bois 

 Reymond's apparatus one induction coil was simply moved away from 

 a fixed coil through which an interrupted current was passed, much 

 in the same manner as the coils in Wiedemann's form of galvanometer 

 are moved. Here no minimum could be obtained. In Dr. Bowditch's 

 form of this apparatus, theoretically a minimum should be obtained, that 

 is, when cosine 8 = 0, or when the axes of the coils were at right angles. 

 An indication of an electrical current is obtained even when the axes 

 of the coils are at right angles, on account of the windings of the coil 

 not being perfectly at right angles to those of the stationary coil. 



That no minimum should be obtained when the axes of the coils 

 are at right angles, and when induction arises from all parts of the 

 circuit, is evident upon an elementary consideration of the subject. 

 We have to deal in this form of instrument with the mutual induction 

 which arises between the fixed coil and the movable one, and also with 

 the self-induction which arises between the spires of the movable coil 

 in the telephone circuit. The mutual induction can be reduced theo- 

 retically to zero by placing the movable coil of the telephone circuit 

 at right angles to the fixed coil. The self-induction can be estimated 

 as follows. Taking Maxwell's discussion for the induction between 

 parallel circuits of radii A and a, we have the coefficient of mutual 

 induction, 



cos e ds dsf 



M 



-ff- 



* Proc. Am. Acad., vol. xi. p. 281. 



