﻿Theory of the Telephone. 297 



phone-piate with the periodic current in the coil. As has 

 already been stated, only a very rough estimate is possible 

 a priori. We will commence by considering the case of an 

 unlimited cylindrical core, divided by a transverse fracture 

 into two parts, and encompassed by an infinite C}'lindrical 

 magnetizing coil containing n turns to the centimetre. If y 

 be the current, the magnetizing force SH due to it is 9 



8H = 47r^7 (5) 



If we regard the core as composed of soft iron, magnetized 

 strongly by a constant force H, the mechanical force with 

 which the two parts attract one another per unit of area is in 

 the usual notation 



I(H + 27rI); 



and what we require is the variation of this quantity, when H 

 becomes H + SH. This may be written 



m{l+(H+4rf)^} (6) 



The value of dljdH. to be here employed is that appropriate 

 to small cyclical changes. It is greatest when I is small, 

 and then * amounts to about 100/47T. As I increases, dl/dH. 

 diminishes, and finally approaches to zero in the state of satu- 

 ration. In order to increase (6) it is thus advisable to 

 augment I up to a certain point, but not to approach satura- 

 tion so nearly as to bring about a great diminution in the 

 value of dl/dH. In the absence of precise information we 

 may estimate that the maximum of (6) will be reached when 

 I is about half the saturation value, or equal to 800 f; and 

 that dl/dH. also has half its maximum value, or 50/47T. At 

 this rate the force due to 5H is about 40,000 SH, reckoned 

 per unit of area of the divided core, or by (5) 



40,000 x47ni7. (7) 



But before (7) can be applied to the core of a telephone 

 electromagnet it must be subjected to large deductions. For 

 in the telephone the total number of windings n is limited to 

 about one centimetre measured parallel to the axis, whereas 

 in (7) the electromagnet is supposed to be infinitely long, and 

 n denotes the number of windings per centimetre. If we are 

 to suppose in (7) that the windings are really limited to one 

 centimetre, lying immediately on one side of the division, 

 there must be a loss of effect which I estimate at 5 times. 



* Phil. Mag. xxiii. p. 225 (1887). 



t Ewiug, ' Magnetic Induction/ 1891, p. 136. 



Phil. Mag. S 5. Vol. 38. No. 232. Sept. 1894. X 



