188 Till: MAGNETIC CIRCUIT [ART. 58 



straight coils and loops of wire in the air is rut her complicated, because 

 of the mathematical tlitlirulties in expressing the iiermeunees of the 

 j.aths. Those interested in the subject will find ample information 

 in Rosa and Coheirs formula and Tables for the Calculation of Mutual 

 >'lf-lmhtcUinct\ in the Bulletins of the Bureau of Standard^, Vol. 

 5 (1908), No. 1. The article contains also quite a complete bibliography 

 on the subject. See also Orlich, Kapazitdt und Inductivitiit (1909), 

 p. 74 et seq. 



Note 2. In the formulae deduced in this and in the two following 

 chapters, it is presupposed that the current is distributed uniformly 

 over the cross-section of the conductors. Such is the case in conductors 

 of moderate size and at ordinary commercial frequencies, unless perchance 

 the material is itself a magnetic substance. With high frequencies, 

 or with conductors of unusually large transverse dimensions, as also with 

 conductors of a magnetic material, the current is not distributed uni- 

 formly over the cross-section of the conductors, the current density 

 being higher near the periphery. The result is that, as the frequency 

 increases, the inductance becomes lower and the ohmic resistance higher. 

 This is known as the skin effect. For an explanation, for a mathematical 

 treatment in a simple case, and for references see Heinke, Handbuch 

 der Elektrotechnik, Vol. 1 (1904) part 2, pp. 120 to 129. Tables and for- 

 mulae will be found in the Standard Handbook, and in Foster's Pocket- 

 Book. See also C. P. Steinmetz, Alternating-Current Phenomena (1908), 

 pp. 206-208, and his Transient Electric Phenomena (1909), Section III, 

 Chapter VII; Arnold, Die Wechselstromtechnik, Vol. 1 (1910), p. 564; A. 

 B. Field, Eddy Currents in Large Slot-wound Conductors, Trans. Amer. 

 Inst. Electr. Engrs., Vol. 24 (1905), p. 761. 



