2 Dr. S. P. Thompson on the Law of the 



where i is the strength of the current, S the number of turns 

 in the coil, k a constant depending on shape and quality of 

 iron, and m the strength of the pole. Joule (1839) showed 

 this rule to he incorrect, and that as the iron became saturated, 

 m ceased to be proportional to Si. 



Midler's Formula. — Muller gave an expression of the 

 form : — 



m = b tan -1 — , 



a ' 



where h and a are constants, depending on the form, quantity, 

 and quality of the core and on the form and disposition of 

 the coils. Yery similar formulae have been used by Yon 

 Waltenhofen, Dub, Cazin, and Breguet. They are purely 

 empirical, fail to represent the facts with accuracy, and have 

 moreover the defect of not lending themselves conveniently 

 to use in the equations of electromagnetic motors, dynamo- 

 electric machines, and other kinds of electric machinery. 



More recently another formula has been coming into use, 

 and is known — for reasons which will presently appear — as 

 Frolich's formula : it is written 



i 

 m = 



a + bi' 



where a and b are again constants, b being the reciprocal of 

 the maximum value of m. This formula, like the preceding, 

 is a perfectly empirical expression not based in itself upon any 

 physical theory, and it accords with the observed facts of the 

 electromagnet better than any of the preceding formulae. 

 Frolich, who in 1878 was using merely Lenz and Jacobi's 

 formula*, appears to have adopted this expression in 1880f, 

 in consequence of the experiments which he had made with 

 dynamo-machines. A similar formula had been used twenty- 

 five years before by Robinson J to express the lifting-power 

 of an electromagnet, and similar formulae have been used by 

 Oberbeck§, Fromme||, ClausiusTT, Ay rton and Perry**, and 

 Ruckertf. 



Now it must be obvious that since almost the whole of 



* Frolich, Die Lehre von der Elektricitdt imd dem Magnetismus, p. 237. 



t Frolich, Berl. Berichte, Nov. 18, 1880, p. 973 ; also Elektrotechnische 

 Zeitschrift, 1881, April, p. 139. 



X Robinson, Trans. Roy. Irish Academy, vol. xxii. p. 1, 1855. 



§ Oberbeck, Pogg. Ann. cxxxv. pp. 74-98, 1868. 



|| Fromrne, Pogg. Ann. civ. p. 305, 1878. 



51 Clausius, Wied. Ann. xx. p. 367, 1883. 



** Ayrton and Peiry, Journ. Soc. Telegr. Eng. and Electr. xii. p. 317, 

 1883. 



ft Riicker, Phil. Mag. ser. 5, xix. p. 463 (June 1885). 



