290 Dr. S. P. Thompson on the Formula of the 



complex formula which he suggested. It has been recently 

 shown by Mr. Bosanquet* that if we take as expressive of the 

 permeability, not the instantaneous value dm/ d%, but the 

 integral value m/a, and treat this on Lamont's plan as pro- 

 portional to the deficit of saturation, 



we deduce at once the formula in question. Dr. Frolich's 

 researches upon the dynamo have given us the most complete 

 and perfect proofs of the adequacy of the formula to represent 

 the facts of the electromagnet as it is used in practice. My 

 former communication was indeed mainly written to point 

 out the extreme value and interest of Dr. Frolich's work 

 from this point of view. 



2. Frolich's simplified Formula of the Electromagnet. 



Since my former communication to the Physical Society 

 was made, a further work on the theory of the dynamo by 

 Dr. Frolich has appeared!. In this work he carries the sim- 

 plification of the formulae of magnet and of dynamo one stage 

 further by introducing considerations somewhat closely con- 

 nected with those which entered into my own work of 1883-4. 



The form adopted by me in 1883 for the Lamont- Frolich 

 formula was 



Gc/cSi 



H = 



i+o-sr 



where H is the resulting average intensity of the magnetic 

 field (in which the armature rotates), k the initial value of the 

 magnetic permeability, Gr a coefficient depending upon such 

 purely geometrical quantities as the form and size of core, 

 pole-pieces, and coils, S the number of windings of the mag- 

 netizing coil, and <r the " saturation -coefficient." This can be 

 transformed at once to Frolich's form by writing M = G/c/a; 

 k = <7 ; #=Si. In 1884 I pointed outf the nature of this 

 saturation-constant and its importance in the resulting equa- 

 tions of the dynamo. It is the reciprocal of that number of 

 ampere-turns which, to mark its importance, I ventured to 

 term "diacritical," namely that number of ampere-turns which 

 will reduce the instantaneous value of the magnetic permeability 

 to half its initial value, or which, in the formula used, will give 



* ' Electrician/ vol. xvi. p. 247, February 1886. 



t Die dynamoelektrische Maschine. Eine physikalische Beschreibung fur 

 den technischen Gebrauch, von Dr. 0. Frolich (Berlin, 1886). 



X ' Dynamoelectric Machinery,' first edition, p. 221 ; also Report Brit. 

 Assoc, Montreal Meeting, 1884. 



