254 Mr. R. S. Brough on the Maximum 



magnets*. The latter supposed the dimensions of the bobbins 

 (as I also do in this paper) to be given, fixed, and immutable ; 

 while the learned Count starts with varying the depth of the 

 bobbin, and piques himself on getting a larger magnetic effect 

 out of it than Mr. Schwendlcr did. The best thickness of wire 

 to wind on a given bobbin, and the best size and shape of bob- 

 bin to employ for a given purpose, are two totally distinct 

 questions. 



While investigating the above problem, the question of the 

 influence of the insulating covering of the wire on the results 

 occurred to Mr. Schwendler ; and he went into it in a subse- 

 quent paper t. 



Mr. Schwendler attacked the problem from the point of view 

 of the resistance of the bobbin ; but it seems to me that it 

 yields more readily and presents a more definite result (the 

 former method gives an equation of the fourth order, which 

 has to be solved by a rather coarse approximation) when we 

 start from the thickness of the wire. This method has also 

 led me to a singularly simple relation existing between the 

 resistance of the electromagnet and the external resistance. 



I shall take the case of an elongated bobbin with straight 

 sides and circular ends, because this is a very common form 

 to give to galvanometer-coils, and because the results can at 

 once be reduced to those applicable to circular bobbins by 

 simply putting the length of the sides equal to nothing in the 

 various exj^ressions. 



Let Y = the magnetic effect of the bobbin, 

 R = the resistance of the bobbin, 

 S = the external resistance, 

 E = electromotive force of the battery, 

 and n = the number of convolutions. 



Then (Jacobi and Dub) 



Y= ''^ 



R + S' 



and the problem is to make Y a maximum J, treating the dia- 

 meter of the wire with which the bobbin is wound as the inde- 

 pendent variable, of which ?2 and R are known functions. 



* Compies Hendus, vol. Ixxvi. pp. 368-371. 



t Philosophical Magazine, Januaiy 1867. 



X The force exerted b}^ a coil on a steel magnet is proportional to Y, 

 whereas the force exerted on a soft-iron armature is proportional to Y" ; 

 but whatever value of the variable makes Y a maximum will also make 

 Y- a maximum : so the one solution meets both cases. 



