LENZ ON ELECTRO-MAGNETISM. 629 



is attained by the ourrent, 



/'(.aximun,) ~ 2 ( ^ 9 + (/> + /3) ^ (^"^ )y • ^^•> 



This expression again shows : 



1. That the maximum of the current stands in direct proportion to 

 f, i. e., to the power of the magnet, or rather to the strength of the 



magnetism which is produced in the armature by the placing on of the 

 magnet, and which again vanishes. 



2. The maximum is more powerful for a thick wire than for a slender 

 one, for we can bring its expression to the form 



/ 

 A B' 



which shows that the whole expression increases with the increase of b. 



3. The maximum decreases with q, i. e. it becomes so much the 

 smaller according to the greatness of the cylinder on which the first 

 series of convolutions is wound, it being assumed that the armature 

 does not on that account become greater. 



4. It becomes smaller with the increase of m, i. e. the greater the 

 free connecting ends of the spirals are, the smaller is the ultimate at- 

 tainable maximum of the current. 



5. Finally, the maximiim increases when a increases, i. e. when the 

 space of the armature upon which a series of convolutions can be 

 wound becomes greater. 



We shall consider the power of the current of a single convolution 

 wound round the armature to be the same as m, then as soon as we 

 put in the general expression (D.) for the current w =: 1 , and a =^b + ^, 

 \ve find _ b^f 



Pi. convolution) - ^(^2 ? -|- 6 + /3) + "" * 



If we divide the expression for the maximum of the current (E.) by 

 this, we may designate the quotients as the maximum of increase, and 

 find that 



29 + (6 + /3)+^ 

 ilic maximum of the increase is ^ — , 2^ j-r r- . . (F.) 



2<7-t-2(6+|3) 



\/C"*) 



Ji I propose to find, for instance, with how many series of convolutions 

 I attain the maximum of the current for my magnet and armature, 

 w hen I take a length of 850 English inches for the wire of the multi- 

 plier and the connecting wires together, I have 



a — 1-6, h + B = 0-065 (wire No. 4) g = 0-335, m = 850. 



The formula n = . f HL gives for « = 1 3-07, and the formula (F.) 

 V «* 

 gives the maximum of increase = 114-8. Wc shall obtain therefore the 



