LENZ ON ELECTRO-MAGNETISM. 627 



in terms of the diameter of the cylindrical armature, and the thickness 

 of the wire and its silky envelope. We have however the semi-dia- 

 meter of a convolution, if half the thickness of the iron cylinders is = q, 



for the first series =■ q -V 



2 



. second = y -h 1. (ft + /3) 



third = 9 + -| (ft + /3) 



nth = 9 + ^-!^ (ft + /3) 



whence we have the length of a convolution or 



c for the first series = Olq-\-(h -\- /3)^ tt 



c second = (^2 g' -)- 3 (ft + (3)") w 



c third = ^2 9 + 5 (ft + /3)^ tt 



c «th = ^2 9 + (2w— 1)(6 + /3)~)t. 



If we substitute the first value of c in the equation for m, we obtain 



^ «i!/ 



^' a TT (^2 9 -H (6 + /3)) + (6 + /3) »; ' 



The electromotive power is for two series of convolutions with regard 

 to the above law, No. 2, 



but the resistance is equal to that of the two series of convolutions, 

 together with the piece m, therefore 



^-^ (2y +ft +/3);r+ ^^ (2 9 f 3 (ft -f /3) ) . + m 



= ft^^ 



_ a Tt (4y + 4 (ft + iS) ) + w (^i + /3) 



6H^ + ^) 

 consequently the power of the current for tM'o series, or 



^« ~ g ^r (4 ^ -h 4 (ft + /3) ) ^^j«_(ftJ-_^ 

 i^ (6 + /3) 



_ 2 a 6Y 



air (4 ^ + 4 (6 + /3) ) -f w (ft -h ^)' 

 \ OL. I Part IV. 2 U 



