522 The Rev. T. R. Robinson's Experimental Researches on the 



Some practical inferences may be drawn from these experiments, for the 

 construction of electro-magnets intended to act with a closed magnetic circuit. 



1. The nearer the spires can be kept to the polar surfaces, the better, for 

 their activity is much diminished as they recede from it : the great superiority 

 of spirals over helices shows this. Thus, the efficiency of {A) is 1'4436 times 

 that of the equiradial {F) ; their mean distances from the poles being 0'07 and 

 107. 



2. The very small decrease caused by increasing the diameter (at least, as 

 far as 7-5, and probably beyond it to an extent not likely to occur in practice) 

 leads to the conclusion that the helices should be as wide as the distance of the 

 cylinders permits, or that b' shall be half that distance ; b will, of course, be as 

 nearly as possible the radius of the cylinders. 



3. The height of the helices and cylinders should be as little as is consistent 

 with lodging a sufficiency of wire to employ to the best advantage the power of 

 the battery which is used. 



4. This height = z may be determined thus : — 



Let iJand -Kbe the constants of the batteries; c? = the diameter of the wire ; 

 d + c that of it when covered with thread (c being in my wire = 0"03) ; 2s = 

 the number of spires in the helices ; and p their resistance. We have 



_^z{ b'-b) , _ 8p.(b' + b){b'-b)xz 

 {d + cy ''' ' d\d + cy 



4/9 



p being a constant, such that the resistance of a unit of the wire = — ^ : for 



copper I find p~\og~^ (5 71018). Then we have for the exciting power with 

 a unit current, 



_ 2sfxE _ 2E(b' -b) fiz 



^^-liV^'~ Ti ''id+cy + 8pz(b'+b)ib'-b) ' 



Ed' 



8p(b' + b)(b'-b) 

 or, putting a = -^^-^ ^ > 



. 2E(b'-b) fiz 



uii- ^5 ' X 



{d^cy+j; 



