Electromagnet and the Equations of the Dynamo. 291 



to the magnet exactly half its maximum magnetism. I further 

 pointed ont in my lectures on the dynamo that year , that, if the 

 number of windings of the coil S is given, there will be a " dia- 

 critical " current, namely a particular value of current which 

 will exactly half-saturate the magnet. Dr. Frolich has inde- 

 pendently made use of this conception, and has applied it to 

 the formula of the electromagnet The argument is his, but 

 I retain the notation I have used. 



Writing (S^) / for the diacritical number of ampere-turns, 

 we have (as I showed in 1884) (Sz) / = l/cr. 



Taking the expression 



GicSi Gtc Si 



H= 



1 + o-Si O" 1 , . 



and writing p 



Y= J 



we have 



Sz 

 H=Y 



St+(Siy 



where Y is obviously the limiting maximum value of H when 

 the excitement is infinitely great. If S is given, then i' is 

 the diacritical current, and the expression becomes 



H=Y/ 



i+r 



which is true for every electromagnet excited by a single 

 current. Two observations made on any electromagnet will 

 determine the two constants Y and i' . Further, if r be the 

 resistance of the magnetizing coil, since ir = e (the potential 

 requisite to send the current through the coil), we may 

 obviously write the equation 



H = Y 



e + e" 



where e' is the diacritical difference of potential, namely that 

 difference of potential which, applied to the coil of resistance 

 r and of S convolutions, will half-saturate the core. 



The extreme convenience of this form of the law of the 

 electromagnet must be at once apparent, since it enables the 

 equation of a given magnet to be instantly adapted to the case 

 of any given current or potential, and is equally applicable to 

 express either the intensity of the field or the magnetic moment 

 of the magnet. To put the matter in a more general way, let 

 -\/r represent current, or potential, or ampere-turns, and let ty' 



