420 BEIJ- SYSTEU TF.CHNICAL JOURNAL 



with a coil. It i^ wondiTful what a fi;cnius can do in one night! He jjointed out the 

 exact relations l.-etween the condenser, the self induction and the frequency which 

 would give the largest current, and he was the first to do this, so far as I know . . ."'' 



Maxwell's letter, which began with the sentence, "Since our conversation 

 yesterday on your experiment on magneto-electric induction, I have con- 

 sidered it mathematically, and now^ send you the result," was dated March 

 27, 1868; it was sent by Grove to the Philosophical Magazine, where it was 

 published in May. Preliminary to the mathematical treatment Maxwell 

 gave in this letter an unusually clear exposition of the analogy existing 

 between certain electrical and mechanical effects, and from the standpoint 

 of pedagogy as well as physics it will be interesting to see the language he 

 used. He expressed himself thus: 



"The machine produces in the primary wire an alternating electromotive force, 

 which we may compare to a mechanical force alternately pushing and pulling at 

 a body. 



"The resistance of the primary wire we may compare to the effect of a viscous 

 fluid in which the body is made to move backwards and forwards. 



"The electromagnetic coil, on account of its self-induction, resists the starting 

 and stopping of the current, just as the mass of a large boat resists the efforts 

 of a man trying to move it backwards and forw^ards. 



"The condenser resists the accumulation of electricity on its surface, just as a 

 railway buffer resists the motion of a carriage towards a fixed obstacle."" 



Using such concepts as these he gave a simple and lucid explanation of 

 the problem without resort to mathematics; and then in a postscript, or 

 appendix, he gave the mathematical theory of the experiment, employing a 

 schematic diagram of the apparatus. Using different, but equivalent, 

 symbols, he derived and solved the now familiar expression for the current i 

 in such a circuit. 



E sin CO/ = I "^^ + i?/ -f J, iidt 

 at C J 



This is recognizable as similar to that set up by Lord Kelvin for the dis- 



/ . . dq\ 



charge of a condenser ( E being zero in that case, and i being equal to ~ 1. 



The solution of this equation is 



E 



^Z^'+i^'--^)' 



from which Maxwell pointed out that the current would be a maximum 

 when wL = -77 (co being proportional to the frequency and L and C being 



