6 Dr. S. P. Thompson on the Law of the 



Series dynamo. 



1 a\ 2R SJ 



Shunt dynamo. 



Compound dynamo (at critical speed for regulation). 



„_1 ( r s (r a + r ) r, 1 , , , i ,x 

 ^1 q, , x ~y K snort shunt). 



e= 



or 



^lf r&+r.) *. •) (1 h 



o-\8(r, + r a + r w ) Z + SJ V 6 " 



where r a , ?* m , r s , and R are the resistances of armature, 

 main-circuit coil, shunt-coil, and external circuit respectively, 

 and e the difference of potentials at the terminals of the 

 machine. These results were announced by the author at the 

 Montreal meeting of the British Association, and were pub- 

 lished by him in his volume on Dynamo-Electric Machinery, 



as was also the important proposition that the factor - (which 



may be called the determinant of the working power of the 

 dynamo, since it appears in every one of the equations, both 

 of current and electromotive force) is that number of ampere- 

 turns which will reduce the effective permeability of the 

 electromagnet, or rather of the magnetic circuit, to half its 

 initial value. It will be seen that all these synthetical results 

 were new, except that for the current of the series dynamo, 

 which is identical with the expression that had been deduced by 

 Dr. Frolich from the current-curve which represented his 

 experimental results. 



Since the publication of the author's treatise, Frolich has 

 further elaborated the equations of the compound-wound 

 machines ; and a more generalized form has been deduced 

 by Prof. Riicker in the masterly paper which he communi- 

 cated to the Physical Society in March last, in which, how- 

 ever, he attributes to Frolich (I know not on what grounds) 

 the general equation for the electromotive force of all kinds 

 of dynamos. Frolich has also verified the adequacy of these 

 formulae by comparing results calculated from them with 

 actual experiments on compound-wound machines. One ex- 

 ample will suffice. 



