294 Dr. 8. P. Thompson on the Formulce of the 



turns). Then 



and 



i = SR' 



SR 



■ -. B (5) 



It appears, then, that the dead turns are proportional to the 

 diacritical current and to the resistance ; and inversely pro- 

 portional to A and Y, the factors of B. It will be noted that 

 i / 2R=E / , the diacritical electromotive force. 

 Again, we have found 



E=nB-E / ; 

 and as E / = n / B, it follows that 



E = (rc-n')B (6) 



This result is interesting in itself, and might have been used 

 as a starting-point for the equations of the dynamo, inasmuch 

 as it is readily found by experiment as a fundamental relation 

 between speed and electromotive force. Following the ana- 

 logy and the nomenclature adopted, we may regard n' (the dead 

 turns) as the diacritical speed. In other words, it is that speed 

 at which, with magnets separately excited to saturation, the 

 induced electromotive force will be diacritical, and will, with 

 the given resistances 2R, give the diacritical current. This 

 equation (6) gives by far the best method of determining the 

 important constant B. Two experiments to observe a pair of 

 values of E and n will suffice to determine both n' and B. 



5. Equations of the Shunt Dynamo. 

 Here we use r s and i s for the resistance and current of the 

 shunt-coil, and r a and i a for those of the armature. We may 

 then calculate the potential at terminals as follows. Writing 

 IA for the resistance of the whole system of machine and 

 its circuits, as measured from brash to brush*, 



T 



E = e + r a i a = e j| = 4wAH, 



H=Y-^, 



e-¥e 



r„, -^ e 



m =nB e+* 



I > 



whence 



«= — : ^ ( 7 ) 



* See my ' Dynamoelectric Machinery,' second edition, p. 298. 



