122 Trans. Acad. Sci. of St. Louis. 



If it is desired that (n') the speed of the motor be 1000 

 rev. pr. min. then 



1000 lorcn .1 



n = — — = 1250 and 



.o 



R=2.25 from eqs. (20) and (21). 



Another value of n' would require a different constant 

 dynamo speed and a different line resistance. 



If on the other hand n were fixed then n' and R could be 

 gotten from the above equations. 



This condition can be very nicely illustrated, or a graphical 

 solution can be gotten by the use of the characteristic surfaces. 



From fig. 8. it is seen that the dynamo surface is ADBC. 

 The motor characteristic at a constant speed of 1000 rev. pr. 

 min. is the line DU. 



Project the motor characteristic upon the dynamo surface 

 and it gives us the line VW, upon the surface which projected 

 upon the ni plane gives the line VX. This line is not neces- 

 sarily straight. See fig. 19. 



The line VX shows that the condition of constant speed of 

 the motor would require varying speed of generator. If we 

 add to the motor characteristic the e. m. f. =Ri, we would 

 have as the result the line DZ which shows what the output 

 of the dynamo must be to give the constant motor speed of 

 1000 r. p.m. when R = 2.25. DZ projected upon the surface 

 gives us the conditions of operation of the dynamo in the 

 line Y"Y. 



This line projected upon the ni plane gives the line Y"Y' 

 which we see is a condition of a constant speed of 1250 rev. 

 pr. min. of the dynamo for all currents. The line Y" is thus 

 the characteristic of the dynamo at a speed of 1250 r. p. m. 



In the solution of the equations (20) and (21) if R had 

 come out negative — see p. 136 — it would be impossible to 

 use those two machines to regulate for constant speed with 

 varying loads. 



From our knowledge of the necessary resistance of the 

 circuit for best regulation, it will be possible to most success- 

 fully design the circuit. 



