110 Trans. Acad. Sci. of St. Louis. 



If we can obtain an algebraic expression for this relation it 

 will be possible to use the surface for many engineering 

 purposes. 



Dr. O. Frolich * started this investigation which can be 

 profitably extended f to include many vexing problems. 



The actual tests of dynamo and motor are given in the second 

 part of this paper, but in this part a more simple condition is 

 used to illustrate the method of examination. 



Symbols. 



e = electro-motive force impressed on the terminals. 



E = total electro-motive force induced in the armature of the 



dynamo. 



E a as counter e. m. f. of the motor, 



i = current. 



n l = rev. pr. sec. 



n = rev. pr. min. of the dynamo, 



n' = rev. pr. min. of the motor. 



H = magnetic density in the air gap. 



H x = max. value of permeability of the magnetic circuit. 



a — a factor depending upon the saturation. 



A = area of the armature coil. 



S = number of turns of wire on the magnates. 



Gr = a constant depending upon the design of the machine. 



R = total resistance of the circuit, 



r = resistance between the terminals. 



The total induced e. m. f. in the armature conductors 

 depends directly on the speed and strength of the field through 

 which the conductors pass — see eq. (l)p. 111. 



The strength of the field in the air gap has a very complex 

 relation to the other conditions of the magnetic circuit. This 



* Berl. Berichte 962, 1880. Electrotechinsche Zeitschrift, ii, 134, 170, 

 1881, vi, 128, 1885; ixNov. 1888. 



t Prof. F. E. Nipher a good many years ago noticed the fact that the em- 

 pirical equation of Frolich was that of an hyperbolic paraboloid. For 

 some years he taught his students that this surface and its elements could 

 be profitably used in examining the operation of dynamo-electric machines. 

 This surface is therefore explained in la of this paper so that the methods 

 suggested in la maybe employed in the remainder of the paper. 



