142 PRINCIPLES OF ELECTRICAL DESIGN 



are entirely ignored, while, in ME. LAMME'S own words, his 

 method of analysis, including as it does more conditions than 

 are usually included, "instead of making the problem appear 

 simpler than formerly . . . makes the problem appear more 

 complex." 1 



In the first place, it may be stated that considerations of a 

 mechanical nature, such as vibration, uneven or oily commutator 

 surface, insufficient or excessive brush pressure, etc., cannot be 

 dwelt upon here, and, in the second place, ideal or "straight- 

 line" commutation will be assumed, and the conditions neces- 

 sary to produce this generally desirable result investigated, 

 in order that a multitude of more or less arbitrary assumptions 

 may not obscure the problem in its early stages. By working 

 from the simplest possible case to the more complex it is thought 

 that the object in view a phj^sical conception of commutation 

 phenomena leading to practical ends will best be served, and 

 influencing factors of relatively small practical importance will 

 be either disregarded or but briefly referred to. 



45. Theory of Commutation. Consider a closed coil of wire 

 of T c turns moving in a magnetic field. At the instant of time 

 t = the total flux of induction passing through the coil is 

 + $0 maxwells, and at the instant of time t = t c sec. the total 

 flux through the coil is + $* maxwells. Then on the assumption 

 that the flux links equally with every turn in the coil, the average 

 value of the e.m.f. developed in the coil during the interval of 

 time t c is 



If R is the ohmic resistance of the coil and e is any instantaneous 

 value of the e.m.f. produced by the cutting of the actual magnetic 

 field in the neighborhood of the wire, the instantaneous value 



o 



of the current in the coil is i = ^, because e is the only e.m.f. 



in the circuit tending to produce flow of current. The usual 

 conception of a distinct flux due to the current i producing a 

 certain flux linkage known as the self-inductance of the circuit 

 is avoided; but its equivalent has not been overlooked, seeing 

 that the magnetomotive force due to the current in the coil is 

 a factor in the production of the flux actually linked with this 

 current at the instant of time considered. It is not suggested 



1 Reply to discussion, Trans. A. I. E. E., vol. XXX, p. 2426 (1911). 



