TransactionsPublished under the care of the General Secretary and the Treasurer . lf = odt and Ae = ri\max = *zmaa; J -^^s + 2 i2„ + -^ ^ / — + ^ ^ j t The chief question is how large is tm ? This time may only be determined by a solution of the differential equation, and, as the J? T computation shows, is almost entirely dependent on J . Since tliese computations are very long, let us satisfy ourselves here withgiving their result Curve I, Fig. 29, represents the ratio ^ 72 T as a function of the constants A = —--zr ^^^ A = 0, that is, the specific resistance of transition E = 0 becomes i,, a
TransactionsPublished under the care of the General Secretary and the Treasurer . lf = odt and Ae = ri\max = *zmaa; J -^^s + 2 i2„ + -^ ^ / — + ^ ^ j t The chief question is how large is tm ? This time may only be determined by a solution of the differential equation, and, as the J? T computation shows, is almost entirely dependent on J . Since tliese computations are very long, let us satisfy ourselves here withgiving their result Curve I, Fig. 29, represents the ratio ^ 72 T as a function of the constants A = —--zr ^^^ A = 0, that is, the specific resistance of transition E = 0 becomes i,, a maximum 832 ARNOLD AND LA COUR: COMMUTATION. on cessation of the commutation, that is, for ~- == 1. If E^ and,therefore, also, A are very large, i^ becomes a maximum when_!5_ = As is evident, curve I begins at 1 and approaches asymptotically the value for very large values of A. From T T curve I the quantity f- -= . = kf has been computed and plotted in curve II as a function of A. For large values of A,curve 11 approaches asymptotically the value 4. By means of. 20 is; 1 10 A Fig. 29. Curves for Determining the MomentOF THE Maximum Value of the AdditionalCurrent. curve 11, the maximum additional current may be calculated in asimple manner: . _ A^ ^zmax 7-> 2). When t is almost equal to T, that is, close to the limit ofcommutation. Since s at the disappearance of the current is a negative dtquantity, the differential equation must, therefore, be possible if fit. ARNOLD AND LA COUR: COMMUTATION. 833 The resistance r is determined by a series of factors of which r> fp the factor ~ •— outweighs all others. Neglecting the minor -K T— t factors, we obtain F^ T— r^^ ^ dt — ^ T— t This condition states that the of the stray induction ofthe additional current at the instant t = T must he less than thepotential difference generated by the additional current betweentJie brush points and the passing commutator segments. If thisis not the case th
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