Alternate Current Measurement . all requirements. It is frequently necessary to consider quantities like N and TsT, such thatone is the differential coefficient of the other. Newtons notation may beconveniently used, not only for the instantaneous values N, 1ST, but also for the corresponding magnitudes N, 1ST, since the latter are constants as regardstime, so that no ambiguity can arise. If A and B are any two cyclic quantities, it will be readily seen that yd) JBljlj — — JtjjflL, JfxxL — U. * Roy. Soc. vol. 61, p. 465. VOL. LXXX.—A. 314 Dr. W. E. Sumpner. [Jan. 21, It follows from (2)
Alternate Current Measurement . all requirements. It is frequently necessary to consider quantities like N and TsT, such thatone is the differential coefficient of the other. Newtons notation may beconveniently used, not only for the instantaneous values N, 1ST, but also for the corresponding magnitudes N, 1ST, since the latter are constants as regardstime, so that no ambiguity can arise. If A and B are any two cyclic quantities, it will be readily seen that yd) JBljlj — — JtjjflL, JfxxL — U. * Roy. Soc. vol. 61, p. 465. VOL. LXXX.—A. 314 Dr. W. E. Sumpner. [Jan. 21, It follows from (2), that for any two quantities N and A we can so chooseL that a right-angled vector triangle is denoted by the equation (i) N = LA + n. From this we have (ii) ft = LA-f li * • and (iii) Ni = LAi + fli. The triangle represented by (iii) is the projection of that denoted by (ii)on the plane determined by (i) or by N, A, and n. By making use of (5),it can be seen that the plane vectors involved in the above equations are. Fig. 1. represented, as in fig. 1, by two similar right-angled triangles with corre-sponding sides perpendicular. It follows that— (7) If N and A are any two cyclic quantities represented by vectors in aplane, the vector projections of N and A on the same plane will be obtainedby turning: each of the vectors N and A through a right angle in the samesense, and by increasing their magnitudes in the same proportion. We might similarly represent N, A, and n by vectors in a plane, andproject on to this plane vectors denoting N, A, and n, and also those denoting$J, A, and ii. Representing the projected vectors by the suffix unity, wehave fig. 2, consisting of three similar right-angled triangles. Ni will berepresented by a vector in the same direction as, but drawn in the oppositesense to, that which represents Ni. This will also be true of the vectorsAi and Ai, etc. Of course, the actual magnitude of N will bear to that ofN a ratio which is dependent on the
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