. The London, Edinburgh and Dublin philosophical magazine and journal of science. In fig. 5, OB A, OCA, OD A are the trianglesfor the several branches of a divided circuit (see fig. 4), with Fig. sin impressed equal to OA. The main current, Im, isthe vector sum of the currents I1? I2, I3 in the branches. Bytaking the projections of the currents upon the line OA, andthen upon a line perpendicular to OA, we obtain the equations Iwtcos^ = I1cos^1 + I2cos #2 + - • . = ^1 cos 0. . (1)Imsin0=I1sin01+I,sin02 + ...=2lBin0. . (2)In the right triangle 0 F A, E L. = \A2+(rfc-L,J (3) 274
. The London, Edinburgh and Dublin philosophical magazine and journal of science. In fig. 5, OB A, OCA, OD A are the trianglesfor the several branches of a divided circuit (see fig. 4), with Fig. sin impressed equal to OA. The main current, Im, isthe vector sum of the currents I1? I2, I3 in the branches. Bytaking the projections of the currents upon the line OA, andthen upon a line perpendicular to OA, we obtain the equations Iwtcos^ = I1cos^1 + I2cos #2 + - • . = ^1 cos 0. . (1)Imsin0=I1sin01+I,sin02 + ...=2lBin0. . (2)In the right triangle 0 F A, E L. = \A2+(rfc-L,J (3) 274 Drs. Bedell and Crehore on the cosfl= . R . . (4) \A2+((i-L<»)2 sin<?= Lc° . . (5) VR/2+(cfe-L)- Substituting in (1) and (2) these values, and similar valuesfor I1? cos 0U sin 6X ; and I2? cos 02, sin 62) &c.; we have I,»cos0 W ^ E /fi = 2 7-= ^ = A. (6) E R,2+(ci-L/w)2 R2+((i,-LwJ 1 1-LW Tm sin 9 _ (J© _ ^ Oca E »,+(^-L-y~ R2+(i-L<B)2 = 2C2RV + (l-CL&,y<B = B(0- • <-7) The letters A and B are introduced to simplify the (7) by (6), tan0=^. ...... (8) Comparing (4) and (6), we obtain A cos20 cos20 A=~BT °r R A~ (J) Comparing (5) and (7),
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
