The Philosophical magazine; a journal of theoretical, experimental and applied physics . radius is BC cos E AC, or BC cos call this circle the E circle. We have now reached the following state of things :— F must lie upon a fixed circle, -•^ 5> 5J JJ JJ and AEF are in one straight line. With these prefatory remarks I now proceed to the solu-tion of the questions particularized at the beginning of thepaper; which will now be seen to be merely the finding out ofthe particular position of E upon its circle, which will make . FEthe ratio -t-f^ as large as possible, or, which is the same t
The Philosophical magazine; a journal of theoretical, experimental and applied physics . radius is BC cos E AC, or BC cos call this circle the E circle. We have now reached the following state of things :— F must lie upon a fixed circle, -•^ 5> 5J JJ JJ and AEF are in one straight line. With these prefatory remarks I now proceed to the solu-tion of the questions particularized at the beginning of thepaper; which will now be seen to be merely the finding out ofthe particular position of E upon its circle, which will make . FEthe ratio -t-f^ as large as possible, or, which is the same thing, AE that of -T^ as small as possible. 9. Let e and / be the two electromotive forces. Take D2 30 Mr. T. II. Blakosley 07i a Geometrical Determination AB equal to <?, and cut off from it BM equal to /. Describethe r circle upon AB, and set off BAD as before, an angle having its tangent equal to Tp-- D is on the F circle. Draw MN perpendicular to AD,and Avith centre D at distance DN describe a circle. Thisis the E circle, for its centre is at D, and its radius= DN= / Through D draw the radius DH pai-allel to AB, H beingon the same side of D that M is of A. Join AH by a straightline cutting the E circle in E and the F circle in F. Thenthese are the particular ])Ositions on the circles which make -,, as here found, is the ,. FE . FE the ratio -1-^^ a maximum -, i. e. x^ AF Ail maximum efficiency. And if DE be joined, the angle ADE will give the phase-difference between the electromotive forces to give this efficiency. FEFor, in the first place, it is clear that the ratio -j^ has some maximum (not a minimum) value between the ]iositions whereE and F coincide, viz. when the two circles intersect. Andbecause DII is parallel to AB, and AH cuts them, thereforethe angle DHE = the angle BAF. But DH, BA pass through the centres of the two circlesresjiectively; therefore AH. making the same angle with BAas it does with DH, must cut the circumlcrenees of the E andF circ
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