The Philosophical magazine; a journal of theoretical, experimental and applied physics . etricalproof of this theorem in Alternating Currents/ It amountssimply to this in the methods of representation here employed,that if we project the revolving line corresponding to anyparticular source of electromotive force upon the direction ofthe final resultant, the power derived from this particularsource will be the product of such projection and the finalresultant divided by twice the resistance. Hence the variouspowers of the different sources will simply be proportional tothe various projections u
The Philosophical magazine; a journal of theoretical, experimental and applied physics . etricalproof of this theorem in Alternating Currents/ It amountssimply to this in the methods of representation here employed,that if we project the revolving line corresponding to anyparticular source of electromotive force upon the direction ofthe final resultant, the power derived from this particularsource will be the product of such projection and the finalresultant divided by twice the resistance. Hence the variouspowers of the different sources will simply be proportional tothe various projections upon the line of the final resultant. IMl. Mag. S. 5. Vol. 25. No. 152. Jan. 1888. D 34 Mr. T. H. Blakoslcy on a Geometrical Determination 7. Suppose, then, that AB, BC are the revolving represen-tatives of two electromotive forces. Then AC is their resultant; CAE is an angle whose tangent is equal to yrr;, as explained ; CE, BF are perpendiculars upon AE. Then AE is the finalresultant or eftective electromotive foice, merely requiringdivision by the resistance to give the current. AE. AE the The power derived from the source of AB is AF _ . AE ^ power transferred to the source of BC is FE -^r— ; and the AE AE^ ^**power heating the circuit is AE -—-;- = -^ As regards the projection of BC, viz. FE, since (as heredrawn) FE is in a contrary direction to AE, there is atransfer of power to its source. Had F been situated nearerto A than E is, the source of BC would do work and assistin heating the circuit. This obviously depends upon whetherBC, AE are inclined to one another at an angle greater orless than a right angle. If we denominate these three powers as the power of theactive source, the power of the recipient source, and theheating-power, they will be to each other in the proportion AF : FE : AE ; FE and the efficiency of transmission will be -^, the ratio of waste beinc AEAF* 8. Since AFB is a right angle, F always lies upon thecircle described upon AB as diameter. Descri
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