420 Mr. T. H. Blakesley on the Differential 



projected point, sometimes on the other. So that such a line 

 has all the properties necessary for representing another 

 magnitude of the same character. 



In this way I shall most generally make the projection 

 represent Electromotive Force, but occasionally Field of 

 Magnetism at a point. As to matter of nomenclature, 

 the only scientific term which I shall employ admitting of 

 any doubtful interpretation, is the Effective Electromotive 

 Force. By this term I intend to convey the idea of that 

 electromotive force which is numerically equal to the product 

 of the current and the resistance, at a point of time. As a 

 department of State has recently employed the term in a 

 totally different sense, this statement has appeared to me to 

 be necessary in the interests of proper explanation. The 

 effective electromotive force is the algebraical sum of all the 

 impressed and induced electromotive forces, and is here 

 represented by E. If V is the sum of all the impressed 

 electromotive forces and F is the sum of all induced electro- 

 motive forces, then the equation among their quantities is 

 V + F=E universally. 



Geometrically, if A B, B C are lines whose projections on 

 some one fixed straight line represent the sum of the im- 

 pressed and the sum of the induced electromotive forces 

 respectively, then the projection of A C will represent the 

 effective electromotive force. 



The three lines must form the sides of a triangle, those 

 corresponding to the impressed and induced electromotive 

 forces being taken the same way round the triangle, that 

 corresponding to E being taken in the opposite direction. 



Now if the actual changes in the magnitudes are harmonic, 

 and of the same period, it is clear that the lines A B, B C, 

 A C must remain of constant length and the triangle must 

 rotate in its own plane at a uniform rate of such a value as 

 to perform a complete revolution in the period of the har- 

 monic change. The triangle thus shows admirably the way 

 in which these magnitudes succeed one another in phase. It 

 also follows from the properties of harmonic motion that if 

 two magnitudes have the same harmonic period, but differ 

 in phases by a quarter of the whole period, the corresponding 

 lines to be projected are at right angles with each other. And 

 hence the rate of variation of an harmonic magnitude differs 

 in phase from the magnitude itself by a quarter of the 

 period. But in the simplest case of a circuit being plied 

 with an harmonic electromotive force V, it is generally 

 considered that the induced electromotive force varies as the 



