L*t 



32 Mr. T. H. Blakesley on a Geometrical Determination 



" If the straight lines AB, BC, 

 CD, ... ST represent the maximum 

 values of different electromotive 

 forces, and, as to direction, are so 

 laid down upon the paper that their 

 projections upon a fixed straight line 

 represent at some point of time the 

 instantaneous values of those elec- 

 tromotive forces, their instanta- 

 neous resultant is the projection of 

 the simple straight line AT." 



5. If, in any particular case, we 

 have taken into consideration all 

 the electromotive forces concerned, 

 then clearly the line representing 

 the resultant corresponds in phase with the instantaneous 

 current; and if by scaling or calculation we find the 

 value of this resultant in volts, we have only to divide by 

 the resistance in ohms to obtain the maximum value of the 

 alternating current resulting from all the component electro- 

 motive forces. This is true even if one of the electromotive 

 forces is that of self-induction. But suppose we have arrived 

 at a preliminary resultant by compounding all the electro- 

 motive forces with the exception of that of self-induction ; we 

 then require the final resultant, and we obtain it by remem- 

 bering that it must be at right angles to the electromotive force 

 of self-induction ; for the electromotive force of self-induction 

 must be greatest when the current is passing through zero : 

 therefore it must have its projection on the fixed line greatest 

 when that of the final resultant (corresponding with the cur- 

 rent) is zero. Therefore the final resultant and the electro- 

 motive force of self-induction must be to the preliminary 

 resultant as the two sides of a right-angled triangle including 

 the right angle, are to the hypothenuse ; and as we already 

 possess the hypotheneuse we have only to determine the ratio 

 of the sides, and upon which side of the hypotheneuse they 

 must be placed, in order fully to determine the position and 

 size of the final resultant and the electromotive force of self- 

 induction. The geometrical construction is as follows. 



From one end of the preliminary c _ A 



resultant set off an angle in the 

 negative direction of rotation whose 

 tangent is equal to the product of 

 the coefficient of self-induction and 

 the angular velocity of rotation di- 

 vided by the resistance, and then 



