54 



Dr. J. Hopkinson and Mr. E. Wilson. [Mar. 17, 



angle X behind the plane of symmetry. If m be the number of con- 

 volutions of the armature, the value of this magnetising force is 



4 7rC^ — = 4\mC opposed to the magnetising force of the fixed coils 



2 7T 



on the magnets. Thus, if we know the lead of the brushes and the 

 current in the armature, we are at once in a position to calculate the 

 effect on the electromotive force of the machine. A further effect of 

 the current in the armature is a material disturbance of the distribu- 

 tion of the induction over the bored face of the pole-piece; the 

 force along BC is by no means equal to that along DE. Draw 

 the closed curve BCGHB, the line integral along CG, and HB is 

 negligible. Hence the difference between force HG and BC is 



equal to 47rC — - = 2 /cmC, where k is the angle COG." 



2 7T 



To verify this formula is one of the principal objects of this 

 paper. 



A pair of brushes having relatively fixed positions near together, 

 and insulated from the frame and from one another, are carried upon 

 a divided circle, and bear upon the commutator. The difference of 

 potential between these brushes was measured in various positions 

 round the commutator, the current in the armature, the potential 

 difference of the main brushes, and the speed of the machine being 

 also noted. 



The results are given in Diagrams Nos. 2, 3, 4, and 5, in which the 

 ordinates are measured potential differences, and the abscissae are 

 angles turned through by the exploring brushes. The potential 

 differences in Diagram No. 2 were measured by a Siemens' volt- 

 meter, and each ordinate is therefore somewhat smaller than the 

 true value, owing to the time during which the exploring brushes 

 were not actually in ^contact with the commutator segments. But 

 this does not affect the results, because the area is reduced in the same 

 proportion as the potential differences. In Diagrams Nos. 3, 4, and 

 5, the potential differences were taken on one of Sir yVilliam 

 Thomson's quadrant electrometers, and are correct. 



Take Diagram No. 2 in which machine No. 1 is a generator. A 

 centimeter horizontally represents 10° of lead, and the ordinates 

 represent differences of potential between the brushes. The area of 

 the curve is 61*3 sq. cm., and represents 130 volts and a total field 



130 1 



of x 29 x = ^'31 x 10 6 lines of induction. This is, of course, 



not the actual field, which is 3 per cent, greater on account of the 

 resistance of the armature, but is represented by an area 3 per cent, 

 greater. An ordinate of 1 cm. will represent an induction of 



~\ x 10 6 = 7 x 10 4 lines in 10°. The area of 10° is 39'5 x 1-73 = 



