326 REPORT- 1889. 



spending values of the current passing round the armature. M. Marcel 

 Deprez ^ demonstrated their practical utility, and (a) showed that, amongst 

 other things, they can be used to determine the current produced by a 

 dynamo in an external circuit of known resistance and containing a constant 

 opposing electromotive force (e.g'., a dynamo charging accumulator cells) ; 

 (h) gave a construction which was practically the first step taken towards 

 the present system of calculation of compound winding of the coils in a 

 dynamo in order to secure a constant E.M.F. through a system of lamps 

 arranged in parallel circuit, or a circuit of lamps arranged in series ; and (c) 

 explained a method of transforming the characteristic carve of one dynamo 

 to that of another having wire of different thickness, but the winding occu- 

 jjying the same volume (i.e. the same skeleton dynamo wound with different 

 wire). The constructions of M. Deprez are given in MM. Mascart and 

 Joubert's ' Treatise on Electricity.' '^ Dr. Hopkinson^ has applied a curve, 

 easily derived from the characteristic, to find the maximum useful work 

 which can be transmitted from a series-wound dynamo to a motor when the 

 resistance of the whole circuit is known. The derived curve has ordinates 



— j-p — ^^*^ abscissee 0, corresponding to E and C respectively of the 



characteristic. The points on it are obtained by a geometrical construc- 

 ts B . 

 tion which depends upon the fact that -yp is the slope of the character- 

 istic curve at any point. 



The characteristic curve of a dynamo requires for its construction an 

 experimental knowledge of the relation between the magnetic field of the 

 armature (which determines the electromotive force) and the correspond- 

 ing current, for every value of the latter. Hence it cannot be applied 

 to those problems in which the best method of constructing the dynamo 

 itself is concerned (with the exception of the particular case in which a 

 dynamo is re-wound). Several attempts have been made to overcome this 

 difficulty, but they give only an approximation to the characteristic, 

 chiefly owing to the fact that the exact relation between the magnetism 

 developed in the iron core of an electro-magnet and the current passing^ 

 through its coil is unknown. Drs. J. and E. Hopkinson '' have made 

 experiments on the magnitude of the waste field of an Edison-Hopkinson 

 dynamo, and, starting from the dimensions of the machine, have calcu- 

 lated a theoretical approximation to its characteristic. They assumed a 

 relation for the magnetisation function and constructed a curve, whicli 

 agrees fairly well with actual experiment. Ayrton and Perry,^ on the other 

 hand, have recently shown that by making two assumptions one can easily 

 obtain a very good approximation to the actual curve. The first of these 

 is that for low values of the current the permeability of the iron part of 

 the magnetic circuit is very great compared with that of the air ; hence, 

 practically, the whole of the magnetic resistance is due to the air gap. 

 This gives for the part of the characteristic near the origin a straight 

 line, which can be drawn when the length of the air gap is known. One 

 point on the upper (curved) part of the characteristic is next determined 



' Marcel Deprez, Comjrtes Bcndus, xcii. (18S1), p. 1152; sciii. (1881), jip. 892 and 

 950. 



2 Mascart and Joubert, Electricity, vol. ii. (Atkinson "s translation), pp. 724-73-5. 



» Hopkinson, Proc. Imt. C. K, April 5, 1883. 



* J. & E. Hopkinson, Phil. Travs., 1886, p. 331. 



i Ayrton & Perry, Phil. May., June 1888, p. 49G ; Proc. Phys. Soc, ix., p. 220. 



