solving certain simple Electrical Problems. 369 



where E stands for electromotive force, C for strength of current, 

 and 11 for resistance, we have at once suggested three different 

 modes of geometrical construction by means of rectangular co- 

 ordinates, the coordinates representing in the three cases respec- 

 tively (1) electromotive force and strength of current, (2) elec- 

 tromotive force and resistance, and (3) strength of current and 

 resistance. 



I, Ordinates represent Electromotive Forces, and Abscisses 



represent Strengths of Current. 



This system, according to which resistance comes to be repre- 

 sented by the slope of a straight line (that is, by the tangent of 

 the angle which the line makes with the axis of abscissae), was 

 lately employed by M. Crova* for the discussion of experiments 

 relating to the degree of constancy possessed by so-called " con- 

 stant " galvanic batteries ; and its application to several other 

 problems, including some of those treated by other methods 

 in this paper, has been still more recentlyf pointed out by the 

 same author. It is therefore not needful to discuss it further 

 in this place. 



II. Ordinates represent Electromotive Forces, and Abscisses 



represent Resistances. 



This system was used long ago by Ohmf, and has been fre- 

 quently employed since his time, though perhaps chiefly by 

 practical electricians§. The following examples may serve to 

 illustrate its application to questions connected with galvanic 

 circuits in which there is a constant electromotive force. 



Let A (Plate VIII. fig. 1) represent the electromotive force 

 of a battery, B the resistance of the battery, and B C the 

 resistance of the remainder of the circuit, this being made up 

 of simple metallic conductors in which no additional electro- 

 motive force acts, then the slope of the straight line AC, or the 

 tangent of the angle A C 0, represents the strength of the cur- 

 rent. It is obvious, by a glance at the figure, that the strongest 

 current that the given battery could produce would be obtained 

 by making the external resistance B C equal to nothing, and 

 that it would be represented by the slope of the line A B, or by 



* Comptes Rendus, Gth April 18/4, vol. lxxviii. p. 965. 



t Journal de Physique (Sept. 1874), vol. Hi. p. 278. 



X Die galvanische Kette mathematisch bearbeitet, 1827. 



§ See, for example, R. S. Culley, e Handbook of Practical Telegraphy,' 

 18/4, pp. 352-355; Latimer Clark, 'Elementary Treatise on Electrical 

 Measurements,' 1868; G. K. Winter, " On Earth-Currents," Journal of 

 the Society of Telegraph-Engineers, vol. ii. pp. 89-101 ; &c. 



