solving certain simple Electrical Problems. 373 



added to the circuit in order to get a second reading of the 

 galvanometer ; then the pulley P' is adjusted so that the cord 

 passing over it may indicate upon the quadrant B the galvano- 

 meter-deflection obtained after introducing the resistance cor- 

 responding to A A' ; and lastly the vertical scale is moved so 

 that a vertical line drawn through the centre of the division- 

 marks and continued downwards to meet the horizontal scale at 

 O may be exactly behind the point Q, where the cords AP and 

 A' P' cross each other. We have then only to read off the hori- 

 zontal and vertical distances, A and Q, to get the perma- 

 nent resistance and electromotive force of the circuit*. To adapt 

 the apparatus to use with a sine-galvanometer, it would be only 

 necessary to replace the vertical scale Q by a quadrant 

 marked with concentric circular arcs, each differing from the next 

 by 1 millim. in radius. 



The following additional examples may be given of the same 

 mode of treatment in connexion with allied problems : — 



Development of Heat in a Galvanic Circuit. — Draw C 

 (fig. 6) horizontally to represent the resistance of the circuit, 

 and OA vertically to represent the electromotive force; from 

 A draw A C and also A D at right angles to AC; then 

 D represents the heat produced in the circuit per unit of 

 time. It is of course to be understood that A denotes not 

 necessarily the electromotive force of the battery, but the resul- 

 tant electromotive force of the whole circuit — that is, the algebraic 

 sum of all the electromotive forces which act anywhere in it. If 

 B denote the resistance of the battery and B C the remaining 

 resistance of the circuit, and if B A ; be drawn vertically, A'E F 

 horizontally, and A' D ; at right angles to A C, E F will denote 

 the heat generated in the battery, and B D' the heat generated 

 in the external part of the circuit. 



Strength of Currents in the different branches of a divided Circuit* 

 — In considering this problem it is needful first of all to have a 

 mode of representing geometrically the combined resistance of 

 two or more conductors connected in (i multiple arc. ,} Let A B 

 and B C in the same straight line (fig. 7) represent the resis- 

 tances of two conductors taken separately. Draw A B' equal to 

 A B and at right angles to it; join B' C, and through B draw a 

 line parallel to A B' and cutting B' C in L ; then B L represents 

 the combined resistance of the two conductors. The same 

 process is applicable to any number of conductors. Thus, let 

 AB, B C, and CD (fig. 8) represent the separate resistances of 

 three conductors connected in multiple arc. Making the con- 



* The quadrant A is made so that it can be turned aside to allow of the 

 vertical scale being brought close up to the zero-point of the horizontal 

 scale when low battery-resistances have to be measured. 



