376 On Methods of solving certain simple Electrical Problems* 



resistance of a conductor and the strength of the current pro- 

 duced in it by a given electromotive force, and let it be required 

 to find the strength of the currents which the same electromotive 

 force would generate in conductors whose resistances are respec- 

 tively represented by the abscissa? m x and m r Through M 

 draw a line MPQ parallel to X, and through m l and m 2 draw 

 m Y P and w? 2 Q parallel toOY; join O P and Q, and let p and 

 q be the points in which P and Q respectively cut M m ; 

 then mp and m q will represent the strengths of the required 

 currents ; and if lines be drawn parallel to X through p so as 

 to intersect m } P in M„ and through q so as to intersect m 2 Q in 

 M 2 , Mj and M 2 will be points whose coordinates, like those of 

 M, represent corresponding values of resistance and strength of 

 current. The points M, 5lj, and M 2 , therefore, lie upon the 

 same rectangular hyperbola. 



In a similar way we may treat many problems of the same 

 sort as those discussed above by aid of what for distinction 

 may be called Ohm's construction ; but as the constructions, 

 arising from the choice of resistance and strength of current as 

 coordinates are usually rather more complex than those previ- 

 ously given, and as I have not come across any cases in which 

 they appear to be decidedly more expressive, I will only give two 

 additional examples. 



• To find the permanent resistance and the electromotive force of a 

 battery from observations of the strengths of two currents corre- 

 sponding to resistances which differ by a known amounts — Let 

 wiM (fig. 14) represent the strength of the current when the 

 resistance of the circuit has an unknown value represented by 

 the (unknown) abscissa m ; and let n N express the strength 

 of the current when the resistance has been increased by a 

 known amount denoted by mn. Through M and N draw 

 straight lines parallel to mn, and let Nj and Mj be the points 

 where these lines respectively intersect n N (produced) and 

 m M. Draw the straight line Nj Mj and produce it to intersect 

 n m produced in ; then m represents the original resistance 

 of the circuit, and the rectangle on the base m with altitude 

 m M, or the rectangle on the base n with altitude n N, repre- 

 sents the electromotive force. 



The heat produced in unit of time by a constant current of given 

 strength traversing a conductor of given resistance can be repre- 

 sented by the volume of a right square prism, two of whose 

 dimensions represent the strength of the current, while the third 

 represents the resistance ; and in the case of a battery of con- 

 stant electromotive force, the relation between the resistance of 

 the circuit and the heat produced in unit of time can be expressed 

 generally as follows : — Take three rectangular axes, OX, Y, 



