78 Intelligence and Miscellaneous Articles. 



sities be produced by the application of correspondingly larger 

 external resistances, and thus Ohm's method be used for ascertaining 

 the comparatively very small internal resistances, a simple calculation 

 shows that unavoidable errors of observation by no means permit the 

 desired certainty of results. 



The design of rendering possible such investigations has led the 

 author to find a method for determining the resistances of circuits 

 which corresponds to the requirements mentioned— a method, that is, 

 which permits the use of very small intensities without the use of very 

 great interpolar resistances. It depends on the following principle. 



If the element under investigation be joined in the inverse direc- 

 tion with another of greater electromotive force, and an extra circuit 

 be introduced, we have three paths for the current between two 

 nodal points, as in Poggendorff 's compensation method. If the re- 

 sistances in the paths of the stronger circuit, the weaker one, and 

 the lateral circuit be respectively denoted by a, /5, and y, and the 

 corresponding intensities by A, B, and C, and assuming that with any 

 values of a, /3, and y, where B will in general be different from 

 nil, by a small variation in a a corresponding alteration of the in- 

 tensities be effected, we arrive by direct deductions from the princi- 

 ples of Ohm's law at the equation 



/WB = yJC, 



or, if the currents running parallel with A be denoted as positive, and 

 thus C as negative, at the equation 



fidB=-ydC. 

 Denoting by C the value which C has when B = 0, integration leads 

 to the relation p# = y (C - C) . 



If by compensation of the circuit investigated B has been made 

 = 0, and thus C = C , and thereupon by a very small alteration of a 

 the equilibrium has been restored, C — C and B give the changes in 

 the current in the circuits y and /3, and the above relation expresses 

 in the form C n — C 



the principle that the quotient of the alterations in the current ob- 

 served after removing compensation in y and (3, multiplied by the 

 resistance of the extra circuit, gives directly the resistance fi and 

 the desired resistance of the circuit. 



This method, then, is distinguished from all previous ones, and espe- 

 cially from Ohm's method, inasmuch as it enables the resistance of 

 the circuit to be investigated in the vicinity of its point of compen- 

 sation, and permits the use of extremely small intensities without 

 using great resistances ; it thus answers the requirement of investi- 

 gating the resistance of a circuit as independent as possible of the dis- 

 turbing influence of polarization — that is, under circumstances in 

 which polarization is reduced to a minimum. 



For measuring B, a multiplier graduated by PoggendorfT's method 

 may be used; for measuring C — C, a Gaugain's tangent compass. 

 The accurately measured y of the extra circuit remains unchanged, 

 while a is measured by arheocord.— Wiener Berichte,vo\. xiv. (1867). 



