Currents in the Branches of a Wheatstone's Bridge. 161 



1. Dal ton was led in 1803 to the conception of atoms of 

 characteristic weight and size by his investigations on the 

 diffusion of gases. From these same investigations he also 

 received the incentive to determine the relative weights and 

 sizes of the atoms of different substances. 



2. In order to render possible the determination of the re- 

 lative weights of the atoms from the results of analysis, he 

 adopted his principle of u greatest simplicity," npon which 

 the empirical laws of chemical synthesis are founded. 



3. Dalton never definitely adopted the hypothesis M/S = C. 



XXVII. Discussion of the Currents in the Branches of a Wheat- 

 stones Bridge, where each branch contains Resistance and 

 Inductance, and there is an harmonic impressed electro- 

 motive force. By Albert Cushing Crehore, Ph.D., 

 Assistant Professor of Physics, Dartmouth College, and 

 George Owen" Squier, Ph.D., First Lieutenant, U.S. 

 Army*. 



THE complete discussion of the currents flowing in the 

 branches of a Wheatstone's Bridge, with a simple 

 harmonic E.M.F., leads by the analytical method to equations 

 which are too cumbersome to be of much practical use. For 

 instance, by the direct method there would be formed as 

 many differential equations as there are branches to the 

 bridge, namely six, and these six simultaneous equations 

 would, by a process of elimination, lead to a single differential 

 equation of the sixth order, the solution of which would give 

 the current in any desired branch. The practical obstacles 

 in the way of finding the single differential equation from 

 the six simultaneous equations, and after that obtaining its 

 solution, are so great that if the same results can be obtained 

 in a simpler way it would be welcomed. Having once written 

 down the equations of current flow in the branches, it is a 

 comparatively easy matter to determine the conditions for 

 zero current in the galvanometer. 



It happens that for this important particular case of zero 

 current in the galvanometer there is a very simple way of 

 determining these conditions for an harmonic E.M. F. Either 

 the analytical or the graphical method will give the result, 

 but the graphical method apparently gives so much more at 

 the same time that it is preferred. 



Referring to fig. 1, let the six branches of the bridge be 



* Communicated by the Authors. 



