22 Mr. R. S. Brough on Wheatstone's Bridge. 



been adduced to explain two such different phenomena as the 

 amount of aberration under the circumstances above detailed, 

 and the existence of terrestrial magnetic currents, that I am jus- 

 tified in regarding this coincidence as corroborative of the truth 

 of both explanations. 



Cambridge, November 17, 1873. 



IV. On Wheatstone's Bridge. By R. S. Brough, Assistant 

 Superintendent of Government Teleyraphs*. 



j~N a paper by Mr. Heaviside, published in the Philosophical 

 -*- Magazine of February 1873, " On the best Arrangement 

 of Wheatstone's Bridge for measuring a given resistance," two 

 equations are given (the author's Nos, 1 and 2) to express gene- 

 rally the strength of the current flowing through the galvano- 

 meter before balance is established. These equations are incor- 

 rect, and they should respectively stand as follows : — 



u== _ (ad— Z>c)E 



(a + c)(b + d)e + (a + b + c + d)ef+(a + b){c + d)f+cd{a + b)+ab(c+d) 



and 



ad— be 



a+b+c+d 



E 



f__±___l±__ , 1 f (a + c)(b + d) A J ad-be y 

 \a + b + c + d "*" f\a + b + c + d ^ J J U + 6 + C + dj 

 From the latter equation the best resistance for the galvano- 

 meter near balance can be at once deduced ; for near balance 



re- 



the term -I = = > may be neglected against the 



La + b + c + dJ J ° ° 



mainder of the denominator of the right-hand member of the 

 equation, and then we have for a maximum of uve : — 

 E== {a + b){c + d ) 

 a+b+c+d 



Obviously the question of the best resistance of the galvano- 

 meter is only independent of the resistance of the battery (so 

 long at least as this is a quantity of relatively finite magnitude) 

 when balance is nearly established, and is not so generally (i. e. 

 away from balance as well as at balance) as Mr. Heaviside's 

 equations would imply. 



It is to be observed, however, that to proceed directly to find 

 the resistance of the galvanometer which makes its magnetic 

 effect a maximum at balance (when no current passes through 

 * Communicated by the Author. 



