Perkins — Methods of Using the Galvanometer. 53 



Art. Y1II.—A. Comparison of Two Ways of Using the Gal- 



vanometer 



by Henry A. Perkins. 



There are a number of instances in laboratory practice 

 where a galvanometer is used to record changes in the resist- 

 ance of a piece of apparatus such as a bolometer, selenium cell 

 or bismuth spiral where the highest degree of sensitiveness is 

 required, and there is a choice between a Wheatstone Bridge 

 arrangement and a simple series connection. The purpose of 

 this paper is to investigate the relative delicacy of the two 

 methods. 



In using the Wheatstone Bridge the variable resistance is 

 introduced in one of the arms, the bridge is balanced and the 

 galvanometer then deflects 

 when the variable arm 

 changes. 



In order to calculate the 

 current that will flow 

 through the galvanometer, 

 we apply KirchhofPs laws, 

 and assume the various 

 resistances ■ equal to r„ r„ 

 r v r a r s, an d 7*6, where r 6 

 is the resistance of the 

 battery, r b that of the gal- 

 vanometer and the others 

 represent the arms of the 

 bridge, r x being the variable resistance. 



In calculating the galvanometer current we shall make use 

 of the following six equations : 



(1) 0,= C.4-C. 



" c 3 = c 4 -c B 

 o = o; 4- A 



E = Cr e 4- 1 r 1 4- C, r, 

 0=0,^-0,^4-0.^ 



C. ■/• - C.r. 



(2) 

 (3) 

 (4) 

 (5) 

 (6) 



= C 2 r 2 



Combining and assembling the coefficients we obtain 

 C 9 (r x + r 2 + r 6 ) + Cj e + r, r 6 = E 

 0,^-0^4- O b {r l 4- r, 4-0 = 

 C. r - C r. - C. r. = O 



6 5 



Solving for C s by determinants 

 E(r 3 r 2 — Ty r 4 ) 

 C. = 



