34 M. L. Schweiidler on the Galvanometer Resistance 



thus 



m=^=S^/g, (4) 



w V AB 



as may be calculated. 



If we express electrical resistances in Siemens' s units, we have 

 to measure 



S 2 and A in square millims., 



B in metres, 



and X is the specific conductivity of the wire 



when the conductivity of pure mercury at 0° is equal to unity. 



Now, the external resistance being given, and m known by 

 formula (4), we may calculate numerically 



Qc*=g < k 



by equation (3) . But as such a calculation, especially for prac- 

 tical use, is inconvenient, it will be better to give an approximate 

 algebraical expression for g } which we may obtain in the follow- 

 ing manner. If we put in equation (3) 



a?== Vg, 

 we have 



g*—kmg \/g—2kg + k 2 = 0, 

 or 



(k-g) 2 = kmg */g, 

 or 



(k-ff) 4 - 



Substituting on the right hand 



g = k-p, 



where p is an unknown positive quantity, i. e. a certain function 

 of and increasing with k and m, we have 



(k-g) 4 =k 2 m' 2 (k-p) 3 ; 



and expanding the right-hand term, we have 



(k-gy^kWikzStfp + SkpZ-p 3 ) ; 



or neglecting all terms with powers of p against k 3 , we have ap- 

 proximately 



(k-g) 4 = kW; 

 or, g developed, 



g=k(\-s/htf) (5) 



This formula gives g a little too small, but near enough for 

 practical use, as the following Table will show : — 



