1895.] Mr Griffiths, The Calibration of a Bridge Wire. 271 



greatest when the wire is thinnest. Now (i) can be altered at will 

 by adjustment of R^ whereas (ii) and (iii) are not under control to 

 the same extent. The greatest value of R^ should be used that is 

 compatible with the limits given by (ii) and (iii). 



Let E be the D. P. of the storage cells. 



Let e be the smallest d. p. which will visibly influence the 

 galvanometer. 



Let r be the resistance of the bridge wire. 



Let I be the length of the bridge wire (in mm.). 



Let X be the smallest difference in the distance between the 

 points d^ and Pj which can be directly determined by 

 the linear measurements. 



Let Ri be the total resistance of the circuit 0^, exterior to the 

 bridge wire. 



Now the value of R^ should be so selected that the D. p. at 

 the ends of a portion of the bridge wire of length X shall be e. 



This will be the case if 



r\ 

 e _ T 

 E~ R, + r' 



hence R^ = r(-.j-lj (a). 



A good high resistance galvanometer will (according to my 

 experience) when properly adjusted be visibly affected when the 

 D. P. of its terminals is 10"" volts, if the conditions as to absence of 

 vibration etc. are favourable ; while a difference of 10"^ volts will 

 give a decided swing. It is safe to assume that a d. p. of 5 x lO"*" 

 volts can always be detected. If the contact makers are supplied 

 with verniers giving 01 mm. then 0'05 mm. is about the limit 

 of accuracy of the linear measurements. I assume therefore that 

 under ordinary conditions e = 5 x 10"" and \ = 0"05 mm. 



Suppose that a wire of length 1 metre and approximate re- 

 sistance 1 ohm is to be calibrated, and that storage cells are used, 



we have E=2, ^ = 1000, r = l. 



Hence eq. (a), we get R=19 ohms. 



And, as we may neglect the internal resistance of the storage 

 cells, the resistance R^ should be 19 ohms, while the total resis- 

 tance of the circuit G^ should be 20 ohms. 



Under ordinary circumstances a wire is not calibrated until it 

 has been finally fixed into the instrument of which it is to form a 



