Dr. E. L. Xichols on the Electrical Resistance qc. 39 



Xow. with the above arrangement of apparatus, if w is very 

 much larger than r (the resistance of the wire a b), so that the 

 current through a b is not sensiblj less than that through the 

 main circuit, we shall have 



E=- = — 



r r J ' 



where C and C / are the currents through a, b and through the 

 shunt, and r is the resistance of the shunt. 

 But 



CK=sinUF, 

 C=tanY£, 

 where TJ is the deflection of the sine-galvanometer and V the 

 constant of the instrument, and where Y is the deflection of 

 the tangent-galvanometer and k the constant of the latter in- 

 strument. 



Then _tanY k _ tanY „ 



— sin U ' ~ sin IT ' ' 

 where 



k 



The length of the wire a b was measured by bringing the 

 two microscopes of a comparator into such position that the 

 terminal a was in focus in the field of one of the microscopes 

 and b in the field of the other. Since these points were quite 

 as near the middle as the end of the wire, every change of 

 temperature caused a movement of both a and b : and it was 

 by taking the differences of these that the true change in the 

 length of ab was determined. As the microscopes were pro- 

 vided with excellent micrometer-scales and screws, a fair 

 degree of accuracy was obtained by this method. Headings 

 of the length of the wire at 20° agreed with a series taken 

 upon a dividing-engine of known accuracy to within "002 

 millim. The distance a b at 20° was found to be 53*5576 

 millim. 



The resistance of the cold wire was found (in terms of TJ, 

 Y, and K) by placing the wire in a naphthaline bath, and ob- 

 taining values of U and Y with various amounts of current. 



From these readings a curve was drawn with - — ^as abscissas 

 te sua L 



and tan 2 Y as ordinates, tan~Y being taken as an expression 



for the heating effect of the current. The point of this curve 



corresponding to tan 2 Y = was taken as the proper value of 



- — tt f° r the coW wire, 

 sin b 



