864 E. L. Nichols— Electrical Resistance and the 
current through ab is _ —— less than that through the 
main circuit, we shall hav 
where C and C’ are the currents BOURh ab and eae the 
shunt, and 7’ is the resistance of the shunt 
But 
C'= sin UX’ 
C=tan Vk 
where U is the deflection of the sine cial ae and k’ the 
constant of the instrument, and where V is the deflection of the 
tangent galvanometer and k'the constant of the latter instru- 
ment. 
Then 
ee 
“sin U #&” sin U 
where K= & y! 
The length of the wire ab 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 ( 
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 (}): and it was by takin 
the differences of these that the true change in the length of ad 
was determined. As the microscopes were provided with 
excellent micrometer scales and screws, a fair degree of 
accuracy was obtained by this method. Readings of the 
length of the wire at 20° agreed with a series taken upon a 
dividing engine of known accuracy, to within 002™. The 
distance ab at 20° was found to be 53°5576™™ 
ge resistance of the cold wire was found—in terms of ayy: 
d K—by placing the wire in a napthaline bath, and obtain- 
see values of U and V with various wage of currents. From 
nv 
these readings a curve was drawn with — anu 3 abscissze and 
tan’V as ordinates, tan*V being taken as an expression for the 
heating effect of the current. The point of this curve corres- 
ta 
ponding to tan*V=0 was taken as the proper value of 7 
for the cold wire. 
In measuring the resistance of the hot wire, the galvano- 
meters were read simultaneously before and after each deter- 
mination of the length. 
