CONDUCTIVITIES OF METALS AND ALLOYS AT LOW TEMPERATURES. 395 
It has been stated that the power supplied was measured by an ammeter in circuit 
and by applying a voltmeter to the ends of the heating coil for the few seconds 
necessary to take a reading. Owing to the resistance of the voltameter, lb = 113 ohms 
at 14° C., not being very great compared to that of the heating coil, R 0 = 6'4 ohms at 
18° C., the measured value P 0 of the volts at the ends of the heating coil is less than 
the value P when the voltameter is not in circuit, and the readings obtained must, 
if v is the resistance external to the coil, and the electromotive force in circuit is 
constant, be multiplied by 
K 0 + Ib r+RoB^Bp + Ih) 
Ri t +R|) 
to give the true volts on the coil, i.e., 
the volts P on the coil = P 0 f 1 + 
Rr 
1 - 
R 0 2 
Ri/ V (R 0 + Ri)(r+R 0 ) 
Since the current was derived throughout from three storage cells kept well 
charged, it will be sufficient in the factor involving r to write r + R 0 = 6/A, and we 
have 
volts P on coil = P 0 + ) ( 1_ 119~4 x G ^~) = 1 ' 05 ^Po (l -0'057A). 
Hence the watts spent on the sleeve 
= 0-954A{l-057(l —0-057A)P 0 —(0-022 + 0-000116 t)A}— 0 > 000020v" C ' 
= 1-008A{(1-0-057 A)Po-(0'021 + 0-00011t)A}-0-000020P / C '. 
Hence H, the total quantity of heat imparted to the bar per second, is given by 
the equation* 
4-19H = r008A{(l—0-057A) P 0 -(0-021 + (POOOIIt) A]-0-000020v" c ,-0-000056v" B . 
Or, since (v" B , v " c ) = (v B , v c ) very nearly, 
4-19H = 1-008A{(1 —0'057A)P u —(0-021 + 0 -00011 r)A}-0 '000020r c , —0-000056 v b . 
Hence 
H = 0-2406A {(1-0-057A)P 0 -(0-021+0-00011t)A}-0-0000048iv-0-000013u b . (17) 
In the small term 0 - 000013r B it will be sufficient if we write v B = v c ,x B /x c ,. 
Thus, for the original equation Q = H — shv c >, p. 386, we must substitute 
Q = 0‘2406A {(1 — 0‘057A) P 0 —(0’021+ 0 , 00011 t) A} 
- (sh + 0^’00000 48 + 0-000013 
\ x c .J 
* For simplicity, the loss of heat along the wires of the upper temperature measuring sleeve, p. 392, is 
treated as if it took place from the heating sleeve. 
3 E 2 
