CONDUCTIVITIES OF METALS AND ALLOYS AT LOW TEMPERATURES. 393 
where V L is the temperature at the junction of the platinoid wire with the copper 
lead, v" c > that of the wire on the sleeve, x is measured from the copper lead, and l is 
the length of the platinoid wire between the copper lead and the sleeve. 
If we neglect the heat generated by the current in the copper lead, and suppose the 
length of the lead to be sufficient for its temperature excess to fall to zero before the 
wire emerges from the containing tube, its temperature excess v x at a point — x from 
the junction with the platinoid is given by the equation 
v x = V L exp. 
M) 
1/2 
X , 
where p x , h u q u k 1 refer to the copper wire and have the usual meanings. 
Since the flow of heat at the copper-platinoid junction is continuous, we must have, 
at x — 0, 
aU dv - a l- dv i 
qn -= q j/Ci -j , 
clx ax 
^.e., 
(phqk) lj2 j sinh 
Hence 
W 
w 
v T = 
4 19L ph 
cosh 
4T9L ph ' L 
’ph' 1/2 
vdcosh (&YlJ ™ -v" c )) = (pMAY'^l 
qk 
4T9Lp/i 
qk 
l-l 
+ v"c> 
The flow of heat out of the exposed platinoid wire into the sleeve is given by the 
value of 
i.e., by 
— qk^ at x = l, 
(as'iIC 
(phqk) 112 f sinh ^ 
1/2 
- 
w 
4T9L ph 
■V T , + 
w 
4T9L ph 
v"c ) cosh 
phV 
qk) 
= | {phqk) 1 ' 2 j sinh (l 
{-[ 
r w 
f W / 
L4T9LpA 
l4T9Lp/d 
j\l/2 
!)+«»„ 
J 
+ 
w 
4T9L ph 
The total flow into the sleeve from the two wires wall therefore be 
v ' d ) cosh ($P}' 
= 2 { {phqk) 112 j sinh 
{ 
4T9LpA[_\ pqk ) 
'(£3&)' l2 s inh(PiYl+ 
qk) 
+ v"c 
+ 
{sms-*°) ■ <ls > 
3 E 
VOL. CCVIII.-A. 
