392 
PROFESSOR C. IE LEES: THERMAL AND ELECTRICAL 
where v A and v B are the mean temperatures over the whole of each platinum wire. 
Hence we have as the connection between the temperature of the rod and the 
observed temperature of the platinum wires, 
(v A , v B ) = (R026 + 29A) (v A , vf) mean value.(12) 
The amount of heat conducted from the sleeve # along the wire at its point of 
contact with the sleeve is equal to the value of qk(dv/dx) at x = 1 , which is 
, ,, cosh oil 
q CT 0 a —i—r-— 
smh at 
- cosh /sinh cd _ qkv 
'o 1-161 
l ~ 7 al 
0 - 00012 x 0 - 166 
0'8 
l 1-053 
l-127'o = 0-000028v'V 
For the two platinum wires of the upper sleeve this amounts to 0-000056V7, which 
must be deducted from the heat supplied to give the heat which flows down the rod 
to the platinum thermometers. 
Corrections for Leads in Power Circuit. 
As in the case of the platinum resistance coils, so in that of the heating coil, the 
No. 40 platinoid wire constituting it was not wholly wound on the sleeve, but at each 
end 0 - 8 centim. projected and served to make contact with the No. 22^ copper wires 
supplying current to the coil. Part, therefore, of the difference of potential measured 
was expended on the leads and on that part of the platinoid wire not on the sleeve. 
On the other hand, the passage of the current through the latter portion of the wire 
raised its temperature above that of the wire on the sleeve, and some of the heat 
generated in it would in consequence reach the sleeve by conduction along the wire. 
We require to determine this amount. 
If W watts are spent in the platinoid wire, and L is the total length of the wire, 
W ■ 
prim-degrees of heat are generated per second in each centimetre of the 
g ' 1 
4-19L 
wire. The equation for the distribution of temperature excess v along the wire in 
the steady state will therefore be 
W j 0 
—phv = 0 , 
( qk -^—5 + 
dx 2 ‘ 4-19L 
where q, k, p, h have the usual meanings. 
The solution of this equation may be put in the form 
(13) 
W 
V 4-19L ph 
-v) smh (&Yl 
qk 
w 
4M9L ph 
-Vi 
sinh ©'T-M 
+ 
W -v" Wnh^Y 
4-19L ph ) \qk) 
x, 
(14) 
* The amount conducted from the sleeve through the wooden support of the leads was too small to be 
taken into account. 
