402 
MESSRS. W. E. AYRTON AND H. KILGOUR ON THE 
for which clH/dx 1 are nought for these two currents in question. It is certainly 
surprising that a calculation based on the assumption that the thermal resistance of 
platinum is the same at all temperatures between 0° C. and 300° C. as it is at 
ordinary temperatures, should have led to the result that, both for a current of 
1*4 ampere and a current of 0'6 ampere passing through this 6-mil wire, d 2 tjdx° 
should be nought, that is, the temperature curve should be flat at almost exactly the 
mean temperature that the wire had in each case. It would, therefore, appear that 
the assumption regarding the thermal resistance of platinum having a constant value 
9’858 at different temperatures has not introduced any serious error. 
If we assume that the vertex of the parabolic curve for dH/dx 3 is in the line along 
which d z xjdt z is reckoned, which is very nearly the case, then 
clH_ 
dx 2 
( 11 ). 
where a is minus the value of dH/dx 2 when x equals nought, and T is the value of t 
when dHjdx 2 equals nought. 
At the point of the wire where the temperature is the highest the temperature 
curve will be flat, that is, dtjdx will be nought, and at the end of the wire where it 
is attached to the support the temperature will have some definitive value, T 0 , in 
other words when 
t = T, f = 0, 
and when 
x = 0, 
dx 
< = T„. 
With these two conditions only and without any reference to the length of the wire, 
it is possible to integrate the equation (11), and the result we arrive at is 
x 
, /T </(t + 2T) - y/3T y/(T 0 + 2T) + y/3T 
^ V 2 a + 2T) + v/3T </(T 0 + 2T) - </3T * ‘ K ’ 
An examination of this equation shows that in order that t may equal T, x must 
equal infinity, and, therefore, in obtaining this integral we have tacitly assumed that 
the maximum temperature of the wire is only obtained at an infinite distance from its 
end. But while great simplicity is obtained by this hypothesis, no more error is 
introduced by its employment than is met with by the use of the ordinary equation 
for the conduction of heat, and which leads to the result that two bodies initially at 
a different temperature take an infinite time to arrive at thermal equilibrium, even 
when connected together by a good conductor of heat. 
On examining the curve for dHjdx 3 on fig. 15, which as already stated has been 
