609 
scissse the axis of the long bar, and for ordinates, the rate of dissi- 
pation of heat from each portion of its surface due to both radia- 
tion and convection. 
IV. If we can by mechanical quadrature, or otherwise, find the 
whole amount of heat dissipated between any point of the long bar 
and its coolest extremity, we have, in truth, the flux of heat passing 
from the hotter extremity of the body across the particular section 
in question ; for the condition of permanence of the temperature of 
the bar arises from the equality of the heat supplied and dissipated. 
But the whole heat dissipated in unit of time is the integral of the 
partial dissipations represented by vertical ordinates of the last- 
named curve, taken between any assumed point x and the farthest 
or cool end of the bar. This quantity, then, is F or the flux across 
unit of section at the point x. 
V. We are now able to resolve the question whether or not the 
flux of heat is in the given bar everywhere proportional to the ra- 
pidity with which the temperature decreases as x increases, or 
dv 
whether the equation holds, F = — the conducting power k 
OjX 
being supposed to be constant. 
The following table (the result of an approximate reduction made 
in 1852) shows that the constancy of k in the case of iron cannot 
be assumed ; on the contrary, that the conductivity diminishes as 
the temperature increases. The first column is the observed tem- 
perature of given points of the bars ; the second and third columns 
give the values of k from the preceding equation — (1.) as deduced 
from experiments on the iron bar with a polished surface ; (2.) when 
the surface was covered with thin paper. The general coincidence of 
the two is satisfactory, since the external cooling was considerably 
different in the two cases. 
Actual Temperature, 
F 
— ; polished bar. 
F 
; covered bar. 
Centigrade. 
dx 
dv 
dx 
25° 
•0136 
0147 
50 
*0130 
•0138 
75 
•0131 . . 
•0123 
100 
•0126 
0113 
1 25 
•0122 
•0107 
150 
•0112 
0107 
1 75 
*0100 
0102 
200 
0087 
