608 
point of tlie axis of the bar at a distance x from the origin). Se- 
condly, That the loss of heat by radiation and convection from the 
surface of the bar is at every point proportional to the same tem- 
perature v. By assuming these principles (the last of which is 
certainly more or less inexact), the well-known solution of the 
problem of the heated bar is, that the temperatures (or excesses of 
temperature) diminish in a geometrical progression from the origin, 
and finally, of course, become insensible. Previous experimenters 
have confined themselves to finding the constants of the logarithmic 
curve for different substances, and thence their relative (not absolute) 
conducting powers. 
In the experiments now described, neither of the above-men- 
tioned principles is assumed. The external loss of heat is di- 
rectly ascertained by experiment, and the admissibility or otherwise 
of the former principle is also directly tested. That principle may 
civ 
be thus symbolised: F — -k--, where F is the flux of heat 
ctx 
across unit of section, k the conducting power for the substance 
employed, and v and x have the same signification as before. 
I. In the first instance, a bar of iron 8 feet long and IJ inch in 
diameter, was heated by means of a crucible at one end, con- 
taining melted solder. Thermometers were inserted at various 
points of its length. The results, v in terms of x, were projected in 
dv 
a curve (approximately a logarithmic), and the values of — were 
ctx 
found by projection or calculation, or both. 
II. Next a short bar (20 inches long), perfectly similar in sec- 
tion and condition of surface to the long bar, is heated to above 200° 
Gent, in a bath of fusible metal, and allowed to cool in free space, 
a thermometer being inserted at the centre of its length. This 
gives us the rate at which such a bar is parting with its heat 
from all causes whatever , in terms of the temperature shown by 
a thermometer in its axis. 
III. The losses of heat in unit of time (one minute) last found 
may be taken as representing the amount of heat dissipated from 
each point of the long bar in the statical experiment (I.), being 
given in terms of the temperature proper to each point of such a 
bar. A curve may thus be constructed, having for its line of ab- 
