490 
MR. C. H. LEES ON THE THERMAL CONDUCTIVITIES 
The heat lost from a nickel-plated surface exposed to air is, therefore, 
•0001804V (l + •008'?’) gram degrees per sq. cm. per second, 
where v is the excess of temperature of the surface over that of the air. 
Statical Experiments. 
These experiments were made with the brass bar before it was cut. One end was 
heated by steam, and the other cooled by water. Eight observations of temperature 
were taken at different points of the bar in the way previously described. 
Let v be the excess of temperature at point x of bar over that of surrounding air, 
p — perimeter of cross-section of bar, 
q = area of cross-section of bar, 
k v — thermal conductivity at temperature excess = v. 
Then, at any point of the surface of the bar, we have 
yq + hv (l + bv) = 0, 
where clv/dn is the rate of change of v along the normal to the surface, s, h, and b 
having the meanings assigned to them in last section. 
At v = 60° C. this gives 
k„ ~ = - -00018 X 60 X 1-5 
an 
= — -0162. 
Now k v will be seen later to have the value "27 approximately. Hence, at a point 
of surface, at the temperature of G0° C. excess, dvjdn = — *06. 
At the same point on the surface dvjdx = 2'5 approximately. Hence, the inclina¬ 
tion of the normal to the isothermal surface at this point to the axis of the bar is 
arctan -06/2-5 = arctan ‘024 — 1° 25'. If the isothermal surface be assumed to be 
part of a sphere, the radius of curvature is about 4 2 cms. At 1 5° C. excess, a similar 
calculation gives the radius of curvature of the isothermal surface to be GO cms. 
Hence we may assume the isothermal surfaces to be planes perpendicular to the 
axis of the bar. 
The equation for the motion of heat in the bar is under these conditions 
?£(*"!) = ^( i + h.(4) 
The conductivity has generally been considered constant in treating this 
equation, but this is scarcely justifiable, as most experimenters find changes of 
