THE THERMAL CONDUCTIVITY OF METALS. ialtyal 
Then the quantity of heat that flows through any hemispherical surface distant 7 
from the end of the wire is 
Bea ee 2 
Q=-hk Tp ot 
and, since the flow is steady 
ad dv 
= ane 16) ad — 
ie ( ap 2777 ) — 0 
Hence 
lv 
Hoye 
Gp Ci, 
which gives 
v= Cpr7!+ C,. 
For r = a let v = V, and for 7 = b let v = @. 



Hence 
V-¢O _ 6b — Va 
v= ab one 
=i Cor 
whence 
Ho al WS © op 
piled inca ake ead, 2 
and 
Wea 
Q = 27k Re ab, 
Ajso 
g=(v,- We 
where V, is the temperature at the hot end of the wire, and / the length of the wire. 
Since V is the temperature of the wire just where it enters the ball, and 6 the 
temperature at the centre of the ball, V — @ is certainly much greater than the 
error, a superior limit to the magnitude of which we wish to ascertain. The heat 
which flows through the wire must be equal to that which flows into the ball ; 
therefore 




T ‘K passe 
(v, nlp V ) a wt ork ni Say ab, 
whence 
Kea (Gita) 
a K (b—a 
=-(V-0+409-V))< ee 
and, therefore, 
@ K (b — a) 
BW ip tb 
Mia’ ay Danaapraossa)i 
te 0 
V4 
