396 
PROFESSOR C. H. LEES: THERMAL AND ELECTRICAL 
Hence in the equation (4) for k (p. 386) we must write for H 
0-2406A{(1-0-057A)P o -( 0‘021 +0-0001 lr)}, 
and for sh 
We thus obtain 
sh + 0-0000048 + 0-000013 
Xr 
M cosh = 0-2406A{(l-0-0S7A)P r (0-021 + 0-00011r)} (itA _ ieASA) 
V B ~V A 
- (sh + 0-0000048 + 0’000013 ^ ) x r ,S P „ 
x C ' 
Finally, substituting for the temperatures of the rod v B and v A in terms of v B and 
v x the observed mean temperatures of the platinum resistances by means of 
equation (12), p. 392, we have 
I-ffCcH, (P h \'\ - 0’2406A{(l-0-057A)P 0 -(0'021 + 0-00011r)}, „ „ , 
qC0S ++ Xc ~ (1-026 + 29A)(«,-C a ) Ai} 
that is, 
kq cosh ( x c 
-(sh + 0-0000048 + 0-000013 ^ ) jc c ,S c ,, 
x c J 
(0"2345 —28A) A {(1 — 0"057A) P 0 —(0*021 + 0-0001 It)} ( Q ox 
— — — V^b^b-^a^a) 
V B -V a 
sh + 0-0000048 + 0-000013^) £c c ,S c ,, (18) 
Xr.i 
where s = i-47 + 0-36 + 0‘11 = 1"94 sq. centims. 
Effect of the use of the Variable State of Temperature Distribution. 
So far the theory has been worked out on the assumption that the temperature 
distribution throughout the apparatus is steady. But it has been stated that the 
measurements were made during the gradual rise of temperature from that of liquid 
air. We have therefore to consider the effect of this on our fundamental equation (4). 
Let v be the temperature of the bar at a cross section distant x from that where 
the bar joins the enclosing tube, and let V be the temperature of the tube. Then v 
satisfies the conditions 
dv 7 d 2 v , , -x n 
w ai = & 3?-A+- v ). 
V = f(t), v = V at x — 0, 
1 
dv 
qk ——b ph (v—V) — Q at x = x c , the free end of the bar, 
ox 
the heat Q being supposed imparted to the bar at its free end. 
