192 
Mr Searle, A method of determining the 
§ 3. Let the mass of the calorimeter be m grammes, let its 
water equivalent be me and let the mass of the water in the 
calorimeter be if grammes. Then, if the temperature of the water 
rise at the rate of R degrees per second when the calorimeter is at 
the temperature of the room, and if H be the rate at which the 
calorimeter and its contents then gains heat by conduction 
through the tube, 
H = R(M -f me) thermal units per second. 
Since the diameter of the tube is small compared with the 
radius of curvature of the axis of the tube where it is immersed in 
the water, we may treat the tube as if it were straight. Hence, if 
6 be the temperature at any point of the tube at a distance r from 
the axis and if K be the thermal conductivity, we obtain for a 
steady flow of heat 
3 _ 9 rr d9 
l 2lTrK dr ’ 
where l is the length of tube immersed in water. If a and b be 
the external and internal radii of the tube and 6 a and 6 b be the 
temperatures of the corresponding faces, we obtain 
Ob - da =e 
H 
2 7 tKI 
!0ge 
Hence, Anally 
lr R (M + me ) , a 
K = ^ log 
Since 
2irl(d b — 6 a ) 
1, a a - b 1 
2 1o S-6 = ^T6 + S 
it may be sufficiently accurate to 
^ log 6 (ajb). Then 
•(!)• 
b 
a — b 
a + b 
write (a — b)j {a + b) for 
+ 
K = 
R (M 4- me) ( a — b) 
( 2 ). 
7 rl (6 b - 0 a ) ( a + b ) 
It will be seen that to this degree of accuracy the result is the 
same as if the tube were replaced by a flat plate of thickness a — b 
and area ^7r/ ( a + b). 
The thermal conductivity of indiarubber (0 0004) is only 
about one-third of that of water (0'0014) and thus we may 
assume that 9 b is practically identical with the temperature 
of the steam passing through the tube and that 9 a is practically 
identical with the temperature shown by the thermometer in the 
calorimeter, when the water is well stirred. 
The amount of heat required to raise the temperature of the 
tube itself is negligible in comparison with that absorbed by the 
calorimeter and thus the assumption that the flow of heat is steady 
leads to no sensible error. 
