492 
MR, C. H. LEES ON THE THERMAL CONDUCTIVITIES 
For the curve which corresponded best with the mean of the three sets of observa¬ 
tions taken, the value of v is represented along the cooler part of the bar by 
”795 cosh ’0378 x -j- 11 ‘86 sinli ’0378 x. 
X. 
v calculated. 
v observed. 
Difference. 
civ 
dx 
0 
•8 
•8 
0 
•448 
10-56 
5-72 
5-72 
0 
•497 
21-04 
11-52 
11-53 
+ -01 
•624 
81'55 
19-17 
19-18 
+ -01 
•852 
32-59 
20-07 
20-09 
+ -02 
•881 
43 15 
31-23 
31-20 
- -03 
1-262 
53-59 
4724 
47-88 
+ -64 
1-971 
64-03 
_ 
70-64 
73-47 
+ 2-83 
3-002 
The differences, with the exception of the last two, are within the limits of error of 
observation, and may be neglected. The last two may be taken into account by 
adding to the above expression for v, between x = 43 and x = 64, an expression of 
the form 
a 
X — 4 o 
10-5 
( X 4t8\^ 
+ b ( — j , where a = '572, b = '06/, 
The values of the differential coefficient of this expression at x — 43T5, 53'59, 
64'03 are 0, T28, '294 respectively. Differentiating the hyperbolic expression for v 
we have dv/dx = '03005 sinh '0378 x -f '4483 cosh ’0378 x, which gives, on substituting 
for x the coordinates of the points of observation, the required values of dv/clx, to 
which, at x = 53'59 and 64'03, Ave must add the quantities T28 and '294 to get the 
true temperature slope. The values thus obtained are given in the above table. 
Having thus got the values of v and dv/dx at eight points on the bar, we can by 
trial determine a so that the equation (6) holds. A few trials sIioav that a is 
positive and equal approximately to '092. It is not necessary to determine a witli 
any great accuracy as it affects very little the subsequent Avork. Assuming a = '002 
we have the following' table of results 
X. 
V. 
, (- n a + b ah , \ 
" ( + r « + rff 
/ rl 1* \ ° 
(5.) 
(6.) 
( 1+ UV Ic) 
0 
•8 
"643 
•201 
-001 
0016 
10-56 
5'72 
33-96 
•253 
•053 
•0015 
21-04 
11-53 
143-3 
•406 
•206 
•00143 
31 - 55 
19-18 
415 
•781 
•581 
•00140 
32-59 
20-09 
459 
•839 
■639 
•00139 
43-15 
31-20 
1174 
1-796 
1-596 
■00136 
53-59 
4780 
3067 
4"666 
4'4-66 
•0ol45 
64-03 
73-47 
8269 
11-860 
11-660 
•00141 
