468 Proceedings of the Royal Society of Edinburgh. [Sess. 
The general procedure was as follows : — 
(a) Cases in which the excess of the final liquid volume (registered 
temperature =T 1 ) over the volume AB was greater than -025 c.c. (approxi- 
mately one-third of the volume of the capillary part BC) were discarded. 
(b) Cases in which the excess of the volume AB over the final liquid 
volume was greater than *150 c.c. were taken as having the registered 
temperature T 1 . 
(c) For all other cases : — 
Temperature Range = 
0° - 600°. 
600° - 1000°. 
Excess of Vol. AB 
over Final Liquid Volume. 
T, 
TV 
- *025 to + -050 
+ ■050 to + TOO 
+ *100 to +*150 
T, - 25 
T x - 15 
H- 5 
Tj -50 
Tj - 30 
Tj-10 
Volume Corrections. 
The volumes 12^5^ 3 anc ^ 1 3A6 ; ^ ven on P* 463, have to he corrected 
for change of pressure. 
Let a, /3, y be the mean compressibility coefficients of quartz-glass, 
mercury, and water respectively. 
Also let «V P denote water- volume at temperature t and pressure p. 
and tV'p denote mercury-volume at temperature t and pressure p. 
The uncorrected initial volume of the water is ^ 2 ~^ 3 or , K V.. 
12*56 15 1 
The corrected initial volume of the water is 15 V P t 
where w \ p = ^(1 - y . p) = "^ (1 - y . p) . . . (1) 
Similarly, the original mercury volume is 15 V' r 
This becomes, as a result of the compression of the mercury, 15 V / i> at 
pressure p, 
where 15 V' p = 15 V\(1 - p .p). 
Finally, if v be the internal volume of dilatometer from A to F at 
atmospheric pressure, this becomes at p atmospheres v (1 — a ' p). 
Hence the corrected change in volume is 
w 4 w 2 -w 3 
13*56 12*56 
•7*P + i5 Y 'i -P-p-v 
a . p . 
(2) 
