66 Proceedings of Royal Soeiety of Edinburgh. [sess. 
To enable us to choose between these formulse we have the 
following comparison with the data for higher pressures in Amagat’s 
second table : — 
Pressure. 
Amagat. 
First formula. 
Second formula. 
1001 
*95596 
*95599 
*95595 
2001 
*92367 
*92337 
•92299 
3001 
*89828 
*89824 
•89741 
The first formula, therefore, represents with remarkable closeness 
the average compressibility of water at 0° C. for any range of 
pressure up to 3000 atmospheres ; while the second obviously gives 
considerably too much compression at higher pressures. Yet there 
is but one numerical difference between the sets of data from which 
these two formulae were derived, and that is merely a matter of 
four units in the fifth decimal place of the volume at 401 atmos- 
pheres ! Thus very small inevitable errors in the data may largely 
affect the values of the constants in the formula. The only certain 
method of overcoming this difficulty would be to work with pres- 
sures of the same order as B. 
The expression which I gave in 1888 for the average compressi- 
bility per atmosphere at 0° C. was {Challenger Reg)ort, Physics and 
Chemistry, Vol. ii. Part 4, p. 36) 
0*001863 
36 - 1 - 2 ? ’ 
the unit for p being 1 ton weight per square inch. To atmospheres 
(152*3 per ton weight per square inch) this is 
0*284 
5483 -hi?’ 
giving 0*0000518 as the compressibility at ordinary pressures. 
This agrees closely with the first, and more accurate, of the two 
formulae just given ; and yet it was derived from data ranging up 
to 450 atmospheres only. I stated at the time that “probably both 
of the constants in this formula ought to be somewhat larger.” 
This would make it still more closely agree with Amagat’s results. 
I have worked out the values of the quantities A and B for 
the ten special temperatures (from 0° to 48° *95 C. inclusive) in 
Amagat’s table No. 2 ; taking for each temperature the data for 
