134 Froceedings of Royal Society of Edinhurgh. [sess. 
His metliod differs from any of mine, for he seeks two temperatures, 
not very different, at which water has the same volume at the same 
pressure. 
So far, I had been dealing with pressures of little more than 
200 atmospheres. Higher pressures led to the result that the 
displacement of the maximum density point increases very much 
faster than does the pressure. For the terms in higher powers of the 
pressure begin to tell more and more ; and another cause comes promi- 
nently into play, depending on the fact that water has a tempera- 
ture of minimum compressibility (about 60° C. at ordinary pressures). 
This affects to a very much greater extent the lowering of the maxi- 
mum density point by pressure than it affects the amount of heat 
developed by the compression. Both of these causes are indicated 
in my formulae as contributing to such a result, but the small 
numerical factors of the terms which express them are not accurately 
known ; and the calculation of the thermal effect of large pressures 
from data obtained by measuring compressibility at different tem- 
peratures is a very severe test of their accuracy. Besides, in giving 
a formula which exactly represented my determinations of the 
change of volume of water, under pressures from 150 to 450 
atmospheres, and at temperatures 0° to 15° C., I expressly said that 
“it must not be extended, in application, much beyond” these 
limits. If, however, we venture to extend it to 500 atmospheres, 
it leads to the following expression, for the heating of water by 
the sudden application of that pressure, 
^ + 3-2 
where t is the original temperature (C) of the water operated on. 
In obtaining this result it is assumed, in accordance with Kopp’s 
data, that the expansibility of water at ordinary temperatures and 
at atmospheric pressure is approximately (^ - 4)/72,000. Other 
experimenters make it somewhat greater. [If the maximum density 
point were lowered 1° for every 50 atmospheres, the heating by 500 
atmospheres would be about (^-f l)/22 only. Comparing this with the 
result above, we see how considerably the causes, alluded to, affect 
the calculated amount of heating.] 
How I find that M. Galopin’s results may be represented very 
