PHYSICAL PROPERTIES OF WATER, ETC. 37 



but highly expressive and apparently important features of the formulas (A) for the 

 separate pressures are, of course, lost. The statement above, as to the greater uncer- 

 tainty of the values the higher the pressure, renders it probable that, in the pressure 

 factor in this formula, both the constants ought to be somewhat larger. It is clear that 

 very small changes in the relative values of the compressions for 1, 2, and 3 tons would 

 make great changes in these constants. In fact, an error of 1 per cent, at 3 tons 

 involves an error of some twenty per cent., nearly, in each of the constants of the 

 pressure factor. 



Again, this last formula would give, for all pressures, minimum compressibility at 

 about 37° C. ; while the former three give 45° C. at 1 ton, 36^5 at 2, and 30°"8 at 3 

 tons : — these minima being 423, 423'4, and 421 respectively. 



If we venture to extend the formula? (A) to atmospheric pressure, we are led to 



520- 3-55/ + 0-03* 2 



I have already shown 1 that this is in close accordance with Buchanan's results at 2° - 5 

 and 12° - 5 C. Buchanan's pressure unit is thoroughly trustworthy; for it was deter- 

 mined by letting down the piezometer, with a Challenger thermometer attached, to a 

 measured depth in the ocean. It would thus appear that the extension of my formulae 

 to low pressures is justified by the result to which it leads. 



This formula gives 415 for the minimum compressibility of water at low pressures, 

 the corresponding temperature being about 60° C. This accords remarkably with the 

 determination made by Pagliani and Vincentini, who discovered it, and placed it at 63° 0. 



On Plate II. I have exhibited graphically a number of known determinations of the 

 compressibility of water for very low pressures at different temperatures. The line 

 marked Hypothetical is drawn from the formula above, the authors of the others are 

 named in the plate. It will be seen at a glance that, if Pagliani and Vincentini had 

 taken Grassi's value of the compressibility of water at 1°'5 C, instead of that at 0° C, 

 as their single assumption, their curve would have coincided almost exactly with my 

 Hypothetical curve ! 



So far matters seemed to have gone smoothly enough. But when I came to reduce 

 the observations made since June 1887, I found that they gave a result differing, 

 slightly indeed but in a consistently characteristic manner, from that already given. 

 The processes of reduction were carried out precisely as before ; and the points deter- 

 mined by the second series of observations are inserted in Plate I., marked with a ©. 

 Curves drawn through them as before are now seen to be parallel to the former curves, 

 but not coincident with them. And the amount of deviation steadily diminishes from 

 the lowest to the highest pressure. These curves, of course, are very closely repre- 



1 See p. 14, above. 



