PHYSICAL PROPERTIES OF WATER, ETC. 33 



Notice that, in the first experiment (. .) failed to give a reading. Also in the 

 fifth and sixth the indications of the two instruments do not agree very closely. The 

 character of the results, however, points apparently to an error in gauging one or other 

 of the instruments. It was the unavoidable occurrence of defects of these kinds that led 

 me to make so many determinations at each temperature and pressure selected. The 

 above specimen contains less than 1 per cent, of my results for fresh water, and I 

 obtained at least as many reduced observations on sea-water. 



To obtain an approximate formula for the full reduction of the observations, I first 

 made a graphic representation, on a large scale, of the results for different pressures 

 at each of four temperatures, adding the compressibility of glass as given in Section VI. 

 above. From this I easily found that the average compressibility for 2 tons pressure 

 (at any one temperature) is somewhat less than half the sum of those for 1 and for 

 3 tons. Thus the average compressibility through any range of pressure falls off more 

 and more slowly as that range is greater. And, within the limits of my experiments, I 

 found that this relation between pressure and average compressibility could be fairly 

 well represented by a portion of a rectangular hyperbola, with asymptotes coincident 

 with and perpendicular to the axis of pressure. Hence at any one temperature 

 (within the range I was enabled to work in), if v lie the volume of fresh water at one 

 atmosphere, v that under an additional pressure p, we have 



o — v _ A 



very nearly, A and I~I being quantities to be found. 



I had two special reasons (besides, of course, its adaptability to the plotted curve) 



for selecting this form of expression. First, it cannot increase or diminish indefinitely 



for increasing positive values of p, and is therefore much to be preferred in a question 



of this kind to the common mode of representation by ascending powers of the variable, 



such as two or more terms of 



B +B L p + B s p 2 + &c, 



or the absolutely indefensible expression, too often seen in inquiries connected with this 

 and similar questions, 



C + Cj'" + &c. 



Second, it becomes zero when^j is infinite, as it ought certainly to do in this physical 

 problem. It appeared also to suggest a theoretical interpretation. But I will say no 

 more about this for the present, as it is simply a matter of speculation. See the latter 

 part of Section X., below. But there is a grave objection to this form of expression, 

 in the fact that small percentage changes in the data involve large percentage changes 

 in A and II, though not in the ratio A/IT. This objection, however, does not apply to 



(PHYp. CHBM. CHALL. EXP. — PART IV. — 1888.) 5 



