36 THE VOYAGE OF H.M.S. CHALLENGER. 



following values were taken at intervals of 5° for the sake of ease of calculation, 

 260 being added to each for the compressibility of glass : — 



0°. 5°. 10°. 15°. 



1 ton, 5044 4874 4723 4594 



2 tons, 4898 4733 4584 446C 



3 tons, 4776 4608 4468 4360 



The fact that water has a temperature of minimum compressibility led me to try to 



represent these numbers by a separate parabolic formula for each pressure. The 



following were easily found : — 



504- 3-60* + 0-04/ 3 , \ 



490 -3-65* + 0-05^ (. . . (A) 



478 -3-701, + 0-06^' j 



for 1, 2, and 3 tons respectively. [The terms independent of t belong to the formula 

 520 — \7p+]f. This will be made use of in future sections.] The utmost difference 

 between the results of these formulae and the numbers from which they were obtained 

 is less than 1/1 0th per cent. No closer approximation could be desired, much less 

 expected, especially when we consider the way in which the * points (on which the 

 whole depends) were themselves obtained. These are represented as follows : — 



In one instance only does the difference reach unit in the third significant place. [It 

 must be remembered that all these numbers commence with the fifth digit after the 

 decimal point.] 



In spite of some remarks above as to uncertainty about temperature, I am con- 

 vinced that the mode of experimenting employed is calculated to insure considerably 

 greater accuracy in the comparison of compressibilities at different temperatures for 

 any one pressure, than in that of compressibilities for different pressures at any one 

 temperature. The displacement of the indices by the expanding water is likely to be 

 more serious the higher the pressure, as the difficulty of effecting the relief quietly is 

 much greater. Probably all the values for the higher pressures are a little too small 

 for this reason. 



The results given above are represented with a fair degree of accuracy by the 



simple formula 



0-001863 /._ 3/ t 2 \ 



36 + 2 > V 400 + 10,0007 



which will amply suffice for ordinary purposes. In this form, however, some small 



