of Water at High Temperatures. 



117 



and RQ=a?=D- 1. If the 

 curve of expansion P Q is a 



, dx 



md ^* jr. 



parabola, x oc y' 



had previously examined the 

 observations of M. Despretz 

 both above and below the mini- 

 mum point, and found that from 

 50° downwards to as far below 

 0° as the liquid condition can 

 (by perfect stillness of the water) 

 be maintained, they could be 

 very accurately represented, not by a parabola, but by an ellipse 

 F P Q, the curvature of expansion below P being greater than 

 that above, and F A, the axis of the ellipse, being inclined to L N, 

 the axis of temperature. On this account the curve was to be 

 considered as only empirical, and therefore of no value in advancing 

 the thermo-molecular physics of water. But now the question 

 occurred, after seeing how the ordinates of graduation ranged, 

 might not the curve above 50° conform to the parabola? might not 

 the small deflection from it in the lower part of the scale be the 

 abnormal effect of the crystallizing force gradually increasing 

 towards the lower temperatures ? 



§ 2. To test this, reference was made to the Table of the 

 expansion of water up to 210°, given in note E of the paper 

 " On Liquid Expansion " above referred to ; and since, if the 

 curve was a parabola, dx or dv oc y or d 2 v constant, it was easy 

 to test the point in question by examining the second differences 

 of the volumes in that Table, which had been carefully reduced 

 to intervals of 5° of the air-thermometer (C.A.). 



The following is the Table with first and second differences : — 



10 

 5 

 

 5 



10 

 15 

 20 

 25 

 30 

 35 

 40 

 45 

 50 

 55 

 60 

 65 



00184 



00068 



00013 



00001 



00025 



00083 



00168 



00280 



00416 



00575' 



00755| 



1-00955 



101 175] 



1 01413 



1-01668 



101940 



dv. 



116 

 55 



24 

 58 

 85 

 112 

 136 

 159 

 180 

 200 

 220 

 238 

 255 

 272 



d 2 V. 



t. 





 65 



61 



70 





75 





80 



34 



85 



27 



90 



27 



95 



24 



100 



23 



105 



21 ! 



110 



20 



115 



20 



120 



18 



125 



17 



130 



17 



135 



18 



140 



01940 

 02230 

 02538 

 02863 

 03205 

 03563 

 03939' 

 04333 

 04 743J 

 05172 

 05620 

 06086 

 OH570 

 07073' 

 07593 

 08130| 



dv. d 2 v. 



272 



290 

 308 

 325 

 342 

 358 

 376 

 394 

 410 

 429 

 448 

 466 

 484 

 503 

 520 

 537 



140 

 145 

 150 

 155 

 160 

 165 

 170 

 175 

 180 

 185 

 190 

 195 

 200 

 205 

 210 



■08130 

 ■08684 

 09257 

 •09847 

 10456 

 11083 

 11731 

 12400 

 13093 

 13811 

 14553 

 15323 

 16124 

 16958 

 17829 



dv. 



537 

 554 

 573 

 590 

 609 

 627 

 648 

 669 

 693 

 718 

 742 

 770 

 801 



8;u 



871 



dh. 



17 



19 

 17 

 19 

 18 

 21 

 21 

 24 

 25 

 24 

 28 

 31 

 33 

 37 



