124 



Mr. J. J. Waterston on the Expansion 



and 7r + */=*204, which, subtracted from 7*29, gives 7*086 as 



corrected denominator, and =1-5363, the volume at 



7'Uob 



320° C.A. 



§ 15. The second column of the following Table was thus 



computed. In the third column are the differences for 1°. 



These are projected as ordinates to the temperatures in fig. 9, 



then equalized as shown by the small dotted curved line. The 



ordinates to this line are read off by scale and set down in the 



fourth column as the equalized differences. These are values of 



dv 



-T-. Now, since the law of liquid expansion requires that these 



differences, divided by their respective volumes, should, when 

 projected as ordinates to the temperatures, range in a conic 

 hyperbola, the reciprocals, if the observations were perfect, ought 

 to range in a straight line. 



1. 



2. 



3. 



4. 



320 C.A. 

 310 „ 

 300 „ 

 290 „ 

 280 „ 

 270 „ 

 260 „ 

 250 „ 

 240 „ 

 230 „ 

 220 „ 

 210 „ 



1 -5363 

 1-4742 

 1-4280 

 1-3856 

 1-3518 

 1-3204 

 1-2912 

 1-2645 

 1-2385 

 1-2171 

 1-1978 

 11800 



•00621 

 •00462 

 •00424 

 •10338 

 •00314 

 •00292 

 •00267 

 •00260 

 •00214 

 •00193 

 •00178 



•00592 

 •00486 

 •00410 

 •00356 

 •00313 

 •00292 

 •00267 

 •00243 

 •00220 

 •00198 

 •00178 



The first reciprocal is - 



1-5052 

 00592 



254-3, which in fig. 10 is set 



off as ordinate to 315°, and so on down to =668, which 



is set off to 215°. 



These points are distinguished by small circles. It will be 

 remarked that they range in a flat ogee curve. The strong 

 broken straight line is drawn through them and transferred to 

 fig. 9, showing that if the equalized differences had been taken 

 from the strong dotted line instead of the faint dotted line, the 

 points in fig. 10 would have ranged exactly in a straight line, as 

 theory requires. The difference this involves in the curve of 

 observations (fig. 8) would hardly be sensible. 



§ 16. Such accordance is indeed much greater than at first 

 sight might be expected from the observations, which in fig. 8 

 are plotted in the rough from the note-book. But the method 



