Mr. J. J. Waterston on Liquid Expansion. 349 



stant ratio to this coefficient, depends on the value of the second 

 differential of expansion ; so that if the series of observations are 

 not sufficiently correct or regular to give a tolerably approximate 

 constancy of value to the second difference, they will fail to afford 

 the test required. 

 The equation is 



- = (-/ ?— I and -xA=F = 504. 



Pi t l — t \dv 1 dv / p 



But instead of this value of F being maintained, after examining 

 graphically and otherwise a considerable number of M. Pierre's 

 tables of observations, I find that it varies from 280 to 380, and 

 that on an average it is less at the lower than at the higher 

 temperatures. 



The discrepancy being so great, and always in one direction, 

 has gradually undermined my confidence in the presumed law of 

 liquid-expansion. 



M. Drion's researches on the dilatability of volatile liquids, 

 published in the Annates de Chimie for May 1859, I had unfor- 

 tunately previously overlooked entirely, although two of the 

 liquids chosen, viz. sulphurous acid and muriatic ether, are per- 

 haps the best that could be selected for testing a theory, as they 

 expand upwards of one-third of their volume on being heated to 

 about 130°, and below this limit of temperature the difference in 

 the march of the thermometers of air and mercury is too small 

 to cause embarrassment. Also they are specifically distinct in 



their chemical relations — one having its elements and S ¥ in a 



burnt condition, and the other, H 2 C . IP CP, having one part 



burnt (H*C1*), and the other part (H 2 C) unburnt. 



On projecting these observations graphically, they are found to 

 be wonderfully free from irregularities; so I trust to not having 

 over-estimated the importance of the results obtained from their 

 graphical analysis, which is presented in the accompanying chart 

 (Plate VII.). 



Instead of the proportionate expansion for 1° being inversely 

 as the temperature below an upper fixed limit, it will be remarked 

 that the evidence is in favour of the absolute expansion for 1° 

 having this ratio. Both values are laid down, the inverse of the 

 proportionate expansion for 1° ranging along a a and c c, the 

 inverse of the absolute expansion for 1° ranging along bb and dd. 

 By employing a straight edge, the exact accordance or discord- 

 ance of the observations with either hypothesis may be ascertained. 



According to the previous hypothesis (the proportionate), the 

 points in a a should not only range in a straight line, but that 

 line ought to be S S, or at least parallel to it, if F held the con- 



