356 M. R. Riihlmann on the Alteration produced by Heat 



Also the conclusions drawn in later treatises of Schrauf, a On 

 the Influence of the Chemical Conditions on the Velocity of 

 Propagation of Light"*, and also " On the Determination of the 

 Refractive Equivalents of the Elements" f> are rendered invalid 

 by the proof that neither M nor N are constants, but that M 

 only may be considered so in rather rough approximation. Two 

 schemes, which are given on pages 357 and 359, give numerical 

 values for M and N for certain substances. The first of these 

 is taken, for the most part, out of the second treatise by Glad- 

 stone and Dale J; the second I have calculated from my own 

 observations for water. 



In the treatise mentioned, Gladstone and Dale suppose there 



^ ,^ 



to be another relation between A and D, namely — ^ — = const., 



or — ^r — = const., while they entirely set aside the constancy 



of yt * I n regard to Schrauf s magnitude M, they say, " The 



( absolute refractive power 3 is evidently not a constant," and 

 prove their assertion by numbers. Eor the calculation of A they 

 employed their own observations, while for the density they used 

 the numbers which Kopp gave in his " Investigations on Specific 

 Gravity and Expansion by Heat, and on the Boiling-Point of 

 some Liquids"§. The employment for one and the same calcu- 

 lation of constants derived from two different kinds of the same 

 liquid cannot be considered trustworthy, because the different 

 degree of chemical purity may give rise to considerable differ- 

 ences. At all events, such great differences in density as are 

 given in the works of Pierre ||, Kopp% andMatthiessen** are to 

 be attributed chiefly to the different degrees of purity in the pre- 

 parations. 



I am quite conscious that I am also so far open to the same 

 reproach, as I have made no determination of the expansion of 

 the water used by me. I have only been prevented from carry- 

 ing out this experiment by want of time. My apparatus for this 

 purpose is already made ; the constants are determined, and the 

 data for water will be adduced in the publication of the continu- 

 ation of my memoir. I believe that the numbers obtained by 

 others may be more safely used in the case of water than in that 



* Pogg. Ann. vol. cxix. pp. 461-480, and pp. 553-572. 



f Ibid. vol. cxxvii.p. 175. 



% "Researches on the Refraction, Dispersion, and Sensitiveness of 

 Liquids/' Phil. Trans, vol. cliii. (1863), pp. 307-343. 



§ Pogg. Ann. vol. lxxii. p. 42. 



|| Ann. de Chim. et de Phys. 1825, Nov. and Dec. p. 325. 



*f[ Pogg. Ann. vol. lxxii. p. 42. 



** Pogg. Ann. vol. cxxviii. pp. 512-540. Report of British Association, 

 1863, p. 37, 



