506 KEPOET— 1888. 



The author finds that liquids near their boiling-point show some 

 deviation in their rates of expansion from those calculated from the above 

 formula, in the sense that the observed expansion is greater than that 

 calculated; e.g., the volume of PBr,, B.P. 173°, is found at 160° to be 

 1-1562; the calculated value (7^= -000841) is 1-1555; on the other 

 hand in one case, that of a paraffin melting at 38°, Beilby has ^ shown 

 that the change in its specific gravity with temperature is from 38° 



to 60° quite constant; — - = —"000727; the deviations of volatile 



at 



liquids from perfect accordance with the law expressed by the formula 

 are nearly always small, but near the boiling-point quite appreciable; 

 and for different liquids the deviations are of different sign ; if 

 we consider Mendelejeff's equation as expressing the ideal form 

 of expansion for liquids by analogy with Gay-Lussac's expression for 

 expansion of gases, then the deviations from the ideal form will be greater, 

 the less the density of the liquid, the greater the cohesion (the value a ^), 

 the less the molecular weight, i.e., the less the vapour-density. Water 

 has a small molecular weight and very great cohesion, the molecular 

 weight being the smallest for all common liquids ; these facts, taken in 

 conjunction with the small difference between the temperatures at which 

 liquid water changes its state of aggregation to the solid and gaseous 

 respectively, account for the anomalies in the expansion of water ; for 

 which, in fact, the equation does not hold, the values of Z; found within 

 different temperature-ranges being quite different. No other liquid shows 

 so rapid a rate of expansion from 4°. 



On p. 132, in a footnote, Mendelejeff refers to a paper by him in 

 which he has shown a dependence of coefficient of expansion of gases 

 on the molecular weight ; this coefficient increases with increasing mole- 

 cular weight. He draws special attention to the case of chlorine, which, 

 therefore, has a large coefficient of expansion : this fact, he says, should 

 be taken into account in regard to the alleged dissociation of the chlorine 

 molecule. 



Thorpe and Eiicler on the Relation of k to Critical Temperature. 



In the paper immediately following Mendelejeff's {he. cit. p. 135), 

 Thorpe and Rlicker discuss the formula given by Mendelejeff in connection 

 with Van der Waals' theories. The result of this paper is to show a 

 simple relation connecting I; Mendelejeff's determinator of expansion, 

 with the critical temperature of the liquid. 



In the Leipzig edition (1881) of Van der Waals' dissertation on the 

 continuity of the gaseous and liquid conditions, on p. 128, he states two 

 general relations, which show that temperatures and pressures are 

 corresponding temperatures and pressures for two different bodies when 

 they are such that the ratio of the absolute temperature in the case 

 of one body to the absolute critical temperature of that body is the same 

 as this ratio for the other body ; for when the pressure, volume of 

 liquid, volume of saturated vapour for the two bodies at these two 

 temperatures are compared, the ratios of these pressures and volumes are 

 found also to be in the same ratio to their values at the critical tempera- 

 ture — the same, that is, for both bodies. Corresponding conditions for two 



' C. S. J. 1883, Trans. 338. ^ C. li. Feb. 14, 1876. 



