110 REPORT — 1886. 



Pressure 40 metres 



„ 100 „ 

 „ 180 „ 

 „ 260 „ 

 „ 320 „ 



It -will be noticed, on calculating the coefficients of dilatation, how 

 very much they differ, in this condition of very high pressure of the sub- 

 stance, from the coefficients at ordinary pressures ; it -will be seen also 

 that the coefficients of dilatation for 1° are smaller, at same pressure, for 

 higher than for lower temperatures. 



In the equation jj (v — a) = b for the straight poi'tions of the line — for 

 high pressures — if p be made infinite v=u : now a is a constant at any 

 given temperature for each gas, which can be determined with fair accu- 

 racy from the equation p (u— ") = p' (^''— «) ^^^ pressures p anip', 

 being a long way apart : and a is therefore a known number : hence the 

 volume taken may be condensed by pressure to a small volume, but never 

 to a volume smaller than a, where a varies very gradually with the tem- 

 perature. 



Vapour-pressures and Temperahtres ; — RegnauU. 



We must now turn to well-known investigations of relations between 

 t)(xpo?ir-pressures and temperatures by Regnault and by others. 



In a magnificent series of investigations on the vapour-pressures 

 (elastic forces) of luater, Regnault ' describes various methods, and gives 

 in separate tables the results for separate series treated by these methods 

 for temperatures ranging from 32° to 230°; and discusses the applicability 

 of a number of different formulae, by which, after determination of the 

 constants in the formula by reference to a few of the determinations the 

 rest of his results were more or less accurately represented. 



The above samples give some idea of the rapid rise of pressure with tem- 

 perature. The empirical formula by which Regnault expressed the results 

 of his observations on other bodies - were of a similar exponential form 

 to those he used for water in t. xxi., the laws. by which Dalton attempted 

 to express the relations being entirely inadequate except over a very short 

 range : these laws of Dalton were — 



(1) The elasticity of vapour of a liquid increases in geometrical pro- 

 gression when the temperatures follow in arithmetical progression. 



(2) The vapours of all liquids have equal elastic forces at tempera- 

 tures equidistant from the boiling points at ordinary atmospheric pressure. 



These laws are replaced by Regnault's tabulated results, and by the 

 empirical formulae he adopted ; for each substance fresh experiments have 

 to be made, and no reliance placed on Dalton's laws. 



For water at low temperatures — e.g. from — 32° to 0° — the formula 

 used was 



F = ft + ta^, where x = t + 32°. 



' Alem. XXT. de TAcaiUmie, mem. viii. pp. 465-633. 

 2 Mem. XXVI. de VAcademie, pp. 335-760. 



