some Thermodynamical Relations. 259 



simply testing (7) ; and, as we find from Regnault's or 

 Rankine's formula (1) or (2) that (7) is untrue, there is 

 nothing further to be said about the four laws in question. 



We draw attention to the fact that Dalton's law, which was 

 the earliest law concerning saturated vapours, and of whose 

 inaccuracy the text-books always warn us, is a much more 

 correct law than the four identical laws which we have been 

 considering. For, to state Dalton's law mathematically, 



|-*w < 8 > 



That is, the rate of change of pressure with temperature is 

 constant at a given pressure for all saturated vapours. Inte- 

 grating (8), we obtain Dalton's law in the shapes 



t + a=ty(p), (9) 



d=t + b (10) 



That is, there is a constant difference between the tempera- 

 tures of two saturated vapours at the same pressure. Now 

 this law has been known to be incorrect for a long time ; but 

 if, assuming this law to be correct, we calculate the tempera- 

 tures of saturation corresponding to various pressures of, say, 

 bisulphide of carbon from those of water, we shall find our 

 errors to be much smaller than those obtained when we use 

 any of the above-mentioned four laws. 



Of the law connecting 6 and t, which has been published 

 in the January number of the Philosophical Magazine, it is 

 easy to see that the two forms in which it has been stated by 

 the authors are inconsistent with one another. Such incon- 

 sistency is not of much importance in the statement of empi- 

 rical laws ; but we think that one of the forms is preferable 

 to the other on account of its symmetry, as it may be put in 

 the form : — The reciprocals of the absolute temperatures of 

 two saturated vapours at corresponding pressures are linear 

 functions of one another, or 



Or, again, it may be put into the shape 



which may be compared with (3). 



In conclusion, it will be observed that in calculating the 

 temperature of a saturated vapour, a small-looking error may 



