258 Professors Ayrton and Perry on 



all be true. Thus III., when stated mathematically, is simply 



4>(p) being the same function of the pressure for all sub- 

 stances. Differentiating (4) with regard to p, we obtain at 

 once law IY. If it had sooner been observed that 



L t dp 



Si~-s 2 J dt 



(5) 



is simply a statement of the Second law of Thermodynamics, 



the authors would probably have examined the truth of the 



law in the shape III. only; since the specific volumes of 



vapours are so difficult to test experimentally, that Rankine, 



to obtain the density of steam, calculated s x — s 2 by dividing 



t dj) 

 the latent heat L by ^v rather than depend on direct 

 J dt j 



measurement. Again, since the first law is = (j)(p) } 



s 1 — s 2 



if we insert L x and ~L 2 , p\ and p 2 , s and a, we see that law II. 



is identical with L, and therefore I., II., III., and IV. are 



merely different methods of stating the same law, and to test 



one is to test them all. 



Now we are sorry to say that we should not have attempted 



to test any of these forms of the law. The form which may be 



tested with most accuracy is III., or, as it may be stated 



mathematically, as in (4) 



or 



dp _ dt 



#~7' 



or 



(=<*■*(?), (6) 



where t is the absolute temperature corresponding to the pres- 

 sure p of a saturated vapour ; a is a number which depends on 

 the nature of the substance, and the function ^jr(p) is the same 

 for all substances. Hence to test laws I., II., III., and IY. 

 it is simply necessary to see whether (6) is true, as (6) is 

 identical with them. Now if (6) is true, it follows that the 

 ratio of the temperatures of two vapours to one another at 

 any pressure is the same as at any other pressure, or 



6 = kt (7) 



In fact, then, we can test laws I., II., III., and IY. by 



