290 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



°> = T 



{dH/dt) 



tfdpm 



provided only that both derivatives are taken in the same direction 

 from the point. Griessmann uses the equation over the whole plane, 

 but makes certain experimentally deduced assumptions which do not 

 now seem to be j ustified. 



The equation is likely to be most useful along the saturation line 

 where dH/dt and dp/dt are both well known. Unfortunately n is not 

 as yet well known at such low temperatures, and it will be interesting 

 to see whether, in the development of the subject, Griessmann's truism 

 turns out to be more useful for the computation of C p at saturation 

 from /* or of /a from C p . 



The only use that will be made of the equation in this paper is to 

 deduce from it the well-known theorem, usually attributed to Rankine, 

 that at ordinary temperatures C p at saturation must be numerically 

 greater than dll^/dt* At most temperatures this condition is so 

 overwhelmingly fulfilled as to be of no value. At 0°C. it requires 

 that C p at saturation be as great as 0.44. Now if Knoblauch's satura- 

 tion curve is continued to temperatures below 100° C, this condition 

 will be found to require, either that the curve passes a minimum 

 between 100° and 0°, or that it must lie somewhat higher between 

 100° and 150° so as to approach smoothly the right value at 0°. The 

 existence of such a minimum has several times been suspected as a 

 result of other indirect computations, and its experimental verification 

 would be a matter of some interest ; in the mean time the other alter- 

 native seems more probable, especially as 

 it brings Knoblauch's values of C p at 

 atmospheric pressure into better, agree- 

 ment with Regnault's. Additional con- 

 firmation of this decision will be found on 

 pages 293 and 300. 



The third of the methods referred to 

 above for connecting C p with ju. is appar- 

 ently new. It involves an equation which, 

 like Griessmann's, is merely a manipula- 

 tive identity or truism. It can be devel- 

 oped as follows. In Figure 10, let ab and 

 cd be parts of two throttling curves on the usual tp diagram, the corre- 

 sponding values of the total heat being H and H + A#. Then at 

 the pressures p and p + &p we have 



40 This follows at once from the fact that both n and Cp are known to be 

 positive. 



p P+Ap 



Figure 10. 



