Bel at ion to Pressure and Temperature. 



497 



inferences as to curvature may be obtained. In table 20 I 

 have entered the two constants in question, supposing that 

 y e =l(yxv/V—?np — nj)% where y Q is a thousand times the 



volume decrement at pressure p. under conditions of constant 



temperature 0. 



Table 20. 



Quadratic constants. 



Substance. 







10 3 x in 



10 6 xn 



Substance. 



e 



10 3 x m 



10 ,; xn 



Ether 



310° 





... 



Diphenylamine 



310° 



197 



92 





185 



776 



990 





185 



113 



54 





100 



340 



346 





100 



64 



3 





65 



224 



170 





65 



62 



12 





29 



167 



107 



Caprinic Acid. 



185 



196 



125 



Alcohol 



310 



_ - — 









100 



116 



46 





185 









65 



92 



27 





100 



178 



209 





30 



71 



5 





65 



111 



28 



Paraffine 



310 



349 



320 





28 



87 



20 





185 



177 



110 



Palmitic AcicL 



310 



315 



267 





100 



110 



43 





185 



161 



93 





65 



83 



9 





100 



100 



36 



Thymol 



310 



435 



484 





65 



88 



25 





185 



159 



85 



Para-Toluidine 



310 



387 



404 





100 



97 



40 





185 



141 



81 





65 



69 



2 





100 



81 



6 





28 



67 



26 





65 



69 



25 













28 



56 



3 











Compressibility increasing inversely as the first power of 



the pressure binomial. 



27. Transition to exponential constants. — These data show 

 that compressibility increases at a rapidly accelerated rate with 

 temperature, and that compressibility m and the datum for 

 curvature n, are intimately related. This suggests the proba- 

 bility of a fundamental relation between y Q and p, independent 



of the material operated on. § 38. In case of alcohol and 

 ether at 31 0°, quadratic constants are manifestly impossible ; 

 for the maximum would lie within the field of observation. 

 This is to some extent true for ether at 185°. Rejecting these 

 exceptional cases, and considering the relation of m and n 

 separately for each substance and collectively for all, it appears 

 that a relation 2n=b(m—a) is available for trial. Since 

 y=?np—np^ y or dy/dp—m(l — 2np/m), replace m by # and 

 2n/?n by «, for the sake of distinction. Then inasmuch as the 

 quadratic equation applies more accurately in proportion as p 

 is small, it may be nearly replaced by dy/dp — d-/\\-\-ap\ whence 



y=.ln(\+ap) ' a . (2) 



This equation has an advantage over the other, since it does 



