Relation to Pteeews and Temperature. 



507 



0-— (1— Y^/k Y,.+p{"A L— Pi)—/*) JcV e \ so that in case of 

 constant volume, temperature varies linearly with pressure, 



small intervals of variation presupposed. The rigorous deduc- 

 tion from {fi) and Mendeleer* equation is kV e 6—— (1— Y c ) + 

 (l+vpji which is linear In proportion as vy> is small com- 

 pared with 1. In §33 it was shown that the relation of 6 and 

 j> is probably linear throughout great intervals. It follow- 

 that (6) is insufficient for large ranges of pressure. Finally 

 regarding Mendeleef s equation, it follows, if and 6 be two 

 consecutive intervals of temperature, the former measured from 

 zero, that Y = l/(l-l\fi,), V ' = l/(l-kJ(0 o +0)), and F = l-t- 



Y e '- V o =(l+k*00 o )/{l-k0) i if k=k /{l-k o e o ). Thus obser- 

 vations may be referred to any convenient temperature as a 

 point of departure. 



35. Computation of hyperbolic constants. — Applying equa- 

 tion (3) to the observations in § 15 to 2-L, I obtained the con- 

 stants given in table 29. Clearly u must be some function of 

 fi ; but the observations are now too crude to indicate its 

 nature. If the ratios of » to p. be found either graphically or 

 by computation, the consecutive values show no discernable 

 march or grouping. Hence I assume this ratio to be constant, 

 and add its mean value in the table. As before the ether and 

 alcohol points at 310° are to be excluded, and the discrejiancy 

 is apparent in the ether point for 185°. 



Table 29. 

 Hyperbolic constants. Direct computation. 



e 



//xlO 6 



i-xlO 6 



d 



fix 10 6 



vxlO 6 



e 



/ux 10 6 



vxlQ* 



Ether 







Toluidine 







Paraffine 







29 



169 



830 



28 



56 



58 



65 



85 



191 



65 



228 



1030 



65 



70 



413 



100 



111 



475 



100 



353 



1570 



100 



81 



110 



185 



181 



845 



185 



1028 



3870 



185 



146 



801 



310 



368 



1510 



A.lcohol 







310 



401 



1730 



Thvmol 







28 



87 



243 



Diphenylamine 







28 



68 



465 



65 



111 



276 



65 



61 



162 



65 



69 



157 



100 



182 



1630 



100 



69 



285 



100 



99 



553 



185 



348 



1755 



185 



114 



613 



185 



162 



715 









310 



215 



889 



310 



465 



2000 



Mean v//z = 4 # 5. 



36. Mean constants. — Utilizing the ratio v//i=4'5, I con- 

 structed the next table. The agreement as a whole is not as 

 good as were the data for # and a in § 30. 



37. The isothermal band. — With the constants of table 30, I 

 computed the actual isothermals, in the way suggested in § 32. 

 Expansion being directly observed, the only hypothesis intro- 

 duced is equation (6). The results so obtained are to be tabu- 

 lated in the manner shown in tables 23 to 28, with which they 



Am. Jour. Sci— Third Series, Vol. XXXIX. Xo. 234.— June, 1890. 

 33 



