( 449 ) 



so tliiit on the isotherm of 20° a fourth point ih acvinired, wiiich 

 renders the slope of tlie i)i\i line a great deal more certain (ef. the 

 coiK'iusion of § J of ('Omni. N". 101''^). Then the cak'nlatioii of /l^ and 

 Ha was i-epeated, and by the aid of these corrected c(»efiicients the 

 isotherm of iY V. was ai^ain caleuhited, and this cah-nhition hy 

 approximation was continued till it caused no longer any change. 

 In this way we found for 20^' C. (for />=r().0()()432) : 



y)rj.,,, = 1.07273 4- 0.0005837 </.,„ -f 0.000000125 r/.^;-' . . (3) 

 With this formula the corrections have l)een calculated for the 

 determinations of isotherms. For the rest the lal ter wei-e treated as 

 ill the preceding coniniiinications. 



§ 4. IiuJlvidual vlrijil co e f fie 'tents . 



We may avail ourselves of the data of table I in order to derive 

 the coeflicients .4.i and /i.i by the aid of the method of least squares. 

 (J A was assumetl according to formula (2) of the [)reL'eding §. For 

 every isotherm j)rA,d = o Wf^'' calculated, and this \'alue was added 

 to the others as if it concerned a new obser\ed point. This calcula- 

 tion was eifected hy the aid of the value .l.(„ = 0.99949, which 

 may l)e derived from the value for the coefti'L'ieurs /it and C'a for 

 (F iinally olitained in the calculation by apju-oximatiou from the 

 conclusion of the [)receding §. Table 11 contains the virial coeflicients 

 and at the same time the ditferences between the given pv-^ 's and 

 the calculated ones. These ditferences are arranged according to the 

 ascending densities. So the lirst column of dilfereuces refers to 

 pf'A,d = o, the others to the data of table 1 in the above succession. 



The calculation of the /J i 's is still uncertain, because for Ca 

 estimated \alues have been assumed. Determinations of y>/\i at greater 

 densities, which wil! render an inde])endent determination of C'.i 

 possible, are in preparation. 



That tiie estimations of C'a cxre not too inaccurate, may be made pro- 

 bable as follows. For 100' follows from table II /i.t „jj^ = 0.000673. 

 On the suppositions on which van dek Waals' equation rests, the value 

 of h may be derived from the value for two temperatures of 

 B=RTb — a with /J =rr /j,i ( J ij and then /> = 0.000432 is found, 

 which does not dilfer much from the value 0.0005, which was first 

 assumed by way of estimation on other grounds. Though the calcu- 

 lation followed here is very uncertain, yeX the found value was 

 [u-eferred to the tirst estimated one, and for this reason the calcu- 

 lations which were tirst made with 0,0005, have been repeated with 

 this new estimation. The ditferences of the results lie within the 

 limit of errors of observation. 



