( 447 ) 



«limeiisions of the |)iezonieter and by the iiuuiometer. The utmost 

 limits of tlie density are 25 and 54 times the normal one. The 

 piezometer aiid fnither auxiliary apparatus were perfectly the same 

 as have served for (he determinations of C. Braak and me (see Comm. 

 N«. lOO Jan. 1908) with hydrogen at 0° C. and 100° C. The satis- 

 factory results obtained then, enhance at the same time the relia- 

 bility of the measurements considered now. 



§ 3. Besu/ts for />r^ . 



The subjoined table contains the results of the determinations. The 

 first column gives the muuber of observation, the second the tempe- 

 rature measured above 0° C. on the absohite scale, the third the 

 pressure in atmospheres, the two following ones the product pvi , 

 and the density r/.i , in which the volume of the gas r^ is expressed 

 in the normal volume (that at 0° C. and 1 atmosphere) and the 

 density dj in the normal density (that at 0° C. and 1 atmosphere). 

 (Compare the corresponding tables of the aboAT meiitioned determi- 

 nations of isotherms of hydrogen). 



The calculation of these i-esults was made as follows : 



First the points of th(^ isotherm of 20^ C. were calculated, (cf. 

 also §8 of Comm. N". 79 (April 1902)) and the coefficients .1^ and 

 /ij of the curve 



1>''A= ^ij+ H (1) 



'•A VA' 



were determined by the 3 points by the aid of the method of least 

 srpiares. For 6j a definite value was assumed, the densities being 

 too small for this coefficient to be determined with sufilicient certainty. If 

 Ave write van dek Waals' etpiation with the second correction for 

 the size of the molecules in the form : 



RTb~a 5 h'T/r 



where r is the volume of the gas under the pressure p at the abso- 

 lute temperature 7, expressed in the theoretical normal volume (see 

 Comm. N". 71 § 3) and if we put the value of Aa at 0^ ^j„ = 1, 

 \\hich approximation is allowed for oni- purpose, we find (cf. Comm. 

 N". 7J § 31 for the value T^^ of C'.i at T 



CA^='UBT}r, 



where 7/ = 0.0036619. The vabie of h was first estimated at 0.0005 

 (cf. the note to § 6 of Comm. K". 96^^ Jaji. 1907), afterwards at 

 0,000432, see § 4. With the coefiicients Aa and /i^ obtained for 20° 



30 

 Proceedings Boyal Acad. Amsterdam. Vol. X. 



