( 777 ) 



For the calculation of these corrections at a definite temperature 

 we might start from the individual virial coefficients in the development 

 into series of the equation of stale (cf. Comm. N". 71, L 901), which 

 we have derived in § 12 of Communication N°. 97". The results 

 obtained in this way show really a regular course 1 ), in spite of the 

 small number of points on the isotherms. 



However, we wished first to adjust the results of the separate 

 isotherms by general formulae of temperature. Both in this case and 

 in general it is very difficult to succeed in this by application of 

 one of the equations of state 1 drawn up in a finite form. Very 

 suitable for such a purpose is the general development into series 

 (or more strictly speaking, development into a polynomial), which 

 has already been mentioned frequently. We chose for this the 

 form VII. 1 (cf. the footnote to § 12 of Comm. N°. 97"). The 

 adjustment takes place by calculating for every isotherm modifications 

 in B and C, AZ? and AC, which we call individual Ll\ and AC, 

 with an approximate value of the correction to the absolute scale, 

 by then representing the values of AC by a general formula of the 

 temperature, and by computing new values for L\l> by successive 

 approximation in such a way that the value for the correction on 

 the absolute scale corresponds to the assumed value of 7'. Finally 

 also the values of LB were represented by a general formula of 

 the temperature. 



If we put the new values of B and C oblained by the aid of 

 these corrections, which special values we denote by VII. H. 2 . 1 in 

 the polynomial of state, then this represents at the same time the 

 determinations of isotherms of Comm. N°. 70 at 20° very satisfactorily, 

 and those of Comm. N°, 78 at 0° and 20° by approximation. 



By means of these general expressions the reductions on the absolute 

 scale have been carried out. 



If B and Care known there is another way to derive the absolute 

 temperature from the observations with the hydrogen thermometer, 

 than by applying the corrections which lead from the hydrogen 

 scale to the absolute temperature scale. In the calculation of the 

 temperature from the observations we may namely take at once into 

 account, that the gas in the thermometer does not follow the law of 

 BOYLE-CHARLES, but that pressure and volume are connected in the 

 way, as is indicated by the development into series with the corrected 

 values of i> and 6'. The formula which may serve for this purpose, 

 is given in § 5. 



i) Only the isotherm of — 135 .7 1 gives a deviating result. (See the conclusion 

 of § 12 of the preceding communication). 



