( 782 ) 



thermometer. Besides the above mentioned values of Lt, which were 

 directly found from the observation it contains the corrections deter- 

 mined according' to the serial formula VII. 1 and those calculated 

 by Callendar and Bkrthelot. Moreover in the last column the 

 corrections, which may be calculated from the experimental values 

 adjusted with VII. H 2 according to formula (4) are given for a 

 comparison. 



Besides the corrections derived from this investigation for the zero- 

 point-pressure of 1000 m.M., also the values found by Berthelot 

 and Callkndar are represented on the plate. The three curves have 

 been indicated by I, II and III in the above mentioned order. Also 

 II and III refer to a zero-point-pressure of 1000 m.M. 



The values derived by Callendar and Berthelot by means of 

 the law of the corresponding states appear to deviate systematically 

 from the experimental ones. With regard to the corrections according 

 to VII. 1., in the derivation of which formula agreement in the 

 region of the equation of state (between 0° and —217° for hydrogen) 

 treated here, was not aimed at, we may observe that a modification 

 is required for VII. 1 to give as good an agreement as possible also 

 in this region. In the first place this agreement would require that 

 for the calculation of VII. 1 those values were assumed for the 

 critical quantities of H 3 which follow from the data of Comm. N°. 97 rt . 

 They are pu = 15 atms. and T k = 43°. This value of T k would 

 considerably increase the corrections given in table XVII according 

 to VII. 1. 



§ 5. Formula to derive the temperature directly from the obser- 

 vations with the gas thermometer of constant volume. 



We suppose that the correction for the ditFerence in pressure at 

 the mercury meniscus and the thermometer-reservoir in consequence 

 of the weight of the thermometer-gas is applied to Ht , and that 

 it is so small that it may be neglected for the small volumes. 



The fundamental formula for the reduction is l ) : 



which may also be written in the form : 



pv = A T (l i-^P+C^p'^ (5) 



We start from this latter formula. The equation for the gas-ther- 

 mometer (cf. formula (1) of § 5 of Comm. N°. 95 e ) becomes now : 



!) Here v is expressed in the theoretical normal volume and hence At = 

 - 1 +0.0036618 S. We call the value for 0° C, at which 6—0, At . It is 1. 



