( 504 ) 



nodal eumes between the lower and the higher tangent-chords form 

 together a closed surface, which bounds the barotropic region. 



If on the other hand 6 max = $ p i remains, till it has reached or 



71 .T 



exceeded the value , and if not a second maximum value for B ]> — 



occurs on the plait, a barotropic plaitpoint will occur at the higher 

 barotropic limiting temperature, whereas at lower temperature a 

 single barotropic tangent-chord on the plait indicates the equilibrium 

 with Vg = vi'. With decreasing temperature this barotropic tangent- 

 chord will at first move along the plait starting from the plaitpoint, 

 but at lower temperatures it will return, and finally (the occurrence 

 of a longitudinal plait being left out of consideration) it will disappear 

 from the plait through a barotropic plaitpoint at the lower barotropic 

 limiting temperature. In this case the barotropic region is bounded 

 on the side towards which the plait extends by barotropic tangent- 

 chords, on the other side by the portions of the connodal curve which 

 are cut off. 



It follows from the above that — when the occurrence of barotropic 

 tangent-chords on the ip-surfaces for a definite pair of substances is 

 attended by the occurrence of barotropic plaitpoints — if Tu > TtpU 

 {higher baratropic plaitpoint temperature) or To <[ Tb p u lower barotropic 

 plaitpoint temperature there always exists at the same time a higher 

 and a lower barotropic tangent-chord ; if Tbph > Tu > T bp n there 

 exists only one barotropic tangent-chord. 



The nature of the barotropic phenomenon for He and H 3 may 

 serve for arriving at an estimation of the critical temperature of He. 

 According to the investigation of one of us (K. See Comm. N°. 96 c.) 

 it is probable that the appearance of a single barotropic tangent- 

 chord for He — H 3 at the temperature of boiling hydrogen would 

 point to T/cHe < about 2°, whereas on the other hand when TkHe 

 is higher, a higher and a lower barotropic tangent-chord is to be 

 expected. Further that, as was already observed in Comm. No. 96 a. 

 (Nov. '06) a barotropic tangent-chord can only appear in the gas- 

 liquid-plait when very unusual relations are satisfied between the 

 properties of the mixed substances, which for the present will most 

 likely only be observed for He and H 2 . 



Whether it is possible that more than one barotropic region occurs, 

 and whether one or more barotropic tangent-chords can move from 

 the plaitpoint past the critical point of contact, is still to be examined. 

 Also whether it is possible that the lower barotropic limiting tem- 

 perature descends lower than Tk„ so that fig. 5 might be realised. 

 With regard to these questions too it is only of practical importance to 



