( 503 ) 



Tii order to examine how a barotropic tangent-chord firs! makes 

 its appearance on the plait on decrease of T, we point out that with 



extension of the plait from 7&, at first — remains positive all over 



d.t 



the liquid branch of the connodal curve, so that at first we have to 

 look for the greatest value of 6 at the plaitpoint, where we shall 

 denote its value by 6 r i. 



When, however, on decrease of T the plait extends over the if'- 

 surface, this need not continue to be the case, and we may tind 



da 



— alternately positive and negative. This is immediately seen when 

 d & 



we notice that this must always be the case when the plait extends 

 all over the \\>- surface. 



If with decrease of T the maximum value of 6 more and more in- 

 creases, and J 7 has fallen so low, that the maximum of # somewhere 



jr 

 in the plait has just ascended to — , then at this 1 the condition for the 



barotropic equilibrium i\, =: v e will be satisfied just for the corre- 

 sponding tangent-chord, and only for this tangent-chord. The higher 

 barotropic limiting temperature is then reached. On further decrease 

 of temperature the barotropic tangent-chord will then split into two 

 parallel barotropic tangent-chords, the higher and the lower tangent- 

 chord, which at first continue to diverge with further falling tempe- 

 rature, so that the higher barotropic tangent-chord may even vanish 

 from the plait through a barotropic plaitpoint, and then, at a lower 

 temperature, make its appearance again through a barotropic plaitpoint 1 ). 

 At still lower temperature it follows from the broadening of the 

 plait in the direction of the y-axis, which at sufficiently low tempe- 

 rature renders the occurrence of a barotropic tangent-chord impossible, 

 that the maximum of 6 falls again, and the barotropic tangent-chords 



n 

 draw again nearer to each other. At #,„ a , r =- the tangent-chords 



coincide again, and the lower barotropic limiting temperature is reached. 

 At lower temperatures u g = i'i is no longer to be realized, and r f , 

 is always ]> n. 



Figs. 2, 3 and 4 represent different cases schematically. In the 

 spacial diagram of the if'- sui 'fa ces for different" temperatures the 

 barotropic tangent-chords supplemented with the portions of the con- 



!) The latter supposes that TtJT^ is not very great; in accepting the contrary 

 we would come in conflict with the supposition that the longitudinal plait does 

 not become of influence. Moreover we preliminarily leave out of account the case 

 that both barotropic tangent-chords follow one anotl er in disappearing or appearing 

 through a barotropic plaitpoint. [Added in the translation]. 



