( 460 ) 



It is llicn easy to niiticijiale. and it is confiniied l)v tlic calcula- 

 tions, that all these quajilities r", ,r" and 5 with the exce[)tion of 1;, 

 are of tiie same order with each other and with t' \ on the contrary 

 not t\ but 7^" is of this same order. 



22. Taking this into consideration the first connodal relation : 



-T— = ^ — (06) 



yields at first a})proximation : 



log (.^•"+è^i) - -^ (2r'-3>c') (r" + 7i) = % (.."-ë7i) - ^ (2y'-3>c') (^"-7^) . (G7) 



or also, subtracting on eitlier side log .v" : 



or, as — is a small quantity of the order of 7^, we get after deve- 

 lopment ijito series and division by 7j : 



^ = i-(2y'-3x').f" (69) 



4 



in which we shortly point out that this formula passes into formula 

 (40) in the plaitpoint, and further that it leads immediately to for- 

 mula (24) of the descrij)li\e part. 



In the same way the second ') connodal relation : 



■ ?^ = ?- (70) 



yields at aj)proximation: 



-4(2y'-3x')(.."-§-7i)+^(/-x')(."-7/').v,-" (71) 



4 2 



or, after reduction and division by 7j : 



1) We must here have recourse to the terms of the order t'^ or tf, as all those of 

 lower order cancel each other. For the sake of clearness we have kept (v" + 7^) 

 and also (v" — 7j) together, tliougli it is evident, that we may write e.g. for {v" + 7^)^ 

 at once 7^^^ on account of the difference in order of v" and i]. 



