KUNGL. SV. VET. AKADEMIENS HANDLINGAR. HAND 47. N:0 4. 



29 



r.. /,(;■. V) e<«\ 



The diagram below graphically represents, for different values of >\ the three 

 functions 



>',/,.(<>. i r). ;-./,. (O. •_>:. v), vJ v (().:, r), 



and very clearly indicates that, for values ^ sensibly smaller than 1, 



rJ„(r.V) 



will converge towards zero for v=<x>, This convergency is the more rapid, the smaller 



■ :t _ ::::: :~:: ::: :: ~2 



















n q __ is __ ___ _ 2 



\j,j. \ 



















0.15 ----- - - - ^ - - - 



\S,'J -|--J- - ^ 















1 - > - C s «" 





C i \ v 31 





















05 Vo \ 







\'" J \^ **- 















^ ~f" 1 !■ "* ■■*■ . 



O i 2 3 4 5 6 7 8' 

 Fig. 3. 



i) is. In the limit of a very small *v (it appears that already D = 0,i is a very fair approxi- 

 mation) we obtain once more our primary solution of chapter B. This, of course, is a 

 necessary consequence, since then the impressing of the small velocity 



— c cos Kx . cos ot 



on the whole system cannot sensibly affect its geometrical configuration. 



It is also obvious that, if the ridge has a sufficient extension, c may well be quite 

 considerable without affecting very much the rapid decay of the coefficients of the higher 

 components. As for the series answering to the roots K v , the exponentials entering in 

 that series will certainly decrease rather slowly; however it should be remembered that 

 the general term contains the factor 



.J 



-i¥) 



