MancJiesier Memoirs, Vol. I. (1906), No. 8. 25 



i + c/'" +<::/'■'■■" +... 



and I + Cj(?"''" + C/"''^" + . . . 



In this case the velocity {qc^"') is given by 



and 



,./._ (i-4>-"")' r 



In this case the point of inflexion in the surface 

 approaches the crest continually as Z, approaches, but 

 is finitely less than, unity,* and the character of the 

 singularity at the crest when ^— i is clearly indicated by 

 the formula. 



We may now obtain the expression employed by 

 Mr. Mitchell. For 



UV 



= r{(i-^.-)*(i-C.-)j ^ 



2kK %\X\ku 



may be written 



w( .-y \V_/ .-^.-- \Vi 



<lVi-{<-'V Vi -&■'■" 7 / 

 _^,| (,-y">!(.-^.-")i ^ 



\ 2 dii- ' 



* To a first approximation the position of the point of inflexion is given 

 by cos kit = ^. 



