— 209 



ax- 



y=ce 



V 



or 



So we have the rotation-volume as follows: 



X=ll 



Vs=7rly^dx=7rc^ I 



l<a— — 



e * ax 



2ali~ -T— 



Aa 



c'e 



1 +Aah+ ^^-J— ' — P"(fc) {n+\-a)\n^ 

 h 13"+' -J 



or 



where «=2a/i--— , i3=2a/i + 4^ and A;=-^ 

 /i fe i3 



Va=''^jy''dx=7icyi,j e ^ ax 



■I) 



'\+4a'h+ "^^^--I^L- ?"(&') (n+l-«')p] 



a^'/j - 



26' 



Aa' 



where a'=2a'/i- ^^' , /3'=2a'ft + -,— and /c'=-^ 

 h h p 



Empirically it will be determined that 



«<1, /3>1 and -"-<1 or «'<1, i3'>1 and -^<1 



i8' 



and 



or 



1 -i'_! — p" (fc) ( 71+ 1 -«) i?i ^ 



/3''+^ 



1-2" 



1 



P 



-P''(k')in + \-a')\nJ=0 



So we have 



2ah- 



Vs== . -c-e 

 Aa 



or' 



9 '1 2'' 



V.'=fl'» 



Aa' 



L h 



From the second equation we have 



Vs 



« An' 



Aa' 



26' 



h J 



