136 SULLA RIFRAZIONE 



dF 



=1 (r'-\- F' ) cos r — r' Y sen r — n Y'= , 



=: (>• — r Y+ Y ) cos r — {r Y+ r +2r Y ) sen r — ìiY =0 , 



dy 

 d"F 



dy 



d'F 

 dy' 



4^ =•■"-* 



dy'' 



d^F 



d'F 



: {r'"- 3 rr" Y- r - 3 r ' r'+ Y'") cos r - (r'" Y+ 3 r'r"+ 3 r" Y 



-r' Y+ dr' Y")senr -n Y"'=0 , 



^ ,•' r '" r- 3 r "" r- 6 r''»-"- 1 2 r' r" Y'+r' '' Y- 6 r'' r"+ F"') cos r 



- (»•'" r+ 4 »•>'"+ 4 »•"■ r'+ 3 r" '— 6 r' V" r+ 6 r" Y"- r' - 4 r' ^ Y' 

 + 4 r' F'") sen r — n F"' = , 



: (/ _ 5 ,-V"' F-1 r'r'" F-10 r"r"'— 20 rr" F'— 1 5 »-V"'— 1 5 r"* F'+l r'V" F 



- 30 r' r" F"+ »•' ' -t- 5 r' ' F'- 1 r^ F"'+ F") cos r - (r'' F+ 5 rV'^'+ 5 r'" F' 

 + 10 rr'"— 10 r'V'" F+ 10 r'" F"— 15 r'r"''Y— 10 r' V" 



- 30 r'' r" F'+ 1 r" Y"'+r''' Y- 1 >•' ^ F"+ 5 r' Y'") sen r - n F"= , 



: (,-^>_ 6 r'r" F— 1 5 r'r'" Y— 1 5 r'V'"— 30 r'r" F'— 1 r '"' F- 60 r' r"r"' 



- 60 r'V" F'+ 20 r'V'" F— 60 rV" F"— 1 5 »•" + 45 j-'V"" F- 45 *•"' Y" 



+ 60r"r"Y'+15r'''r"-60r'r"Y"'-r'^Y+lbr''Y"-lbr''Y"+Y'")cosr 

 -(r^'F+6r'r^+ 6 r"'F'+ 15rV^- 15-r'%-'^F+ 15 r'^ Y"+ 10 r'"' 



- 60 r'r'r'" F- 20 r' 'r'"- 60 r'%-'" Y'+ 20 ■/" F'"- 15 >•"' F- 45 r'\"' 



- 90 r'r"'F'+ 15 »-'V"F- 90 r'V" F"+ 15 r" F"'+ r'^+ 6 r' F' 

 -20r''F"'+6r'F^)sen»--nF'"=0 , 



- — = (r'"- 7 rV"'F-21 rV'F- 21 r'V^-42 *VF'- 35»-"'i-'"F- lOSr'rV"' 



- 105 r'r'" Y'+ 35 r'V'" F— 105 rV F"~ 70 rV" '— 70 r'''F' - 105 r"V"' 

 + 210 r' V"r"' F- 210 r"r"' F"+ 35 r V"'+ 140 r' V'" F'- 140 r'/" F'" 



+ 105>-V"'F+ 105 j-'V"V 315r'V"'F'- 105r""F"+ 210r'^r"F" 



- 21 /-'\-"F-105 /-VF^-r' - 7 r'''Y'+ 35 r''* F'"- 21 r'^Y''+ F"") cosr 



- (r"" F+ 7 rV'''+ 7 r"' F'+ 2 1 /r"- 2 1 »-'\-^ F+ 2 1 r" F"+ 35 r"'r" 



- 105 r'r'r''' Y- 35 r' V'"- 105 r'V'^F'+ 1 5 »-'^F"+ 20 r" F'" 

 ' — 70/r'" F— 105>-"V"'F— 210>-'V"F"'— 420»-'rV"'F' 



.,3 



+ 35 r' r" Y- 210 r r" F"+ 35 r" F'^- 105 r'r"'- 105 r F' 

 + 105 r\" Y— 315 rV" F"+ 21 r' V"+ 90 r'V"F'— 210 /r"Y"' 

 + 21 /'FM- 21 r'^F"- 35 / F'"+ 7 >•' F"'-r''F) sen r-n F""=0. 



