354 Prof. Adams on the Application of Screw-Blades 



=ip t c0*r 4 {2ksm6-klog e {l+k 2 )(6 + %sm20)-2tan-nsmd , 



+ 2£ 2 tan- 1 k (sin 0-£ sin 3 6) ) 

 = i py-r* \ (k- tan" 1 k) x -68404--Hog e (1 + P) x -67046 



+ k* tan- 1 kx -65737} 

 = \?^ I* 3 ('22801 - '67046 + -65737) 



-yfc 5 (-13681 --33523 + -21912) + &c.} 

 = i /0y o)V{Fx -21492-^x -0207}. 

 The moment on the two floats becomes 



1 pph* {k?0 + 3(k - tan" 1 k) sia 6- log e (1 + /c 2 ) x 6 



+ |log e (1 + £ 2 )(0 + J sin 2<9) +\ tan" 1 k (sin 0-£ sin 3 (9) 



-(l+^)[(^-tan-^)2sm^ + ilog e (l+A; 2 X^ + isin2(9) 

 -f \ tan- 1 £ (sin 6— J sin 3 0)] 



+ |(1 + 2£) 2 [log e (l +/; 2 )(0-Hsin20) + 2tan- 1 £(sin0-isin 3 0)] j. 

 = ip i ft)V{(^- tan- 1 £)(sin<9-4£sin 0) +(£ 2 -log e (1 + £ 2 )) x 



- i£log e ( 1 + F) (0 + isin20) + p 2 log e (l + * 2 )(0 + isin20) 

 4-^tan- 1 k (sin Q-\ sin 3 0)} 



= i, /ft >v{(f - J)(l-4*) sin0 + **- g_J) ( + i sln2 0) } 



+ £ (0 + i sin 20) + (>- ^(sin 0--^ sin 3 (9) } 



= i / o i 6)V{F(-11401- -33523 -f -32868) 

 + k 4 { - -45604 + -17453 + -33523) 



- £ 5 (-06840 - -16761 + -10956) } 



= i/o i o) 2 r 5 {A: 3 x -10746 + k 4 x -05372 -& 5 x -01035}. « 



Hence the resistance on a pair of floats 



= i / j / ft) 2 r 4 {-513256~(l + 2X:) x -234563-i(l -4F) x -259202 



-£ 3 x-21492 + Fx-0207} 

 = i^«)V{-149092-^x -469126 + A: 2 x-518404-Fx '21492 



+ & 5 x-0207}. 



