358 Prof. AdamS on the Application of Screiv-Blades 



= ^©V-T ( q cos Odd— 1 tan- 1 q cos Odd 



-f (X cot 7 - ^ f cos 2 log (1 + q*)dO 



+ (X cot y — — ) j cos 3 . tan -1 qdO k 



M = ip / w 2 r 5 T' (¥ ^ + (W cot 7 cos 0i0 



- f| (1 -3X 2 cot 2 y cos 2 (9) log (1 + q*) dd 



- f (3-X 2 cot 2 7 cos 2 0) . X cot y cos 6 tan" 1 gtf0 



" ©7 [ f ? cos ^ + r cot y cos2 e log ^ + g2 ^ 



- ( (1 -X 2 cot 2 y cos 2 0) cos 6 tan" 1 §<?# J 

 + i.^ r2 Jcos 2 01og(l + 9 2 )^ 



H — ^ . X cot 7 1 cos 3 tan -1 j.d^ 



+ j X cot 7 . g cos &/0— I X cot 7 . tan -1 q . cos &/0 



+ 2 (x cot 7-— )[Wcos 6d6— j tan" 1 g cos 0.do\ 

 + \ (\ cot 7- — )(3X cot 7- — \ fcos 2 6 log (1 + q*) d6 



+ Xcoty(Xcot7 \ A cos 3 6 . tan -1 qdd k 



These equations for R and M will apply to all cases by giving 

 different values to X, y, and the limit of 0, and by putting q = k 

 if any portion of the screw-blade of width kr be cut away, — re- 

 membering that the radius of the wheel = r cot 7(1 +X), and 

 that the axis of the screw-blade is at a distance equal to \r cot 7 



