ANIMAL MECHANICS. 



287 



Therefore, finally 



8 = - i 0.2065 = - 5.70 inches. 



The negative sign of § denotes, that the axis of rotation 

 of maximum work lies at the near side of the vertex O. 

 Draw PQ perpendicular to OX, so that 



OC = 5.70 inches, 



then C is the centre of the conic (59), and its minor axis, 

 PQ, is the axis of rotation, which would produce the maxi 

 mum work in the motion of the wing. 



In order to construct the conic, let us divide equation (59) 

 by sin j3 sin j3', and we obtain 



^w^ , = La:3 + Mx + N '' (63) 



where 



L = X + Y cot-)3 cot j3' - Z (cot j3 + cot /3 ) ; 

 if = (6 + b ) X - Z (b cot j3' + cot j3) ; 

 iV = bb' X, 



Substituting, in these expressions, the values already giver 

 we obtain 



sin /sin 0' = °- 2 ° 6 + 2 '3?5 * + 4 702. 



This equation gives us, when y = o, 



l \ = - 5.700 + 3.138 inches, 



