314 ANIMAL MECHANICS. 



showing that the equilibrium is always stable, and 



« , 1. 1230 ^ 



S = 2 =3.65. 



0-1537 



The actual distance of the socket from OP' is j^nds of an 

 inch. 



(d.) Wing of the Macaw. — The following measurements on 

 the wing of the Macaw are made in 32nds of an inch : — 



Wing of Macaw. 



Angle. 



l-V 



/ sin 9 



V sin 9 



o° 



42 



+ 39 



+ 9 



10 



46 



+ 33 



+ 6 



20 



54 



+ 27 



+ 4 



30 



70 



+ 21 



+ 2 



40 



96 



+ 9 



+ 1 



50 



106 



- 10 



— 2 



60 



114 



- 32 



- 3 



70 



127 



- 59 



- 4 



80 



143 



-89 



- 8 



90 



112 



- 9i 



- 10 



From these measurements, the following Table is calcu- 

 lated : — 



Wing of Macaw. 



Angle. 



1 



{I + V) sin 9 



IV sin 2 9 





l-V 



l-V 



o° 



0.02381 



+ r. 1428 



8.36 



10 



0.02174 



+ 0. 8480 



4-3° 



20 



0.01852 



+ °-574i 



2.00 



3° 



0 01415 



+ 0. 3286 



0. 60 



40 



0 01041 



f 0. 1042 



0. 09 



5° 



0.00943 



— 0. 1 1 32 



o.ig 



60 



0.00877 



- 0. 3070 



0.84 



70 



0. 00787 



- 0. 4960 



1.86 



80 



0. 00699 



-0 6783 



5.00 



90 



0. 00893 



- 0. 9018 



8.12 



Sum, 0-13062 



0-5014 



31-36 



