300 



ANIMAL MECHANICS. 



From these measurements, the following results were ob- 

 tained by calculator* : — 



Wing of Pheasant. 



Angle. 



1 



[t + I ) COS v 



11 COS 6 U 





I -I' 



l-V 



o° 



0. 07692 



6. 231 



15300 



5 



0. 02500 



2.750 



45-9° 



IO 



0-01515 



i.515 



29. 00 



'5 



0.01351 



1 .6892 



28.38 



20 



0. 01000 



1 • 35°° 



20. 06 



2 5 



0. 00833 



1.2500 



16.88 



3° 



0. 006 14 



1.1717 



15 20 



35 



0.00547 



1.0765 



13.07 



40 



0.00503 



i . 0704 



11. 16 



45 



0. 00463 



1. 0231 



9 77 



Sum, 



0.17018 



19.5805 



342.42 



Hence, the axis PQ, passing through the centre of the Conic 

 (66), lies at a distance from the vertex 0, equal to — 



1 I 9-5 8o 5 



57-53- 



0.1701c 



The actual distance of the axis ST is 51. 

 In equation (66), 



3/ 2 .= Lac 2 + Mx + N t 



the axis OX will not intersect the conic in real points unless 



IP ~ aLJY 



be positive. This, therefore, becomes the condition for the 

 existence of axes of unstable equilibrium, and for the existence 

 of the ellipse of unstable equilibrium. We are, therefore, bound 

 to ascertain that this condition is fulfilled in the wings of the 

 birds already investigated. The following Table shows that 

 they all satisfy this test : — 



