ANIMAL MECHANICS. 



317 



Difference between Calculation and Observation in the position 

 of the Socket in the Wings of Birds. 



Bird. 



Axis of maximum 

 instability. 



Axis of minimum 

 stability. 



Albatross, . . . 

 Wood Pigeon, . . 

 Heron, .... 

 Macaw, .... 

 Pheasant, . . . 



o. 10 inch. 

 0.14 „ 

 O.14 „ 

 0.05 „ 

 0. 20 ,, 



0. 30 inch. 

 0.27 ,, 

 0. 10 

 0.41 

 0.15 » 



Mean Error, 0.126 inch. 



0.246 inch. 



The differences between calculation and theory shown in 

 the foregoing Table (one-eighth and one-quarter of an inch) 

 are not greater than should be expected in such a class of 

 observations. It may be noted, also, that the mean error in 

 the calculation of the axis of maximum instability (which is the 

 more important of the two axes) is only half the mean error 

 in the calculation of the axis of minimum stability. 



We have seen by Prop. E, applied to the shoulder and 

 hip joints of various animals, that muscles intended to produce 

 the maximum work by rotation round axes perpendicular to 

 their plane are incapable of producing a rotation round any 

 axis lying in their plane. Let us now inquire how muscles 

 like those of the pectoral muscles of birds, intended to produce 

 the maximum work round an axis lying in their plane, behave 

 with regard to the axis of rotation perpendicular to their plane 

 drawn through the socket of the shoulder joint. 



It will be readily seen, by reference to the proof given of 

 equation (44), Prop. B, that it is independent of the shape of 

 the bones, whether straight or curved ; so that if k, 6, 0, be 

 given, there are an infinite number of muscles capable of pro- 

 ducing the same work. This equation — 



Work done = 2&Sw sin ^ sin 0, 



