2(52 



ANIMAL MECHANICS. 



by the angle SOI becoming a right angle, and the gastro- 

 cneme muscles are acquiring their maximum effect upon the 

 ankle joint, by the angle GBY becoming a right angle, that 

 both these muscles act at a considerable disadvantage upon 

 the knee joint; for the angles CI 0 and CGB become very 

 acute, when the angles SOI and 6ri?Fpass through right 

 angles. Still, both hamstring and gastrocneme muscles tend 

 to flex the knee joint, in every position of the legs ; an effect, 

 which would be disastrous to the combined movement of the 

 muscles of the hip and ankle, when the Tiger walks, rims, or 

 springs upon its prey. Therefore, the flexing effect of these 

 muscles »pon the knee, is always counteracted by the extend- 

 ing effect of the rectus femoris, and its allies, upon the same 

 joint ; and these antagonist muscles are called into action, to 

 an extent necessary to keep the knee joint from bending, or, 

 in some motions of the leg, to an extent that actually extends 

 the leg upon the thigh. 



It is very interesting, therefore, to observe that the rectus 

 femoris, which is the natural ally of the hamstring and gas- 

 trocneme muscles, acting in the line H.rf., is at right angles 

 to the lever cR, at the same time that the angles SOI and 

 GBY, of the hamstring and gastrocneme muscles, pass 

 through 90 0 . 



In Propositions A and B, we have considered the case of 

 two bones, lying in the same plane, and united by a quadri- 

 lateral sheet of muscular fibres ; one bone being supposed 

 fixed, and the other bone compelled to turn round an axis of 

 rotation perpendicular to the plane. We nave now to ex- 

 amine the more complex case in which the moveable bone 

 turns round some axis lying in the plane of the two bones ; 

 an action, by which the plane quadrilateral becomes a gauche 

 quadrilateral, and the muscular fibres form the surface known 

 as an hyperboloid of one sheet. 



I shall first suppose the axis of rotation to be perpendi- 



