12 PROCEEDINGS OF THE NATIONAL MUSEUM vol. 123 



the new resultant force is F'. (Clock directions herein always refer 

 to the skull as viewed from its left side.) The rotational effect of 

 force F' on the quadrate is P. It is clear that variation in the angle 

 of the depressor mandibulae can increase or reduce P (fig. 7a) and that 

 the muscle-ligament combination could even produce retraction of 

 the upper jaw (fig. 76). The neutral angle of the muscle is the angle 

 at which contraction of the depressor mandibulae produces no motion 

 of either jaw. Bock's force analysis (1964, fig. 9) is incorrect because 

 he neglected to transfer the backward component of force of the 

 depressor mandibulae (H in fig. 6 of this paper) to the jaw articulation 

 along with the upward component (V) . It is not true that the pres- 

 ence of the ligament would cause protraction upon contraction of the 

 depressor mandibulae under all conditions, as implied by his analysis; 

 rather, the force and amount of protraction obtained and the amount 

 of depression of the lower jaw as well depend upon the two variables 

 mentioned above, and these forces could reach zero (the neutral state) 

 under conditions that are not very different from those existing in 

 birds. The conditions producing a neutral angle of the depressor 

 mandibulae are not found in birds when the jaws are closed because 

 such conditions would prevent opening of both jaws. Birds in which 

 the geometry of the jaw-support system departs most strongly from 

 a neutral arrangement probably represent special adaptations for 

 coordination of the jaws through the depressor mandibulae. 



Just as components V' and H' are altered by variations in the angle 

 of F, their effect upon protraction varies with changes in the relative 

 lengths of the force and work arms (B and A) when the muscle angle 

 remains the same. If B is increased relatively more than A, V 

 increases but H' remains the same, with the result that P increases. 

 By contrast, P may be reduced to zero if B becomes relatively 

 shortened. 



Were the fine of force of the depressor mandibulae to parallel the 

 long axis of the quadrate (regardless of its angle to the long axis of 

 the mandible), its protraction force (P) would be zero only when B 

 equalled A. In birds, B is always greater than A and the depressor 

 commonly is nearly parallel to the long axis of the quadrate with the 

 result that a protraction force exists. The force of protraction can be 

 increased by relative lengthening of the retroarticular process of the 

 mandible or by shifting the angle of pull of the depressor muscles in a 

 counterclockwise direction, or by both. The amount of protraction 

 possible depends upon the relative lengths of A and of B, of the 

 quadrate, and of the muscle fibers in the depressor mandibulae, as 

 well as the geometry of the palate and upper jaw. A relative increase 

 in A with respect to B would increase the degree of protraction with 

 a given contraction of the depressor muscles, at the same time re- 



