10 PROCEEDINGS OF THE NATIONAL MUSEUM ™l. 123 



special adaptions rather than typical conditions. To better under- 

 stand these complex kinetic relationships, three main questions must 

 be answered: (1) How does the postorbital ligament produce coordina- 

 tion of the two jaws? (2) How can the jaws be alternately "coupled" 

 and "uncoupled"? (3) What factors produce coordination in addition 

 to or in the absence of the postorbital ligament? The first question 

 is dealt with in the following section, and the second and third, under 

 "Coordination and Independence of Jaw Action." 



Angle of the Depressor Mandibulae 



Zusi (1959) postulated that the depressor mandibulae could cause 

 protraction of the upper jaw if part or all of the muscle pulled at an 

 angle (forward and upward) with respect to the long axis of the 

 quadrate. He stated that the forward component of force with 

 respect to the quadrate would be transmitted to the quadrate through 

 the lower jaw. Bock (1964, pp. 16, 17) disagreed, saying that the 

 only point of relevance was whether or not the pull of the depressor 

 had a component directed forward along the axis of the lower jaw, 

 and he pointed out that such a forward component would diminish 

 or disappear as the lower jaw was depressed. In addition, he indicated 

 that any analysis of muscle angle should include the postorbital 

 ligament when it is present. Here I shall present such an analysis 

 in detail because it is of considerable importance for understanding 

 adaptations of the kinetic mechanism, whereas the effect of muscle 

 angle on a simplified system of weightless and frictionless levers as 

 presented by Zusi (1959) and Bock (1964, pp. 16, 17) is probably 

 irrelevant to the situation in the avian jaw, even in birds lacking a 

 postorbital ligament. 



To explain the relationship between the postorbital ligament and 

 motion of both jaws through force analysis, it is necessary to discuss 

 two important variables diagrammed in figure 6: first, the relative 

 lengths of the segments from the mandibular attachment of the post- 

 orbital ligament to the center of rotation of the jaw articulation (A) 

 and from the ligament's attachment to the insertion of the depressor 

 mandibulae (B); and second, the angle of the depressor mandibulae 

 in relation to its neutral axis. The force of the depressor mandibulae 

 (F) can be replaced by two components, H and V, running in line 

 with and vertical to the force arm B. To determine the effect of 

 these components on the quadrate, one must transfer both compo- 

 nents, H' and V, to the jaw-quadrate articulation. The clockwise 



VXB 



rotational component V is increased by the amount V= — — 



whereas the counterclockwise component H' remains the same, and 



