Location of the vector of jaw muscle force in mammals

Previous work has suggested that the third molar lies just in front of the point where the resultant vector of jaw muscle force, estimated from dissections, intersects the tooth row. This point meets the jaw such that the vector is 30% of jaw length from the jaw joint. Thus, the vector divides the jaw in the ratio of 3:7 when measurements are taken perpendicular to the vector. In practice, however, distances along mammalian jaws are typically measured on an easily determined line such as a line from one end of the tooth row to the other. The position of the jaw joint is then projected onto this line. As a rule, such a line is not perpendicular to the vector and so the distance from the projection of the joint, out to the rear of the third molar (and the vector's intersection), is different in different mammals. Rarely is this distance 30% of total jaw length. However, when the location of the vector's intersection is measured along the tooth row, this position varies directly with the inclination of the vector; a vector inclined posteriorly intersects the tooth row far from the projection of the joint and an anterior vector's intersection is relatively close. Only a vector perpendicular to the line from one end of the tooth row to the other intersects at 30%. This obvious point suggests a way to test the above hypotheses when the inclination of the vector is not known exactly. The predicted relationship between the distance to the molar, as a percentage of the total jaw length, and the approximate inclination of the vector derived from muscle weights (posterior or anterior depending on whether the temporalis or the masseter/pterygoid, respectively, is dominant) was observed in a sample of 46 different mammals.