GREGORY, QUADRUPEDAL LOCOMOTION 279 



Applying this to Fig. 6, II, we see that in the horse, the muscles fig- 

 ured are inserted at more open angles of insertion (a, /?, y) than in the 

 mastodon or elephant and that their rotation components are therefore 

 relatively greater, the centripetal components relatively less. 



The foregoing principles were worked out independently by the writer, 

 but Luciani 36 gives similar principles for human locomotion. He states 

 that not all of the muscular force is available for the movement of the 

 skeleton, that this is only the case when the insertion of the muscle on 

 the bone reaches almost a right angle, as in the case of the masseters, 

 which can exert their whole strength in pressing the lower jaw against 

 the upper jaw. He says that generally, owing to the conditioning form 

 of the skeleton, the muscle is attached more or less obliquely, so that the 

 direction of its fibers makes a more or less acute angle with the long axis 

 of the bone. In all these cases, a great part of the total force of the 

 muscle is lost as regards movement. In every case, however, whatever 

 the form of the muscle or the size of the angle of insertion may be, by 

 resolving the total pull into its components, in accordance with the law 

 of the parallelogram of forces, one can determine how much of the total 

 pull is expended in the movement of the bone, assuming the other bones 

 to be stationary. Luciani 37 also shows that the more acute the angle of 

 insertion is, the smaller will be the component of rotation, and the nearer 

 the angle of insertion approaches a right angle, the greater will be the 

 component of rotation. 



Relations of speed of movement and angle of insertion. — Eeturning to 

 Fig. 2, we see that if DB contracts to DB', the point of insertion will 

 move from B to B'. If now the angle of insertion be increased to a and 

 db (equal to DB) contracts to db' (equal to DB'), then the point of in- 

 sertion moves only through bb', which is less than BB'. If the contrac- 

 tion time as well as the distance be constant, then B will move faster 

 than b ; that is, when the rate of contraction and length of muscle are 

 constant the speed of the insertion point varies inversely with the angle 

 of insertion. 



It is also evident that if the angle of insertion and other factors re- 

 main constant the speed of the distal end of a long bone will increase as 

 the point of insertion is moved toward the head of the bone. (Because 

 BC will be larger.) 



Variableness of the rotation component. — From Fig. 2, it will be seen 

 that the angle ab'd is somewhat greater than abd, that is, both the angle 

 of insertion and the rotation component increase as the muscle contracts. 



30 Physiologie des Menschen, Siebente Lieferung, p. 115. 



31 IUd., p 116. 



