284 ANNALS NEW YORK ACADEMY OF SCIENCES 



gives a relatively high moment of power (proportional to W) to the 

 calf muscles and a relatively low "moment of resistance" (proportional 

 to Va') to the great pressure of the shaft of the limb upon the astrag- 

 alus. A considerable part of this ''moment of resistance" is also sub- 

 tracted by the supporting effect of the great pad of elastic tissue under- 

 neath the foot. oSTo doubt the specimen from which Fig. 3, II, was 

 drawn should have been mounted with the feet more nearly vertical; 

 this would greatly shorten Va' and further increase the advantage of 

 m X bV. As the plantar pad is raised from the ground, more weight is 

 thrown on the toes, but, at the same time, they are brought further back 

 almost beneath the astragalus, thus reducing Va' to a minimum, so that 

 the load decreases as the muscles contract. This arrangement not only 

 compensates for the fact that the greatest absolute force of a muscle is 

 developed when it is stretched to its full psysiological length, but it also 

 permits the muscle to perform a greater total quantity of work than 

 would be the case if the load were increasing instead of diminishing 

 (p. 280). 



Similarly, in the horse, the greatest "moment of resistance" is when 

 the foot is fully flexed forward (which is at the instant the foot touches 

 the ground) ; the action of the extensor muscles is thus suddenly checked; 

 this conditions physiologically a corresponding and sudden increase in 

 the available energy (p. 277). By the raising of the heel the moment 

 of resistance ("W X BA'), as in the case of the elephant, also decreases, 

 i. e., the load diminishes; but in the elephant, the motion of the foot is 

 relatively slow and the acceleration increment of the stride (p. 275) is 

 therefore slight, whereas in the horse the motion of the foot is very 

 rapid, and the acceleration increment (through the high velocity im- 

 parted to the relatively light body by the spring-like extension or open- 

 ing of the angles at the stifle, hock, fetlock and pastern) is very great, 

 so much so that at least three of the feet are off. the ground during a 

 great portion of the time. In brief, short feet (as in the Proboscidea) 

 slightly bending at the ankle, raise a heavy load through a short distance 

 with a minimal acceleration increment of the stride; long feet (as in 

 the horse), sharply bending at the ankle, throw a smaller load a long 

 distance, with a maximal acceleration increment. 



Metatar so- femoral ratios.* — That in cursorial animals the hind foot 

 is long as compared with the femur, while in graviportal animals the 



*° The investigation of limb- and arch-form and proportions, and especially the estab- 

 lishment and significance of definite ratios between the limb segments, were suggested 

 by Professor Osborn and taken up conjointly by him and the writer in the Eocene sec- 

 tion of the Titanothere Monograph; the following observations on limb ratios are in 

 part a preliminary publication of the joint results attained. 



