542 On the Effect of Impacts and Strains [July, (From the American Naturalist, July, 1881.) ON THE EFFECT OF IMPACTS AND STRAINS ON THE FEET OF MAMMALIA.1 BY E. D. COPE. THE principal specializations in the structure of the feet of the Mammalia may be summarized as follows: I. The reduction of the number of the toes to one in the Peris- sodactyla (horses, etc.), and two in the Artiodactyla (cloven feet). II. The second hinge-joint in the tarsus of the Artiodactyla. 1 Read before the National Academy of Sciences, April, 1881. Abstract. Some of the points of this paper have already been discussed in the Naturalist (April), but the present abstract contains additional matter. 1881.] on the Feet of Mammalia. 543 III. The trochlear ridges and keels at the various movable articulations of the limbs. These are as follows: i. Looking downwards— a, Intertrochlear crests of the humerus. ft. On the carpal end of the radius. Y' Metacarpals, distal ends. S. Tibia distally. e. Metatarsals distally. 2. Looking upwards— a> Radius distally. ft. Astragalus, edges. Y' Astragalus distally (Artiodaclyla). S. Phalanges (very weak). The following observations may be made respecting the struc- tures included under division III: The trochlear keels which look downwards are much the most prominent and important. Those enumerated as looking upwards are weak and insignificant, or of a different character from the down-looking ones. The latter are all projections from the middles of the ends of the respective elements. The up-looking are generally projections of the edges of bones. Such are the lateral crests of the astragalus, Fig. i. Fig. 2. Fig. i.—Right posterior foot of a species of Coryphodon from New Mexico, one- hnlf nat. size. From Report Expl. W. of iooth Mer., G. M. Wheeler, iv, PI. LIX. Fig. 2.—Right posterior foot of Aphelops viegalodus Cope, from Colorado, one- halt natural size. From Report U. S. Geol. Surv. Terrs., F. V. Hayden, IV, PI. cxxx. and the adjacent edges of the cuboid and navicular bones which 544 On the Effect of Impacts and Strains [July, cause the distal emargination of the astragalus in the Artiodac- iyla. The proximal ridges of the phalanges are very weak, and the concavities in the extremity of the radius cannot be called trochlear, as they are adaptations to the carpal bones. I. The reduction in the number of toes is supposed to be due to the elongation of those which slightly exceeded the others in length, in consequence of the greater number of strains and im- pacts received by them in rapid progression, and the complement- ary loss of material available for the growth of the smaller ones. This is rendered probable from the fact that the types with reduced digits are dwellers on dry land in both orders, and those that have more numerous digits are inhabitants of swamps and mud. In geological history it is supposed that the Perissodactyles Fir. 3. Fig. 4. Fig. 3.—Right posterior foot of Protohippus sejiinctus Cope from Colorado, about one-half natural size. From Report U. S. Geol. Surv. Terrs., h. V. Hayden, iv. Fig. 4.—Right posterior foot of Poebrotherium labiatum Cope, from Colorado three-fifths nat. size. From Hayden’s Report, iv, PI. cxv. 1881.] on the Feet of Mammalia. 545 (figures 2-3) originated from the Amblypoda, or primitive Ungu- lata (figure 1), which first assumed terrestrial habits, while the Artiodactyla (figures 4 and 9— 11), originating from the same order, long continued as mud dwellers ; as witness the hippo- potami and hogs of to-day. The mechanical effect of walking in the mud is to spread the toes equally on opposite sides of the middle line. This would encourage the equal development of the digits on each side of the middle line, as in the cloven-footed types. In progression on hard ground, the longest toe (the third) will receive the greatest amount of shock from contact with the earth. There is every reason to believe that shocks, if not excessive, encourage growth in the direction of the force applied. This is strongly suggested by the relations between the length of the legs and the rate of speed of animals; and the lengths of the teeth and their long-continued use. Certain it is that the lengths of the bones of the feet of the Ungulate orders have a direct relation to the dryness of the ground they inhabit, and the possibility of speed which their habitat permits them, or necessarily imposes on them. II. The hinge between the first and second series of tarsal bones in the Artiodactyla, may be accounted for by reference to the habits which are supposed to have caused the cloven-footed char- acter. Observation on an animal of this order walking in mud, shows that there is a great strain anteroposteriorly transverse to the long axis of the foot, which would readily cause a gradual loosening of an articulation like that connecting the two series of tarsals in the extinct Amblypoda. Any one who has examined this part of Coryphodon will see that a little additional mobility at this point would soon resemble the second tarsal joint of the hogs. In the case of animals which progress on hard ground, no such cross-strain would be experienced, and the effect would be to consolidate by flattening the fixed articulation. III. The trochleae. These prominences, which form the tongues of the tongue and groove articulations, exhibit various degrees of development in the different Mammalia. Those of different parts of the skeleton coincide in their condition in any one type of am- bulatory Mammalia, and so may be all considered together. This fact suggests strongly that they are all due to a common cause. They are all imperfect in the Rodentia and Carnivora (figures 5-6) (except the Leporidce, which are especially characterized by 546 On the Effect of Impacts and Strains [July, their great speed). Among ungulates they are very imperfect in the Proboscidea. The orders mention- ed all have elastic pads on the under sides of their feet or toes. The same is true of the lowest types of both the Ar- tiodactyla and Perissoaactyla, the hip- popotami and rhinoceroses. In the Ruminantia the trochleae are well de- veloped (figure io) with one ex- Fig. 5. Fig. 6. Fig. 8. Fig. 7. Fig. 5.—Distal extremity of tibia of Amblyctonus sinosus Cepe. Fig. 6.—Distal extremity of tibia of Oxytzna morsitans Cope. Both flesh-eaters and two-thirds nat- ural size. From Report Expl. and Surv. W. of iooth Mer., G. M. Wheeler, iv, Pt. II. Fig. 7.— End of tibia and astragalus of Archcelurus debilis. Fig. 8. — Femur of Nimravus gomphodus. Carnivora, one-third natural size. Mus. Cope. ception, and that is the distal metacarpal and metatarsal keels of the Camelidcz (figure 9). These animals confirm the probability of the keels being the effect of long-continued shocks, for they are the only Ruminants which have elastic pads on the inferior sides of their digits. That these processes may be displacements due to shocks long ■ continued, is rendered probable by the structure of the bones themselves. (1) They project mostly in the direction of gravity. Constant jarring on the lower extremity of a hollow cylinder with soft (medullary) contents, and flexible end walls would tend to a decurvature of both inferior and superior adjacent end walls. If the side walls are wide and resistant, the projection will be median, and will be prolonged in the direction of the 1881.] on the Feet of Mammalia. 547 flexure of the joint. (2) They fit entering grooves of the proxi- mal ends of corresponding bones. These will be the result of the same application of force and displacement, as the protrusion of the inferior, commencing with a concavity (.Elephas); becoming Fig. 9. Fig. io. Fig ii. Fig. 9.—Part of anterior foot of Procamelus occicientalis from New Mexico. From Report of Capt. G. M. Wheeler, Vol. iv, Pt. II. 10.—Metacarpals of Cosoryx furcatus from Nebraska, two thirds natural size; a, anterior face; b, posterior; c, proximal end; d, distal end. Fig. ii.—Left forefoot with part of radius of Poebrotherium vilsoni Leidy, from Colorado, three-filths natural size. From Hayden’s Report, iv. more concave (Fig. 7), and becoming finally a groove. (3) When the dense edge of a bone, as in the case of the lateral walls of the astragalus, is presented upwards, a groove is produced in the 547 On the Effect of Impacts, etc. [July, down-looking bone ; e. g., the lateral grooves of the distal end of the tibia. (4) When the inferior bones are the denser, the superior articular face yields; e. g., the distal end of the radius to the first row of carpals (Fig. 11). (5) The metapodial keels commence in the lower types on the posterior side of the distal extremity of the bone. This is partly due to the presence there of a pair of sesamoid bones, which with the tendons in which they are developed, sustain and press on the lateral parts of the extremities, and leave the middle line without support. Published June 27, iSSl.