MOTION. 



459 



they may form the greatest base of support, has 

 been mathematically investigated by Parent 

 and Barthez. According to the latter, the tra- 

 pezium which forms the base of support will 

 be a maximum when the prolongations of the 

 lines drawn through the central line of each 

 foot and passing through the centre of each 

 heel form an angle of 38 56". 



The calculation of Parent is defective, from 

 its being based upon the hypothesis that the 

 foot turns as upon a pivot about its articula- 

 tion with the leg, instead of around the heel. 

 When the body stands erect upon both legs, 

 and presses equally on each, the legs will form 

 equal angles with the vertical line passing 

 through the centre of gravity; but if the two 

 legs form different angles with that line, the 

 pressure upon the legs will be unequal, and 

 will vary with the angles of inclination, 

 for example, in jig. 249, a d is perpendicular 

 and g i parallel to the horizon ; if a b 



Fig. 249. 



e - 



and a g represent the entire force exerted by 

 the legs to support the whole body, a d and a i 

 will be the corresponding portion of these forces 

 necessary to sustain the weight of the body, 

 and will also together represent that weight ; 

 and if a d and a i be found by experiment, the 

 absolute forces, a b, a g, will be found.* In 

 standing, the limbs serve merely to support the 

 body, and to preserve the centre of gravity at a 

 certain height above the plane of position, 

 within the base of support, which is a necessary 

 condition to prevent it from falling. In addi- 

 tion to these functions they translate the trunk, 

 during progression, from point to point, and 

 keep it in equilibrium, in all the varied move- 

 ments and under the action of all the extra- 

 neous forces incidental to locomotion. f 



* See Borelli de motu animal, prop. 138, p. 173. 



t When a man stands with his centre of gravity 

 at a vertical height H, ahove the plane of the hori- 

 zon, if his weight be I', then the amount of force 

 which he expends in order to stand is, according 

 to Poisson, equal to rn. Traite de Mcch. Paris, 

 1833, 688. 



Walking. In walking or running, the body 

 may be divided into two portions, namely, the 

 trunk, head, neck, and arms, which constitute 

 the burden that is to be borne, and the legs 

 which support and carry the burden along. 

 The former cannot, however, be considered as a 

 merely passive or dead weight, as the trunk 

 and arms contribute to keep in equilibrio the 

 forces acting on the centre of gravity during 

 progression. In walking, the trunk is carried 

 forwards with its major axis directed nearly 

 perpendicularly to the horizon, like a rod poised 

 endways on the hand. The power to keep the 

 trunk thus poised whilst it is moved forwards 

 is attained only after considerable experience 

 during the earlier period of man's career, when 

 his unsteady gait, numerous trials, and frequent 

 falls afford practical illustrations of the difficulty 

 of the process. Every movement of the legs, 

 arms, head, or trunk, as well as the bearing of 

 burdens in various positions, requires a compen- 

 sating movement of some other part, in confor- 

 mity to the theorv of parallel forces, to preserve 

 the whole in equilibrio; therefore, in order to 

 keep the supported parts poised on the rounded 

 head of either femur, whilst the body is trans- 

 ferred from one to the other, and carried forwards 

 in the air, either against or in the same direc- 

 tion as the wind, there must be a continued in- 

 terchange of compensating movements, and 

 these actions are placed under the controul of 

 the excito-motory division of the nervous sys- 

 tem. It is well known that when any portion 

 of a rigid body receives motion from a neigh- 

 bouring body, all the parts of the rigid body 

 will partake of the same motion, only when 

 the direction of the force passes from the point 

 of contact through the centre of gravity. If this 

 is not the case, as, for example, when the upper 

 extremity of the propelling leg acts on the 

 lower part of the trunk of the human body in 

 the erect position, the lower part would be pro- 

 pelled forwards and upwards, whilst the centre 

 of gravity of the trunk would be left behind, 

 and fall backwards ; but if this centre be in- 

 clined forwards at the beginning of the step, the 

 weight of the body and its required momen- 

 tum will propel it forwards and downwards ; 

 hence the resultant of the several forces will be 

 a force which propels the body forwards in a 

 direction which, by experience, is found to be 

 nearly horizontal : but there is also another 

 force which affects the trunk, namely, the re- 

 sistance of the air, which tends to turn the 

 trunk backwards, and must be counteracted by 

 the force of gravity, through the inclination of 

 the trunk forwards. The amount of this con- 

 stant inclination of the trunk must be estimated 

 by the resistance which it encounters from the 

 air in walking and running. It must therefore 

 be greater in rapid progression, because the 

 resistance of the air is then more powerful than 

 in more deliberate motion. Without this incli- 

 nation it would still be possible to preserve a 

 uniform position of the body in walking and 

 running, not, however, by the force of its own 

 gravity, but by means of the power of the mus- 

 cles, which connect it with the limbs ; but this 



