MOTION. 



471 



their steps will equal the time of oscillation, and 

 the case is nearly the same in a slower pace. 

 We observe, therefore, that when children and 

 grown persons, or tall and little men, are walk- 

 ing together in the pace most easy and natural 

 to them, they move in a different time. It is 

 true the movements of the legs, like those of 

 any other member, may be accelerated by means 

 of the muscular force and made to move 

 quicker than when they are merely impelled 

 by their own gravity in swinging from behind 

 forward, but when so continued an exercise of 

 muscular power is required, such an unnatural 

 pace cannot long be sustained. 



In the estimate already given of the forces 

 which have an influence in walking, it will be 

 observed that as long as the force of the exten- 

 sion of the legs in a vertical direction upwards, 

 is equal to that of gravity upon the body acting 

 vertically downwards, the centre of gravity will 

 move in a direction perfectly horizontal ; but 

 experience shows that as soon as the force of 

 the extension of the supporting leg ceases, the 

 centre of gravity falls below the horizontal path 

 in which it was previously moving; but the 

 instant the other leg stands perpendicularly it 

 will rise again to its former level. The mathe- 

 matical theory of walking proves that from the 

 figure of the human machine there must of ne- 

 cessity be a sinking of the centre of gravity in 

 order that progression may be accomplished. 

 By varying the time of the sinking of the body 

 at the end of each step, the effect of the resist- 

 ance of the air and other extraneous influences 

 which would disturb the horizontal velocity of 

 the trunk, are compensated. In a favourable 

 wind, when it travels at a greater velocity than 

 the walker, it is necessary he should increase 

 the time of sinking to counteract its effect, and 

 preserve a mean uniform motion. 



The application of mechanical principles 

 does not accord with slow as it does with that 

 of quick walking, for the former is too much 

 under the control of the will of the walker, and 

 the limbs are not suffered to swing freely by 

 their own gravity as in quick walking, in which 

 this volition diminishes, according to Weber, 

 at least when the slightest exertion is continued 

 for any length of time, and it is in this condition 

 alone that theory and experiment nearly ap- 

 proximate. We must, however, remember that 

 the control exercised by the muscular system 

 over the limbs in slow walking is a new force 

 which animals are enabled to interpose in 

 order to vary the effects which result from the 

 physical laws in operation during locomotion,* 

 and by no means refutes the theory of the 

 influence of those forces which affect, not only 

 the locomotion of animals, but the motion 

 of matter universally. 



Running. The laws which regulate running 

 in many of the lower animals, such as qua- 

 drupeds and birds, are nearly the same as in 

 Man. It will therefore be necessary to enter 

 into the details of this movement in reference 

 to the latter only. 



The principles upon which walking and 

 running differ. In running as in walking it 

 may be considered as a fundamental law that 



the same motions of the body recur after each 

 double step ; and that both legs exercise equal 

 and alternate actions in these movements. In 

 running the object is to acquire a greater velo- 

 city in progression than can be attained in 

 walking. In order to accomplish this, instead 

 of the body being supported on each leg alter- 

 nately, the action is divided into two periods, 

 during one of which the body is supported 

 on one leg, and during the other it is not sup- 

 ported at all. The latter condition constitutes 

 the principal difference between these two 

 modes of progression. When the body is pro- 

 jected upwards so as to swing freely in the 

 air, the hinder lee: must be raised from the 

 ground before the advanced swinging leg has 

 reached the vertical position ; hence, in run- 

 ning, the duration of the step is less than the 

 half-duration of the oscillation of the leg, be- 

 cause, when the advanced leg has reached the 

 vertical position and is again placed on the 

 ground, the hinder leg has already begun to 

 describe a portion of its arc of oscillation. By 

 these means the duration of the step is di- 

 minished, whilst the length is increased, both 

 of which tend to augment the velocity. The 

 length of the step is consequently greater than 

 that side of a right-angled triangle, whose 

 hvpotheneuse is the extended leg, and the 

 other side the elevation of the centre of gravity 

 above the ground. In running the step may 

 be divided into two periods; the first, the time 

 t, during which the body is supported on one 

 leg, and the second, the time T t, during 

 which it is not supported at all. 



Forces employed in running. The forces 

 which act in running are the same as in walking; 

 first, extension ; secondly, gravity ; thirdly, 

 resistance. In running, a horizontal move- 

 ment of the centre of gravity is not practicable 

 as in walking, for although the extensor power 

 might be so regulated that the centre should 

 continue at the same elevation so long as the 

 body poised on one leg, it would evidently fall 

 during the time it was left unsupported. Now, 

 as it is found after the whole time of a step 

 to have neither sunk nor risen, and since no 

 instantaneous elevation of the centre of gravity 

 takes place between the termination of the pre- 

 ceding and the commencement of the following 

 step ; it follows that during the time t, it 

 must ascend just as much as it sinks during 

 the time -r t. The effects of gravity and 

 resistance have been sufficiently explained in 

 the theory of walking.* 



The conditions for regular progression in 



* By an analysis based on data similar to those 

 for walking, Messrs. \Veber have deduced the 

 following equations which express the general 

 laws of running. 



(h 

 (A 



S 



t 



T 



(29) 

 (30) 

 (31) 



(32) 



