474 



MOTION. 



the attitude of the annexed design by Flaxman 

 (Jig. 266), in which it will be seen that the 

 whole mass of the body lies posterior to the 

 vertical line a c b, passing through the base of 

 support, whereas the preceding theory shews 

 that in quick walking and running the swinging 

 leg never passes beyond the vertical d c, which 

 cuts the head of the femur. This figure has 

 therefore been drawn upon false principles. 



TABLE 12. 



A Table of fifty-six experiments on running 

 with various velocities. Space passed through 

 43.43 intt. 142'2504,/f^. 



From this table we see that the length of 

 step increases rapidly, whilst the duration va- 

 ries but very little ; and that the duration is 

 always equal to a half oscillation of a pen- 

 dulum. 



Duration of spring .. 0'2618 1 ,- 



T- n ir -i -. f difference 



Duration of half oscil-J ^ 



lation of pendulum i j 



Hence we perceive that the duration of the 

 spring is less than the oscillation of the le^ as a 

 pendulum by a very small fraction only, which 

 is probably due to muscular action. 



In quick running the length of step rapidly 

 increases, whilst the duration slowly dimi- 

 nishes; but in slow running the length dimi- 

 nishes rapidly, whilst the time remains nearly 

 the same. The time of a step in quick run- 

 ning, compared to that in quick walking, is 

 nearly as two to three, whilst the lengths of the 

 steps are as two to one, consequently a person 

 can run in a given time three times as fast as 

 he can walk. The velocity in running is usually 

 at the rate of about ten miles in an hour, but 

 there are many persons who for a limited period 

 can exceed this velocity. 



In the human race, however, the velocity in 

 running varies considerably, depending on 

 a variety of physical conditions, such as age, 

 sex, stature, muscular power, the nature of the 

 surface on which the progression is performed, 

 and the angle of elevation above, or depression 

 below the plane of the horizon. Man is ex- 

 ceeded in speed by many of the lower animals, 

 owing to differences in the structure of the 



locomotive organs, and the physical laws which 

 they obey. 



Leaping or jumping. This mode of pro- 

 gression is adopted by a great number of 

 animals; some of which resort to it only for 

 the accomplishment of a particular object, 

 others as a regular means of locomotion. 



In most of the orders of the animal king- 

 dom there are some species which transfer 

 themselves from place to place by a succession 

 of impulses, in air, in water, and on solids : it 

 is to the latter we shall confine our attention, 

 having already briefly mentioned the former in 

 the sections on flying and swimming. 



In leaping, the object to be attained is to 

 take the greatest length of step without refer- 

 ence to its duration ; and herein it differs from 

 running, in which the greatest steps are taken 

 in the least possible lime. 



The height to which animals of different 

 orders are capable of springing* varies, but, 

 according to Strans-Durckheim, all those in 

 the same order leap to equal elevations. 



Amongst insects, the Grasshopper and Cricket, 

 and in the order Felis, the Cat, the Leopard, 

 and the Tiger, all rise to the same elevations 

 above the positions of their respective centres of 

 gravity at the instant when their feet quit the 

 ground. 



This appears at first to be inconsistent with 

 the computations made on the proportion of 

 the force of muscles to the mass of animals of 

 different dimensions. If we select four diffe- 

 rent animals of the same order, in which the 

 dimensions of one kind are as 1, 2, 3, 4, 

 their weights will be as the cubes of these 

 numbers, or, as 1, 8, 27, 64 ; but since the force 

 of a muscle depends on the number of its 

 fibres, and therefore increases in the ratio of its 

 transverse section ; that is, as the square of one 

 of these dimensions, the muscular forces of the 

 animals will be as 1, 4, 9, 16, and the velocities 

 (supposing the muscles to act instantaneously) 

 will be as the forces divided by the weights,'or as 

 1, , ^, \, and the heights of the leaps being 

 as the squares of the velocities would be 

 as 1, .}, i, -,' 5 . Now, as they are all found to 

 arrive at the same height, this may be ex- 

 plained by supposing that the muscles do not 

 act instantaneously, but as constantly accele- 

 rating forces during thecontinuanceof the spring. 

 The force on an unit of mass in the Cat is to 

 that on an unit in the Tiger, as 1 to { ; and since 

 the dimensions of the latter are four times those 

 of the former, the tiger passes through four 

 times the space the Cat passes over, reckoned 

 from the beginning to the end of the time the 

 muscles act, until the animal quits the ground, 

 and therefore is elevated to the same height as 

 the cat.f 



From these principles we see the reason why 



* The spring is that portion of the leap which 

 takes place before the feet quit the ground. 



t Thus : Let ~ the space passed through 

 during the spring of the cat, /= the muscular 

 force employed in the time t of a spring, then, 

 by equation (3), 



s = 4/* 8 . 



Now, as the tiger passes through a space = 4s, 



