I.—PHYSIOLOGY. 163 
jump as well as a flea he could easily clear the top of St. Paul’s Cathedral. 
It is a matter only of elementary mechanics to show, on the assumption 
that a woman can project herself vertically with a velocity proportional 
to that with which she can project herself horizontally, the constant of 
the proportion being the same as for the case of a man, that both the high 
jump and the long jump in the two sexes should be in the ratio not of the 
velocities but of the squares of the velocities. The maximum range and the 
maximum height of a projectile vary as the square of the velocity of 
projection. Thus it is right to compare, for men and women, not the height 
of the high jump or the distance of the long jump, but the square roots 
of these quantities, if we wish to study their relative performance in 
jumping as compared with running. This being 80, we find that the high 
jump of a woman, as measured by its square root, is 87 per cent of that 
of a man”; the long jump, measured in a similar way, is 81-5 per cent. 
These compare closely with their relative performances for very short 
times of running, where a woman, as shown above, can run 84 per cent. 
asfastasaman. It is amusing to find simple mechanics explaining such 
_ apparent differences between the sexes. 
The Characteristic Oxygen-Requirement-Speed Curve. 
The curves given in fig. 2 define the economy with which movements 
are carried out. By such means can be shown the amount of energy 
_ required, in terms of oxygen used, in order, say, to run or swim for a minute 
at any given speed. The curves will vary largely from one individual to 
another. Some men move more efficiently than others at all speeds: 
A may be moreefficient at one speed than B is, but less efficient at another. 
For most kinds of muscular exercise the characteristic curve of fig. 2 is 
ascertainable by experiment. In some cases, as in swimming, experi- 
mental difficulties might be considerable, at any rate at higher speeds. 
It is obvious, however, that such a curve must exist for any person 
performing any kind of continuous muscular exercise. In it we have 
_a characteristic of that given individual for that particular form of work. 
Skill. 
Some people are much more skilled than others. To a large degree, 
of course, the skill and grace associated with athletic prowess is natural 
and inborn ; to a large degree, however, it can be produced by training 
and breeding. All the movements required in the violent forms of mus- 
alae exertion here discussed are rapid ones, far too rapid to be directly 
and continuously subject to the conscious intelligence : they are largely, 
indeed mainly, reflex, set going by the will but maintained by the interplay 
of proprioceptive nervous system and motor apparatus. The nature of 
-mouscular skill cannot be discussed here; possibly, however, above all 
other factors it is the foundation of athletic prowess. Such skill has a 
physiological basis as it has a psychological aspect. It is a fit subject 
for discussion alike by physiologists, psychologists, students of physical 
ain hanes 
2 It would really be fairer to compare the heights jumped, less the initial heights 
of the centres of gravity, say 3:1 feet and 2°8 feet respectively. This gives 
 2°2/3°51 = -63 as the ratio of the heights, of which the square root is ‘79, a close 
agreement with the long jump. 
M 2 
