Man is always under the influence of gravitation, and therefore, his structure and function are related to it. The determination of the centre of gravity is one of the most important problem in the study of man from the mechanical point of view. Hitherto, several methods have been used to determine the centre of gravity statically, such as BORELLI'S (1677, a board counterpoised at the centre), REYMOND'S (1900, one lever and two fulcrums one of which is laid on the scale), etc. But, the fact that the centre of gravity is not a fixed point in the body but is constantly moving has been disregarded in the methods employed thus far. The centre of gravity has always been measured in the overlaying posture and we must seek another way if we wish to know the centre of gravity at any given posture.
From about thirty years ago, A. BASLER has been studying its characteristics. He asserts that it is affected even by the pulse and it is necessary, therefore, to use a swing; the subject being made to stand in a given posture with a constant force applied against the swing, as a result of which the angle of deflection will be directly due to the height of the centre of gravity and the weight of the subject. His method, I think, is superior to the old ones, but has some faults, for example, if the subject changes his posture even slightly, the influence over the angle of deflection is considerable, and is more than the change of the height of gravity centre that must be measured.
Our method is free of this fault. We use the swing method, not statically, but dynamically: if the physical pendulum is made to oscillate, its period (T) is exclusively due to the distance from the axis to the centre of gravity and the moment of inertia of the rigid body (1)-(2). Man's moment of inertia is, however, difficult to determine as well as the centre of gravity, and so some rigid body, of which both of these are known, is fixed to the pendulum. Again measure the period (T'), and you will find the distance to be obtained by eliminating the moment of inertia (3) -(4). The resistance of the air in proportion to the velocity and the friction of the bearings, which are attached to decrease the friction which operates to counter the direction of the velocity are both measured and found not to give rise to any need for correction of the results ((6), Fig. 6).
Such a complex computation as this causes necessarily considerable error in the result which is derived from each measurement. Formula (7) shows the relation of error and it is notable that the success of this experiment should depend on the measures of the T, T', and that accuracy should increase in proportion as T' is much more than T.
On the principle above explained, we measured the centre of gravity in several postures of one subject, and those in normal standings of 13 subjects. Though the sample size is too small to justify definite conclusions, the correlation between the relative value of leg length and that of height of the centre of gravity was relatively high, which is contrary to SCHEIDT'S statements. This will be a matter of future research.
