[mechanical] The center of gravity of a body is that point about which it will be balanced though placed in any position, hence it is the center of parallel pressures. It may be determined experimentally by suspending the body in different successive positions and hanging a plumb line against the face. The common point of the numerous intersections of the plumb line will correspond with the center of gravity. In regular figures or solids the center of gravity corresponds with their geometrical center. The common center of gravity of two bodies is in a point which divides the distance between their individual centers of gravity in the inverse ratio of their weights. The common center of gravity of more than two bodies combined in one system is found by first obtaining the common center of any two of them, and then obtaining the common center of those two with the third, and so on till all are included. [Horner, J. G. ; Dictionary of Terms Used in Mechanical Engineering; The Technical Press, Ltd., London, England, 1960]
"notes which are produced by the two primes, 3 and 5. As the quadrant contains all the angles which give the different proportions in form, so does the ratio of 1:2, or the area of an octave, contain all the different notes in music. The ratio of 1:2 corresponds to unity, and, like the square and the circle in form, admits of no varieties. Half the length of a string gives an octave when the string is homogeneous and uniform; if the one half has more gravity than the other, the center of gravity of the whole string gives the octave. The ratio of 1:2 rests on the center of gravity. [Scientific Basis and Build of Music, page 27]
"An elongated uniform body, e.g., a dressed lath of pine, has three primary centers - the center of gravity, the center of oscillation, and the center of velocity. The center of gravity is the center of the body; the center of oscillation is two-thirds from the end as the point of suspension; the center of velocity is at two-thirds of one-third from the end; i.e., at two-ninths from the end as the point of suspension.
"This elongated body suspended at the end, or at one-third from the end, the oscillations are the same. The one-third above the point of suspension so balances the two-thirds below that the oscillations are performed in the same time for both suspensions. When it is suspended at two-thirds of the one-third. i.e., one-ninth of the whole length above the center of oscillation, one-ninth above balances two-ninths below; the oscillating part is thus, as it were, one-ninth shorter than at the center of oscillation, and gives rise to the center of velocity." [Scientific Basis and Build of Music, page 92-93]
"The two poles are, therefore, poles of still Magnetic Light around which the divided electric pairs can manifest their light of motion. The two poles, thus divided, have within them the desire to be united as one, by uniting the two divided pairs of conditions as one. In this manner the two poles which have united, become the common center of gravity of the whole gravity shaft of the mass controlled by it." [Atomic Suicide, page 182]