[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]
But let us proceed with our development, for we need another fifth, a lower one, a subdominant for our minor scale. Well, let us divide A5 by 3 and we have D1 2/3, the root of the lowest fifth; and if we divide A5 by 5 we have for our middle to this fifth F1, and this is F just as we find it at the major start, and identical in quantity in both major and minor. But let us examine the D1 2/3. It is not easy to compare D1 2/3 with D27 of the major; let us bring it up a few octaves by multiplying by 2. This will not alter its quantity, but simply give us the same quantity in a higher octave, in which we may more easily compare it with the major D1 2/3 multiplied by 2 is 3 1/3; multiplied again by 2 is 6 2/3; once more by 2 it is 13 1/3; and once more by 2 it is 26 2/3. Now we can compare it with D27 of the major, and we find this strange fact, that it is a little lower than the major D. The two D's are at the center of the dual system, but the center of the system is neither in the one D nor in the other, but as an invisible point between them, like the center of gravity in a double star; for the minor D is pushed a little below the center, and the major D is pushed a little above the center of the two modes of the system. [Scientific Basis and Build of Music, page 32]
So the dual system of Music revolves round a mathematical point which is in none of its notes, but in the empty space between the two D's. Like the earth, it is hung upon nothing. This is an exceedingly interesting musical phenomenon. In that comma of vacant space is music's center of gravity.
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 at 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. [Scientific Basis and Build of Music, page 92]
When a uniform dressed lath is held at the center of gravity and struck, it vibrates freely with a low tremor; when held at the center of velocity and struck at the center of gravity, it vibrates freely, and goes into large sections. But if it be struck at two-thirds of one-third from the other end, its own center of percussion, it has not the least tendency to vibrate. But if it be held at the center of velocity, and at its own center of percussion at the other end, and struck at the center of gravity, these two places will become points of rest, and the lath will move freely in all the other parts. [Scientific Basis and Build of Music, page 93]
"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]
In oscillatory motion these centers act conjointly, but not simultaneously; but in vibratory motion these centers act simultaneously, and on each side of the center of gravity. [Scientific Basis and Build of Music, page 93]
are always when they have returned to the side from which they were started. The Pendulographer, also, when writing the beautiful pictures which the musical ratios make when a pen is placed under the control of the pendulums, always finds his figure to begin again when the pendulums have finished their period, and have come for a fresh start to the side from which the period began. This confirms our author's definition of an oscillation of a pendulum. Fig. 3 is an illustration of the correct definition of a Musical Vibration, as also given in this work. Although the definition of an oscillation is not identical with that of a vibration, yet on account of their movement in the same ratios the one can be employed in illustration of the other as we have here done. Fig. 4 is a uniform rod suspended from the end as a pendulum; it will oscillate, of course, at a certain speed according to its length. In such a pendulum there are three centers related in an interesting way to the subject of Music in its three chords - subdominant, tonic, and dominant, which roots are F, C, and G. The center of gravity in the middle of the rod at 2, suspended at which the rod has no motion, corresponds to F, the root of the subdominant, in which there is the maximum of musical gravity. The center of oscillation at 3, which is one-third of the length of the rod from the end, is like the root of the tonic whose number is 3 in the genesis of the scale from F1. In this point of suspension the oscillations are the same as when suspended from the end at 1. The point at 9 is at a ninth from the center of oscillation. Our author discovered that, if suspended at this point, the pendulum had its highest rate of speed. Approaching the end, or approaching the center of oscillation from this point, the rate of speed decreases. Exactly at one-ninth from the center of oscillation, or two-ninths from the end, is this center of velocity, as Ramsay designated it; and it corresponds in some sort also to the root of the dominant G, which is 9 in the genesis of the scale from F1; its rate of vibration is nine times that of F1. The dominant chord is the one in which is the maximum of levity and motion in music. [Scientific Basis and Build of Music, page 105]
This plate sets forth the essential duality of the musical system of vibrations. It is a remarkable fact that the numbers of the vibrations of the major mode are the numbers for the string proportions of the minor mode; and vice versa, the string proportions in the major are the numbers of the vibrations in the minor. We have, however, to see that we use the proper notes and numbers; we must know the secret of Nature. This secret rests in the duality of the notes, and begins from the two D's. The center of gravity of the musical system of vibrations is found in the comma space between the two D's as they are found in the genesis of the two modes. In these two D's the vibration number and string proportions are nearly identical. Starting from this point as the center of gravity in the [Scientific Basis and Build of Music, page 118]
"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]
The speed with which light presumably travels is 186,400 miles per second. The distance between stars is so great that the speed of light is computed as light years, for the distance computed by lesser units of time would yield figures so great that they would be meaningless.
Light only seems to travel. It is but one more of the countless illusions caused by wave motion. Waves of the ocean seem to traverse the ocean but they only appear to do so, for waves are pistons in the universal engines, and pistons operate up and down. Wave pistons of light, or of the ocean, operate radially and spirally inward and outward, toward and away from gravity.
Waves of light do not travel. They reproduce each other from wave field to wave field of space. The planes of zero curvature which bound all wave fields act as mirrors to reflect light from one field into another. This sets up an appearance of light as traveling, which is pure illusion.
The sunlight we feel upon our bodies is not actual light from the sun. What actually is happening is that the sun is reproducing its own condition on the earth by extending the reproductions out through cold space into ever enlarging wave fields until those reproductions begin to converge again toward our center of gravity into ever smaller wave fields. The heat we feel and the light we see are dependent entirely upon the ability of the wave fields to reproduce the light and heat, and that ability is conditioned upon the amount of moisture in the atmosphere.
If there were no moisture in the atmosphere, our bodies would carbonize from the heat thus reproduced. One cannot consistently think of that heat as direct rays of the sun, for that same sunlight was intensely cold during its reproduced journey through the immensely expanded wave fields of space between the sun and earth.
The light and heat which appear to come from the star or sun have never left the star or sun.
That which man sees as light and feels as heat are the reproduced counterparts of the light and heat which are its cause.
The rate of vibration in a wave field depends upon its volume. Vibration in a wave field means the pulse of interchange between its compressed core and the space surrounding that core. A slow vibration in a large wave field would cool one's body, or even freeze it, while fast pulsing interchange in extremely small wave fields could burn one's body.
A lens which multiplies light and heat toward a focal point which sets paper on fire merely compresses larger wave fields into smaller ones. The rate of vibration increases for the same reason that the planets nearest the sun move much faster in their small orbits than those which are far away from the sun. Kepler 's law covering the speeds of planets will apply to rates of vibration in wave fields as appropriately as with the movements in the solar system. [Walter Russell, The Secret of Light, pages 169-171]