The breaking down or splitting into discrete quantities from an harmonic state or condition such as white or invisible light refracting it into its constituent or aliquot parts or as splitting out discrete music scale notes from its fundamental or keynote tone.
Differentiation is not unlike refraction wherein a WHOLE is divided into its constituent parts; i.e., a rainbow, for instance, divided into its three main components - viz. - HEAT (infrared / red), LIGHT (yellow / white) and CHEMICAL (blue / ultraviolet) rays. (This is one of the great base ideas Keely discovered in Hughes' Harmonies of Tones and Colours - Developed by Evolution - the triple nature of a whole.)
"Electricity is the result of three differentiated sympathetic flows, combining the celestial and terrestrial flows by an order of assimilation negatively attractive in its character." [Vibratory Physics - The Connecting Link between Mind and Matter]
"No such thing as discord exists in the molecule. Discordance results from chords producing differentiation and may be equated by the proper chord of harmony. Every gaseous molecule is a resonator to any and all vibrations, whether concordant or discordant. That which we term discord exists in sound itself, not in matter." Snell Manuscript
"Differentiation, by compound negative vibration of their neutral centres, causes antagonism, and thus the great attractive power that aggregates them becomes one of dispersion or expansion, accompanied by immense velocity of rotation, which carries its influence through the whole volume of air, 230 cubic inches contained in sphere, within its 33 1/3 chord of its circle of coincidence. By this wire of platinum and silver the current of force is now passed to run the vibratory disk, thus altogether upsetting the "compressed air" theory of Professor Barkes, Dr. Hall, and others of less note." [Keely, Keely and His Discoveries]
"The breaking up of a cyclone will open a field for future research, if any way can be discovered for obtaining the chord of mass of the cyclone. To differentiate the chord of its thirds would destroy it;" [Chapter 9 of Keely and His Discoveries]
"Like poles do not repel each other, simply because there is a perfect sympathetic equation between them; the same in unlike poles. If a differentiation of 33 1/3 against 100 is established between them, whether like or unlike, they become attractive to each other. They become repellent after differentiating them, 66 2/3 of the one against 100 of the other, by sympathetic vibration." [Keely and His Discoveries]
"The normal brain is like a harp of many strings strung to perfect harmony. The transmitting conditions being perfect, are ready, at any impulse, to induce pure sympathetic assimilation. The different strings represent the different ventricles and convolutions. The differentiations of any one from its true setting is fatal, to a certain degree, to the harmony of the whole combination. If the sympathetic condition of any physical organism carries a positive flow of 80 per cent on its whole combination, and a negative one of 20 per cent, it is the medium of perfect assimilation to one of the same ratio, if it is distributed under the same conditions to the mass of the other. If two masses of metal, of any shape whatever, are brought under perfect assimilation, to one another, their unition, when brought into contact, will be instant.
"If we live in a sympathetic field we become sympathetic, and a tendency from the abnormal to the normal presents itself by an evolution of a purely sympathetic flow towards its attractive centers. It is only under these conditions that differentiation can be broken up, and a pure equation established. The only condition under which equation can never be established is when a differential disaster has taken place, of 66 2/3 against the 100 pure, taking the full volume as one. If this 66 2/3 or even 100 exists in one organ alone, and the surrounding ones are normal, then a condition can be easily brought about to establish the concordant harmony or equation to that organ. It is as rare to find a negative condition of 66 2/3 against the volume of the whole mass, as it is to find a coincident between differentiation; or, more plainly, between two individuals under a state of negative influence. Under this new system, it is as possible to induce negations alike as it is to induce positives alike. Pure sympathetic concordants are as antagonistic to negative discordants as the negative is to the positive; but the vast volume the sympathetic holds over the non-sympathetic, in ethereal space, makes it at once the ruling medium and readjuster of all opposing conditions if properly brought to bear upon them." [Keely and His Discoveries, Chapter 7]
"Like poles do not repel each other, simply because there is a perfect sympathetic equation between them; the same in unlike poles. If a differentiation of 33 1/3 against 100 is established between them, whether like or unlike, they become attractive to each other. They become repellent after differentiating them, 66 2/3 of the one against 100 of the other, by sympathetic vibration." [Vibratory Physics - The Connecting Link between Mind and Matter]
All abnormal discordant aggregations in these resonating convolutions produce differentiation to concordant transmission; and according as these differentiations exist in volume, so the transmissions are discordantly transferred, producing antagonism to pure physical action. Thus, in motor ataxy, a differentiation of the minor thirds of the posterior parietal lobule produces the same condition between the retractors and extendors of the leg and foot, and thus the control of the proper movements is lost through this differentiation. The same truth can be universally applied to any of the cerebral convolutions that are in a state of differential harmony to the mass of immediate cerebral surroundings. Taking the cerebral condition of the whole mass as one, it is subservient to one general head centre; although as many neutrals are represented as there are convolutions. The introductory minors are controlled by the molecular; the next progressive third by the atomic; and the high third by the etheric. All these progressive links have their positive, negative, and neutral position. When we take into consideration the structural condition of the human brain, we ought not to be bewildered by the infinite variety of its sympathetic impulses, inasmuch as it unerringly proves the true philosophy that the mass-chords of such structures are governed by vibratory etheric flows. There is no structure whatever - animal, vegetable, or mineral - that is not built up from the cosmic ether. Certain orders of attractive vibration produce certain orders of structure; thus the infinite variety of effects; more especially in the cerebral organs. Discordance cannot exist in the molecule proper. Discordance in any mass is the result of differentiated groups induced by antagonistic chords, and any differentiated mass can be brought to a condition of harmony or equation by proper chord media, and an equated sympathy produced whether the mass be metal or brain. [Vibratory Physics - The Connecting Link between Mind and Matter]
"There is good reason for believing that insanity is simply a condition of differentiation in the mass-chords of the convolutions, which creates an antagonistic molecular bombardment towards the neutral or attractive centres of such convolutions. This may be compared to a knot on a violin string. As long as this knot remains, it is impossible to elicit, from its sympathetic surroundings, the condition which transfers pure concordance to its resonating body. Discordant conditions (i.e., differentiation of mass) produce negatization to coincident action. Pure sympathetic concordants are as antagonistic to negative discordants as the negative is to the positive; but the vast volume the sympathetic holds over the non-sympathetic, in ethereal space, makes it at once the ruling medium and re-adjuster of all opposing conditions, when properly brought to bear upon them. Josiah Royce is right as regards correspondent sympathetic association between two conditions. If concordance can be established, even of unlike states, no matter whether it be of the high tenuous forces of nature, gases with liquids, liquids with solids, solids with gases, the structural conditions can be perfectly adverse. Their neutral centres are the focalized seat of sympathetic concordance for controlling any differentiation that may exist outside, or in the mass that surrounds them. Certain orders of vibration can reach these centres and establish a concordant flow of sympathy, independent of any mass antagonism; in other words, certain orders of sympathetic vibratory transmission can correct and equate all differentiation that may exist between physical organisms and their cerebellic flows. Discord is disease. Harmony is health.''" - [Keely." [[Vibratory Physics - The Connecting Link between Mind and Matter]
This same phenomenon occurs in all octaves of Creation - As Above So Below.
"One of the greatest errors in reactor construction is the use of aluminum tubes for uranium containers. Aluminum would become charged with radioactive death very quickly in comparison with silver, gold or any other metal on the blue side of the spectrum. Steel is on the red side, but its density is so much greater than aluminum that it is a better metal than aluminum for that purpose. Nickel would be better than steel, for nickel is on the blue side." [Atomic Suicide, page 17. See spectrum]
The division of sexless Oneness into pairs could not be a part of Nature's process without also dividing the Oneness of Light. God's Magnetic Light is white because it is still. It has no tensions or strains in it, for it is not divided. It is invisible to the senses because it has no motion in it. The moment motion begins the Light of the Creator's energy is divided into pairs which multiply their red and blue intensities in the ratio of their extension from their cathode beginnings, just as electric potential multiplies its intensity for the same reason. [Atomic Suicide, page 92]
"By the year 1821, Fresnel was able to show via mathematical methods that polarization could be explained by the wave theory of light and only if light was entirely transverse, with no longitudinal vibration whatsoever." https://en.wikipedia.org/wiki/Light#Wave_theory
Akasa - Ether: The First Duality
differentiation of mass
differentiation to concordant transmission
index of refraction
Law of Refractive Indices
Table of Cause and Effect Dualities