The forty laws that govern harmony, sound and vibration.
"Coextensive and coeternal with space and duration, there exists an infinite and unchangeable quantity of atomoles, the base of all matter; these are in a state of constant vibratory motion, infinite in extent, unchangeable in quantity, the initial of all forms of energy."
(2) Law of Corporeal Vibrations
"All coherent aggregates when isolated from like bodies, or when immersed or confined in media composed of matter in a different state, vibrate at a given ascertainable pitch."
(3) Law of Corporeal Oscillations
"All coherent aggregates not isolated from like bodies, oscillate at a period-frequency varying with the tensions that augment and diminish the state of equilibrium."
(4) Law of Harmonic Vibrations
"All coherent aggregates are perpetually vibrating at a period-frequency corresponding to some harmonic ratio of the fundamental pitch of the vibrating body; this pitch is a multiple of the pitch of the atomole."
(5) Law of Transmissive Vibraic Energy
"All oscillating and vibrating coherent aggregates create, in the media in which they are immersed, outwardly propagated concentric waves of alternate condensation and rarefaction, having a period-frequency identical with the pitch of the aggregate.
Scholium: All forms of transmissive energy can be focussed, reflected, refracted, diffracted, transformed, and diminished in intensity inversely as the square of the distance from the originating source."
(6) Law of Sympathetic Oscillation
"Coherent aggregates immersed in a medium pulsating at their natural pitch simultaneously oscillate with the same frequency, whether the pitch of the medium be a unison, or any harmonic of the fundamental pitch of the creative aggregate."
"Juxtaposed coherent aggregates vibrating in unison, or harmonic ration, are mutually attracted."
"Juxtaposed coherent aggregates vibrating in discord are mutually repelled."
"Coherent aggregates harmonically united constitute centers of vibration bearing relation to the fundamental pitch not multiples of the harmonic pitch, and the production of secondary unions between themselves generate pitches that are discords, either in their unisons, or overtones with the original pitch; from harmony is generated discord, the inevitable cause of perpetual transformation."
"Any aggregate in a state of vibration develops in addition to its fundamental pitch a series of vibration in symmetrical sub-multiple portions of itself, bearing ratios of one, two, three, or more times its fundamental pitch."
"Energy manifests itself in three forms: Creative, the vibrating aggregate; Transmissive, being the propagation of isochronous waves through the media in which it is immersed; Attractive, being its action upon other aggregates capable of vibrating in unisons or harmony."
(12) Law of Oscillating Atomic Substances
"Coherent atomic substances are capable of oscillating at a pitch varying directly as the density, and inversely as the linear dimensions from one period of frequency per unit of time to the 21st octave above, producing the creative force of Sonity, whose transmissive force (Sound) is propagated through the media of solids, liquids, and gases, and whose static effect (Sonism) produces attractions and repulsions between sympathetically vibrating bodies according to the Law of Harmonic Attraction and Repulsion."
"Internal vibrations of atomic substances and atomic molecules are capable of vibrating at a period-frequency directly as their density, inversely as their linear dimensions, directly as the coefficient of their tension from the 21st to the 42nd octaves, producing the creative force (Sono-thermity), whose transmissive force (Sono-therm) is propagated in solid, liquid, gaseous, and ultra-gaseous media, statically producing adhesions and molecular unions, or disintegration, according to the Law of Harmonic Attraction and Repulsion."
"All atoms when in a state of tension are capable of oscillating at a pitch inversely as the cube of their atomic weights, and directly as their tension from 42 to 63 octaves per second, producing the creative forcce (Thermism), whose transmissive force (Rad-energy) propagated in solid, liquid, and gaseous ether, produces the static effects (Cohesion and Chemism) on other atoms of association, or dissociation, according to the Law of Harmonic Attraction and Repulsion.
Scholium: Dark radiant heat begins at absolute zero temperature, and extends through light, chemical rays, actinic rays, and infra-violet rays, up to the dissociation of all molecules to the 63rd octave."
(15) Law of Vibrating Atomolic Substances
"Atoms are capable of vibrating within themselves at a pitch inversely as the Dyne (the local coefficient of Gravity), and as the atomic volume, directly as the atomic weight, producing the creative force (Electricity), whose transmissive force is propagated through atomolic solids, liquids, and gases, producing induction and the static effect of magnetism upon other atoms of attraction or repulsion, according to the Law of Harmonic Attraction and Repulsion.
Scholium: The phenomenon of Dynamic Electricity through a metallic conductor and of induction are identical. In a metallic conductor, the transmission is from atom to atom, through homologous interstices, filled with ether, presenting small areas in close proximity. In crystalline structures, heat, which expands the atoms, by twisting them produces striae, increases the resistance, etc. Between parallel wires and through air the induction takes place from large areas through a rarefied medium composed of a mixture of substances, whose atoms are separated by waves of repulsion of various pitches, discordant to electric vibrations; the said atoms sympathetically absorb the vibrations and dissipate from themselves, as centers, concentric waves of electric energy which produces heat and gravism."
(16) Law of Oscillating Atomoles
"Atomoles oscillating at a uniform pitch (determined by their uniform size and weight) produce the creative force Atomolity, whose transmissive form, Gravism, is propagated through more rarefied media, producing the static effect upon all other atomoles, denominated Gravity."
(17) Law of Transformation of Forces
"All forces are different forms of Universal Energy unlike in their period- frequency, merging into each other by imperceptible increments; each form representing the compass of 21 octaves. Each form or pitch may be transformed into an equivalent quantity of another pitch above or below it in the scale of 105 octaves. The transformation can occur only through its static effect, developing vibrations of harmonic pitches above or below their fundamental vibration, or developing with juxtaposed aggregates, resultant and difference, or third order, as the case may be.
Scholium: A table of the intervals and harmonics of the normal harmonic scale will indicate the ratios in which the transformation of forces will occur."
"Atoms have each a different and definite pitch, at which they naturally vibrate.
Scholium: Atomic pitch is determined directly
from its simple spectrum.Scholium: Atomic pitch is determined by computations from its associate spectrum with all other atoms, as in known spectra.
Scholium: Atomic pitches are more important working data than atomic weights; tables of atomic pitches must be precise."
(19) Law of Variation of Atomic Pitch by Rad-energy
"The higher harmonics and overtones of projected rad-energy are of a pitch sufficiently high to cause the atom to expand; by causing the atomoles to vibrate systematically the same influence will cause the atom to contract, and thus by changing the volume, atomic pitch is varied."
(20) Law of Variation of Atomic Pitch by Electricity and Magnetism
"Electricity and Magnetism produce internal vibrations in the atom, which are followed by proportional changes in volume and, therefore, pitch."
(21) Law of Variation of Atomic Pitch by Temperature
"Atoms in chemical combination oscillate with increasing amplitude directly as the temperature, and simultaneously absorb overtones of higher harmonics, producing expansion of volume and diminution of pitch.
Rule: The gradual approach of the temperature of harmonic combination can be observed by mutually comparing superimposed spectra; chemical combination commences when the fundamental lines of each spectrum bear harmonic ratios by linear measurement."
(22) Law of Pitch of Atomic Oscillation
"Atoms not isolated and in a state of tension between forces that oppose and increase the equilibrium oscillate bodily at a pitch that is a resultant of the atomic weight, atomic volume, and tension."
(23) Law of Variation of Pitch of Atomic Oscillation by Pressure
"The frequency of atomic oscillation increases and diminishes inversely as the square of the pressure."
(24) Law of Variation of Atomic Oscillation by Temperature
"The force of cohesion diminishes inversely as the square of the distance the atoms are apart, and the force of the chemical affinity diminishes in the same ratio. Heat increases the amplitude of the oscillations in a direct ratio to the temperature of the natural scale.
Scholium: New thermometers and accurate thermometric tables, on the natural base, wherein doubling the temperature doubles the pitch of the transmissive energy, are required. Such a table of temperature will bear natural relations to atomic weights, pitches, specific heats, chemical affinities, fusions, solubilities, etc., and will disclose new laws. One table for each must be constructed."
(25) Law of Variation of Atomic Oscillation by Electricity
"The electric current destroys cohesion and chemical tension directly as square of current in amperes, inversely as the resistance in ohms, inversely as the chemical equivalent, and conversely as the coefficient of the difference between the freezing and volatilizing temperature of mass acted upon."
(26) Law of Variation of Atomic Oscillation by Sono-thermism
"Diminishes the tensions directly as the quantity of heat developed, and in antithetical proportion to the harmonics absolved."
"Atoms whose atomic pitches are in either unison, harmonic or concordant ratios, unite to form molecules.
Corollary: When two atoms are indifferent, they may be made to unite by varying the pitch of either, or both.
Scholium: This necessitates the construction of tables, representing variation of atomic pitches by temperature, pressure, etc.
Scholium: Tables of all harmonics and concords, and harmonics founded upon a normal harmonic scale, are equally essential.
Scholium: Optical instruments may be made to measure pitches of energy."
(28) Law of Chemical Dissociation
"If the pitch of either atom, in a molecule, be raised or lowered; or, if they both be unequally raised or lowered in pitch until the mutual ratio be that of a discord; or, if the oscillation amplitude be augmented by heat until the atoms are with the concentric waves of attraction, - the atoms will separate."
(29) Law of Chemical Transposition
"New molecules must be harmonics of the fundamental pitch."
(30) Law of Chemical Substitution
"(too complex for brief statement)"
"The presence of harmonics and discords."
(32) Law of Molecular Synthesis and Combination (Organic)
"The molecular pitch must be a derived harmony of the radicals.
Scholium: Reconstruction of electric units to represent pitches and amplitudes."
(33) Law of Chemical Morphology
"The angle of crystallization is determined by the relation between the molecular pitch of the crystallizing substance to the variation- density of the liquid depositing it."
(34) Law of Atomic Dissociation
"Overtones of high rad-energy pitches produce separation of the atomoles and recombinations among the atomolic molecules of the atoms."
(35) Law of Atomolic Synthesis of Chemical Elements
"Harmonic pitches of atomolity produce association of etheric-atomolic particles to form atoms; the kind of atom is determinable by the pitches employed."
"Atoms under the tension of chemical combination oscillate with an amplitude directly as the temperature, inversely as the pressure, and as the square of the specific heat. Diminishing the pitch of oscillation inversely as the square of the distance of the atoms apart, and simultaneously increasing the vibrating pitch of the atom by absorption of overtones and higher harmonics."
(37) Law of Electro-Chemical Equivalents
"An atom vibrates sympathetically under the influence of electric energy, such undertones of which are absorbed as are a harmonic or harmony of the electric pitch; the amount of energy absorbed being directly as the arithmetical ratio of the undertone of the fundamental electric pitch.
Scholium: A table of electro-chemical equivalents on the normal basis will indicate the electrical conditions and amount of chemical change."
"The cohesion between atoms diminishes directly as the square root of the pressure and temperature, and as the square of electric intensity."
(39) Law of Refractive Indices
"A table of the refractive indices of substances indicates their molecular pitch; and in connection with crystalline form the phase of molecular oscillation."
(40) Law of Electric Conductivity
"Electric energy is transmitted through homogeneous bodies with a completeness in direct proportion as the atoms are more or less perfect harmonics of the electric pitch, but not at all through substances whose atoms are discordant to the electric pitch; also through molecular substances, when their resultant notes are harmonics of the electric pitch, - the transmissions being inversely as the temperature, directly as the density diminished in proportion to the amount of crystallization, and inversely as the cube of the dyne, also directly as the reciprocal of the local magnetic intensity."