By use of a resonant circuit and electric magnetic ether waves of very short length, Hertz produced frequencies of 100,000,000 per second, with waves of about one meter in length. Righi, with his oil oscillator for electric current, produced frequencies of 11,000,000,000 with wave length of 2.6 cm. Lebedow Lampa and Boses produced with their electromagnetic waves, frequencies of 50,000,000,000 with wave length of .6 cm which are the highest known to science of the present day (1934). The longest radiant heat ray is .01 cm with a frequency of 3,000,000,000,000, orange colored light has a wave length of .00006, with frequency of 500,000,000,000,000, and the shortest ultra violet light ray, observed by Schumann and Lyman, is .00001, with frequency of 3,000,000,000,000,000.

Using only an atmospheric medium, Keely produced 519,658,633 vibrations per second. By passing the vibrations through hydrogen he states that on the enharmonic third a frequency is induced that can only be represented in "sound colors" and "cannot be set down in figures."

He mentions the following frequencies, measured in sound colors: Molecular frequency inducted in homexar by harmonic thirds, 100,000,000 that inducted by enharmonic sixths, 300,000,000, that induced by diatonic ninths, 900,000,000, that inducted by dominant etheric sixths, 8,100,000,000, that inducted by interetheric ninths, 24,300,000,000. In the trexar the "compounding of the triple triple (chords in three octaves) will give a frequency from the ninth node that, set down, would make a "string of figures a mile long."

He says: "The highest range of vibrations I ever induced was in the experiment in which I liberated ozone by molecular percussion, inducing luminosity. A percussive molecular pressure of 110,000 lbs. per square inch was registered on the testing lever. The sphere and its accessories were so strained by the pressure that the decarbonized steel compressors moved as if composed of putty, and the machine was "unshipped" making repairs necessary before further experiments could be performed.

Concerning vibrations of the different states of matter, he says:

"The frequency of heat, a vibro-atomic element, is not more than 14,000 per second at its greatest intensity."

"The vibrational frequency governing the magnetic flow ranges from 300,000 to 780,000 per second. The order of the magnetic flow is the "first interatomic" and is the first order above odor."

"The diamagnetic receding movement of metallic silver, which it exhibits toward a magnetic field, is caused by "some 800,000 corpuscular percussions" per second, or "interatomic bombardment."

"The oscillating frequency of matter increases with its tenuity, according to the subdivision to which it belongs, the molecular frequency being the least. The molecular subdivision Keely claimed vibrates in arithmetical progression, as:

1 : 3 : 9 : 27 : 81 : 243 : etc.

The atomic vibrates in geometric progression, as:

3 : 9 : 81 : 6561 : 43,046,721 : etc.

and soon passes into mathematical infinity. The same progression is believed to take place in all orders above the molecular.