It took Keely eight years to perfect the Trexar and the **Trexnonar** (Trexar used with nine nodes, the first three of silver, the second three of gold and the third three of platinum). He states that during the time he was perfecting the **Trexnonar** the intermissions of vibratory transmission through the wire were so frequent and of such length, preventing continuity of mechanical motion, that he was about to give up when a seeming accident revealed the truth of his former theory of the law governing the atomic triplets in their association. He states that compound negative vibration of the neutral centers of the molecules in the Trexar and **Trexnonar** causes antagonism by differentiation and the attractive power of aggregation becomes radiant force with immense rotational velocity, carrying the "force" beyond the molecular inner one-third sphere of coincidence. [see Law of Cycles]

When using the Trexar or **Trexnonar**, a "slight tap on the chladna wave plate" accelerates the normal molecular frequency from 20,000 to 180,000 or 9 times. The sectional ratio is 3:6:9 or (^{9}/_{3})^{2} or 9 times. Here the nine nodes touch the extreme end, and next to the mass being operated on, in which position they are not in use.

"*Now if we shift a gold node along the third or platinum section the oscillatory multiplication will be 9 X 9 or 81 times the normal 20,000 or 1,620,000 oscillations per second. A gold node shifted over the extreme section will hold the frequency to 1,620,000 per second with the introductory chord of B third octave.*"

"*When using nine nodes, silver, gold and platinum nodes come in the order given, but when associating the seventh node (Trisexar) the gold node comes first and platinum, its third higher, comes last. I always end with the triplet higher.*"

"*Using the second node of platinum raises this frequency to the 81st power, or 1,620,000 ^{81} or far beyond computation and represents the effect of only two nodes.*"

"*Transmitting the order of sympathetic atomic vibration through a three-node transmitter (Trextrinar) induces interatomic percussion resulting in triple atomic subdivision not by oscillation of the atoms across their diameter but by infinite acceleration of the atomic film or etheric capsule, and at the same time permitting the extension of atomic vibration far enough to set free the gaseous atomic element.*" (This last must refer to the force generated by multiplication of vibratory frequencies in the Trexar as used with the different node combinations. This disintegration Keely claimed was caused chiefly by accelerating the atomic envelope.)

"*To rotate the neutral center indicator of the focalizing disk (of the magnetic engine) through a soft steel attractor requires transmission of the full triple-triple chord, or 156,057,552,198,220,000 corpuscular oscillations per second, resulting in 110 revolutions per minute on the neutral center indicator. This is only multiplication by the one gold node.*"

"*By using the second node of platinum we can raise this frequency to its 81st power, or 156,057,552,198,220,000 ^{81} or infinitely beyond computation. This frequency represents the effect of only two nodes.*"

"*I have induced rotation up to 123 revolutions per second on a neutral indicator, which required billions of vibrations per second, but even this frequency is only a minute fraction of the frequencies governing the vitality of the far-luminous centers.*"

"*The compounding of the triple-triple or chords in three octaves, will give from the ninth node a frequency that, set down in figures, would represent a number a mile long.*"