"Both attraction and repulsion are exhibited by the action of the dual magnetic force. However, like or unlike magnetic poles become attractive when their frequency ratios become 33 1/3 of one against 100 of the other, simply by sympathetic resonant vibration." The Snell Manuscript
"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, ATTRACTION PROPULSION ETC]
Attraction and Repulsion of Magnets
3:6:9 - This quote seems to clearly explain the significance of the ratio 3:6:9 - "The relative frequency of all sympathetic streams is in the ratio 3:6:9. Those whose relative frequencies are 3:9 are mutually attractive, while those having the relation of 6:9 are mutually repellant." [Keely, SYMPATHETIC STREAMS - Snell, LAWS OF MOLECULAR BEING, Sympathetic Stream, Modes of Vibration, Modes of Vibration - Annotated]
For a more complete description by Keely on what magnetism is and how a magnet works see ANSWERS MADE IN LETTERS FROM MR. KEELY - TO QUESTIONS ASKED OF HIM.
See Also
3.17 - Magnetic Electric Poles
Figure 7B.16 - Bar Magnets shown separate then joined as one
Figure 7B.18 - Four Poles of a Bar Magnet
7B.20 - Magnetism
16.20 - Magnetic Pole Reversal
16.21 - Magnetic Flow
Figure 16.08 - Two bar magnets becoming one magnet