A Short Method for the Discovery of Neptune

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Abstract
The mathematical basis is described of a method for the discovery of Neptune that involves far less numerical calculation. The time of heliocentric conjunction can be found solely from considerations of the discrepancy in the longitude of Uranus. This information alone makes prediction possible within less than 15° on the basis of Bode's law. By finding the distance in a circular orbit appropriate to the best fit of the observations a prediction can be made comparable in accuracy with that achieved by Le Verrier. It is shown how by suitable combination of the equations of condition the number of unknowns can be reduced to three (as compared with eight in the original methods) for any assumed mean distance, and the same process removes certain awkward features that would otherwise enter for orbits near the 2:1 resonance.

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