Adams presented his findings to the Royal Astronomical Society on November 13, 1846, approximately two and half months after Le Verrier's calculations had been made public at a meeting of the Royal Academy of Sciences in Paris. In his paper An Explanation of the Observed Irregularities in the Motion of Uranus: On the Hypothesis of Disturbances Caused By a More Distant Planet; With a Determination of the Mass, Orbit, and Position of the Disturbing Body (London: W. Clowes & Sons, 1846) Adams discussed his own interest in the problem and attempts to resolve the issue but ultimately credited Le Verrier and Johann Galle with the discovery of what we now know as the planet Neptune.
I mention these dates merely to show that my results were arrived at independently, and previous to the publication of M. Le Verrier, and not with the intention of interfering with his just claims to honours of the discovery; for there is no doubt that his researches were first published to the world, and led to the actual discovery of the planet by Dr. Galle, so that the facts stated above cannot detract, in the slightest degree, from the credit due to M. Le Verrier.Adams then goes into details of his attempts to calculate the orbit and the various methods that he employed. This was a tedious process of testing various hypotheses and then calculating the predicted orbit from those equations and comparing the predictions to observed data.
Rauner's copy of Adam's paper is a presentation copy from the author to a Lieutenant W. S. Swafford, R.N. Ask for Rare Book QB 681 .A32 1846.