Entered according to Act of Congress, in the year 1875, by

JOHN N. STOCKWELL, M.A.,

In the Office of the Librarian of Congress, at Washington.

PREFACE.

AN abstract of the following investigation was published in Nos. (2024-2026) of the Astronomische Nachrichten. But, a few verbal inaccuracies, together with numerous typographical errors, being found in the work as printed, it was decided to reprint the whole investigation, giving the mathematical developments more in detail, and also developing the formula for the latitude of the moon, a subject not touched upon in that investigation. The author hopes to find leisure for the complete development of the perturbations of the moon's motions, by means of the differential equations given in this first chapter. It is believed that these equations will give the co-ordinates of the moon in a more direct and simple manner than any combination of the general differential equations of motion hitherto employed for that purpose.

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