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mentioned which, as the theory has since verified, were real onward steps. The perusal of this chapter will shew to what extent we are indebted to our great philosopher; at the same time we cannot fail being impressed with reverence for the genius and perseverance of the men who preceded him, and whose elaborate and multiplied hypotheses were in some measure necessary to the discovery of his simple and single law.

I take this opportunity of acknowledging my obligations to several friends, whose valuable suggestions have added to the utility of the work.

HUGH GODFRAY.

St. John's College, Cambridge,

April, 1853.

In the present edition, besides the change of form and the incorporation of the figures with the text, which it is hoped will render the work more commodious, very few alterations have been thought necessary; and, except in one or two instances, where additional paragraphs have been introduced, nothing but the wording of some of the sentences has been altered.

October, 1859.

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CHAPTER III.

DIFFERENTIAL EQUATIONS,

19 Formation of the Differential Equations.

22 Orders of the Small Quantities introduced

23 Values of the Forces P, T, S

24 Order of the Sun's disturbing Force

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CHAPTER IV.

INTEGRATION OF THE DIFFERENTIAL EQUATIONS.

25 General Process described

27 Terms of a higher order which must be retained

30 Solution to the first order

35 Introduction of c and g

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