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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.
St. John's College, Cambridge,
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.
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
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
61 Second Method. Values deduced by the Solution of a large
number of simultaneous Equations