An Elementary Treatise On the Planetary Theory, With a Collection of Problems
The book An Elementary Treatise On the Planetary Theory, With a Collection of Problems was written by author Charles Hartwell Horne Cheyne Here you can read free online of An Elementary Treatise On the Planetary Theory, With a Collection of Problems book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Elementary Treatise On the Planetary Theory, With a Collection of Problems a good or bad book?
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51. The principal part of the coefficient of a term in E, of tJie form P cos { (pn + qn') t + Q} is of the order p + q. This term arises from the multiplication of such terms as P x C ° S {{Jen - Jen) t+ Q t ), with P 2 1™ {[( P -k)n+(q + Jc) n'] t+Q,}, and P 3 C ° S {[(p + 7c)n+(q- Jc) «'] t + Q 3 ], sm and as in the last Article, the order of the principal part of P will be equal to the lesser of those of P, and P 3 . 48 PLANETARY THEORY. Now the order of the principal part of P 2 will be the... least value which the arithmetical sum oip~k and q + k can assume, for different values of k. (i) Suppose k less than p ; then this sum =p —k+q+k =p + q. (ii) Suppose k not less thanp; then this sum = k —p + q + k, the least value of which (by putting k equal to p) =p + q. Similarly it may be shewn that p + q will be the order of the principal part of P 3 . Hence it follows that p + q will be the order of the principal part of P. In Art. 44 we have assumed that (a 2 + a' 1 — 2aa' cos )~" can be expanded in a series of cosines of and its multiples, we shall now give a proof of this and shew how the coeffi- cients may be calculated.
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