The problem as thus presented was one of the most difficult we can
perceive of, but the difficulty was only an incentive to attacking
it with all the greater energy. So long as the motion was supposed
purely elliptical, so long as the action of the planets was
neglected, the problem was a simple one, requiring for its
solution only the analytic geometry of the ellipse. The real
difficulties commenced when the mutual action of the planets was
taken into account. It is, of course, out of the question to give
any technical description or analysis of the processes which have
been invented for solving the problem; but a brief historical
sketch may not be out of place. A complete and rigorous solution
of the problem is out of the question--that is, it is impossible
by any known method to form an algebraic expression for the co-
ordinates of a planet which shall be absolutely exact in a
mathematical sense. In whatever way we go to work the expression
comes out in the form of an infinite series of terms, each term
being, on the whole, a little smaller as we increase the number.
So, by increasing the number of these various terms, we can
approach nearer and nearer to a mathematical exactness, but can
never reach it.
Pages:
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285