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Mr. D.K. Picken has done well to direct attention to the unsatisfactory nature of the elementary discussion of the Simple Pendulum, current in the text-books.
What is usually passed off as a proof is a downright wicked deceit, and deserves the serious attention of the advocate of rigour, when he can spare time to look elsewhere, beyond a fundamental axiom or a convergency test.
* v. Mathematical Gazette, vol. vii. p.173.