Rational Logarithms.

I HAVE recently been considering how best the theory of logarithms could be presented to a beginner without such a paralysing opening as used to be the practice (see Todhunter). I do not know what is done now. But the result of this consideration has been the development of a complete exposition of the whole fundamental principle of the logarithm without any of the mathematical treatment which, so far as I know, is universally employed. The idea, of course, is that this should be an introduction to the usual mathematical treatment, not a substitute for it.