In the investigation of a little curiosity in the matter of annuities, I had occasion to want four or five terms of log (a + bx + cx2 + …), and, by Arbogast's rules I accordingly wrote down the following, without a stroke of the pen more than is here given:—

This I might have continued to any number of terms for little beyond the trouble of writing. The method is easy to demonstrate and easy to practice; and it struck me that I might, in a few pages, give an account of it sufficient for use and detached from anything else. I therefore append it to the problem.