The following collection of problems is intended to serve two purposes—first, as a continuation of a former article, published in vol. x. of this Magazine, under the title of “Solutions of the Compound-Survivorship Assurance Problems,” which treats of cases involving three lives only; and secondly, as an introduction, or preliminary step, to a complete exposition of the writer's method of constructing mortality and annuity tables upon Mr. Gompertz's celebrated hypothesis, a brief account of which method will be found in the eighth and ninth volumes.

With the exception of the publication on a more limited scale (and which will be hereafter referred to), of that which is now to be developed, there exists at present no ready and practical method of forming to more than seven places the logarithms of numbers of more than seven or eight figures. The great extent of the tables requisite, if formed on the plan of our present seven-figure tables, is not only likely ever to prove a bar to their construction, but it would also render them too cumbrous, if constructed, to be easily and readily used. In the present method, the end in view is sought to be attained in another way. The principle of the method is the resolution of the number whose logarithm is required, by a direct and easy process, into factors of a peculiar form, the logarithms of which, to the requisite extent, admit of easy tabulation. The logarithms of the factors, then, being taken from the table, their sum is the logarithm of the given number.

The Mythological Astronomy of the ancients; part the second: or the key of Urania, the wards of which will unlock all the mysteries of antiquity. Norwich, 1823, 12mo.

A Companion to the Mythological Astronomy, &c., containing remarks on recent publications. … Norwich, 1824, 12mo.

A new Theory of the Earth and of planetary motion; in which it is demonstrated that the Sun is vicegerent of his own system. Norwich, 1825, 12mo.

The analyzation of the writings of the Jews, so far as they are found to have any connexion with the sublime science of astronomy. [This is pp. 97–180 of some other work, being all I have seen.]