^{page 1 note *} The present author thinks it right to state that the following paper was prepared before he had an opportunity of seeing Mr. Davies's work.

^{page 2 note *} De Morgan on Probabilities (Lardner's Cyclopædia), p. 190.

^{page 3 note *} De Morgan on Probabilities, p. 228.

^{page 6 note *} By adding unity to the tabular value of an annuity on the given age, agreeably to (8).

^{page 9 note *} For when n = I, A_y ^n-1 becomes A_y ^o which is equal to unity, whatever the value of A_y may be.

^{page 10 note *} This is a decreasing series in geometrical progression, whose common ratio is A_y. The rule for summing such series is to be found in all elementary works on Algebra. It is as follows:—Multiply the last term by the common ratio; subtract the product from the first term; and divide the remainder by the excess of unity over the common ratio.

page 16 note *_** Part II., containing the PRAXIS, will appear in a subsequent Number.