s afterwards, I went to him and very gravely told him that I had
discovered the law of human mortality in the Carlisle Table, of which he
thought very highly. I told him that the law was involved in this
circumstance. Take the table of expectation of life, choose any age, take
its expectation and make the nearest integer a new age, do the same with
that, and so on; begin at what age you like, you are sure to end at the
place where the age past is equal, or most nearly equal, to the expectation
to come. "You don't mean that this always happens?"--"Try it." He did try,
again and again; and found it as I said. "This is, indeed, a curious thing;
this _is_ a discovery." I might have sent him about trumpeting the law of
life: but I contented myself with informing him that the same thing would
happen with any table whatsoever in which the first column goes up and the
second goes down; and that if a proficient in the higher mathematics chose
to palm a figment upon him, he could do without the circle: _a corsaire,
corsaire et demi_,[617] the French proverb says. "Oh!" it was remarked, "I
see, this was Milne!"[618] It was _not_ Milne: I remember well showing the
formula to him some time afterwards. He raised no difficulty about [pi]; he
knew the forms of Laplace's results, and he was much interested. Besides,
Milne never said stuff! and figment! And he would not have been taken in:
he would have quietly tried it with the Northampton and all the other
tables, and would have got at the truth.

{287}

EUCLID WITHOUT AXIOMS.

The first book of Euclid's Elements. With alterations and familiar
notes. Being an attempt to get rid of axioms altogether; and to
establish the theory of parallel lines, without the introduction of any
principle not common to other parts of the elements. By a member of the
University of Cambridge. Third edition. In usum serenissimae filiolae.
London, 1830.

The author was Lieut. Col. (now General) Perronet Thompson,[619] the author
of the "Catechism on the Corn Laws." I reviewed the fourth edition--which
had the name of "Geometry without Axioms," 1833--in the quarterly _Journal
of Education_ for January, 1834. Col. Thompson, who then was a contributor
to--if not editor of--the _Westminster Review_, replied in an article the
authorship of which could not be mistaken.

Some more attempts upon the problem, by the same author, will be found in
the sequel. They are all of acute and le