It's _half-and-half_, the gentleman means; Don't you see he talks of _score_?

That's the bit of memorandum That we chalk behind the door.

_Semi-definite_'s outlandish; But I see, in half a squint, That he speaks of the lubbers who call for a quart, When they can't manage more than a pint.

Now I'll read it into English, And then you'll answer me this: If it isn't good logic all the world round, I should like to know what is?

When you call for a pot of half-and-half, If you're lost to sense of shame, You may leave it _semi-definite_, But you pay for it all just the same.

I am unspeakably comforted when I look over the above in remembering that the question is not whether it be Pindaric or Horatian, but whether the copy be as good as the original. And I say it is: and will take no denial.

Long live--long will live--the glad memory of William Hamilton, Good, Learned, Acute, and Disputatious! He fought upon principle: the motto of his book is:

"Truth, like a torch, the more it's shook it shines."

There is something in this; but metaphors, like puddings, quarrels, rivers, and arguments, always have two sides to them. For instance,

"Truth, like a torch, the more it's shook it shines; But those who want to use it, hold it steady.

They shake the flame who like a glare to gaze at, They keep it still who want a light to see by."

{344}

ANOTHER THEORY OF PARALLELS.

Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the Equiangular Spiral. By Lieut-Col. G. Perronet Thompson.[721] The same, second edition, revised and corrected. The same, third edition, shortened, and freed from dependence on the theory of limits. The same, fourth edition, ditto, ditto. All London, 1840, 8vo.

To explain these editions it should be noted that General Thompson rapidly modified his notions, and republished his tracts accordingly.

SOME PRIMITIVE DARWINISM.

Vestiges of the Natural History of Creation.[722] London, 1840, 12mo.

This is the first edition of this celebrated work. Its form is a case of the theory: the book is an undeniable duodecimo, but the size of its paper gives it the look of not the smallest of octavos. Does not this ill.u.s.trate the law of development, the gradation of families, the transference of species, and so on? If so, I claim the discovery of this esoteric testimony of the book to its own contents; I defy any one to point out the reviewer who has mentioned it. The work itself is described by its author as "the first attempt to connect the natural sciences into a history of creation."

The attempt was commenced, and has been carried on, both with marked talent, and will be continued. Great advantage will result: at the worst we are but in the alchemy of some new chemistry, or the astrology of some new astronomy. Perhaps it would be as well not to be too sure on the matter, until we have an antidote to possible consequences as exhibited under another theory, on which {345} it is as reasonable to speculate as on that of the _Vestiges_. I met long ago with a splendid player on the guitar, who a.s.sured me, and was confirmed by his friends, that he _never practised_, except in thought, and did not possess an instrument: he kept his fingers acting in his mind, until they got their habits; and thus he learnt the most difficult novelties of execution. Now what if this should be a minor segment of a higher law? What if, by constantly thinking of ourselves as descended from primeval monkeys, we should--if it be true--actually _get our tails again_? What if the first man who was detected with such an appendage should be obliged to confess himself the author of the _Vestiges_--a person yet unknown--who would naturally get the start of his species by having had the earliest habit of thinking on the matter? I confess I never hear a man of note talk fluently about it without a curious glance at his proportions, to see whether there may be ground to conjecture that he may have more of "mortal coil" than others, in anaxyridical concealment. I do not feel sure that even a paternal love for his theory would induce him, in the case I am supposing, to exhibit himself at the British a.s.sociation,

With a hole behind which his tail peeped through.

The first sentence of this book (1840) is a cast of the log, which shows our rate of progress. "It is familiar knowledge that the earth which we inhabit is a globe of somewhat less than 8,000 miles in diameter, being one of a series of eleven which revolve at different distances around the sun."

The _eleven_! Not to mention the Iscariot which Le Verrier and Adams calculated into existence, there is more than a septuagint of _new_ planetoids.

ON RELIGIOUS INSURANCE.

The Const.i.tution and Rules of the Ancient and Universal 'Benefit Society' established by Jesus Christ, exhibited, and its advantages and claims maintained, against all Modern and {346} merely Human Inst.i.tutions of the kind: A Letter very respectfully addressed to the Rev. James Everett,[723] and occasioned by certain remarks made by him, in a speech to the Members of the 'Wesleyan Centenary Inst.i.tute'

Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith.[724] 12mo, (pp. 8.)

The Wesleyan minister addressed had advocated provision against old age, etc.: the writer declares all _private_ provision un-Christian. After decent maintenance and relief of family claims of indigence, he holds that all the rest is to go to the "Benefit Society," of which he draws up the rules, in technical form, with chapters of "Officers," "Contributors" etc., from the Acts of the Apostles, etc., and some of the early Fathers. He holds that a Christian may not "make a _private_ provision against the contingencies of the future": and that the great "Benefit Society" is the divinely-ordained recipient of all the surplus of his income; capital, beyond what is necessary for business, he is to have none. A real good speculator shuts his eyes by instinct, when opening them would not serve the purpose: he has the vizor of the Irish fairy tale, which fell of itself over the eyes of the wearer the moment he turned them upon the enchanted light which would have destroyed him if he had caught sight of it. "Whiles it remained, was it not thine own? and after it was sold, was it (the purchase-money) not in thine own power?" would have been awkward to quote, and accordingly nothing is stated except the well-known result, which is rule 3, cap. 5, "Prevention of Abuses." By putting his principles together, the author can be made, logically, to mean that the successors of the apostles should put to death all contributors who are detected in not paying their full premiums.

{347}

I have known one or two cases in which policy-holders have surrendered their policies through having arrived at a conviction that direct provision is unlawful. So far as I could make it out, these parties did not think it unlawful to lay by out of income, except when this was done in a manner which involved calculation of death-chances. It is singular they did not see that the entrance of chance of death was the entrance of the very principle of the benefit society described in the Acts of the Apostles. The family of the one who died young received more in proportion to _premiums_ paid than the family of one who died old. Every one who understands life a.s.surance sees that--_bonus_ apart--the difference between an a.s.surance office and a savings bank consists in the adoption, _pro tanto_, of the principle of community of goods. In the original const.i.tution of the oldest a.s.surance office, the _Amicable Society_, the plan with which they started was nothing but this: persons of all ages under forty-five paid one common premium, and the proceeds were divided among the representatives of those who died within the year.

THE TWO OLD PARADOXES AGAIN.

[I omitted from its proper place a ma.n.u.script quadrature (3.1416 exactly) addressed to an eminent mathematician, dated in 1842 from the debtor's ward of a country gaol. The unfortunate speculator says, "I have labored many years to find the precise ratio." I have heard of several cases in which squaring the circle has produced an inability to square accounts. I remind those who feel a kind of inspiration to employ native genius upon difficulties, without gradual progression from elements, that the call is one which becomes stronger and stronger, and may lead, as it has led, to abandonment of the duties of life, and all the consequences.] {348}

1842. Provisional Prospectus of the Double Acting Rotary Engine Company. Also Mechanic's Magazine, March 26, 1842.

Perpetual motion by a drum with one vertical half in mercury, the other in a vacuum: the drum, I suppose, working round forever to find an easy position. Steam to be superseded: steam and electricity convulsions of nature never intended by Providence for the use of man. The price of the present engines, as old iron, will buy new engines that will work without fuel and at no expense. Guaranteed by the Count de Predaval,[725] the discoverer. I was to have been a Director, but my name got no further than ink, and not so far as official notification of the honor, partly owing to my having communicated to the _Mechanic's Magazine_ information privately given to me, which gave premature publicity, and knocked up the plan.

An Exposition of the Nature, Force, Action, and other properties of Gravitation on the Planets. London, 1842, 12mo.

An Investigation of the principles of the Rules for determining the Measures of the Areas and Circ.u.mferences of Circular Plane Surfaces ...

London, 1844, 8vo.

These are anonymous; but the author (whom I believe to be Mr. Denison,[726]

presently noted) is described as author of a new system of mathematics, and also of mechanics. He had need have both, for he shows that the line which has a square equal to a given circle, has a cube equal to the sphere on the same diameter: that is, in old mathematics, the diameter is to the circ.u.mference as 9 to 16! Again, admitting that the velocities of planets in circular orbits are inversely as the square roots of their distances, that is, admitting Kepler's law, he manages to prove that gravitation is inversely as the square _root_ of the distance: and suspects magnetism of doing the difference between this and Newton's law. {349} Magnetism and electricity are, in physics, the member of parliament and the cabman--at every man's bidding, as Henry Warburton[727] said.

The above is an outrageous quadrature. In the preceding year, 1841, was published what I suppose at first to be a Maori quadrature, by Maccook. But I get it from a cutting out of some French periodical, and I incline to think that it must be by a Mr. M^cCook. He makes [pi] to be 2 + 2[root](8[root]2 - 11).

THE DUPLICATION PROBLEM.

Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728]

ent.i.tled "A method of making a cube double of a cube, founded on the principles of elementary geometry," wherein his principles are proved erroneous, and the required solution not yet obtained. By Robert Murphy.[729] Mallow, 1824, 12mo.

This refutation was the production of an Irish boy of eighteen years old, self-educated in mathematics, the son of a shoemaker at Mallow. He died in 1843, leaving a name which is well known among mathematicians. His works on the theory of equations and on electricity, and his papers in the _Cambridge Transactions_, are all of high genius. The only account of him which I know of is that which I wrote for the _Supplement_ of the _Penny Cyclopaedia_. He was thrown by his talents into a good income at Cambridge, with no social training except penury, and very little intellectual training except mathematics. He fell into dissipation, and his scientific career was almost arrested: but he had great good in him, to my knowledge.

A sentence in {350} a letter from the late Dean Peac.o.c.k[730] to me--giving some advice about the means of serving Murphy--sets out the old case: "Murphy is a man whose _special_ education is in advance of his _general_; and such men are almost always difficult subjects to manage." This article having been omitted in its proper place, I put it at 1843, the date of Murphy's death.

A NEW VALUE OF [pi].

The Invisible Universe disclosed; or, the real Plan and Government of the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.

The book opens abruptly with: