Here is General Thompson again, with another paradox: but always master of the subject, always well up in what his predecessors have done, and always aiming at a useful end. He desires to abolish temperament by additional keys, and has constructed an enharmonic organ with forty sounds in the octave. If this can be introduced, I, for one, shall delight to hear it: but there are very great difficulties in the way, greater than stood even in the way of the repeal of the bread-tax.

In a paper on the beats of organ-pipes and on temperament published some years ago, I said that equal temperament appeared to me insipid, and not so agreeable as the effect of the instrument when in progress towards being what is called out of tune, before it becomes offensively wrong. There is throughout that period unequal temperament, determined by accident. General Thompson, taking me one way, says I have launched a declaration which is likely to make an epoch in musical practice; a public musical critic, taking me another way, quizzes me for preferring music _out of tune_. I do not think I deserve either one remark or the other. My opponent critic, I suspect, takes _equally tempered_ and _in tune_ to be phrases of one meaning. But by equal temperament is meant equal distribution among all the keys of the error which an instrument _must_ have, which, with twelve sounds only in the octave, professes to be fit for all the keys. I am reminded of the equal temperament which was once applied to the postmen's jackets. The coats were all made for the average man: the {186} consequence was that all the tall men had their tails too short; all the short men had them too long. Some one innocently asked why the tall men did not change coats with the short ones.

A diagram ill.u.s.trating a discovery in the relation of circles to right-lined geometrical figures. London, 1863, 12mo.

The circle is divided into equal sectors, which are joined head and tail: but a property is supposed which is not true.

An attempt to a.s.sign the square roots of negative powers; or what is [sqrt] -1? By F.H. Laing.[321] London, 1863, 8vo.

If I understand the author, -a and +a are the square roots of -a^2, as proved by multiplying them together. The author seems quite unaware of what has been done in the last fifty years.

BYRNE'S DUAL ARITHMETIC.

Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863, 8vo.

The plan is to throw numbers into the form a(1.1)^{b} (1.01)^{c} (1.001)^{d}... and to operate with this form. This is an ingenious and elaborate speculation; and I have no doubt the author has practised his method until he could surprise any one else by his use of it. But I doubt if he will persuade others to use it. As asked of Wilkins's universal language, Where is the second man to come from?

An effective predecessor in the same line of invention {187} was the late Mr. Thomas Weddle,[323] in his "New, simple, and general method of solving numeric equations of all orders," 4to, 1842. The Royal Society, to which this paper was offered, declined to print it: they ought to have printed an organized method, which, without subsidiary tables, showed them, in six quarto pages, the solution (x=8.367975431) of the equation

1379.664 x^{622} + 2686034 10^{432} x^{152} - 17290224 10^{518} x^{60} + 2524156 10^{574} = 0.

The method proceeds by successive factors of the form, a being the first approximation, a 1.b 1.0c 1.00d.... In my copy I find a few corrections made by me at the time in Mr. Weddle's announcement. "It was read before that learned body [the R. S.] and they were pleased [but] to transmit their thanks to the author. The en[dis]couragement which he received induces [obliges] him to lay the result of his enquiries in this important branch of mathematics before the public [, at his own expense; he being an usher in a school at Newcastle]." Which is most satirical, Mr.

Weddle or myself? The Society, in the account which it gave of this paper, described it as a "new and remarkably simple method" possessing "several important advantages." Mr. Rutherford's[324] extended value of [pi] was read at the very next meeting, and was printed in the _Transactions_; and very properly: Mr. Weddle's paper was excluded, and very very improperly.

HORNER'S METHOD.

I think it may be admited that the indisposition to look at and encourage improvements of calculation which once {188} marked the Royal Society is no longer in existence. But not without severe lessons. They had the luck to accept Horner's[325] now celebrated paper, containing the method which is far on the way to become universal: but they refused the paper in which Horner developed his views of this and other subjects: it was printed by T. S. Davies[326] after Horner's death. I make myself responsible for the statement that the Society could not reject this paper, yet felt unwilling to print it, and suggested that it should be withdrawn; which was done.

But the severest lesson was the loss of _Barrett's Method_,[327] now the universal instrument of the actuary in his highest calculations. It was presented to the Royal Society, and refused admission into the _Transactions_: Francis Baily[328] printed it. The Society is now better informed: "_live and learn_," meaning "_must live, so better learn_," ought to be the especial motto of a corporation, and is generally acted on, more or less.

Horner's method begins to be introduced at Cambridge: it was published in 1820. I remember that when I first went to Cambridge (in 1823) I heard my tutor say, in conversation, there is no doubt that the true method of solving equations is the one which was published a few years ago in the _Philosophical Transactions_. I wondered it was not taught, but presumed that it belonged to the higher mathematics. This Horner himself had in his head: and in a sense it is true; for all lower branches belong to the higher: but he would have stared to have been told that he, Horner, {189} was without a European predecessor, and in the distinctive part of his discovery was heir-at-law to the nameless Brahmin--Tartar--Antenoachian--what you please--who concocted the extraction of the square root.

It was somewhat more than twenty years after I had thus heard a Cambridge tutor show sense of the true place of Horner's method, that a pupil of mine who had pa.s.sed on to Cambridge was desired by his college tutor to solve a certain cubic equation--one of an integer root of two figures. In a minute the work and answer were presented, by Horner's method. "How!" said the tutor, "this can't be, you know." "There is the answer, Sir!" said my pupil, greatly amused, for my pupils learnt, not only Horner's method, but the estimation it held at Cambridge. "Yes!" said the tutor, "there is the answer certainly; but it _stands to reason_ that a cubic equation cannot be solved in this s.p.a.ce." He then sat down, went through a process about ten times as long, and then said with triumph: "There! that is the way to solve a cubic equation!"

I think the tutor in this case was never matched, except by the country organist. A master of the instrument went into the organ-loft during service, and asked the organist to let him _play the congregation out_; consent was given. The stranger, when the time came, began a voluntary which made the people open their ears, and wonder who had got into the loft: they kept their places to enjoy the treat. When the organist saw this, he pushed the interloper off the stool, with "You'll never play 'em out this side Christmas." He then began his own drone, and the congregation began to move quietly away. "There," said he, "that's the way to play 'em out!"

I have not scrupled to bear hard on my own university, on the Royal Society, and on other respectable existences: being very much the friend of all. I will now clear the Royal Society from a very small and obscure slander, simply because I know how. This dissertation began with {190} the work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer published, in 1849, a method of calculating logarithms.[329] First, a long list of instances in which, as he alleges, foreign discoverers have been pillaged by Englishmen, or turned into Englishmen: for example, O'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical parabola claimed by the Saxons under the name of _Neal_: the grandfather of this mathematician was conspicuous enough as _Neal_; he was archbishop of York. This list, says the writer, might be continued without end; but he has mercy, and finishes with his own case, as follows:--"About twenty years ago, I discovered this method of directly calculating logarithms. I could generally find the logarithm of any number in a minute or two without the use of books or tables. The importance of the discovery subjected me to all sorts of prying. Some a.s.serted that I committed a table of logarithms to memory; others attributed it to a peculiar mental property; and when Societies and individuals failed to extract my secret, they never failed to traduce the inventor and the invention. Among the learned Societies, the Royal Society of London played a very base part. When I have more s.p.a.ce and time at my disposal, I will revert to this subject again."

Such a trumpery story as this remains unnoticed at the time; but when all are gone, a stray copy from a stall falls into hands which, not knowing what to make of it, make history of it. It is a very curious distortion.

The reader may take it on my authority, that the Royal Society played no part, good or bad, nor had the option of playing a part. {191} But I myself _pars magna fui_:[331] and when the author has "s.p.a.ce and time" at his disposal, he must not take all of them; I shall want a little of both.

ARE ATOMS WORLDS?

The mystery of being; or are ultimate atoms inhabited worlds? By Nicholas Odgers.[332] Redruth and London, 1863, 8vo.

This book, as a paradox, beats quadrature, duplication, trisection, philosopher's stone, perpetual motion, magic, astrology, mesmerism, clairvoyance, spiritualism, h.o.m.oeopathy, hydropathy, kinesipathy, Essays and Reviews, and Bishop Colenso,[333] all put together. Of all the suppositions I have given as actually argued, this is the one which is hardest to deny, and hardest to admit. Reserving the question--as beyond human discussion--whether our particles of carbon, etc. are _cl.u.s.ters_ of worlds, the author produces his reasons for thinking that they are at least single worlds. Of course--though not mentioned--the possibility is to be added of the same thing being true of the particles which make up our particles, and so down, for ever: and, on the other hand, of our planets and stars as being particles in some larger universe, and so up, for ever.

"Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so _ad infinitum._ And the great fleas themselves, in turn, have greater fleas to go on; While these again have greater still, and greater still, and so on."[334]

I have often had the notion that all the nebulae we see, including our own, which we call the Milky Way, may be particles of snuff in the box of a giant of a proportionately {192} larger universe. Of course the minim of time--a million of years or whatever the geologists make it[335]--which our little affair has lasted, is but a very small fraction of a second to the great creature in whose nose we shall all be in a few tens of thousands of millions of millions of millions of years.

All this is quite possible, and the probabilities for and against are quite out of reach. Perhaps also all the worlds, both above and below us, are fac-similes of our own. If so, away goes free will for good and all; unless, indeed, we underpin our system with the hypothesis that all the fac-simile bodies of different sizes are actuated by a common soul. These acute supplementary notions of mine go far to get rid of the difficulty which some have found in the common theory that the soul inhabits the body: it has been stated that there is, somewhere or another, a world of souls which communicate with their bodies by wondrous filaments of a nature neither mental nor material, but of a _tertium quid_ fit to be a go-between; as it were a corporispiritual copper encased in a spiritucorporeal gutta-percha. My theory is that every soul is everywhere _in posse_, as the schoolmen said, but not anywhere _in actu_, except where it finds one of its bodies. These _a priori_ difficulties being thus removed, the system of particle-worlds is reduced to a dry question of fact, and remitted to the decision of the microscope. And a grand field may thus be opened, as optical science progresses! For the worlds are not fac-similes of ours in time: there is not a moment of _our_ past, and not a moment of _our_ future, but is the _present_ of one or more of the particles. A will write the death of Caesar, and B the building of the Pyramids, by actual observation of the processes with a power of a thousand millions; C will discover the commencement of the Millennium, and D the {193} termination of Ersch and Gruber's Lexicon,[336] as mere physical phenomena. Against this glorious future there is a sad omen: the initials of the forerunner of this discovery are--NO!

THE SUPERNATURAL.

The History of the Supernatural in all ages and nations, and in all Churches, Christian and Pagan: demonstrating a universal faith. By Wm.

Howitt.[337] London, 2 vols. 8vo. 1863.

Mr. Howitt is a preacher of spiritualism. He cements an enormous collection of alleged facts with a vivid outpouring of exhortation, and an unsparing flow of sarcasm against the scorners of all cla.s.ses. He and the Rev. J.

Smith[338] (_ante_, 1854) are the most thoroughgoing universalists of all the writers I know on spiritualism. If either can insert the small end of the wedge, he will not let you off one fraction of the conclusion that all countries, in all ages, have been the theaters of one vast spiritual display. And I suspect that this consequence cannot be avoided, if any part of the system be of truly spiritual origin. Mr. Howitt treats the philosophers either as ignorant babies, or as conscious spirit-fearers: and seems much inclined to accuse the world at large of dreading, lest by the actual presence of the other world their Christianity should imbibe a spiritual element which would unfit it for the purposes of their lives.

{194}

FROM MATTER TO SPIRIT.

From Matter to Spirit. By C. D. With a preface by A. B.[339] London, 1863, 8vo.

This is a work on Spiritual Manifestations. The author upholds the facts for spiritual phenomena: the prefator suspends his opinion as to the cause, though he upholds the facts. The work begins systematically with the lower cla.s.s of phenomena, proceeds to the higher cla.s.s, and offers a theory, suggested by the facts, of the connection of the present and future life. I agree in the main with A. B.; but can, of course, make none but horrescent reference to his treatment of the smaller philosophers. This is always the way with your paradoxers: they behave towards orthodoxy as the thresher fish behaves towards the whale. But if true, as is said, that the drubbing clears the great fish of parasites which he could not otherwise get rid of, he ought to bear no malice. This preface retorts a little of that contempt which the "philosophical world" has bestowed with heaped measure upon those who have believed their senses, and have drawn natural, even if hasty, inferences. There is philosophercraft as well as priestcraft, both from one source, both of one spirit. In English cities and towns, the minister of religion has been tamed: so many weapons are bared against him when he obtrudes his office in a dictatory manner, that, as a rule, there is no more quiet and modest member of society than the urban clergyman.

Domination over religious belief is reserved for the exclusive use of those who admit the right: the rare exception to this mode of behavior is laughed at as a bigot, or shunned as a nuisance. But the overbearing minister of nature, who snaps you with _unphilosophical_ as the clergyman once frightened you with _infidel_, is still a recognized member of society, wants taming, and will get it. He wears the priest's cast-off {195} clothes, dyed to escape detection: the better sort of philosophers would gladly set him to square the circle.

The book just named appeared about the same time as this Budget began in the _Athenaeum_. It was commonly attributed, the book to my wife, the preface to myself. Some time after, our names were actually announced by the publisher, who ought to know. It will be held to confirm this statement that I announce our having in our possession some twenty reviews of different lengths, and of all characters: who ever collects a number of reviews of a book, except the author?

A great many of these reviews settle the matter _a priori_. If there had been spirits in the matter, they would have done this, and they would not have done that. Jean Meslier[340] said there could be no G.o.d over all, for, _if_ there had been one, He would have established a universal religion. If J. M. _knew_ that, J. M. was right: but if J. M. did not know that, then J. M. was on the "high priori road," and may be left to his course. The same to all who know what spirits would do and would not do.

A. B. very distinctly said that he knew some of the a.s.serted facts, believed others on testimony, but did not pretend to know whether they were caused by spirits, or had some unknown and unimagined origin. This he said as clearly as I could have said it myself. But a great many persons cannot understand such a frame of mind: their own apparatus is a kind of spirit-level, and their conclusion on any subject is the little bubble, which is always at one end or the other. Many of the reviewers declare that A. B. is a secret believer in the spirit-hypothesis: and one of them wishes that he had "endorsed his opinion more boldly." According to this reviewer, any one who writes "I boldly {196} say I am unable to choose," contradicts himself. In truth, a person who does say it has a good deal of courage, for each side believes that he secretly favors the other; and both look upon him as a coward. In spite of all this, A. B. boldly repeats that he feels a.s.sured of many of the facts of _spiritualism_, and that he cannot pretend to affirm or deny anything about their cause.

The great bulk of the illogical part of the educated community--whether majority or minority I know not; perhaps six of one and half-a-dozen of the other--have not power to make a distinction, cannot be made to take a distinction, and of course, never attempt to shake a distinction. With them all such things are evasions, subterfuges, come-offs, loopholes, etc. They would hang a man for horse-stealing under a statute against sheep-stealing; and would laugh at you if you quibbled about the distinction between a horse and a sheep. I divide the illogical--I mean people who have not that amount of natural use of sound inference which is really not uncommon--into three cla.s.ses:--First cla.s.s, three varieties: the Niddy, the Noddy, and the Noodle. Second cla.s.s, three varieties: the Niddy-Noddy, the Niddy-Noodle, and the Noddy-Noodle. Third cla.s.s, undivided: the Niddy-Noddy-Noodle. No person has a right to be angry with me for more than one of these subdivisions.

The want of distinction was ill.u.s.trated to me, when a boy, about 1820, by the report of a trial which I shall never forget: boys read newspapers more keenly than men. Every now and then a bench of country magistrates rather astonishes the town populations, accustomed to rub their brains[341]

against one another. Such a story as the following would, {197} in our day, bring down grave remarks from above: but I write of the olden (or Eldon[342]) time, when nothing but conviction in a court of record would displace a magistrate. In that day the third-cla.s.s amalgamator of distinct things was often on the bench of quarter-sessions.

An attorney was charged with having been out at night poaching. A clear _alibi_ was established; and perjury had certainly been committed. The whole gave reason to suspect that some ill-willers thought the bench disliked the attorney so much that any conviction was certain on any evidence. The bench did dislike the attorney: but not to the extent of thinking he could snare any partridges in the fields while he was asleep in bed, except the dream-partridges which are not always protected by the dream-laws. So the chairman said, "Mr. ----, you are discharged; but you should consider this one of the most fortunate days of your life." The attorney indignantly remonstrated, but the magistrate was right; for he said, "Mr. ----, you have frequently been employed to defend poachers: have you been careful to impress upon them the enormity of their practices?" It appeared in a wrangling conversation that the magistrates saw little moral difference between poaching and being a poacher's professional defender without lecturing him on his wickedness: but they admitted with reluctance, that there was a legal distinction; and the brain of N^3 could no further go. This is nearly fifty years ago; and Westernism was not quite extinct.

If the present lords of the hills and the valleys want to shine, let them publish a true history of their own order. I am just old enough to remember some of the last of the squires and parsons who protested against teaching the poor to read and write. They now write books for the working cla.s.ses, give them lectures, and the like. There is now no cla.s.s, as a cla.s.s, more highly educated, broadly educated, and deeply educated, {198} than those who were, in old times, best described as partridge-popping squireens. I have myself, when a boy, heard Old b.o.o.by speaking with pride of Young b.o.o.by as having too high a spirit to be confined to books: and I suspected that his dislike to teaching the poor arose in fact from a feeling that they would, if taught a little, pa.s.s his heir.

A. B. recommended the spirit-theory as an hypothesis on which to ground inquiry; that is, as the means of suggestion for the direction of inquiry.