Chapter XIII: Part 13

Mr. Hind announces to the _Times_ that he has received a letter from Dr. Bruennow, of the Royal Observatory at Berlin, giving the very important information that Le Verrier's planet was found by M. Galle, on the night of September 23. "In announcing this grand discovery," he says, "I think it better to copy Dr. Bruennow's[800] letter."

"Berlin, Sept. 25.

"My dear Sir--M. Le Verrier's planet was discovered here the 23d of September, by M. Galle.[801] It is a star of the 8th magnitude, but with a diameter of two or three seconds. Here are its places:

h. m. s. R. A. Declination.
Sept. 23, 12 0 14.6 M.T. 328 deg. 19' 16.0" -13 deg. 24' 8.2"
Sept. 24, 8 54 40.9 M.T. 328 deg. 18' 14.3" -13 deg. 24' 29.7"

The planet is now retrograde, its motion amounting daily to four seconds of time.

"Yours most respectfully, BRUeNNOW."

"This discovery," Mr. Hind says, "may be justly considered one of the greatest triumphs of theoretical astronomy;" and he adds, in a postscript, that the planet was observed at Mr. Bishop's[802] Observatory, in the Regent's Park, {387} on Wednesday night, notwithstanding the moonlight and hazy sky. "It appears bright," he says, "and with a power of 320 I can see the disc. The following position is the result of instrumental comparisons with 33 Aquarii:

Sept. 30, at 8h. 16m. 21s. Greenwich mean time--
Right ascension of planet 21h. 52m. 47.15s.
South declination 13 deg. 27' 20"."

THE NEW PLANET.

"Cambridge Observatory, Oct. 15.

"The allusion made by Sir John Herschel, in his letter contained in the _Athenaeum_ of October 3, to the theoretical researches of Mr. Adams, respecting the newly-discovered planet, has induced me to request that you would make the following communication public. It is right that I should first say that I have Mr. Adams's permission to make the statements that follow, so far as they relate to his labors. I do not propose to enter into a detail of the steps by which Mr. Adams was led, by his spontaneous and independent researches, to a conclusion that a planet must exist more distant than Uranus. The matter is of too great historical moment not to receive a more formal record than it would be proper to give here. My immediate object is to show, while the attention of the scientific public is more particularly directed to the subject, that, with respect to this remarkable discovery, English astronomers may lay claim to some merit.

"Mr. Adams formed the resolution of trying, by calculation, to account for the anomalies in the motion of Uranus on the hypothesis of a more distant planet, when he was an undergraduate in this university, and when his exertions for the academical distinction, which he obtained in January 1843, left him no time for pursuing the research. In the course of that year, he arrived at an approximation to the position of the supposed planet; which, however, he did not consider to be worthy of confidence, on account of his not {388} having employed a sufficient number of observations of Uranus. Accordingly, he requested my intervention to obtain for him the early Greenwich observations, then in course of reduction;--which the Astronomer Royal immediately supplied, in the kindest possible manner. This was in February, 1844. In September, 1845, Mr. Adams communicated to me values which he had obtained for the heliocentric longitude, excentricity of orbit, longitude of perihelion, and mass, of an assumed exterior planet,--deduced entirely from unaccounted-for perturbations of Uranus. The same results, somewhat corrected, he communicated, in October, to the Astronomer Royal. M. Le Verrier, in an investigation which was published in June of 1846, assigned very nearly the same heliocentric longitude for the probable position of the planet as Mr. Adams had arrived at, but gave no results respecting its mass and the form of its orbit. The coincidence as to position from two entirely independent investigations naturally inspired confidence; and the Astronomer Royal shortly after suggested the employing of the Northumberland telescope of this observatory in a systematic search after the hypothetical planet; recommending, at the same time, a definite plan of operations. I undertook to make the search,--and commenced observing on July 29. The observations were directed, in the first instance, to the part of the heavens which theory had pointed out as the most probable place of the planet; in selecting which I was guided by a paper drawn up for me by Mr. Adams. Not having hour xxi. of the Berlin star-maps--of the publication of which I was not aware--I had to proceed on the principle of comparison of observations made at intervals. On July 30, I went over a zone 9' broad, in such a manner as to include all stars to the eleventh magnitude. On August 4, I took a broader zone and recorded a place of the planet. My next observations were on August 12; when I met with a star of the eighth magnitude in the zone which I had gone over on July 30,--and which did not then {389} contain this star. Of course, this was the planet;--the place of which was, thus, recorded a second time in four days of observing. A comparison of the observations of July 30 and August 12 would, according to the principle of search which I employed, have shown me the planet. I did not make the comparison till after the detection of it at Berlin--partly because I had an impression that a much more extensive search was required to give any probability of discovery--and partly from the press of other occupation. The planet, however, was _secured_, and two positions of it recorded six weeks earlier here than in any other observatory,--and in a systematic search expressly undertaken for that purpose. I give now the positions of the planet on August 4 and August 12.

Greenwich mean time.

Aug. 4, 13h. 36m. 25s. {R.A. 21h. 58m. 14.70s.
{N.P.D. 102 deg. 57' 32.2"

Aug. 12, 13h. 3m. 26s. {R.A. 21h. 57m. 26.13s.
{N.P.D. 103 deg. 2' 0.2"

"From these places compared with recent observations Mr. Adams has obtained the following results:

Distance of the planet from the sun 30.05
Inclination of the orbit 1 deg. 45'
Longitude of the descending node 309 deg. 43'
Heliocentric longitude, Aug. 4 326 deg. 39'

"The present distance from the sun is, therefore, thirty times the earth's mean distance;--which is somewhat less than the theory had indicated. The other elements of the orbit cannot be approximated to till the observations shall have been continued for a longer period.

"The part taken by Mr. Adams in the theoretical search after this planet will, perhaps, be considered to justify the suggesting of a name. With his consent, I mention _Oceanus_ as one which may possibly receive the votes of astronomers.--I {390} have authority to state that Mr. Adams's investigations will in a short time, be published in detail.

"J. CHALLIS."[803]

ASTRONOMICAL POLICE REPORT.

"An ill-looking kind of a body, who declined to give any name, was brought before the Academy of Sciences, charged with having assaulted a gentleman of the name of Uranus in the public highway. The prosecutor was a youngish looking person, wrapped up in two or three great coats; and looked chillier than anything imaginable, except the prisoner,--whose teeth absolutely shook, all the time.

Policeman Le Verrier[804] stated that he saw the prosecutor walking along the pavement,--and sometimes turning sideways, and sometimes running up to the railings and jerking about in a strange way. Calculated that somebody must be pulling his coat, or otherwise assaulting him. It was so dark that he could not see; but thought, if he watched the direction in which the next odd move was made, he might find out something. When the time came, he set Bruennow, a constable in another division of the same force, to watch where he told him; and Bruennow caught the prisoner lurking about in the very spot,--trying to look as if he was minding his own business. Had suspected for a long time that somebody was lurking about in the neighborhood. Bruennow was then called, and deposed to his catching the prisoner as described.

_M. Arago._--Was the prosecutor sober?

_Le Verrier._--Lord, yes, your worship; no man who had a drop in him ever looks so cold as he did.

_M. Arago._--Did you see the assault?

_Le Verrier._--I can't say I did; but I told Bruennow exactly how he'd be crouched down;--just as he was.

{391}

_M. Arago (to Bruennow)._--Did _you_ see the assault?

_Bruennow._--No, your worship; but I caught the prisoner.

_M. Arago._--How did you know there was any assault at all?

_Le Verrier._--I reckoned it couldn't be otherwise, when I saw the prosecutor making those odd turns on the pavement.

_M. Arago._--You reckon and you calculate! Why, you'll tell me, next, that you policemen may sit at home and find out all that's going on in the streets by arithmetic. Did you ever bring a case of this kind before me till now?

_Le Verrier._--Why, you see, your worship, the police are growing cleverer and cleverer every day. We can't help it:--it grows upon us.

_M. Arago._--You're getting too clever for me. What does the prosecutor know about the matter?

The prosecutor said, all he knew was that he was pulled behind by somebody several times. On being further examined, he said that he had seen the prisoner often, but did not know his name, nor how he got his living; but had understood he was called Neptune. He himself had paid rates and taxes a good many years now. Had a family of six,--two of whom got their own living.

The prisoner being called on for his defence, said that it was a quarrel. He had pushed the prosecutor--and the prosecutor had pushed him. They had known each other a long time, and were always quarreling;--he did not know why. It was their nature, he supposed. He further said, that the prosecutor had given a false account of himself;--that he went about under different names. Sometimes he was called Uranus, sometimes Herschel, and sometimes Georgium Sidus; and he had no character for regularity in the neighborhood. Indeed, he was sometimes not to be seen for a long time at once.

The prosecutor, on being asked, admitted, after a little hesitation, that he had pushed and pulled the prisoner too. {392} In the altercation which followed, it was found very difficult to make out which began:--and the worthy magistrate seemed to think they must have begun together.

_M. Arago._--Prisoner, have you any family?

The prisoner declined answering that question at present. He said he thought the police might as well reckon it out whether he had or not.

_M. Arago_ said he didn't much differ from that opinion.--He then addressed both prosecutor and prisoner; and told them that if they couldn't settle their differences without quarreling in the streets, he should certainly commit them both next time. In the meantime, he called upon both to enter into their own recognizances; and directed the police to have an eye upon both,--observing that the prisoner would be likely to want it a long time, and the prosecutor would be not a hair the worse for it."

This quib was written by a person who was among the astronomers: and it illustrates the fact that Le Verrier had sole possession of the field until Mr. Challis's letter appeared. Sir John Herschel's previous communication should have paved the way: but the wonder of the discovery drove it out of many heads. There is an excellent account of the whole matter in Professor Grant's[805] _History of Physical Astronomy_. The squib scandalized some grave people, who wrote severe admonitions to the editor. There are formalists who spend much time in writing propriety to journals, to which they serve as foolometers. In a letter to the _Athenaeum_, speaking of the way in which people hawk fine terms for common things, I said that these people ought to have a new translation of the Bible, which should contain the verse "gentleman and lady, created He them." The editor was handsomely fired and brimstoned!

{393}

A NEW THEORY OF TIDES.

A new theory of the tides: in which the errors of the usual theory are
demonstrated; and proof shewn that the full moon is not the cause of a
concomitant spring tide, but actually the cause of the neaps.... By
Comm^r. Debenham,[806] R.N. London, 1846, 8vo.

The author replied to a criticism in the _Athenaeum_, and I remember how, in a very few words, he showed that he had read nothing on the subject. The reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr. Critic." Had he read any of the actual investigations on the usual theory, he would have known that to this day the sun and moon continue to be called _planets_--though the phrase is disappearing--in speaking of the tides; the sense, of course, being the old one, wandering bodies.

A large class of the paradoxers, when they meet with something which taken in their sense is absurd, do not take the trouble to find out the intended meaning, but walk off with the words laden with their own first construction. Such men are hardly fit to walk the streets without an interpreter. I was startled for a moment, at the time when a recent happy--and more recently happier--marriage occupied the public thoughts, by seeing in a haberdasher's window, in staring large letters, an unpunctuated sentence which read itself to me as "Princess Alexandra! collar and cuff!" It immediately occurred to me that had I been any one of some scores of my paradoxers, I should, no doubt, have proceeded to raise the mob against the unscrupulous person who dared to hint to a young bride such maleficent--or at least immellificent--conduct towards her new lord. But, as it was, certain material contexts in the shop window suggested a less {394} savage explanation. A paradoxer should not stop at reading the advertisements of Newton or Laplace; he should learn to look at the stock of goods.

I think I must have an eye for double readings, when presented: though I never guess riddles. On the day on which I first walked into the _Panizzi_ reading room[807]--as it ought to be called--at the Museum, I began my circuit of the wall-shelves at the ladies' end: and perfectly coincided in the propriety of the Bibles and theological works being placed there. But the very first book I looked on the back of had, in flaming gold letters, the following inscription--"Blast the Antinomians!"[808] If a line had been drawn below the first word, Dr. Blast's history of the Antinomians would not have been so fearfully misinterpreted. It seems that neither the binder nor the arranger of the room had caught my reading. The book was removed before the catalogue of books of reference was printed.

AN ASTRONOMICAL PARADOXER.

Two systems of astronomy: first, the Newtonian system, showing the rise
and progress thereof, with a short historical account; the general
theory with a variety of remarks thereon: second, the system in
accordance with the Holy Scriptures, showing the rise and progress from
Enoch, the seventh from Adam, the prophets, Moses, and others, in the
first Testament; our Lord Jesus Christ, and his apostles, in the new or
second Testament; Reeve and Muggleton, in the third and last Testament;
with a variety of remarks thereon. By Isaac Frost.[809] London, 1846,
4to.

{395}

A very handsomely printed volume, with beautiful plates. Many readers who have heard of Muggletonians have never had any distinct idea of Lodowick Muggleton,[810] the inspired tailor, (1608-1698) who about 1650 received his commission from heaven, wrote a Testament, founded a sect, and descended to posterity. Of Reeve[811] less is usually said; according to Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself with one specimen of Mr. Frost's science:

"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when the reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs in support of his theory of the earth revolving round the sun: all the rest is assertion without any proofs.'--'What are they?' inquired the Doctor.--'Well,' I said, 'they are, first, the power of {396} attraction to keep the earth to the sun; the second is the power of repulsion, by virtue of the centrifugal motion of the earth: all the rest appears to me assertion without proof.' The Doctor considered a short time and then said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the credit of completing the system, but really he has only half done his work.'--'How is that,' inquired my friend the Doctor. My reply was this: 'You will observe his system shows the earth traverses round the sun on an inclined plane; the consequence is, there are four powers required to make his system complete:

1st. The power of _attraction_.
2ndly. The power of _repulsion_.
3rdly. The power of _ascending_ the inclined plane.
4thly. The power of _descending_ the inclined plane.

You will thus easily see the _four_ powers required, and Newton has only accounted for _two_; the work is therefore only half done.' Upon due reflection the Doctor said, 'It certainly was necessary to have these _four_ points cleared up before the system could be said to be complete.'"

I have no doubt that Mr. Frost, and many others on my list, have really encountered doctors who could be puzzled by such stuff as this, or nearly as bad, among the votaries of existing systems, and have been encouraged thereby to print their objections. But justice requires me to say that from the words "power of repulsion by virtue of the centrifugal motion of the earth," Mr. Frost may be suspected of having something more like a notion of the much-mistaken term "centrifugal force" than many paradoxers of greater fame. The Muggletonian sect is not altogether friendless: over and above this handsome volume, the works of Reeve and Muggleton were printed, in 1832, in three quarto volumes. See _Notes and Queries, 1st Series_, v, 80; 3d Series, iii, 303. {397}

[The system laid down by Mr. Frost, though intended to be substantially that of Lodowick Muggleton, is not so vagarious. It is worthy of note how very different have been the fates of two contemporary paradoxers, Muggleton and George Fox.[813] They were friends and associates,[814] and commenced their careers about the same time, 1647-1650. The followers of Fox have made their sect an institution, and deserve to be called the pioneers of philanthropy. But though there must still be Muggletonians, since expensive books are published by men who take the name, no sect of that name is known to the world. Nevertheless, Fox and Muggleton are men of one type, developed by the same circumstances: it is for those who investigate such men to point out why their teachings have had fates so different. Macaulay says it was because Fox found followers of more sense than himself. True enough: but why did Fox find such followers and not Muggleton? The two were equally crazy, to all appearance: and the difference required must be sought in the doctrines themselves.

Fox was not a _rational_ man: but the success of his sect and doctrines entitles him to a letter of alteration of the phrase which I am surprised has not become current. When Conduitt,[815] the husband of Newton's half-niece, wrote a circular to Newton's friends, just after his death, inviting them to bear their parts in a proper biography, he said, "As Sir I. Newton was a _national_ man, I think every one ought to contribute to a work intended to do him justice." Here is the very phrase which is often wanted to signify that {398} celebrity which puts its mark, good or bad, on the national history, in a manner which cannot be asserted of many notorious or famous historical characters. Thus George Fox and Newton are both _national_ men. Dr. Roget's[816] _Thesaurus_ gives more than fifty synonyms--_colleagues_ would be the better word--of "_celebrated_," any one of which might be applied, either in prose or poetry, to Newton or to his works, no one of which comes near to the meaning which Conduitt's adjective immediately suggests.

The truth is, that we are too _monarchical_ to be _national_. We have the Queen's army, the Queen's navy, the Queen's highway, the Queen's English, etc.; nothing is national except the _debt_. That this remark is not new is an addition to its force; it has hardly been repeated since it was first made. It is some excuse that _nation_ is not vernacular English: the _country_ is our word, and _country man_ is appropriated.]

Astronomical Aphorisms, or Theory of Nature; founded on the immutable
basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.

This is by the framer of the Weather Almanac, who appeals to that work as corroborative of his theory of planetary temperature, years after all the world knew by experience that this meteorological theory was just as good as the others.

{399}

The conspiracy of the Bullionists as it affects the present system of
the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).

This pamphlet is one of a class of which I know very little, in which the effects of the laws relating to this or that political bone of contention are imputed to deliberate conspiracy of one class to rob another of what the one knew ought to belong to the other. The success of such writers in believing what they have a bias to believe, would, if they knew themselves, make them think it equally likely that the inculpated classes might really believe what it is _their_ interest to believe. The idea of a _guilty_ understanding existing among fundholders, or landholders, or any holders, all the country over, and never detected except by bouncing pamphleteers, is a theory which should have been left for Cobbett[818] to propose, and for Apella to believe.[819]

[_August_, 1866. A pamphlet shows how to pay the National Debt. Advance paper to railways, etc., receivable in payment of taxes. The railways pay interest and principal in money, with which you pay your national debt, and redeem your notes. Twenty-five years of interest redeems the notes, and then the principal pays the debt. Notes to be kept up to value by penalties.]

THEISM INDEPENDENT OF REVELATION.

The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price _2d._ Is
there sufficient proof of the existence of God? 8vo. 1847.

This acorn of the holy oak was forwarded to me with a manuscript note, signed by the editor, on the part of the {400} "London Society of Theological Utilitarians," who say, "they trust you may be induced to give this momentous subject your consideration." The supposition that a middle-aged person, known as a student of thought on more subjects than one, had that particular subject yet to begin, is a specimen of what I will call the _assumption-trick_ of controversy, a habit which pervades all sides of all subjects. The tract is a proof of the good policy of letting opinions find their level, without any assistance from the Court of Queen's Bench. Twenty years earlier the thesis would have been positive, "There is sufficient proof of the non-existence of God," and bitter in its tone. As it stands, we have a moderate and respectful treatment--wrong only in making the opponent argue absurdly, as usually happens when one side invents the other--of a question in which a great many Christians have agreed with the atheist: that question being--Can the existence of God be proved independently of revelation? Many very religious persons answer this question in the negative, as well as Mr. Holyoake. And, this point being settled, all who agree in the negative separate into those who can endure scepticism, and those who cannot: the second class find their way to Christianity. This very number of _The Reasoner_ announces the secession of one of its correspondents, and his adoption of the Christian faith. This would not have happened twenty years before: nor, had it happened, would it have been respectfully announced.

There are people who are very unfortunate in the expression of their meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded a pamphlet on the existence of God, and said that the Society trusted I "may be induced to give" the subject my "consideration." How could I know the Society was one person, who supposed I had arrived at a conclusion and wanted a "_guiding word_"? But so it seems it was: Mr. Holyoake, in the _English {401} Leader_ of October 15, 1864, and in a private letter to me, writes as follows:

"The gentleman who was the author of the argument, and who asked me to send it to Mr. De Morgan, never assumed that that gentleman had 'that particular subject to begin'--on the contrary, he supposed that one whom we all knew to be eminent as a thinker _had_ come to a conclusion upon it, and would perhaps vouchsafe a guiding word to one who was, as yet, seeking the solution of the Great Problem of Theology. I told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he must be content to wait. On some day of courtesy and leisure he might have the kindness to write.' Nor was I wrong--the answer appears in your pages at the lapse of seventeen years."

I suppose Mr. Holyoake's way of putting his request was the _stylus curiae_ of the Society. A worthy Quaker who was sued for debt in the King's Bench was horrified to find himself charged in the declaration with detaining his creditor's money by force and arms, contrary to the peace of our Lord the King, etc. It's only the _stylus curiae_, said a friend: I don't know _curiae_, said the Quaker, but he shouldn't style us peace-breakers.

The notion that the _non_-existence of God can be _proved_, has died out under the light of discussion: had the only lights shone from the pulpit and the prison, so great a step would never have been made. The question now is as above. The dictum that Christianity is "part and parcel of the law of the land" is also abrogated: at the same time, and the coincidence is not an accident, it is becoming somewhat nearer the truth that the law of the land is part and parcel of Christianity. It must also be noticed that _Christianity_ was part and parcel of the articles of _war_; and so was _duelling_. Any officer speaking against religion was to be cashiered; and any officer receiving an affront without, in the last resort, attempting to kill his opponent, was also to be cashiered. Though somewhat of a book-hunter, I {402} have never been able to ascertain the date of the collected remonstrances of the prelates in the House of Lords against this overt inculcation of murder, under the soft name of _satisfaction_: it is neither in Watt,[821] nor in Lowndes,[822] nor in any edition of Brunet;[823] and there is no copy in the British Museum. Was the collected edition really published?

[The publication of the above in the _Athenaeum_ has not produced reference to a single copy. The collected edition seems to be doubted. I have even met one or two persons who doubt the fact of the Bishops having remonstrated at all: but their doubt was founded on an absurd supposition, namely, that it was _no business of theirs_; that it was not the business of the prelates of the church in union with the state to remonstrate against the Crown commanding murder! Some say that the edition was published, but under an irrelevant title, which prevented people from knowing what it was about. Such things have happened: for example, arranged extracts from Wellington's general orders, which would have attracted attention, fell dead under the title of "Principles of War." It is surmised that the book I am looking for also contains the protests of the Reverend bench against other things besides the Thou-shalt-do-murder of the Articles (of war), and is called "First Elements of Religion" or some similar title. Time clears up all things.]

* * * * *

Notes

[1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p 61.

[2] In the first edition this reference was to page 11.

[3] In the first edition this read "at page 438," the work then appearing in a single volume.

[4] "Just as it would surely have been better not to have considered it (i.e., the trinity) as a mystery, and with Cl. Kleckermann to have investigated by the aid of philosophy according to the teaching of true logic what it might be, before they determined what it was; just so would it have been better to withdraw zealously and industriously into the deepest caverns and darkest recesses of metaphysical speculations and suppositions in order to establish their opinion beyond danger from the weapons of their adversaries.... Indeed that great man so explains and demonstrates this dogma (although to theologians the word has not much charm) from the immovable foundations of philosophy, that with but few changes and additions a mind sincerely devoted to truth can desire nothing more."

[5] Mrs. Wititterly, in _Nicholas Nickleby_.--A. De M.

[6] The brackets mean that the paragraph is substantially from some one of the _Athenaeum Supplements_.--S. E. De M.

[7] "It is annoying that this ingenious naturalist who has already given us more useful works and has still others in preparation, uses for this odious task, a pen dipped in gall and wormwood. It is true that many of his remarks have some foundation, and that to each error that he points out he at the same time adds its correction. But he is not always just and never fails to insult. After all, what does his book prove except that a forty-fifth part of a very useful review is not free from mistakes? Must we confuse him with those superficial writers whose liberty of body does not permit them to restrain their fruitfulness, that crowd of savants of the highest rank whose writings have adorned and still adorn the _Transactions_? Has he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill himself?"

[8] "Let no free man be seized or imprisoned or in any way harmed except by trial of his peers."

[9] "The master can rob, wreck and punish his slave according to his pleasure save only that he may not maim him."

[10] An Irish antiquary informs me that Virgil is mentioned in annals at A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of Saltzburg] died in Germany in the thirteenth year of his bishoprick." No allusion is made to his opinions; but it seems he was, by tradition, a mathematician. The Abbot of Aghabo (Queen's County) was canonized by Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be much damaged by the character given to the real bishop, if there were anything in it to dilapidate.--A. De M.

[11] "He performed many acts befitting the Papal dignity, and likewise many excellent (to be sure!) works."

[12] "After having been on the throne during ten years of pestilence."

[13] The work is the _Questiones Joannis Buridani super X libros Aristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio. It also appeared at Paris in editions of 1499, 1513, and 1518, and at Oxford in 1637.

[14] Jean Buridan was born at Bethune about 1298, and died at Paris about 1358. He was professor of philosophy at the University of Paris and several times held the office of Rector. As a philosopher he was classed among the nominalists.

[15] So in the original.

[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the pantheistic philosopher, excommunicated from the Jewish faith for heresy, was born at Amsterdam in 1632 and died there in 1677.

[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire, Scotland, and died about 1291. He was one of the best known savants of the court of Emperor Frederick II, and wrote upon astrology, alchemy, and the occult sciences. He was looked upon as a great magician and is mentioned among the wizards in Dante's _Inferno_.

"That other, round the loins
So slender of his shape, was Michael Scot,
Practised in every slight of magic wile." _Inferno_, XX.

Boccaccio also speaks of him: "It is not long since there was in this city (Florence) a great master in necromancy, who was called Michele Scotto, because he was a Scot." _Decameron_, Dec. Giorno.

Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_, is well known:

"In these fair climes, it was my lot
To meet the wondrous Michael Scott;
A wizard of such dreaded fame,
That when, in Salamanca's cave,
Him listed his magic wand to wave,
The bells would ring in Notre Dame!"

Sir Walter's notes upon him are of interest.

[18] These were some of the forgeries which Michel Chasles (1793-1880) was duped into buying. They purported to be a correspondence between Pascal and Newton and to show that the former had anticipated some of the discoveries of the great English physicist and mathematician. That they were forgeries was shown by Sir David Brewster in 1855.

[19] "Let the serpent also break from its appointed path."

[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at Florence in 1803; died at Fiesole in 1869. His _Histoire des Sciences Mathematiques_ appeared at Paris in 1838, the entire first edition of volume I, save some half dozen that he had carried home, being burned on the day that the printing was completed. He was a great collector of early printed works on mathematics, and was accused of having stolen large numbers of them from other libraries. This accusation took him to London, where he bitterly attacked his accusers. There were two auction sales of his library, and a number of his books found their way into De Morgan's collection.

[21] Philo of Gadara lived in the second century B.C. He was a pupil of Sporus, who worked on the problem of the two mean proportionals.

[22] In his _Histoire des Mathematiques_, the first edition of which appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died at Versailles in 1799. He was therefore only thirty-three years old when his great work appeared. The second edition, with additions by D'Alembert, appeared in 1799-1802. He also wrote a work on the quadrature of the circle, _Histoire des recherches sur la Quadrature du Cercle_, which appeared in 1754.

[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the first four books of the conics of Apollonius of Perga (247-222 B.C.). He also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and on the two books on Equilibrium of Archimedes (287-212 B.C.)

[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His famous arithmetic appeared in 1677 and went through many editions. It was written in a style that appealed to teachers, and was so popular that the expression "According to Cocker" became a household phrase. Early in the nineteenth century there was a similar saying in America, "According to Daboll," whose arithmetic had some points of analogy to that of Cocker. Each had a well-known prototype in the ancient saying, "He reckons like Nicomachus of Gerasa."

[25] So in the original, for Barreme. Francois Barreme was to France what Cocker was to England. He was born at Lyons in 1640, and died at Paris in 1703. He published several arithmetics, dedicating them to his patron, Colbert. One of the best known of his works is _L'arithmetique, ou le livre facile pour apprendre l'arithmetique soi-meme_, 1677. The French word _bareme_ or _barreme_, a ready-reckoner, is derived from his name.

[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom Cato or Tully could have acknowledged for their countryman." His works on arithmetic, music, and geometry were classics in the medieval schools.

[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV (1261-1264). He was one of the early medieval translators of Euclid from the Arabic into Latin, and the first printed edition of the _Elements_ (Venice, 1482) was from his translation. In this work he probably depended not a little upon at least two or three earlier scholars. He also wrote _De computo ecclesiastico Calendarium_, and _De quadratura circuli_.

[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the circumference to the diameter of a circle.

[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in 1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged and inaccurate, but it is still a helpful bibliography. De Morgan speaks somewhere of his indebtedness to it.

[30] Abraham Gotthelf Kaestner was born at Leipsic in 1719, and died at Goettingen in 1800. He was professor of mathematics and physics at Goettingen. His _Geschichte der Mathematik_ (1796-1800) was a work of considerable merit. In the text of the _Budget of Paradoxes_ the name appears throughout as Kastner instead of Kaestner.

[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in 1476; died at Rome in 1558. He was an astrologer and mathematician, and was professor of mathematics at Ferrara in 1531. In 1545 he became bishop of Civita Ducale.

[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in 1892. He and Leverrier predicted the discovery of Neptune from the perturbations in Uranus.

[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811, and died at Paris in 1877. It was his data respecting the perturbations of Uranus that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in 1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De Morgan refers, appeared at Leyden in 1594.

[35] The title is: _In hoc libra contenta.... Introductio i geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere. Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boueelles, Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He was canon and professor of theology at Noyon. His _Introductio_ contains considerable work on star polygons, a favorite study in the Middle Ages and early Renaissance. His work _Que hoc volumine contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at Paris in 1509-10.

[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions of honor in the church, including the bishopric of Brescia. He was made a cardinal in 1448. He wrote several works on mathematics, his _Opuscula varia_ appearing about 1490, probably at Strasburg, but published without date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and at Basel in 1565.

[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was one of the most successful printers of his day. He was known as _Typographus Parisiensis_, and to his press we owe some of the best works of the period.

[38] Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was born at Estaples, near Amiens, in 1455, and died at Nerac in 1536. He was a priest, vicar of the bishop of Meaux, lecturer on philosophy at the College Lemoine in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy, theology, and mathematics.

[39] Claude-Francois Milliet de Challes was born at Chambery in 1621, and died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660, and published a _Cursus seu mundus mathematicus_, which included a short history of mathematics, in 1674. He also wrote on mathematical geography.

[40] This date should be 1503, if he refers to the first edition. It is well known that this is the first encyclopedia worthy the name to appear in print. It was written by Gregorius Reisch (born at Balingen, and died at Freiburg in 1487), prior of the cloister at Freiburg and confessor to Maximilian I. The first edition appeared at Freiburg in 1503, and it passed through many editions in the sixteenth and seventeenth centuries. The title of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita phylosophica tractans de omni genere scibili: Cum additionibus: Quae in alijs non habentur_.

[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura circuli demonstratio ex Campano_, that appeared without date about 1507.

[42] Born at Liverpool in 1805, and died there about 1872. He was a merchant, and in 1865 he published, at Liverpool, a work entitled _The Quadrature of the Circle, or the True Ratio between the Diameter and Circumference geometrically and mathematically demonstrated_. In this he gives the ratio as exactly 3-1/8.

[43] "That it would be impossible to tell him exactly, since no one had yet been able to find precisely the ratio of the circumference to the diameter."

[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno Christi ... MDXIIII," as appears by the colophon of the second volume to which De Morgan refers.

[45] Regiomontanus, or Johann Mueller of Koenigsberg (Regiomontanus), was born at Koenigsberg in Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at Vienna under the great astronomer Peuerbach, and was his most famous pupil. He wrote numerous works, chiefly on astronomy. He is also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germanus de Regiomonte, etc.

[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble in 1535. He was professor of theology at Cologne and also at Turin. After the publication of his _De Occulta Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp in 1530, and each passed through a large number of editions. A French translation appeared in Paris in 1582, and an English one in London in 1651.

[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in 1600. He was a jurist and historian, and held the office of procurator general to the Duke of Lorraine.

[48] This was at the storming of the city by the British on May 4, 1799. From his having been born in India, all this appealed strongly to the interests of De Morgan.

[49] Orontius Finaeus, or Oronce Fine, was born at Briancon in 1494 and died at Paris, October 6, 1555. He was imprisoned by Francois I for refusing to recognize the concordat (1517). He was made professor of mathematics in the College Royal (later called the College de France) in 1532. He wrote extensively on astronomy and geometry, but was by no means a great scholar. He was a pretentious man, and his works went through several editions. His _Protomathesis_ appeared at Paris in 1530-32. The work referred to by De Morgan is the _Quadratura circuli tandem inventa & clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556 edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_, published at Paris, the subtitle is: _Quibus inter caetera, Circuli quadratura Centum modis, & supra, per eundem Orontium recenter excogitatis, demonstratus_, so that he kept up his efforts until his death.

[50] Johannes Buteo (Boteo, Buteon, Bateon) was born in Dauphine c. 1485-1489, and died in a cloister in 1560 or 1564. Some writers give Charpey as the place and 1492 as the date of his birth, and state that he died at Canar in 1572. He belonged to the order of St. Anthony, and wrote chiefly on geometry, exposing the pretenses of Finaeus. His _Opera geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De quadratura circuli libri duo_ at Lyons in 1559.

[51] This is the great French algebraist, Francois Viete (Vieta), who was born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603. His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His _Opera mathematica_ was edited by Van Schooten in 1646.

[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_, that appeared in Paris in 1556. For the title page see Smith, D. E., _Rara Arithmetica_, Boston, 1908, p. 280.

[53] The title is correct except for a colon after _Astronomicum_. Nicolaus Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De astronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oder Algebra_ (1601).

[54] Born at Dole, Franche-Comte, about 1550, died in Holland about 1600. The work to which reference is made is the _Quadrature du cercle, ou maniere de trouver un quarre egal au cercle donne_, which appeared at Delft in 1584. Duchesne had the courage of his convictions, not only on circle-squaring but on religion as well, for he was obliged to leave France because of his conversion to Calvinism. De Morgan's statement that his real name is Van der Eycke is curious, since he was French born. The Dutch may have translated his name when he became professor at Delft, but we might equally well say, that his real name was Quercetanus or a Quercu.

[55] This was the father of Adriaan Metius (1571-1635). He was a mathematician and military engineer, and suggested the ratio 355/113 for [pi], a ratio afterwards published by his son. The ratio, then new to Europe, had long been known and used in China, having been found by Tsu Ch'ung-chih (428-499 A.D.).

[56] This was Jost Buergi, or Justus Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante editionem Neperianam viam praeiverunt ad hos ipsissimos logarithmos." He constructed a table of antilogarithms (_Arithmetische und geometrische Progress-Tabulen_), but it was not published until after Napier's work appeared.

[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610. It was he who first carried the computation of [pi] to 35 decimal places.

[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.

[59] I do not know this edition. There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae," 4to, in 1591.

[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions, irrationals, and the duplication of the cube.

[61]

_The Circle Speaks._
"At first a circle I was called,
And was a curve around about
Like lofty orbit of the sun
Or rainbow arch among the clouds.
A noble figure then was I--
And lacking nothing but a start,
And lacking nothing but an end.
But now unlovely do I seem
Polluted by some angles new.
This thing Archytas hath not done
Nor noble sire of Icarus
Nor son of thine, Iapetus.
What accident or god can then
Have quadrated mine area?"

_The Author Replies._
"By deepest mouth of Turia
And lake of limpid clearness, lies
A happy state not far removed
From old Saguntus; farther yet
A little way from Sucro town.
In this place doth a poet dwell,
Who oft the stars will closely scan,
And always for himself doth claim
What is denied to wiser men;--
An old man musing here and there
And oft forgetful of himself,
Not knowing how to rightly place
The compasses, nor draw a line,
As he doth of himself relate.
This craftsman fine, in sooth it is
Hath quadrated thine area."

[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in 1601. His work on the Mystery of Numbers is one of the most exhaustive and erudite ones of the mystic writers. The first edition appeared at Bergamo in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in 1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls the second, in 1591. Other editions, before the Paris edition to which he refers, appeared in 1599 and 1614; and the colophon of the Paris edition is dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.

[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got him into numerous literary quarrels, being the subject of frequent satire.

[64] Thomas Galloway (1796-1851), who was professor of mathematics at Sandhurst for a time, and was later the actuary of the Amicable Life Assurance Company of London. In the latter capacity he naturally came to be associated with De Morgan.

[65] Giordano Bruno was born near Naples about 1550. He left the Dominican order to take up Calvinism, and among his publications was _L'expulsion de la bete triomphante_. He taught philosophy at Paris and Wittenberg, and some of his works were published in England in 1583-86. Whether or not he was roasted alive "for the maintenance and defence of the holy Church," as De Morgan states, depends upon one's religious point of view. At any rate, he was roasted as a heretic.

[66] Referring to part of his _Discours de la methode_, Leyden, 1637.

[67] Bartholomew Legate, who was born in Essex about 1575. He denied the divinity of Christ and was the last heretic burned at Smithfield.

[68] Edward Wightman, born probably in Staffordshire. He was anti-Trinitarian, and claimed to be the Messiah. He was the last man burned for heresy in England.

[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649; grammarian, philologist, and satirist.

[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in 1613. He was a jurist of some power.

[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He wrote on the history of philosophy (1731-36, and 1742-44).

[72] Daniel Georg Morhof, born at Wismar in 1639, died at Luebeck in 1691. He was rector of the University of Kiel, and professor of eloquence, poetry, and history.

[73] In the _Histoire des Sciences Mathematiques_, vol. IV, note X, pp. 416-435 of the 1841 edition.

[74] Colenso (1814-1883), missionary bishop of Natal, was one of the leaders of his day in the field of higher biblical criticism. De Morgan must have admired his mathematical works, which were not without merit.

[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in 1866. He was an excellent linguist and a critical student of the Bible. He became librarian at Lambeth in 1838.

[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the opponents of the Roman Catholic Relief bill, the Reform bill, and the Jewish Civil Disabilities Relief bill.

[77] We have, in America at least, almost forgotten the great stir made by Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of the nineteenth century. He was professor of Hebrew at Oxford, and canon of Christ Church.

[78] That is, his _Magia universalis naturae et artis sive recondita naturalium et artificialium rerum scientia_, Wuerzburg, 1657, 4to, with editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott (Koenigshofen 1608, Wuerzburg 1666) was a physicist and mathematician, devoting most of his attention to the curiosities of his sciences. His type of mind must have appealed to De Morgan.

[79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum naturalis, tum geometrica_, etc., 1608.--_Consideratio nova in opusculum Archimedis de circuli dimensione_, etc., 1609.

[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of biographies which was published at Heidelberg and Frankfort from 1615 to 1620.

[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were related to the Zwinglians, and opposed all power of excommunication and the infliction of penalties by a church.

[82] See Acts xii. 20.

[83] Theodore de Bese, a French theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in 1605.

[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time through his attempt to introduce music and written prayers into the service of the Scotch Presbyterian church.

[85] Born at Veringen, Hohenzollern, in 1512; died at Roeteln in 1564.

[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His _Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was an influential work.

[87] The title was carelessly copied by De Morgan, not an unusual thing in his case. The original reads: A Plaine Discovery, of the whole Revelation of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ... London ... 1611.

[88] I have not seen the first edition, but it seems to have appeared in Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition was the third.

[89] It seems rather certain that Napier felt his theological work of greater importance than that in logarithms. He was born at Merchiston, near (now a part of) Edinburgh, in 1550, and died there in 1617, three years after the appearance of his _Mirifici logarithmorum canonis descriptio_.

[90] Followed, in the third edition, from which he quotes, by a comma.