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    Re: "Impossible" Lunars: Nauticus v. Maskelyne, 1786
    From: George Huxtable
    Date: 2010 Sep 9, 16:27 +0100

    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Frank Reed" 
    To: 
    Sent: Tuesday, September 07, 2010 9:15 AM
    Subject: [NavList] "Impossible" Lunars: Nauticus v. Maskelyne, 1786
    
    
    Below is the more or less complete text of a small booklet published in
    1786 by a man who called himself "Nauticus". It details and extends a
    correspondence between himself and the Royal Astronomer, Nevil Maskelyne,
    whom Nauticus refers to as "The Compiler," which was carried out mostly in
    the letters section of the "London Gazetteer" newspaper in 1785-86. The
    objects of discussion are some example "lunar" problems in the Second
    Edition of the Tables Requisite, published in 1781. Nauticus finds them a
    great "shame". He is an amateur with respect to this material, but of
    course all students are amateurs when they start so the issue he raises was
    bound to confuse other beginners eventually. As I have noted in other
    posts, it is totally incorrect to dismiss these examples by quoting Euclid
    like biblical commandments, as he does. The replies from Maskelyne are also
    interesting since they certainly highlight that petty, easily enraged side
    of this Royal Astronomer that some of his contemporaries complained about.
    
    Note: There are a fair number of Latin quips and quotations tossed in by
    Nauticus. Some of these may be copied down incorrectly. Also, the usage
    "instant" and "ultimo" referring to calendar dates may be unfamiliar for
    some. They mean here "of this month" and "of last month" respectively. I
    have done only a partial proofreading so please ask if there's any text
    that doesn't make sense. In a later letter in the series, Nauticus goes off
    on a tangent about how foreigners are debasing British achievements in
    astronomy. He talks about how they refer to the "Georgium Sidus" as
    "Herschel". This was the controversy over the naming of the planet "Uranus"
    which seems rather quaint today. He also complains that "Poor Robin"
    published notice of a transit of Mercury before the official Nautical
    Almanac. This "Poor Robin" was a privately published common almanac,
    comparable to the modern "Farmer's Almanac". This issue, while totally
    irrelevant here, does highlight a tension that would become more serious in
    later decades: the Nautical Almanac back then was BOTH a navigator's
    almanac and an astronomer's almanac. Eventually it made sense to separate
    these functions.
    
    -FER
    
    Enjoy:
    ------------------------------------------
    
    MYSTICAL MATHEMATICS
    Applied to
    MOON-HAULING,
    
    or,
    The Science of Non-Entities,
    As full set forth in
    The New Requisite Tables,
    Published by Order of the Board of Longitude;
    In Four Extremely Extreme Exemplifying
    Problems:
    and the
    Correspondence, on that Subject,
    between
    Nauticus and the Compiler
    As published in the Gazetteer.
    
    London:
    Printed for
    [...various booksellers...]
    
    M.DCC.LXXXVI.
    Price One Shilling.
    
    ------------------
    
    PREFACE
    
    The writer of the following sheets is perfectly aware into what oblivion
    the temporary nature of the subject will naturally propel them; and he is
    likewise conscious that the public can little care for either party's
    arguments, or for whosoever may have the advantages of reason and truth, in
    the present contest. But, within every man's breast, (except in the most
    depraved,) there is placed a principle, which cautions him to preserve his
    character, among those who honour him with friendship. Those, to whom the
    author is known, and of whose esteem he boasts himself careful, have urged
    him to exculpate his conduct, and prove the veracity of his assertions, by
    a fairly collected statement of the contest, and by plain reference to the
    principles of mathematics. In obedience, therefore, to friendly dictates,
    he throws before the public an impartial recital of the paper-war; and he
    trusts he shall stand excused in making use of the weapons that justice has
    occasionally offered to him, --ridicule and irony,
    
    --ridentem dicere verum
    Quid vetat?
    
    ------------------
    
    MYSTICAL MATHEMATICS.
    
    Scientia quavis, a justitia et reliqua virtute sejuncta, calliditat, non
    autem sapientia, videtur esse. -Plato.
    
    Never did a man more unwillingly take up his pen in his own justification
    than the writer of this, who, though compelled to it by the illiberality of
    his opponent, will endeavour as much as possible not to defile paper in
    like manner, but leave the reader to conceive what language would have best
    retaliated the abuse.
    
    In December, 1785, Nauticus, having occasion to examine some of the
    examples in the new Requisite Tables, published by order of the Board of
    Longitude, was surprised to find them such as could not exist in the nature
    of things, although they were there introduced as elucidations of rules,
    established, on the clearest geometrical principles, by Mess. Lyons and
    Dunthorne; men, who, in their profession, were ornaments to their country.
    
    The consequence was the following letter, published in the Gazetter, Dec.
    20, 1785.
    
    ------------------
    
    Numb. I.
    To ASTRONOMERS.
    
    Gentlemen,
    I Am a seaman, and can say I have seen many sights, sailed at all seasons,
    studied the situations of ths Sun, Saturn, and satellites; and have stated,
    in several simple schemes, the best methods of determining the longitude.
    But, of all the sights I have seen, I never saw the solution of an
    impossible triangle, till, in my last voyage, I was reading the new
    Requisite Tables, published by order of the Commissioners of Longitude. The
    preface of this useful book is larded with the names of many mighty men,
    who have assisted the astronomer-royal in the compilation of the work, sed
    mirabile dictu! -We there see wonders! Two miracles Wrought! (examples 3d
    and 4th, pages 35 and 36!) Two triangles solved, in which the observed
    distances are considerably greater than the respective zenith distances of
    the objects observed. In the first, one side is greater than the other two
    by above three degrees; in the other, nearly six degrees. This would have
    heen laughed at two thousand years ago. Surely we are not to have mysteries
    in the mathematics, as well as in mythology; but perhaps without them the
    mystic ministers of M---- will miss the money taken for the passport into
    the wooden world, long the habitation of ...
    NAUTICUS.
    
    ------------------
    
    Before the publication of the above, another egregious example was
    discovered, which, (who could have thought it?) upon examination, proved to
    be one of those mentioned above, solved after Mr. Lyons's method, improved.
    This was the occasion of the following letter, published in the Gazetteer
    Dec. 26, 1785.
    
    ------------------
    
    Numb. II.
    To ASTRONOMERS.
    Addendum to my last letter in the Gazetteer of the 20th instant.
    
    Gentlemen,
    In the Requisite Tables, published by the authority of the Commissioners of
    Longitude, I have since discovered a more egregious error than the two
    before mentioned, viz. in page 31, example the IVth, the sun's zenith
    distance is given above 71 degrees, the moon's 19 degrees, and the apparent
    distance of their centres 103 one-half degrees, consequently impossible;
    for one side of the triangle is longer than the other two by above 13
    degrees. Shame! Shame! How degraded is the dignity of a British astronomer!
    NAUTICUS.
    
    ------------------
    
    A fourth equally horrid blunder, example III, p.30, of the Requisite
    Tables, was discovered the same day, which proved to be the other example
    mentioned in No. I. solved after Mr. Lyons's improved method. A few days
    after, the following angry letter, No III. appeared in the Gazetteer, which
    was followed by No IV. Feb. 3, 1786, being a partial reply from Nauticus,
    who confines himself to one example only, and does not even notice the
    possibility or impossibility of the mistake of the ill-made 4 for a 7, but
    leaves the rest of the filth ad referendum; which never would have been
    seen by the public, had not the illiberal rejoinder, No. V. appeared in the
    Gazetteer, April 29, 1786, containing a repetition of the principal part of
    No. III. and a curious conclusion or *ne plus ultra, anglice*, not an inch
    beyond his nose.
    
    The two notes following No. V. appeared in the Gazetteer, one in April, the
    other in May; the first pf which, Nauticus surmises, must relate to No. V.
    as he knows of no other late astronomical dispute in the Gazetteer.
    
    ----------------------------------
    
    Numb. III.
    To the EDITOR of the GAZETTEER.
    Dec. 31, 1785.
    
    Sir,
    In your Gazetteer of the 20th instant a person, under the signature of
    Nauticus, has censured two examples which are made use of in the New Tables
    Requisite to be used with the Nautical Almanack, and in your paper of
    yesterday he has repeated his attacj. The directors, as well as the
    compiler of that work, always feel themselves obliged to those who tell
    them in a friendly way, of any errors which have crept into that work; and
    they will make a proper use of their information, let it come in what wyhat
    way or with what design it will.
    
    The examples he censures were taken from real observations, and no error
    has been committed by the compiler in the first of them; I mean that on
    p.30 and 35. This example was selected for the purpose of exemplifying an
    extreme case; namely, that where the objects are on or near the same
    vertical circle; and it is *possible* ["possible" is italicized in the
    original] the editor might choose this example for the very reason that
    Nauticus founds his objections on. It is certainly better on that account;
    for if Nauticus had employed himself in making useful observations, instead
    of "studying the situations of Saturn and his satellites," by means of
    which we may conclude his "simple schemes for the best determining the
    longitude" are effected, he would have known by experience that the best
    observers are liable to some errors in observing altitudes, both of the
    moon and stars, in the night-time, and especially when they are very near
    the zenith, or very near the horizon. And when the objects are nearly on
    the same vertical circle, since these errors are as likely to be in excess
    as in defect, it is not improbable that the circumstance which has happened
    in the observation, from which this example is taken, may frequently happen
    in others, which might puzzle a beginner; but this example will shew him,
    that, in working by either of the methods which this is worked by, no error
    or puzzle whatever can arise from it. This is a circumstance which the
    sagacity of a critic, ignorant in a great measure of the subject he writes
    on, and determined to find fault only, would never discover.
    
    In the 4th example, the editor undoubtedly committed a mistake, in taking
    an ill-made 4 for a 7; and as that example also is taken from a real
    observation, he did not examine into the agreement of the several parts of
    the triangle in the manner he most likely would have done, if he had formed
    it out of his own mind; but iy would be affectation to express much sorrow
    on the occasion, because the error creates no absurdity in the operation;
    nor can any person be ither puzzled or led wrong by it. The editor of the
    Requisite Tables has long been convinced, from experience, that nothing
    which is the production of his head of hands will be perfect. Nauticus, if
    we may judge from the arrogance and triumphant manner in which he writes,
    and the contempt and scurrility with which he treats those he thinks have
    slipped into error, has not yet learned that he also is subject to
    imperfections; yet, unfortunately for him, in his first essay, though it
    consists but of 25 lines, has had committed as many errors as he accuses
    the compiler of commiyying in a pretty large octavo volume, of the most
    difficult matter. He says, "In the first, one side [of a triangle] is
    greater than the other two by above three degrees; and in the other *nearly
    six degrees*. [italicized in the original]" Now, if this brilliant critic
    has been able to add two numbers together, and take a third from their sum,
    he must have seen that the excess is *more than thirteen degrees!*
    [italicized in the original] He also asserts, that the editor has solved
    two triangles, in each of which one side is greater than the sum of the
    other two; a falsehoos which must either have originated in his ignorance
    or the the meaning of the word he uses, or in the insolence of not
    regarding what he writes, while he thinks himself safe from detection under
    the mask of an anonymous signaturel for the editor has not resolved any
    triangle in the operations which he alludes to. But this is a trifle to
    what he has done in his second essay. He has, since he wrote his former,
    discovered the first of these mistakes, and has now introduced it as a
    *third* mistake of the editor's, with (if possible) more insolent triumph
    than he had found himself able to express before. Surely, when a man points
    out the mistakes of another, and, without the least provocation, treats him
    with contempt and scurrility on account of them, he should be exceedingly
    careful not to make more mistakes himself than he accuses the other of;
    much more ought he to be careful, not, by his own blunders, to exhibit the
    same error twice over for different ones, and, tinker-like, make more holes
    than he mends.
    
    It is impossible to say what villainous meaning is intended to be converyed
    by the words "perhaps without them [the mistakes he has been exposing *]
    the mystic Ministers of M---- will miss the money taken for passport into
    the wooden world." I have observed above that Nauticus seems to have no
    scruples of conscience about him, while he writes *with safety* [italicized
    in the original] under the mask of an anonymous signature; bu the compiler
    of the New Requisite Tables dares him, or any other person, to mention,
    under his real name, a single instance where he has been concerned in any
    such dirty work as appears to be hinted at by them; and if he cannot, after
    such insinuation, the public will be at no loss for the sirname (it cannot
    be the Christian name) which ought to be annexed to Nauticus.
    
    The Compiler of the Requisite Tables
    
    P.S. This, and several other errors, will be given in the first publication
    which the Board makes; and a publication would have been made some time ago
    on purpose, if they had been of any importance.
    
    ----------------------------------
    
    * This is a reference curiously acccurate. Vide No I.
    
    ----------------------------------
    
    Numb. IV.
    February 3, 1786.
    
    Quenadmodum qui expectant obsidionem omnia parant sub hostium adventum, ita
    adversus assulium iracundiae praecepsis philosophiae muniendus est animus.
    
    Little did Nauticus think his alliterated allusions to the absurdities of
    an astronomer would had adduced the illiberal abus announced in the
    Gazetteer of the 31st ultimo. Adieu, euphonic alliteration: come, ye
    children of Cadmus, in any order ye please; and, O ye Genii, eldest sons of
    Arabas brains, who preside over the magic rules of addition and
    subtraction, descend, inspire your humble votary, clear his eyes from mist,
    let him not fall into error, nor mistake a quadrate four for a descending
    seven. Why so angry, *Mr. Compiler of the Requisite Tables?* I hope you are
    not the person who took the observations, from which example II page 35, is
    copied; if so, I am sure Miss Nancy, with her nine-inch globe, or Master
    Jacky, with his four-inch Gunter's quadrant, would have determined the
    altitudes of the moon and star much nearer truth than three degrees fifty
    min. (the quantity the observed distance exceeds the two zenith distances)
    suppsing them in the same certical, and allowing half the error to each
    altitude. Unluckily for me, and luckily, or designedly, for, or by the
    compiler, the latitude and time are not given when the observations were
    taken. I have looked over the quarto volume of observations, published by
    Mr. Wales, which were made in his tour round the world, to see whether that
    gentleman ever observed so carelessly as to be out three or four degrees in
    one or both of his altitudes together, but have perceived no such blunders.
    But, since Mr. Compiler builds so much upon this extremely extreme
    exemplifying case, let us examine that only, and leave the filth *ad
    referendum*. From the *data* there is a moral certainty that the
    observations must have been taken between or near the tropics; that the
    objects were, one to the eastward and the other westward of the zenith, and
    that they must be in or very near the same vertical. Then, in the name of
    Euclid, why that prolix mystical solutions? Every one, who knows what
    parallax and refraction mean, must know that their difference, added or
    subtracted, in such a case, to or from the observed distance, will give the
    trus distance of the objects as truly as the *data* will admit: in all
    other *possible* cases there are shorter, plained, and more easy, methods
    than any exhibited in the Requisite Tables, [Latin comment unreadable].
    
    Mr. Compiler says, this extremely extreme exemplifying case may prevent a
    beginner from being puzzled: this indeed is a circumstance that the
    *sagacity* of none but a *critic* can discover. Again, it is certain that
    in the night the horizon is nearer the observer's eye than in the day,
    consequently the apparent altitudes will be proportionately greater; but
    this militates much against the possibility of the example being drawn from
    actual observation, if the soltuion be any thing near truth. Now to suppose
    all or the greater part of the error in the star's altitude, is not
    consistent with reason; therefore it must have been in the moon's; and
    supposing it so, (but what hand must the observer have been!) the true
    distance in the example is jumbled out justly just.
    
    For the honour of my country, I would advise that honourable board, the
    Commissioners of Longitude, to order the sheets containing the subject off
    this essay to be cancelled. Let us no longer be the laughing stocks of our
    neighbors, who have kicked the planet Georgium Sidus out of the heavens,
    and given its place to the indefatigable Herschel; printed our countryman
    Gardiner's Logarithms; afforded Poor Robin an opportunity of announcing to
    the public the transit of Mercury on the fourth of May this year as soon as
    the Nautical Almanack; also the disapppearance and re-appearance of
    Saturn's ring in the years 1789 and 1790, neither of which were noticed by
    our Astronomers twelve months ago. -- Shame! Shame! How degrading to the
    dignity of a British astronomer!
    
    NAUTICUS.
    
    --------------------------
    
    Numb. V,
    April 29, 1786.
    To the EDITOR of the GAZETTEER.
    
    Sir,
    I. In the Gazetteer of December 20, 1785, Nauticus asserts, that the
    Compiler of the Requisite Tables has solved two impossible triangles;
    whereas the Compiler has not solved any triangle whatever in the operations
    referred to.
    II. Nauticus asserts also, that "the preface to that USEFUL book is larded
    with the names of many mighty men who have assited the astronomer royal in
    the compilation of the work;" but every person, who will take the trouble
    of reading that preface, will see that there is but ONE person mentioned,
    as having any thing to in the compilation of it.
    III. In the Gazetteer of Dec. 26, 1785, Nauticus assued his readers, that
    he had found a third example of the Compiler's, more absurd than either of
    the two which he had taken notice of before; when the truth was, it was the
    same with one of them, in which Nauticus had himself blundered so
    egregiously as not to know it again.
    IV. In the Gazetteer of February the 3d, Nauticus asserts that our
    neighbours "had afforded Poor Robin an opportunity of announcing to the
    public the transit of Mercury on the 4th of May this year as soon as the
    Nautical Almanack:" the real matter of fact is, that the transit of
    Mercury, though omitted in the Almanack for 1786, was inserted as an
    erratum in that for 1787, which was published in the autumn of the year
    1783. No foreign Ephemerides, announcing that transit, reached England till
    the December following; and as Poor Robin is published annually about the
    middle of November, it is plain that writer could avail himself of it
    before Novmber 1784, more than a year after the Nautical Almanack had made
    the transit public.
    V. Nauticus is not more scrupulous of telling verbal lies than written
    ones: he declared to several of the Compiler's friends and acquaintance,
    that he did not know who the Compiler was, or he would not have printed his
    first piece of elegant composition; yet he admits, in that elegant morsel,
    that he had read the *larded* preface, where the Compiler's name and place
    of abode stand at full length.
    
    Nauticus is pleased to ask, in his *facetious* way, "Why so angry, Mr.
    Compiler?" Mr. Compiler was never yet in a situation where he could not
    fully and truly answer even impertinent questions; and now affords Mr.
    Nauticus, that it was not the poignancy of his wit that made him so; though
    there can be no doubt but Nauticus thinks himself possessed of a wonderful
    fund of it: it is not uncommon for conceited persons to mistake their own
    ribaldry for wit. Neither was it because he has been detected in an error:
    he knows too well how subject he and every one, even Nauticus himself, are
    to it. But he was angry at finding his reputation attacked, in the most
    wanton and unprovoked manner, by a person with a mask on his face; and who,
    because he thought himself unknown, did not scruple to assert the most
    impudent falsehoods, and to accuse him of errors which he never committed;
    and not even content with that, but insinuating also that he committted
    them wilfully, and for the basest of purposes. Yet this man complains of
    being treated with illiberaility and abuse!
    
    Nauticus, in his last publication, has been weak enough to suffer the snake
    to be discovered by its tail. "There are shorter, plainer, and more easy,
    methods of reducing the distance than any exhibited in the Requisite
    Tables," which we are to suppose (believe it who will) the Board of
    Longitude has rejected; and therefore this mighty stickler for the honour
    of his country is resolved to be the first to pull it down, by insinuating
    that foreigners hold our publications, and particularly the Nautical
    Almanack, cheap; whereas it is well known, that this publication is held in
    the highest esteem all over Europe; that it is used every where, and
    expressly copied into their own Ephemerides; that no foreign publication of
    the kind comes near it, in the number and exactness of its original
    calculations; and that it reflects the highest honour on the Board of
    Longitude and the British astronomers who are concerned in it; and it is
    the fullest and most unequivocal proof of its merit, that the sale is
    continually and rapidly increasing; a very large impression now constantly
    sold off longer before the year commencing to which it belongs.
    
    The Compiler of the Requisite Tables.
    
    P.S. Since the above was sent to the printer, I have discovered the
    unfortunate step which has drawn down the wrath of Mr. Nauticus upon me.
    This man is employedd by Messrs. M. and P. to manufacture and new-vamp old
    books of navigation; and, having learned that mathematical
    instrument-makers can divide quadrants with greater exactness into 96 parts
    than into 90, sagely concluded, that it would be a wonderful improvements
    to compute the tables of difference of latitude and departure to 96ths of a
    quadrant rather than to degrees, as is usual; and had address enough to
    persuade his employers to adopt this absurdity, and print an edition of
    Haselden's Seaman's Daily Assistant, with the tables so computed. As many
    of this book are used in the school which I am intrusted with the care of,
    a parcel of them was sent mel but as it is my business to teach the
    children, committed to my care, navigation in a rational way, and not the
    wild schemes of Nauticus, I returned these books to our counting-house, and
    they were sent to Messrs. M. amd P. with a request that some of the old
    sort might be sent instead of them, as those were of no use to us. What
    passed between Mr. A and his employers, in consequence of this, I cannot
    tell, nor yet hor those gentlemen got rid of a large impression of such an
    absurd work; but as another edition was printed immediately, and some of it
    sent to me, I never either thought or heard of this circumstances, which
    happened more than a year ago, till yesterday, when I was told that I had
    injured Mr. A. in the eye of his employers; that the Board of Longitude had
    neglected some of his schemes; and that they had also withdrawn the sale of
    the Nautical Almanack from his employers. A long catalogue of injuries
    truly! To which I shall add, that I have never seen any of their
    *twice-laid stuff* bu the book above-mentioned, and that whiach *was*
    Atkinson's Epitome; and I could point out as many errors in the first as
    would almost fill a column of the Gazatteer, and as many absurdities and
    insonsistencies in the latter as would fill another; but having now placed
    Nauticus *in propria persona* before the public, and also his actions, and
    motives for them, in their true colours, I have done with him. A fly maye
    be very troublesome on a man's nose; but when he has brushed it off, and
    the pain ceases, the insect then becomes too contemptible to be pursued
    farther.
    
    ------------------
    
    Note I. which appeared in the Gazetteer in April, 1786.
    
    ***Mr Wales complains of partiality without reason. The letter to which his
    is an answer, was delayed longer than his manuscript; and such matters, as
    they are not of much importance, must give way to more temporary
    subjects --His letter, he may be assured, shall be inserted the first open
    day. We are by no means interested or concerned about the controversy. --It
    is a mere astronomical dispute, and, knowing neither of the parties, we are
    indifferent how it terminates.
    
    Note II. which appeared in the Gazetteer in May, 1786.
    
    ***The petulant and ___ gentleman, who signs himself W.W. of Christ's
    Hosptial, may be ____; for it is not likely that we should insult our
    readers by any mention of a matter so trifling.
    
    ==============================
    
    Here ended our public news-paper contest. The following was written, and
    intended to be published through the same channel; but, on consideration,
    it was thought a more extensive channels would be preferable, for seeveral
    reasonsl one especially, the difficulty the editor met with in finding room
    for such uninteresting matter.
    
    To the EDITOR of the GAZETTEER.
    
    Just before your paper of the 29th of April was put into my habds, I had
    luckily read the XIVth chapter of Proverbs, verse 17, or, as sure as the
    Pole-Star is in the Little Bear's tail, I must have been two-thirds to
    three-fourths inclined to be angry with Mr. Compiler of the Requisite
    Tables; who seems to have forsaken not only the point in question, but even
    the very language of a gentleman and astronomer, perfering that which
    cannot be said to belong either to a liberal education or to liberal
    sentiments. The ribaldry he has adduced in his last essay requires such a
    treatment as cannote be either amusing or interesting to your readers,
    therefore the reply, and further investigation of the matter, must be in
    another channel. However, I crave the favour of your to insert the
    remaining part, or referenda, of my last answer to his *polite* and
    *gentleman-like* essay of Dec. 31, 1785.
    
    The many illiberal epithets bestowed, and equally illiberal expressions
    there used, cannot add much to the credit or support of the argument on his
    side, particularly the curious parathetic reference of the relative to its
    antecedent, (vide note, No III. p. 6,) by which one may surmise that this
    might man is not less capable of breaking Priscian's head than of cracking
    Euclid's scull. In the prostscript he says, "This and several other errors
    will be given in the first publication the Board *makes*." Have there not
    been two different lists or errata already printed to the very book in
    question? Have not three Ephemeridea, and several editions of those out od
    print, been published, by the order of the Board, since the Requisite
    Tables, without any notice being taken of the blunders alluded to, even of
    the ill-made 7 ? It is true, some trifling errors have been notices; but
    neith the defect of the natural since of 45 degrees, nor some others,
    perhaps slips of the pen or neglects of the corrector, which it would
    ill-become Nauticus to take advantage of, though *lex talionis* would
    jsutify him so to do. Mr. Compiler takes advantage of the alliteration in
    No. I. and simply haprs upon Saturn's satellites; then shelters himself
    (and a bad shelter it is) under the three sides given not making a
    triangle; but converts them into an arc of the same vertical, which every
    Tyro knows cannot be, except the Compiler can demonstrate that 89 degrees
    58 minutes, and 86 degrees 8 minutes, of the same circle, are equal.
    Nauticus, for want of an expression, called the blunders impossible
    triangles, which, in fact, was calling them nothing. There are four of
    them, or two, twice told, and solved; neither *ens*, nor *ens rationis*; &
    *ex nihilo nihil fit*, except a perfect vacuum in the upper regions of some
    body. Oh Lyons! oh Dunthorne! ye sleep in peace; but little did ye ever
    think your rules, established on geometry's strong base, could be so far
    improved as to out-geometrize geometry itself.
    
    In No. V. the Compiler recapitulates, in great part, what he before had
    said, and numerically registers his assertions, which will be notice in
    order.
    
    I. This was answered above.
    II. That the word *Compiler* was taken in too general a sense must be
    confessed; but to use the Compiler's words, "it would be affectation to
    express too much sorrow on the occasion;" and in the metaphorical sense of
    the word, every hod-carrier may be said to assist in compiling a building.
    III. This has been answered before.
    IV. Neither Nauticus nor many others had seen the preface to the Almanack
    for 1787. This is the only part of the last paragraph in No. IV. the
    Compiler has notices. However, there has lately appeared a flying
    half-sheet, stuck into the Nautical Almanacks, containing the places of the
    Georgian Planet; but we are not told from what tables those places were
    calculated. *Our naighbours have published tables of the planet* Herschel's
    *motions*.
    V. In reading this curious head the reader will be apt to conceive that the
    mask was pellucid, and that the snake was not in the grass with his
    tailonly sticking out, notwithstanding Mr. Compiler's asseveration. It is
    true, Nauticus mentioned his reasons for publishing No. I. and II. to
    several persons, perhaps the Compiler's friends; and, for his sake, wished
    the matter had dropped; or that, like a gentleman, (to which character this
    paragraph gives lye direct) he had acknowledhed his erros, it would have
    spared much pain on both sides; for, as St. Paul says, "it is hard to kick
    against the pricks, and foght with the beasts at Ephesus." The rest of this
    head is too scurrilous to merit attention, and speaks more against the
    author than words can express. There remains now but the postscript to
    noticel and I wish I could be silent.
    
    John Adama,s a person wll known at Waltham-Abbey, Ratcliff-Cross, and
    Edmonton, being unemployed, in his distress, in the year 1780, conceived
    that a quarter of the compass divided into 96 parts, would be more
    convenient for seamen than the present division of 90, because every point
    of the compasss would then consist of 12 parts instead of 11(1/4) and the
    quarter point of 3 parts instead of 2d 48' 45", consequently fractions
    avoided, and the tables rendered more extensive and useful. Mr. Rust, of
    St. Catharine's, Mr Adams's friend, a man of no small philanthropy,
    undertook to print and publish the said tables; and had caused some sheets
    to be printed, when the worthy gentlemen, whom the Compiler alludes to,
    sent to Mr. Rust and bought the copy, which was printed, sold and esteemed
    by sensible men. Mr. Rust informed Nauticus, that one of his correspondents
    sent him word those tables were reprinted in Holland four years ago. It is
    true, some enemies of improvement, and others who could not perceive that
    those tables, in their operation, (but with more convenience,) were exactly
    the same as the former, cavilled at them; upon which the gentlemen
    immediately ordered the old tables to be printed.
    
    What is become of so large an impression of that *absurd work*, (as the
    Compiler calls it,) Nauticus cannot say; but can assure him, that three
    years ago a copy could not be procured.
    
    The remainder of his postscript must fall so heavy upon the writer's head,
    Nauticus cannot wish to add to the weight there, though far more able to
    bear it than the cartilaginous gristle of his nose.
    
    Nauticus holds the Board of Longitude, in general, in the highest esteem,
    and is fully sensible of the great utility of the Nautical Almanack, and
    must confess the Requisite Tables have their use. But why those mystical
    precepts? Did the Compiler think Lyons's and Dunthorne's demonstrations of
    no use? Are there not many navigators who understand geometry, &c. that
    must, mole-like, work in the dark, or purchase the old tables to enlighten
    themselves? For Urania's sake, let us make things as plain as possible. As,
    for example, why is not the reader told, in the explanation of Tab. XVI.
    for determining the latitude by two altitudes, that the logarithm of half
    the elapsed time is the cosecant of the time, reduced into degrees, &c.
    that the logarithm of the middle time is the sine of the same in degrees,
    added to the logarithm of s, and the log-rising is the versed sine of the
    time in degrees; and why is not the demonstration added? For a minute let
    us look at the general introduction to the Requisite Tables, pages 1 and 2,
    and see how we are to adjust a Hadley's quadrant: strangely, indeed! for
    the last adjustment is explained first, and the first not noticed. The dark
    glass is to be placed on the hithher side of the little speculum, and that
    to be set parallel to the great speculum, how much soever the latter may
    incline from a perpendicular to the plane of the quadrant. This may account
    for some part of Mr. Compuler's error in his real observation, as he calls
    it, in No. III. Could any one have imagined, after what has been said on
    Hadley's quadrant by Mr. Ludlam, Magellan, and others, such an explanation
    would have been produced of that useful instrument. Mr. Compiler surely
    must know, that, if the index-glass be not perpendicular to the plane of
    the quadrant, the other adjustmenst will not enable him to measure an arc
    of a great circle truly. But enough of this. And now to the doctrine of
    non-entities, or a review of the surprising exemplifying problems; and
    first, in example III. page 30, Requisite Tables, there is given the
    altitude of the star 5d 6', the altitude of the moon's center 88d 46',
    their apparent distance 89d 58' 6"; consequently the star's zenith distance
    84d 54', and the moon's zenith distance 1d 14'.These two zenith distances,
    with the observed distance, must either form a spherical triangle, or be in
    the same vertical; in either case, the trus distance may be found, but here
    we see the observed distance greater than the sum of the other two by 3d
    50' 6"; therefore it is impossible to draw a conclusion by any method
    whatever. The same example is pretended to be solved by Dunthorne's method,
    page 35. *Surprising!* Example the IVth, pages 31 and 26, are more
    suprising still; for there one side is longer than the other two by 13d 39'
    5". This, as well as the former, if we believe Mr. Compiler, was taken from
    an actual observation, but he mistook 71 degrees for 41 degrees; yet 30
    degrees are of no consequence to the conclusion. So far both Mess. Lyons's
    and Dunthorne's methods are improved, believe it who will.
    
    But let us examine example II. pages 29 and 34. Here both objects are
    nearly in the same vertical, the one on one side of the meridian, and the
    other on the other; consequently nothing more is necessary than to open the
    Requisite Tables, and take out the effect of parallax and refraction, for
    the moon 52' 3", and the same for the sun 5'; their difference, 51' 58"
    subtracted from the observed distance, 90d 21' 13", gives the trus distance
    nearly, viz. 89d 29' 15", which ought to be 89d 29' 16". But the Compiler,
    in two extremely extreme exemplifying tedious solutions, makes the true
    distance by Lyons's method 89d 29' 10" and by Dunthorne's method 89d 29'
    14"; and no where hints the great advantage of taking the distance of the
    moon from the sun or star when they are nearly in the same vertical, though
    a case that may frequently happen, and save almost all the labour of
    determining the longitude.
    
    And now for a word at parting: therefore, Mr. Compiler, instead of a modern
    insincere compliment, accept a little advice. If, by some peculiar
    conformation of your nature, you should feel any compunction, and yet be
    backward to forsake your erratic path, believe me, your character will run
    little hazard by a confession of your faults. Why, man, you have a wit on
    your side: dean Swift says, "A man, who confesses his error, does but
    confess that he is wiser today than he was yesterday."
    
    Let these words of Horace, then, seek for an application among others:
    
    Video meliora, proboque; deteriora sequor.
    
    Embrace this new faith: *Do justice, and be esteemed!*
    
    THE END
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