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we cannot be sure of being right on such a point within about a second, so that it might happen that the true full moon would be half a second before twelve o'clock, in which case Easter Sunday would begin in one half second more. But if we were arguing with a divine of the sixteenth century, we should state the case as follows, which would be quite in keeping with the style of thinking of that period. Suppose the full moon to happen exactly at the moment at which the centre of the sun was opposite to the visible meridian which (before the invention of clocks) must have been the admitted time of midnight. The full moon in that case happens neither on Saturday nor Sunday. Which then is Easter Sunday; the one which begins with full moon, or the next? A catholic would have referred to the church, but it is not likely that all the college of cardinals would have been of one mind; and protestants (many of whom hadamore than ceremonial veneration for correct Easter) would have been sadly puzzled.
The rule given for finding Easter takes the average moon and sun, or two imaginary bodies which move uniformly at the average rate of the real ones. But the real places of the sun and moon are found by making various corrections of these average places,* which, as to the moon, might make more than a quarter of an hour of difference. And it is very likely that various Easters in different years are wrongly calculated on this account. Such an occurrence would not now give much concern perhaps to a single individual on the face of the globe; nevertheless, many might like, as. a matter of curiosity, to know how to find Easter-day for themselves: we shall therefore give the following application of arithmetic to hot crossed buns, extracted from f Delambrc's Hist, d'Ast. Mod.
* See the paper on the Moon's Orbit, in the Companion to the Almanac for 1834.
t The form in which this rule is given, is extracted from Sir Harris Nicolas's useful Chronology of History, (in Lardnei^s Cyclopaedia,) by permission. We have compared it with Delambre.
It gives also the golden number, the epact, and the dominical letter. It may appear long, but it is broken up into the smallest subdivisions.
The given years.
(a) Add one to the given year.
(b) Divide the given year by 4, and keep the quotient only; reject the remainder.
(c) Take 16 from the number of centuries in the given year, divide by 4, and keep the quotient only.
(d) Take 16 from the number of centuries in the given year.
(e) Add together (a) (b) and (c) and subtract (d).
(f) Divide (e) by 7, keeping 'the remainder only.
(g) Subtract (f) from 7; and the dominical letter is under the remainder below.
12 3 4 5 6 7 ABCDEFG
(h) Divide (a) by 19, the remainder is the golden number, or 19 is the golden number if the remainder be 0.
(i) From the number of centuries in the given year subtract 17, divide by 25, and keep the quotient only.
fited by it. For as long as he * lived, he would neither return nor copy it; and I suspect he meant to pass it as his own." We now come to a curious specimen of the way in which a sentence is handed down by compilation from generation to generation. Edward Sherburne, in the notes to his translation of Manilius, London 1675, writes as follows: "But the work of his chiefly pertinent to our subject, and [whose loss cannot be sufficiently deplored, was his Harmonicon Coeleste, which, being communicated to Mersennus, was by some perfidious acquaintance of that honest-minded person, surreptitiously taken from him, and irrecoverably lost or suppressed, to the unspeakable detriment of the lettered world.] Vide Bidliald. &c. The learned Golius had it, and Sir Alexander Hume from hence imparted another copy; both which, 'tis feared, are lost, there being no impression made thereof; and Golius being since dead, his collections (whereof he had many in Arabick) are said to be dispersed, and (which is to be pitied) carried back by a Jew into Turkey." Benjamin Martin, in his Biographia Philosophica, 1764, repeats the clause in brackets; and Dr. Hutton, in his Mathematical Dictionary, 1815, does the same, substituting only " great" for " unspeakable," and "literary" for " lettered." The assertion about Golius
* Iste; there is such confusion about this sentence, that we quote it entire; " Hie vir optimus et facilis a quodam viro non bo i ia! fidei illo libro emunctus est, ita ut nee ipsum Pu tea no reddere potuerit, nee respub. literaria fructum aliquem ex eo capere. Quamdiu enim vixit, iste nee reddere voluit nee copiam illius facere; et, nisi fa 1 lor, meditabatur sibi adrogare Viette hoc opus, veri authoris nomine suppresso." From the first clause in italics, we should suppose Bouillaud did not know who it was took the book (though quidam is there ambiguous); from the second, that he did know. And what we have presently to say makes this whole assertion still more inexplicable. Both Mersenue and Puteanus were alive when this was written: P. Puteanus and Bouillaud were not only known to each other, but were, as long after the publication of the Ast. Philol. as 1679, engaged in a joint production (the catalogue of the library of Vieta's friend, the president De Thou.)
and Sir A. Hume, has some reference to the preface of Vieta's collected works by Schooten, published in 1646, in which it is stated that the editor had a copy of the Harmonicon, but not sufficiently complete to publish; but that he had received another copy from Alexander Hume, which would appear in a subsequent work, together with anecdotes (u>«tSora) of Vieta. No such work, however, was ever published.
This question being already sufficiently obscure, the writer of this article, some years ago, requested the late
distinguished and excellent mathematician M. to
make some inquiry upon the subject at Paris; and that gentleman soon found a circumstance which makes Bouillaud's assertion most singular: for, in the manuscripts of this very Bouillaud, he states that he, Bouillaud, had had the manuscript,* and had lent it, in 1662, to Prince Leopold of Tuscany, the protector of the Accadernia del Cimento; from which the gentleman alluded to supposed that it might be now at Florence. Though our expectations are but slender, we do not entirely despair of seeing this curious relic dug out of some Italian library or other.
Appended to the Life of Dr. Edward Bernard, published in Latin by Dr. Thomas Smith, London 1704, is a collection, entitled " Veterum Mathematicorum scripta quae reperiri potuerunt, voluminibus xiv." This is either a collection of works which Bernard had made, or a synopsis of such a collection as he conceived might have
* The following passages are from the letters of M.
to the writer: "Le manuscrit original de Harmonicon Cceleste est h. Florence. Bouillaud, astronome Francais, a prete ce livre, en 1662, au prince Leopold de Toscane, protecteur de l'academie del Cimento." On some surprise being expressed at this, in connexion with Bouillaud's printed assertion in early life, the following confirmation was given: "Le fait coucernant le manuscrit de Harmonicon Cceleste, prete par Bouillaud au prince Leopold des Medicis est consigne' dans
les manuscrits de Bouillaud, et M. "(naming a very
celebracted mathematician) " savant gebmetre, m'en a donue I'assurance. II faut chercher dans les manuscrits. ou dans les ouvrages publics par les auteurs, la verite de l'histoire."
been made. But he says, page 23, " accedant quaedam de Vietae Harmonico Coelesti; cujus mentio in Astronomia Philol." Whether this be actual or hypothetical, might be ascertained by examination of Bernard's manuscripts, if he left any: Bernard was Savilian professor at Oxford, and died in 1703, being succeeded by Dr. Gregory.
IV.—Chaucer's work on the Astrolabe. This astronomical work of our oldest poet is the first work on any science in English of which we have any knowledge. It was written (says the black-letter edition of Chaucer, of 1602) in 1391, and the preface will show to whom and why.
"Little Lowis my sonne, I perceiue well by certaine euidences, thine abilitie to learne sciences touching numbers and proportions, and also wel consider I thy busie prayer in especiall to learne the Treatise of the Astrolabie. Then for as much as a philosopher saith, he wrapeth him in his friend, that condiscendeth to the rightfull prayers of his friend. Therefor I haue giuen thee a sufficient Astrolabie for our orizont, compouned after the iatitude of Oxenford: upon the which, by meditation of this little treatise, I purpose to teach thee a certaine number of conclusions pertayning to this same instrument. I say a certaine [number] of conclusions, for three causes, the first cause is this: Trust well, that all the conclusions that haue be. founden, or els possibly might bee found in so noble an instrument as in the Astrolaby, ben unknowen perfidy to any mortall man in this region, as I suppose. Another cause is this, that soothly in any carts of the Astrolabie that I haue yseene, there ben some conclusions, that woll not in all thyngs perfourme her behests; and some of hem beene too hard to thy tender age of ten yeare, to conceiue. This treatise deuided in flue parts, will I shewe the woonder-light rules and naked words in English, for Latine ne canst thou not yet but smale, my little sonne. But neuer the lesse, suffiseth to thee these true conclusions in English, as well as sufficeth to this noble clerkes, Greekes, these same conclusions in Greeke, and to the Arabines in Arabike, and to Jewesin Hebrewe, and to the Latin folke in Latine; which Latin folke had