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.

(b) Divide the given year by 4)1836

4)1851

4, and keep the quotient only; reject the remainder.

2294

2312

7)2312

rem. 5.

rem. 2.

(f) Divide (e) by 7, keeping 7)2294 the remainder only.

(g) Subtract (f) from 7; and the dominical letter is under the remainder below.

1 2 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.

This gives nothing till

(i) From the number of centuries in the given year subtract 17, divide by 25, and keep the quotient A.D. 4200. only.

To find what is the difference between the old and new styles, add together 10 and (d). Thus for 1836 and 1851 there is a difference of 12 days.

Something equivalent to the preceding process, though shortened, when done on a large scale, by help of tables, must be gone through for all future time before Easter can be found. It may well be asked why the 30th of March, or any other day, would not do as well? Why should the moon and sun both be necessary to regulate the time of a religious festival, when the sun only would be a much more intelligible guide. The Jews had a lunar year; and therefore the passover, as well as all other observances, depended on the moon; but the existence of a lunar year in religious rites, and of a solar year in civil matters, is a great deal of trouble for nothing. There are no Vietas now, to drive heretical Easter-finders from the congregations of the pious.

III.—A story about an old book, which concerns nobody but an astronomer, was lost no one knows how but Leopold de' Medici, and has never been found. We must bring Vieta again upon the carpet, in a better character than that in which he last appeared in our pages, and to show that if a book of his has been preserved which does not advance his credit, another has been lost which might have done so. And we shall be the more specific as there is a single chance left of recovering a curious work, if this lucubration should find any reader who is interested in astronomy and has credit at Florence.

Vieta wrote a work, entitled Harmonicon Caleste,* on astronomy. This we learn from Bouillaud (Latinized Bullialdus,) in the Prolegomena to his Astronomia Philolaica, Paris, 1645, as follows: "He had written a book called Harmonicon Caleste, which the distinguished Peter Puteanus (or Dupuis) lent to Father Mersenne, &c. &c. This excellent and affable (facilis) man was deprived of the book by some dishonest person, so that he could neither return it to Puteanus, nor could the world be bene

*This has, we believe, been the title of several works. Vincent Wing certainly published one book of that name.

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 Cœleste, which, being com. municated 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 Bulhald. &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

66

* Iste; there is such confusion about this sentence, that we quote it entire; "Hic vir optimus et facilis à quodam viro non bonæ fidei illo libro emunctus est, ita ut nec ipsum Puteano reddere potuerit, nec respub. literaria fructum aliquem ex eo capere. Quamdiu enim vixit, iste nec reddere voluit nec copiam illius facere; et, nisi fallor, meditabatur sibi adrogare Vietæ 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 Mersenne 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 (avéκdora) 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 Accademia 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 quæ 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 Cœleste est à Florence. Bouillaud, astronome Français, a prêté ce livre, en 1662, au prince Leopold de Toscane, protecteur de l'académie 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 concernant le manuscrit de Harmonicon Cœleste, prêté par Bouillaud au prince Leopold des Medicis est consigné dans les manuscrits de Bouillaud, et M. (naming a very celebracted mathematician) "savant géométre, m'en a donné l'assurance. Il faut chercher dans les manuscrits. ou dans les ouvrages publiés par les auteurs, la verité de l'histoire."