taken by Vieta. This Rubeus says, in his dedication, by permission, "Since, most holy father, this matter, of which the cognisance belongs to you, has been agitated, I have thought proper, under your most sacred name, to give this my admonition publicly, to the end that every handle of provocation may be taken away from Vieta, and an end put to this controversy by your authority." Such language never could have been addressed to a Pope by a priest, "permissu superiorum," unless the sentiment contained had been avowed by the party addressed. Vieta, however, died that same year, and thus perhaps escaped what we would rather had fallen upon him than upon the liberal and charitable Galileo. We imagine the illustrious Frenchman (for illustrious he was in many ways) would have been somewhat astonished had he been told that a future age would say his paschal lucubrations proved nothing except that it is not wise for a man of note to write in anger anything which is likely to last a couple of centuries.

II.—On the method of finding Easter above-mentioned. We owe the confusion attending moveable feasts, to the idea already alluded to, that the proper time of holding Easter was a matter of religious importance. But we may easily show that, in that case, a perfect performance of religious duties is unattainable, without a geometrically accurate knowledge of the sun, moon, and planets. Supposing it granted, that Easter Sunday ought to be the Sunday following the full moon which follows the 21st of March, and that if that full moon happen on a Sunday, the next is Easter Sunday: the following case

might happen. Astronomical prediction might place the time of full moon at half a second after twelve o'clock on Saturday night, or Sunday morning, in which case Easter Sunday should be the next Sunday. But even at this period, 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 had a more 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

See the paper on the Moon's Orbit, in the Companion to the

Almanac for 1834.

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 * Delambre's Hist. d'Ast. Mod.

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 form in which this rule is given, is extracted from Sir Harris Nicolas's useful Chronology of History, (in Lardner's Cyclopædia,) by permission. We have compared it with Delambre.

VOL. I.

0

2296

2314

2 (d)

2 (d)

(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

A B C D E F G

(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 centu

7)2312

rem. 5.

7

5

2

rem. 2.

༡

2

5

gives nothing till

ries in the given year subtract 17, A. D. 4200. divide by 25, and keep the quotient

only.

The rule now subdivides into two branches.

When the epact (m) is 23, or | When the epact (m) is greater less, as for year 1836.

(n) Subtract the epact from 45: this gives 33.

(0) Subtract the epact from 27,

than 23, as for year 1851.

(n) Subtract the epact from 75; this gives 47.

(0) Subtract the epact from

divide by 7, and take the remain-57, divide by 7, and take the re

der.

12 from 27 leaves 15, divide

by 7, remainder 1.

mainder.

28 from 57 leaves 29, divide by 7, remainder 1.

The two rules are now the same again.

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 exist