"First demonstration. Concerning the centre: showing that, because the centre is an innermost point at an equal distance between two extreme points of a right line, and from every two relative and opposite intermediate points, it is composed of the two extreme internal points of each half of the line; each extreme internal point attracting towards itself all parts of that half to which it belongs...."

Of course the circle is squared: and the circ.u.mference is 3-1/21 diameters.

SOME MODERN ASTROLOGY.

Combination of the Zodiacal and Cometical Systems. Printed for the London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)

What this London Society was, or the "combination," did not appear. There was a remarkable comet in 1843, the tail of which was at first confounded with what is called the _zodiacal light_. This nicely-printed little tract, evidently got up with less care for expense than is usual in such works, brings together all the announcements of the astronomers, and adds a short head and tail piece, which I shall quote entire. As the announcements are very ordinary {351} astronomy, the reader will be able to detect, if detection be possible, what is the meaning and force of the "Combination of the Zodiacal and Cometical Systems":

"_Premonition._ It has pleased the AUTHOR _of_ CREATION to cause (to His _human and reasoning_ Creatures of this generation, by a '_combined_'

appearance in His _Zodiacal_ and _Cometical_ system) a '_warning Crisis_'

of universal concernment to this our GLOBE. It is this '_Crisis_' that has so generally 'ROUSED' at this moment the '_nations throughout the Earth_'

that no equal interest has ever before been excited by MAN; unless it be in that caused by the 'PAGAN-TEMPLE IN ROME,' which is recorded by the elder Pliny, '_Nat. Hist._' i. 23. iii. 3. HARDOUIN."

After the accounts given by the unperceiving astronomers, comes what follows:

"Such has been (_hitherto_) the only object discerned by the '_Wise of this World_,' in this _twofold union_ of the '_Zodiacal_' and '_Cometical_'

systems: yet it is nevertheless a most '_Thrilling Warning_,' to _all_ the inhabitants of this precarious and transitory EARTH. We have no authorized intimation or reasonable prospective contemplation, of '_current time_'

beyond a year 1860, of the present century; or rather, except '_the interval which may now remain from the present year 1843, to a year 1860_'

([Greek: hemeras HEXeKONTA]--'_threescore or sixty days_'--'_I have appointed each_ "DAY" _for a_ "YEAR,"' _Ezek._ iv. 6): and we know, from our '_common experience_,' how speedily such a measure of time will pa.s.s away.

"No words can be '_more explicit_' than these of OUR BLESSED LORD: viz.

'THIS GOSPEL _of the Kingdom shall be preached in_ ALL the EARTH, _for a Witness to_ ALL NATIONS; AND THEN, _shall the_ END COME.' The '_next 18 years_' must therefore supply the interval of the '_special Episcopal forerunners_.'

(Matt. xxiv. 14.)

"See the 'JEWISH INTELLIGENCER' of the present month (_April_), p. 153, for the '_Debates in Parliament_,' respecting {352} the BISHOP OF JERUSALEM, _viz._ Dr. Bowring,[731] Mr. Hume,[732] Sir R. Inglis,[733] Sir R.

Peel,[734] Viscount Palmerston.[735]"

I have quoted this at length, to show the awful threats which were published at a time of some little excitement about the phenomenon, under the name of the _London Society_. The a.s.sumption of a corporate appearance is a very unfair trick: and there are junctures at which harm might be done by it.

THE NUMBER OF THE BEAST.

_Wealth_ the name and number of the Beast, 666, in the Book of Revelation. [by John Taylor.[736]] London, 1844, 8vo.

Whether Junius or the Beast be the more difficult to identify, must be referred to Mr. Taylor, the only person who has attempted both. His cogent argument on the political secret is not unworthily matched in his treatment of the theological riddle. He sees the solution in [Greek: euporia], which occurs in the Acts of the Apostles as the word for wealth in one of its most disgusting forms, and makes 666 in the most straightforward way. This explanation has as good a chance as any other. The work contains a general {353} attempt at explanation of the Apocalypse, and some history of opinion on the subject. It has not the prolixity which is so common a fault of apocalyptic commentators.

A practical Treatise on Eclipses ... with remarks on the anomalies of the present Theory of the Tides. By T. Kerigan,[737] F.R.S. 1844, 8vo.

Containing also a refutation of the theory of the tides, and afterwards increased by a supplement, "Additional facts and arguments against the theory of the tides," in answer to a short notice in the _Athenaeum_ journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission to the Royal Society just before the publication of his book.

A new theory of Gravitation. By Joseph Denison,[738] Esq. London, 1844, 12mo.

Commentaries on the Principia. By the author of 'A new theory of Gravitation.' London, 1846, 8vo.

Honor to the speculator who can be put in his proper place by one sentence, be that place where it may.

"But we have shown that the velocities are inversely as the square roots of the mean distances from the sun; wherefore, by equality of ratios, the forces of the sun's gravitation upon them are also inversely as the square roots of their distances from the sun."

EASTER DAY PARADOXERS.

In the years 1818 and 1845 the full moon fell on Easter Day, having been particularly directed to fall before it in the act for the change of style and in the English missals and prayer-books of all time: perhaps it would be more correct to say that Easter Day was directed to fall after the full moon; "but the principle is the same." No explanation was given in 1818, but Easter was kept by the tables, {354} in defiance of the rule, and of several protests. A chronological panic was beginning in December 1844, which was stopped by the _Times_ newspaper printing extracts from an article of mine in the _Companion to the Almanac_ for 1845, which had then just appeared. No one had guessed the true reason, which is that the thing called the moon in the Gregorian Calendar is not the moon of the heavens, but a fict.i.tious imitation put wrong on purpose, as will presently appear, partly to keep Easter out of the way of the Jews' Pa.s.sover, partly for convenience of calculation. The apparent error happens but rarely; and all the work will perhaps have to be gone over next time. I now give two bits of paradox.

Some theologians were angry at this explanation. A review called the _Christian Observer_ (of which Christianity I do not know) got up a crushing article against me. I did not look at it, feeling sure that an article on such a subject which appeared on January 1, 1845, against a publication made in December 1844, must be a second-hand job. But some years afterwards (Sept. 10, 1850), the reviews, etc. having been just placed at the disposal of readers in the _old_ reading-room of the Museum, I made a tour of inspection, came upon my critic on his perch, and took a look at him. I was very glad to remember this, for, though expecting only second-hand, yet even of this there is good and bad; and I expected to find some hints in the good second-hand of a respectable clerical publication. I read on, therefore, attentively, but not long: I soon came to the information that some additions to Delambre's[739] statement of the rule for finding Easter, belonging to distant years, had been made by Sir Harris Nicolas![740] Now as I myself furnished my friend Sir H. N. with Delambre's digest of {355} Clavius's[741] rule, which I translated out of algebra into common language for the purpose, I was pretty sure this was the ignorant reading of a person to whom Sir H. N. was the highest _arithmetical_ authority on the subject. A person pretending to chronology, without being able to distinguish the historical points--so clearly as they stand out--in which Sir H. N. speaks with authority, from the arithmetical points of pure reckoning on which he does not pretend to do more than directly repeat others, must be as fit to talk about the construction of Easter Tables as the Spanish are to talk French. I need hardly say that the additions for distant years are as much from Clavius as the rest: my reviewer was not deep enough in his subject to know that Clavius made and published, from his rules, the full table up to A.D. 5000, for all the movable feasts of every year! I gave only a glance at the rest: I found I was either knave or fool, with a leaning to the second opinion; and I came away satisfied that my critic was either ignoramus or novice, with a leaning to the first. I afterwards found an ambiguity of expression in Sir H. N.'s account--whether his or mine I could not tell--which might mislead a novice or content an ignoramus, but would have been properly read or further inquired into by a competent person.

The second case is this. Shortly after the publication of my article, a gentleman called at my house, and, finding I was not at home, sent up his card--with a stylish west-end club on it--to my wife, begging for a few words on pressing business. With many well-expressed apologies, he stated that he had been alarmed by hearing that Prof. De M. had an intention of altering Easter next year. Mrs. De M. kept her countenance, and a.s.sured him that I had no such intention, and further, that she greatly doubted my having the power to do it. Was she quite sure? his authority was very good: fresh a.s.surances given. He was greatly relieved, for he had some horses training for after Easter, which {356} would not be ready to run if it were altered the wrong way. A doubt comes over him: would Mrs. De M., in the event of her being mistaken, give him the very earliest information?

Promise given; profusion of thanks; more apologies; and departure.

Now, candid reader!--or uncandid either!--which most deserves to be laughed at? A public instructor, who undertakes to settle for the world whether a reader of Clavius, the constructor of the Gregorian Calendar, is fool or knave, upon information derived from a compiler--in this matter--of his own day; or a gentleman of horse and dog a.s.sociations, who, misapprehending something which he heard about a current topic, infers that the reader of Clavius had the ear of the Government on a proposed alteration. I suppose the querist had heard some one say, perhaps, that the day ought to be set right, and some one else remark that I might be consulted, as the only person who had discussed the matter from the original source of the Calendar.

To give a better chance of the explanation being at once produced, next time the real full moon and Easter Day shall fall together, I insert here a summary which was printed in the Irish Prayer-book of the Ecclesiastical Society. If the amus.e.m.e.nt given by paradoxers should prevent a useless discussion some years hence, I and the paradoxers shall have done a little good between us--at any rate, I have done my best to keep the heavy weight afloat by tying bladders to it. I think the next occurrence will be in 1875.

EASTER DAY.

In the years 1818 and 1845, Easter Day, as given by the _rules in_ 24 Geo.

II cap. 23. (known as the act for the _change of style_) contradicted the _precept_ given in the preliminary explanations. The precept is as follows:

"_Easter Day_, on which the rest" of the moveable feasts "depend, is always the First Sunday after the Full Moon, which happens upon or next after the Twenty-first Day of {357} _March_; and if the Full Moon happens upon a Sunday, _Easter Day_ is the Sunday after."

But in 1818 and 1845, the full moon fell on a Sunday, and yet the rules gave _that same Sunday_ for Easter Day. Much discussion was produced by this circ.u.mstance in 1818: but a repet.i.tion of it in 1845 was nearly altogether prevented by a timely[742] reference to the intention of those who conducted the Gregorian reformation of the Calendar. Nevertheless, seeing that the apparent error of the Calendar is due to the precept in the Act of Parliament, which is both erroneous and insufficient, and that the difficulty will recur so often as Easter Day falls on the day of full moon, it may be advisable to select from the two articles cited in the note such of their conclusions and rules, without proof or controversy, as will enable the reader to understand the main points of the Easter question, and, should he desire it, to calculate for himself the Easter of the old or new style, for any given year.

1. In the very earliest age of Christianity, a controversy arose as to the mode of keeping Easter, some desiring to perpetuate the _Pa.s.sover_, others to keep the _festival of the Resurrection_. The first afterwards obtained the name of _Quartadecimans_, from their Easter being always kept on the _fourteenth day_ of the moon (Exod. xii. 18, Levit. xxiii. 5.). But though it is unquestionable that a Judaizing party existed, it is also likely that many dissented on chronological grounds. It is clear that no _perfect_ anniversary can take place, except when the fourteenth of the moon, and with it the pa.s.sover, falls on a Friday. Suppose, for instance, it falls on a Tuesday: one of three things must be {358} done. Either (which seems never to have been proposed) the crucifixion and resurrection must be celebrated on Tuesday and Sunday, with a wrong interval; or the former on Tuesday, the latter on Thursday, abandoning the first day of the week; or the former on Friday, and the latter on Sunday, abandoning the paschal commemoration of the crucifixion.

The last mode has been, as every one knows, finally adopted. The disputes of the first three centuries did not turn on any _calendar_ questions. The Easter question was merely the symbol of the struggle between what we may call the Jewish and Gentile sects of Christians: and it nearly divided the Christian world, the Easterns, for the most part, being _Quartadecimans_.

It is very important to note that there is no recorded dispute about a method of predicting the new moon, that is, no general dispute leading to formation of sects: there may have been difficulties, and discussions about them. The Metonic cycle, presently mentioned, must have been used by many, perhaps most, churches.

2. The question came before the Nicene Council (A.D. 325) not as an astronomical, but as a doctrinal, question: it was, in fact, this, Shall the _pa.s.sover_[743] be treated as a part of Christianity? The Council resolved this question in the negative, and the only information on its premises and conclusion, or either, which comes from itself, is contained in the following sentence of the synodical epistle, which epistle is preserved by Socrates[744] and Theodoret.[745] "We also send {359} you the good news concerning the unanimous consent of all in reference to the celebration of the most solemn feast of Easter, for this difference also has been made up by the a.s.sistance of your prayers: so that all the brethren in the East, who formerly celebrated this festival _at the same time as the Jews_, will in future conform _to the Romans and to us_, and to all who have of old observed _our manner_ of celebrating Easter." This is all that can be found on the subject: none of the stories about the Council ordaining the astronomical mode of finding Easter, and introducing the Metonic cycle into ecclesiastical reckoning, have any contemporary evidence: the canons which purport to be those of the Nicene Council do not contain a word about Easter; and this is evidence, whether we suppose those canons to be genuine or spurious.

3. The astronomical dispute about a lunar cycle for the prediction of Easter either commenced, or became prominent, by the extinction of greater ones, soon after the time of the Nicene Council. Pope Innocent I[746] met with difficulty in 414. S. Leo,[747] in 454, ordained that Easter of 455 should be April 24; which is right. It is useless to record details of these disputes in a summary: the result was, that in the year 463, Pope Hilarius[748] employed Victorinus[749] of Aquitaine to correct the Calendar, and Victorinus formed a rule which lasted until the sixteenth century. He combined the Metonic cycle and the solar cycle presently described. But {360} this cycle bears the name of Dionysius Exiguus,[750] a Scythian settled at Rome, about A.D. 530, who adapted it to his new yearly reckoning, when he abandoned the era of Diocletian as a commencement, and constructed that which is now in common use.

4. With Dionysius, if not before, terminated all difference as to the mode of keeping Easter which is of historical note: the increasing defects of the Easter Cycle produced in time the remonstrance of persons versed in astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752]

Cardinal Cusa,[753] Regiomonta.n.u.s,[754] etc. From the middle of the sixth to that of the sixteenth century, one rule was observed.

5. The mode of applying astronomy to chronology has always involved these two principles. First, the actual position of the heavenly body is not the object of consideration, but what astronomers call its _mean place_, which may be described thus. Let a fict.i.tious sun or moon move in the heavens, in such manner as to revolve among the fixed stars at an average rate, avoiding the alternate accelerations and r.e.t.a.r.dations which take place in every planetary motion. Thus the fict.i.tious (say _mean_) sun and moon are always very near to the real sun and moon. The ordinary clocks show time by the mean, not the real, sun: and it was always laid down that Easter depends on the opposition (or full moon) of the mean sun and moon, not of the real ones. Thus we see that, were the Calendar ever so correct {361} as to the _mean_ moon, it would be occasionally false as to the _true_ one: if, for instance, the opposition of the mean sun and moon took place at one second before midnight, and that of the real bodies only two seconds afterwards, the calendar day of full moon would be one day before that of the common almanacs. Here is a way in which the discussions of 1818 and 1845 might have arisen: the British legislature has defined _the moon_ as the regulator of the paschal calendar. But this was only a part of the mistake.

6. Secondly, in the absence of perfectly accurate knowledge of the solar and lunar motion (and for convenience, even if such knowledge existed), cycles are, and always have been taken, which serve to represent those motions nearly. The famous Metonic cycle, which is introduced into ecclesiastical chronology under the name of the cycle of the golden numbers, is a period of 19 Julian[755] years. This period, in the old Calendar, was taken to contain exactly 235 _lunations_, or intervals between new moons, of the mean moon. Now the state of the case is:

19 average Julian years make 6939 days 18 hours.