A Budget of Paradoxes Volume I Part 32

XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be greater than VII.,) and subtract XIV., the result is the day of March, or if more than 31, subtract 31, and the result is the day of April, on which Easter Sunday (old style) falls. (37; Easter Day is April 6).

These rules completely represent the old and new Calendars, so far as Easter is concerned. For further explanation we must refer to the articles cited at the commencement.

The annexed is the table of new and full moons of the Gregorian Calendar, cleared of the errors made for the purpose of preventing Easter from coinciding with the Jewish Pa.s.sover.

The second table (page 370) contains _epacts_, or ages of the moon at the beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to 1999: should the New Zealander not have arrived by that time, and should the churches of England and Rome then survive, the epact table may be continued from their liturgy-books. The way of using the table is as follows: Take the epact of the required year, and find it in the first or last column of the first table, in line with it are seen the calendar days of new and full moon. Thus, when the epact is 17, the new and full moons of March fall on the 13th and 28th. The result is, for the most part, correct: but in a minority of cases there is an error of a day. When this happens, the error is almost always a fraction of a day much less than twelve hours. Thus, when the table gives full moon on the 27th, and the real truth is the 28th, we may be sure it is early on the 28th.

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------------------------------------------------------------------------- |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.| ------------------------------------------------------------------------- 1 | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | 1 | 14 | 13 | 14 | 13 | 12 | 11 | 10 | 9 | 7 | 7 | 5 | 5 | ------------------------------------------------------------------------- 2 | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | 2 | 13 | 12 | 13 | 12 | 11 | 10 | 9 | 8 | 6 | 6 | 4 | 4 | ------------------------------------------------------------------------- 3 | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | 3 | 12 | 11 | 12 | 11 | 10 | 9 | 8 | 7 | 5 | 5 | 3 | 3 | ------------------------------------------------------------------------- 4 | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | 4 | 11 | 10 | 11 | 10 | 9 | 8 | 7 | 6 | 4 | 4 | 2 |2,31| ------------------------------------------------------------------------- 5 | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | 5 | 10 | 9 | 10 | 9 | 8 | 7 | 6 | 5 | 3 | 3 | 1 |1,30| ------------------------------------------------------------------------- 6 | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | 6 | 9 | 8 | 9 | 8 | 7 | 6 | 5 | 4 | 2 |2,31| 30 | 29 | ------------------------------------------------------------------------- 7 | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | 7 | 8 | 7 | 8 | 7 | 6 | 5 | 4 | 3 | 1 |1,30| 29 | 28 | ------------------------------------------------------------------------- 8 | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | 8 | 7 | 6 | 7 | 6 | 5 | 4 | 3 |2,31| 30 | 29 | 28 | 27 | ------------------------------------------------------------------------- 9 | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | 9 | 6 | 5 | 6 | 5 | 4 | 3 | 2 |1,30| 29 | 28 | 27 | 26 | ------------------------------------------------------------------------- 10 | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 | 10 | 5 | 4 | 5 | 4 | 3 | 2 |1,31| 29 | 28 | 27 | 26 | 25 | ------------------------------------------------------------------------- 11 | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 | 9 | 11 | 4 | 3 | 4 | 3 | 2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 | ------------------------------------------------------------------------- 12 | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 | 9 | 8 | 12 | 3 | 2 | 3 | 2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 | ------------------------------------------------------------------------- 13 | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 | 9 | 8 | 7 | 13 | 2 | 1 | 2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | ------------------------------------------------------------------------- 14 | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 | 9 | 8 | 7 | 6 | 14 |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | ------------------------------------------------------------------------- 15 | 15 | 13 | 15 | 13 | 13 | 11 | 11 | 9 | 8 | 7 | 6 | 5 | 15 | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | ------------------------------------------------------------------------- 16 | 14 | 12 | 14 | 12 | 12 | 10 | 10 | 8 | 7 | 6 | 5 | 4 | 16 | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | ------------------------------------------------------------------------- 17 | 13 | 11 | 13 | 11 | 11 | 9 | 9 | 7 | 6 | 5 | 4 | 3 | 17 | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | ------------------------------------------------------------------------- 18 | 12 | 10 | 12 | 10 | 10 | 8 | 8 | 6 | 5 | 4 | 3 | 2 | 18 | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | ------------------------------------------------------------------------- 19 | 11 | 9 | 11 | 9 | 9 | 7 | 7 | 5 | 4 | 3 | 2 |1,31| 19 | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | ------------------------------------------------------------------------- 20 | 10 | 8 | 10 | 8 | 8 | 6 | 6 | 4 | 3 | 2 |1,31| 30 | 20 | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | ------------------------------------------------------------------------- 21 | 9 | 7 | 9 | 7 | 7 | 5 | 5 | 3 | 2 |1,31| 29 | 29 | 21 | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | ------------------------------------------------------------------------- 22 | 8 | 6 | 8 | 6 | 6 | 4 | 4 | 2 |1,30| 30 | 28 | 28 | 22 | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | ------------------------------------------------------------------------- 23 | 7 | 5 | 7 | 5 | 5 | 3 | 3 |1,31| 29 | 29 | 27 | 27 | 23 | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | ------------------------------------------------------------------------- 24 | 6 | 5 | 6 | 5 | 4 | 3 | 2 |1,30| 29 | 28 | 27 | 26 | 24 | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | ------------------------------------------------------------------------- 25 | 5 | 4 | 5 | 4 | 3 | 2 |1,31| 29 | 28 | 27 | 26 | 25 | 25 | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 | ------------------------------------------------------------------------- 26 | 4 | 3 | 4 | 3 | 2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 | 26 | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 | ------------------------------------------------------------------------- 27 | 3 | 2 | 3 | 2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 | 27 | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 | 9 | 9 | ------------------------------------------------------------------------- 28 | 2 | 1 | 2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | 28 | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 | 8 | 8 | ------------------------------------------------------------------------- 29 |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | 29 | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 | 9 | 9 | 7 | 7 | ------------------------------------------------------------------------- 30 | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | 30 | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 | 8 | 8 | 6 | 6 | ------------------------------------------------------------------------- |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.| -------------------------------------------------------------------------

{370}

======================================================= | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ------------------------------------------------------- 185 | 17 | 28 | 9 | 20 | 2 | 12 | 23 | 4 | 15 | 26 ------------------------------------------------------- 186 | 7 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 ------------------------------------------------------- 187 | 28 | 9 | 20 | 1 | 12 | 23 | 4 | 15 | 26 | 7 ------------------------------------------------------- 188 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 | 28 ------------------------------------------------------- 189 | 9 | 21 | 1 | 12 | 23 | 4 | 15 | 26 | 7 | 18 ------------------------------------------------------- 190 | 29 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 ------------------------------------------------------- 191 | 19 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 ------------------------------------------------------- 192 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 ------------------------------------------------------- 193 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 ------------------------------------------------------- 194 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 ------------------------------------------------------- 195 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 ------------------------------------------------------- 196 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 ------------------------------------------------------- 197 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 ------------------------------------------------------- 198 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 | 22 ------------------------------------------------------- 199 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 | 13 =======================================================

For example, the year 1867. The epact is 25, and we find in the table:

J. F. M. AP. M. JU. JL. AU. S. O. N. D.

New 5+ 4 5+ 4 3+ 2 1,31 29 28- 27 26 25 Full 20 19- 20 19- 18 17 16 15 13- 13 11+ 11

When the truth is the day after + is written after the date; when the day before, -. Thus, the new moon of March is on the 6th; the full moon of April is on the 18th. {371}

I now introduce a small paradox of my own; and as I am not able to prove it, I am compelled to declare that any one who shall dissent must be either very foolish or very dishonest, and will make me quite uncomfortable about the state of his soul. This being settled once for all, I proceed to say that the necessity of arriving at the truth about the a.s.sertions that the Nicene Council laid down astronomical tests led me to look at Fathers, Church histories, etc. to an extent which I never dreamed of before. One conclusion which I arrived at was, that the Nicene Fathers had a knack of sticking to the question which many later councils could not acquire. In our own day, it is not permitted to Convocation seriously to discuss any one of the points which are bearing so hard upon their resources of defence--the cursing clauses of the Athanasian Creed, for example. And it may be collected that the prohibition arises partly from fear that there is no saying where a beginning, if allowed, would end. There seems to be a suspicion that debate, once let loose, would play up old Trent with the liturgy, and bring the whole book to book. But if any one will examine the real Nicene Creed, without the augmentation, he will admire the way in which the framers stuck to the point, and settled what they had to decide, according to their view of it. With such a presumption of good sense in their favor, it becomes easier to believe in any claim which may be made on their behalf to tact or sagacity in settling any other matter. And I strongly suspect such a claim may be made for them on the Easter question.

I collect from many little indications, both before and after the Council, that the division of the Christian world into Judaical and Gentile, though not giving rise to a sectarian distinction expressed by names, was of far greater force and meaning than historians prominently admit. I took _note_ of many indications of this, but not _notes_, as it was not to my purpose.

If it were so, we must admire the discretion of the Council. The Easter question was the {372} fighting ground of the struggle: the Eastern or Judaical Christians, with some varieties of usage and meaning, would have the Pa.s.sover itself to be the great feast, but taken in a Christian sense; the Western or Gentile Christians, would have the commemoration of the Resurrection, connected with the Pa.s.sover only by chronology. To s.h.i.+ft the Pa.s.sover in time, under its name, _Pascha_, without allusion to any of the force of the change, was gently cutting away the ground from under the feet of the Conservatives. And it was done in a very quiet way: no allusion to the precise character of the change; no hint that the question was about two different festivals: "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." The Judaizers meant to be keeping the Pa.s.sover _as_ a Christian feast: they are gently a.s.sumed to be keeping, _not_ the Pa.s.sover, _but_ a Christian feast; and a doctrinal decision is quietly, but efficiently, announced under the form of a chronological ordinance. Had the Council issued theses of doctrine, and excommunicated all dissentients, the rupture of the East and West would have taken place earlier by centuries than it did. The only place in which I ever saw any part of my paradox advanced, was in an article in the _Examiner_ newspaper, towards the end of 1866, after the above was written.

A story about Christopher Clavius, the workman of the new Calendar. I chanced to pick up "Albertus Pighius Campensis de aequinoctiorum solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis, De que Rest.i.tutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On the t.i.tle-page were decayed words followed by ".._hristophor.. C..ii_, 1556 (or 8)," the last blank not entirely erased by time, but showing the lower halves of an _l_ and of an _a_, and {373} rather too much room for a _v_.

It looked very like _E Libris Christophori Clavii_ 1556. By the courtesy of some members of the Jesuit body in London, I procured a tracing of the signature of Clavius from Rome, and the shapes of the letters, and the modes of junction and disjunction, put the matter beyond question. Even the extra s.p.a.ce was explained; he wrote himself Cla_u_ius. Now in 1556, Clavius was nineteen years old: it thus appears probable that the framer of the Gregorian Calendar was selected, not merely as a learned astronomer, but as one who had attended to the calendar, and to works on its reformation, from early youth. When on the subject I found reason to think that Clavius had really read this work, and taken from it a phrase or two and a notion or two. Observe the advantage of writing the baptismal name at full length.

A COUPLE OF MINOR PARADOXES.

The discovery of a general resolution of all superior finite equations, of every numerical both algebraick and transcendent form. By A. P.

Vogel,[761] mathematician at Leipzick. Leipzick and London, 1845, 8vo.

This work is written in the English of a German who has not mastered the idiom: but it is always intelligible. It professes to solve equations of every degree "in a more extent sense, and till to every degree of exactness." The general solution of equations of _all_ degrees is a vexed question, which cannot have the mysterious interest of the circle problem, and is of a comparatively modern date.[762] Mr. Vogel {374} announces a forthcoming treatise in which are resolved the "last impossibilities of pure mathematics."

Elective Polarity the Universal Agent. By Frances Barbara Burton, auth.o.r.ess of 'Astronomy familiarized,' 'Physical Astronomy,' &c.

London, 1845, 8vo.[763]

The t.i.tle gives a notion of the theory. The first sentence states, that 12,500 years ago [alpha] Lyrae was the pole-star, and attributes the immense magnitude of the now fossil animals to a star of such "polaric intensity as Vega pouring its magnetic streams through our planet." Miss Burton was a lady of property, and of very respectable acquirements, especially in Hebrew; she was eccentric in all things.

1867.--Miss Burton is revived by the writer of a book on meteorology which makes use of the planets: she is one of his leading minds.[764]

SPECULATIVE THOUGHT IN ENGLAND.

In the year 1845 the old _Mathematical Society_ was merged in the Astronomical Society. The circle-squarers, etc., thrive more in England than in any other country: there are most weeds where there is the largest crop. Speculation, though not encouraged by our Government so much as by those of the Continent, has had, not indeed such forcing, but much wider diffusion: few tanks, but many rivulets. On this point I quote from the preface to the reprint of the work of Ramchundra,[765] which I superintended for the late Court of Directors of the East India Company.

{375}

"That sound judgment which gives men well to know what is best for them, as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced without, a great taste for pure speculation among the general ma.s.s of the people, down to the lowest of those who can read and write. England is a marked example. Many persons will be surprised at this a.s.sertion. They imagine that our country is the great instance of the refusal of all _unpractical_ knowledge in favor of what is _useful_. I affirm, on the contrary, that there is no country in Europe in which there has been so wide a diffusion of speculation, theory, or what other unpractical word the reader pleases. In our country, the scientific _society_ is always formed and maintained by the people; in every other, the scientific _academy_--most aptly named--has been the creation of the government, of which it has never ceased to be the nursling. In all the parts of England in which manufacturing pursuits have given the artisan some command of time, the cultivation of mathematics and other speculative studies has been, as is well known, a very frequent occupation. In no other country has the weaver at his loom bent over the _Principia_ of Newton; in no other country has the man of weekly wages maintained his own scientific periodical. With us, since the beginning of the last century, scores upon scores--perhaps hundreds, for I am far from knowing all--of annuals have run, some their ten years, some their half-century, some their century and a half, containing questions to be answered, from which many of our examiners in the universities have culled materials for the academical contests. And these questions have always been answered, and in cases without number by the lower order of purchasers, the mechanics, the weavers, and the printers' workmen. I cannot here digress to point out the manner in which the concentration of manufactures, and the general diffusion of education, have affected the {376} state of things; I speak of the time during which the present system took its rise, and of the circ.u.mstances under which many of its most effective promoters were trained. In all this there is nothing which stands out, like the state-nourished academy, with its few great names and brilliant single achievements. This country has differed from all others in the wide diffusion of the disposition to speculate, which disposition has found its place among the ordinary habits of life, moderate in its action, healthy in its amount."

THE OLD MATHEMATICAL SOCIETY.

Among the most remarkable proofs of the diffusion of speculation was the Mathematical Society, which flourished from 1717 to 1845. Its habitat was Spitalfields, and I think most of its existence was pa.s.sed in Crispin Street. It was originally a plain society, belonging to the studious artisan. The members met for discussion once a week; and I believe I am correct in saying that each man had his pipe, his pot, and his problem. One of their old rules was that, "If any member shall so far forget himself and the respect due to the Society as in the warmth of debate to threaten or offer personal violence to any other member, he shall be liable to immediate expulsion, or to pay such fine as the majority of the members present shall decide." But their great rule, printed large on the back of the t.i.tle page of their last book of regulations, was "By the const.i.tution of the Society, it is the duty of every member, if he be asked any mathematical or philosophical question by another member, to instruct him in the plainest and easiest manner he is able." We shall presently see that, in old time, the rule had a more homely form.

I have been told that De Moivre[766] was a member of this {377} Society.

This I cannot verify: circ.u.mstances render it unlikely; even though the French refugees cl.u.s.tered in Spitalfields; many of them were of the Society, which there is some reason to think was founded by them. But Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and others of known name, were certainly members. The Society gradually declined, and in 1845 was reduced to nineteen members. An arrangement was made by which sixteen of these members, who where not already in the Astronomical Society became Fellows without contribution, all the books and other property of the old Society being transferred to the new one. I was one of the committee which made the preliminary inquiries, and the reason of the decline was soon manifest. The only question which could arise was whether the members of the society of working men--for this repute still continued--were of that cla.s.s of educated men who could a.s.sociate with the Fellows of the Astronomical Society on terms agreeable to all parties. We found that the artisan element had been extinct for many years; there was not a man but might, as to education, manners, and position, have become a Fellow in the usual way. The fact was that life in Spitalfields had become harder: and the weaver could {378} only live from hand to mouth, and not up to the brain. The material of the old Society no longer existed.

In 1798, experimental lectures were given, a small charge for admission being taken at the door: by this hangs a tale--and a song. Many years ago, I found among papers of a deceased friend, who certainly never had anything to do with the Society, and who pa.s.sed all his life far from London, a song, headed "Song sung by the Mathematical Society in London, at a dinner given Mr. Fletcher,[771] a solicitor, who had defended the Society gratis."

Mr. Williams,[772] the a.s.sistant Secretary of the Astronomical Society, formerly Secretary of the Mathematical Society, remembered that the Society had had a solicitor named Fletcher among the members. Some years elapsed before it struck me that my old friend Benjamin Gompertz,[773] who had long been a member, might have some recollection of the matter. The following is an extract of a letter from him (July 9, 1861):

"As to the Mathematical Society, of which I was a member when only 18 years of age, [Mr. G. was born in 1779], having been, contrary to the rules, elected under the age of 21. How I came to be a member of that Society--and continued so until it joined the Astronomical Society, and was then the President--was: I happened to pa.s.s a bookseller's small shop, of second-hand books, kept by a poor taylor, but a good mathematician, John Griffiths. I was very pleased to meet a mathematician, and I asked him if he would give me some lessons; and his reply was that I was more capable to teach him, but he belonged to a society of mathematicians, and he would introduce me. I accepted the offer, and I was elected, and had many scholars then to teach, as {379} one of the rules was, if a member asked for information, and applied to any one who could give it, he was obliged to give it, or fine one penny. Though I might say much with respect to the Society which would be interesting, I will for the present reply only to your question. I well knew Mr. Fletcher, who was a very clever and very scientific person. He did, as solicitor, defend an action brought by an informer against the Society--I think for 5,000l.--for giving lectures to the public in philosophical subjects [i.e., for unlicensed public exhibition with money taken at the doors]. I think the price for admission was one s.h.i.+lling, and we used to have, if I rightly recollect, from two to three hundred visitors. Mr. Fletcher was successful in his defence, and we got out of our trouble. There was a collection made to reward his services, but he did not accept of any reward: and I think we gave him a dinner, as you state, and enjoyed ourselves; no doubt with astronomical songs and other songs; but my recollection does not enable me to say if the astronomical song was a drinking song. I think the anxiety caused by that action was the cause of some of the members' death. [They had, no doubt, broken the law in ignorance; and by the sum named, the informer must have been present, and sued for a penalty on every s.h.i.+lling he could prove to have been taken]."

I by no means guarantee that the whole song I proceed to give is what was sung at the dinner: I suspect, by the completeness of the chain, that augmentations have been made. My deceased friend was just the man to add some verses, or the addition may have been made before it came into his hands, or since his decease, for the sc.r.a.ps containing the verses pa.s.sed through several hands before they came into mine. We may, however, be pretty sure that the original is substantially contained in what is given, and that the character is therefore preserved. I have had myself to repair damages every now and then, in the way of conjectural restoration of defects caused by ill-usage. {380}

THE ASTRONOMER'S DRINKING SONG.

"Whoe'er would search the starry sky, Its secrets to divine, sir, Should take his gla.s.s--I mean, should try A gla.s.s or two of wine, sir!

True virtue lies in golden mean, And man must wet his clay, sir; Join these two maxims, and 'tis seen He should drink his bottle a day, sir!

"Old Archimedes, reverend sage!

By trump of fame renowned, sir, Deep problems solved in every page, And the sphere's curved surface found,[774] sir: Himself he would have far outshone, And borne a wider sway, sir, Had he our modern secret known, And drank a bottle a day, sir!

"When Ptolemy,[775] now long ago, Believed the earth stood still, sir, He never would have blundered so, Had he but drunk his fill, sir: He'd then have felt[776] it circulate, And would have learnt to say, sir, The true way to investigate Is to drink your bottle a day, sir!

"Copernicus,[777] that learned wight, The glory of his nation, With draughts of wine refreshed his sight, And saw the earth's rotation; {381} Each planet then its...o...b..described, The moon got under way, sir; These truths from nature he imbibed For he drank his bottle a day, sir!

"The n.o.ble[778] Tycho placed the stars, Each in its due location; He lost his nose[779] by spite of Mars, But that was no privation: Had he but lost his mouth, I grant He would have felt dismay, sir, Bless you! _he_ knew what he should want To drink his bottle a day, sir!

"Cold water makes no lucky hits; On mysteries the head runs: Small drink let Kepler[780] time his wits On the regular polyhedrons: He took to wine, and it changed the chime, His genius swept away, sir, Through area varying[781] as the time At the rate of a bottle a day, sir!

"Poor Galileo,[782] forced to rat Before the Inquisition, _E pur si muove_[783] was the pat He gave them in addition: {382} He meant, whate'er you think you prove, The earth must go its way, sirs; Spite of your teeth I'll make it move, For I'll drink my bottle a day, sirs!

"Great Newton, who was never beat Whatever fools may think, sir; Though sometimes he forgot to eat, He never forgot to drink, sir: Descartes[784] took nought but lemonade, To conquer him was play, sir; The first advance that Newton made Was to drink his bottle a day, sir!