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.

235 average lunations make 6939 days 16 hours 31 minutes.

So that successive cycles of golden numbers, supposing the first to start right, amount to making the new moons fall too late, gradually, so that the mean moon of this cycle gains 1 hour 29 minutes in 19 years upon the mean moon of the heavens, or about a day in 300 years. When the Calendar was reformed, the calendar new moons were four days in advance of the mean moon of the heavens: so that, for instance, calendar full moon on the 18th usually meant real full moon on the 14th.

7. If the difference above had not existed, the moon of the heavens (the mean moon at least), would have returned {362} permanently to the same days of the month in 19 years; with an occasional slip arising from the unequal distribution of the leap years, of which a period contains sometimes five and sometimes four. As a general rule, the days of new and full moon in any one year would have been also the days of new and full moon of a year having 19 more units in its date. Again, if there had been no leap years, the days of the month would have returned to the same days of the week every seven years. The introduction of occasional 29ths of February disturbs this, and makes the permanent return of month days to week days occur only after 28 years. If all had been true, the lapse of 28 times 19, or 532 years, would have restored the year in every point: that is, A.D. 1, for instance, and A.D. 533, would have had the same almanac in every matter relating to week days, month days, sun, and moon (mean sun and moon at least). And on the supposition of its truth, the old system of Dionysius was framed. Its errors, are, first, that the moments of mean new moon advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that the average Julian year of 3651/4 days is too long by 11 m. 10 s.

8. The Council of Trent, moved by the representations made on the state of the Calendar, referred the consideration of it to the Pope. In 1577, Gregory XIII[756] submitted to the Roman Catholic Princes and Universities a plan presented to him by the representatives of Aloysius Lilius,[757] then deceased. This plan being approved of, the Pope nominated a commission to consider its details, the working member of which was the Jesuit Clavius. A short work was prepared by Clavius, descriptive of the new Calendar: this {363} was published[758] in 1582, with the Pope's bull (dated February 24, 1581) prefixed. A larger work was prepared by Clavius, containing fuller explanation, and entitled Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti Explicatio. This was published at Rome in 1603, and again in the collection of the works of Clavius in 1612.

9. The following extracts from Clavius settle the question of the meaning of the term moon, as used in the Calendar:

"Who, except a few who think they are very sharp-sighted in this matter, is so blind as not to see that the 14th of the moon and the full moon are not the same things in the Church of God?... Although the Church, in finding the new moon, and from it the 14th day, uses neither the true nor the mean motion of the moon, but measures only according to the order of a cycle, it is nevertheless undeniable that the mean full moons found from astronomical tables are of the greatest use in determining the cycle which is to be preferred ... the new moons of which cycle, in order to the due celebration of Easter, should be so arranged that the 14th days of those moons, reckoning from the day of new moon inclusive, should not fall two or more days before the mean full moon, but only one day, or else on the very day itself, or not long after. And even thus far the Church need not take very great pains ... for it is sufficient that all should reckon by the 14th day of the moon in the cycle, even though sometimes it should be more than one day before or after the mean full moon.... We have taken pains that in our cycle the new moons should follow the real new moons, so that the 14th of the moon should fall either the day before the mean full moon, or on that day, or not long after; and this was done on purpose, for if the new moon of the cycle fell on the same day as the mean new moon of the {364} astronomers, it might chance that we should celebrate Easter on the same day as the Jews or the Quartadeciman heretics, which would be absurd, or else before them, which would be still more absurd."

From this it appears that Clavius continued the Calendar of his predecessors in the choice of the fourteenth day of the moon. Our legislature lays down the day of the full moon: and this mistake appears to be rather English than Protestant; for it occurs in missals published in the reign of Queen Mary. The calendar lunation being 291/2 days, the middle day is the fifteenth day, and this is and was reckoned as the day of the full moon. There is every right to presume that the original passover was a feast of the real full moon: but it is most probable that the moons were then reckoned, not from the astronomical conjunction with the sun, which nobody sees except at an eclipse, but from the day of first visibility of the new moon. In fine climates this would be the day or two days after conjunction; and the fourteenth day from that of first visibility inclusive, would very often be the day of full moon. The following is then the proper correction of the precept in the Act of Parliament:

Easter Day, on which the rest depend, is always the First Sunday after the fourteenth day of the calendar moon which happens upon or next after the Twenty-first day of March, according to the rules laid down for the construction of the Calendar; and if the fourteenth day happens upon a Sunday, Easter Day is the Sunday after.

10. Further, it appears that Clavius valued the celebration of the festival after the Jews, etc., more than astronomical correctness. He gives comparison tables which would startle a believer in the astronomical intention of his Calendar: they are to show that a calendar in which the moon is always made a day older than by him, represents the heavens better than he has done, or meant to do. But it must be observed that this diminution of the real moon's age has {365} a tendency to make the English explanation often practically accordant with the Calendar. For the fourteenth day of Clavius is generally the fifteenth day of the mean moon of the heavens, and therefore most often that of the real moon. But for this, 1818 and 1845 would not have been the only instances of our day in which the English precept would have contradicted the Calendar.

11. In the construction of the Calendar, Clavius adopted the ancient cycle of 532 years, but, we may say, without ever allowing it to run out. At certain periods, a shift is made from one part of the cycle into another. This is done whenever what should be Julian leap year is made a common year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times to correct the error of 1 h. 19 m., before referred to, in each cycle of golden numbers: Clavius, to meet his view of the amount of that error, put forward the moon's age a day 8 times in 2,500 years. As we cannot enter at full length into the explanation, we must content ourselves with giving a set of rules, independent of tables, by which the reader may find Easter for himself in any year, either by the old Calendar or the new. Any one who has much occasion to find Easters and movable feasts should procure Francoeur's[759] tables.

12. Rule for determining Easter Day of the Gregorian Calendar in any year of the new style. To the several parts {366} of the rule are annexed, by way of example, the results for the year 1849.

I. Add 1 to the given year. (1850).

II. Take the quotient of the given year divided by 4, neglecting the remainder. (462).

III. Take 16 from the centurial figures of the given year, if it can be done, and take the remainder. (2).

IV. Take the quotient of III. divided by 4, neglecting the remainder. (0).

V. From the sum of I, II, and IV., subtract III. (2310).

VI. Find the remainder of V. divided by 7. (0).

VII. Subtract VI. from 7; this is the number of the dominical letter

1 2 3 4 5 6 7 (7; dominical letter G). A B C D E F G

VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the golden number. (7).

IX. From the centurial figures of the year subtract 17, divide by 25, and keep the quotient. (0).

X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep the quotient. (1).

XI. To VIII. add ten times the next less number, divide by 30, and keep the remainder. (7).

XII. To XI. add X. and IV., and take away III., throwing out thirties, if any. If this give 24, change it into 25. If 25, change it into 26, whenever the golden number is greater than 11. If 0, change it into 30. Thus we have the epact, or age of the Calendar moon at the beginning of the year. (6).

When the Epact is 23, or less.

XIII. Subtract XII., the epact, from 45. (39).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder. (7)

When the Epact is greater than 23.

XIII. Subtract XII., the epact, from 75.

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 {367} the result is the day of April, on which Easter Sunday falls. (39; Easter Day is April 8).

In the following examples, the several results leading to the final conclusion are tabulated.

======================================================== GIVEN YEAR 1592 1637 1723 1853 2018 4686 I. 1593 1638 1724 1854 2019 4687 II. 398 409 430 463 504 1171 III. - 0 1 2 4 30 IV. - 0 0 0 1 7 V. 1991 2047 2153 2315 2520 5835 VI. 3 3 4 5 0 4 VII. 4 4 3 2 7 3 VIII. 16 4 14 11 5 13 IX. - - 0 0 0 1 X. 0 0 0 1 1 10 XI. 16 4 24 21 15 13 XII. 16 4 23 20 13 0 say 30 XIII. 29 41 22 25 32 45 XIV. 4 2 4 7 7 6 XV. 29 43 28 27 32 49 Easter Day Mar.29 Apr.12 Mar.28 Mar.27 Apr.1 Apr.18

13. Rule for determining Easter Day of the Antegregorian Calendar in any year of the old style. To the several parts of the rule are annexed, by way of example, the results for the year 1287. The steps are numbered to correspond with the steps of the Gregorian rule, so that it can be seen what augmentations the latter requires.

I. Set down the given year. (1287).

II. Take the quotient of the given year divided by 4, neglecting the remainder (321).

V. Take 4 more than the sum of I. and II. (1612).

VI. Find the remainder of V. divided by 7. (2).

VII. Subtract VI. from 7; this is the number of the dominical letter

1 2 3 4 5 6 7 (5; dominical letter E). A B C D E F G

VIII. Divide one more than the given year by 19, the remainder (or 19 if no remainder) is the golden number. (15).

XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there be no remainder) is the epact. (12).

{368}

When the Epact is 23, or less.

XIII. Subtract XII., the epact, from 45. (33).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder, (1).

When the Epact is greater than 23.

XIII. Subtract XII., the epact, from 75.

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 Passover.

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.

{369}

- 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 assertions 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 Passover 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 Passover only by chronology. To shift the Passover 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 Passover as a Christian feast: they are gently assumed to be keeping, not the Passover, 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 Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On the title-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 space was explained; he wrote himself Clauius. 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, authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c. London, 1845, 8vo.[763]

The title 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 mass 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 assertion. 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 circumstances 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 passed 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 title page of their last book of regulations, was "By the constitution 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: circumstances render it unlikely; even though the French refugees clustered 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 class of educated men who could associate 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 passed 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 Assistant 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 pass 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 shilling, 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 shilling 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 scraps containing the verses passed 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 glass—I mean, should try A glass 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 orb described, The moon got under way, sir; These truths from nature he imbibed For he drank his bottle a day, sir!

"The noble[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!

"D'Alembert,[785] Euler,[786] and Clairaut,[787] Though they increased our store, sir, Much further had been seen to go Had they tippled a little more, sir! Lagrange[788] gets mellow with Laplace,[789] And both are wont to say, sir, The philosophe who's not an ass Will drink his bottle a day, sir!

"Astronomers! what can avail Those who calumniate us; Experiment can never fail With such an apparatus: Let him who'd have his merits known Remember what I say, sir; Fair science shines on him alone Who drinks his bottle a day, sir!

{383} "How light we reck of those who mock By this we'll make to appear, sir, We'll dine by the sidereal[790] clock For one more bottle a year, sir: But choose which pendulum you will, You'll never make your way, sir, Unless you drink—and drink your fill,— At least a bottle a day, sir!"

Old times are changed, old manners gone!

There is a new Mathematical Society,[791] and I am, at this present writing (1866), its first President. We are very high in the newest developments, and bid fair to take a place among the scientific establishments. Benjamin Gompertz, who was President of the old Society when it expired, was the link between the old and new body: he was a member of ours at his death. But not a drop of liquor is seen at our meetings, except a decanter of water: all our heavy is a fermentation of symbols; and we do not draw it mild. There is no penny fine for reticence or occult science; and as to a song! not the ghost of a chance.



1826. The time may have come when the original documents connected with the discovery of Neptune may be worth revising. The following are extracts from the Athenaeum of October 3 and October 17:



LE VERRIER'S[792] PLANET.

We have received, at the last moment before making up for press, the following letter from Sir John Herschel,[793] {384} in reference to the matter referred to in the communication from Mr. Hind[794] given below:

"Collingwood, Oct. 1.

"In my address to the British Association assembled at Southampton, on the occasion of my resigning the chair to Sir R. Murchison,[795] I stated, among the remarkable astronomical events of the last twelvemonth, that it had added a new planet to our list,—adding, 'it has done more,—it has given us the probable prospect of the discovery of another. We see it as Columbus saw America from the shores of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis, with a certainty hardly inferior to that of ocular demonstration.'—These expressions are not reported in any of the papers which profess to give an account of the proceedings, but I appeal to all present whether they were not used.

"Give me leave to state my reasons for this confidence; and, in so doing, to call attention to some facts which deserve to be put on record in the history of this noble discovery. On July 12, 1842, the late illustrious astronomer, Bessel,[796] honored me with a visit at my present residence. On the evening of that day, conversing on the great work of the planetary reductions undertaken by the Astronomer Royal[797]—then in progress, and since published,[798]—M. Bessel remarked that the motions of Uranus, as he had satisfied {385} himself by careful examination of the recorded observations, could not be accounted for by the perturbations of the known planets; and that the deviations far exceeded any possible limits of error of observation. In reply to the question, Whether the deviations in question might not be due to the action of an unknown planet?—he stated that he considered it highly probable that such was the case,—being systematic, and such as might be produced by an exterior planet. I then inquired whether he had attempted, from the indications afforded by these perturbations, to discover the position of the unknown body,—in order that 'a hue and cry' might be raised for it. From his reply, the words of which I do not call to mind, I collected that he had not then gone into that inquiry; but proposed to do so, having now completed certain works which had occupied too much of his time. And, accordingly, in a letter which I received from him after his return to Koenigsberg, dated November 14, 1842, he says,—'In reference to our conversation at Collingwood, I announce to you (melde ich Ihnen) that Uranus is not forgotten.' Doubtless, therefore, among his papers will be found some researches on the subject.

"The remarkable calculations of M. Le Verrier—which have pointed out, as now appears, nearly the true situation of the new planet, by resolving the inverse problem of the perturbations—if uncorroborated by repetition of the numerical calculations by another hand, or by independent investigation from another quarter, would hardly justify so strong an assurance as that conveyed by my expressions above alluded to. But it was known to me, at that time, (I will take the liberty to cite the Astronomer Royal as my authority) that a similar investigation had been independently entered into, and a conclusion as to the situation of the new planet very nearly coincident with M. Le Verrier's arrived at (in entire ignorance of his conclusions), by a young Cambridge mathematician, Mr. Adams;[799]—who will, I hope, {386} pardon this mention of his name (the matter being one of great historical moment),—and who will, doubtless, in his own good time and manner, place his calculations before the public.

"J. F. W. HERSCHEL."

Discovery of Le Verrier's Planet.

Mr. Hind announces to the Times that he has received a letter from Dr. Bruennow, of the Royal Observatory at Berlin, giving the very important information that Le Verrier's planet was found by M. Galle, on the night of September 23. "In announcing this grand discovery," he says, "I think it better to copy Dr. Bruennow's[800] letter."



"Berlin, Sept. 25.

"My dear Sir—M. Le Verrier's planet was discovered here the 23d of September, by M. Galle.[801] It is a star of the 8th magnitude, but with a diameter of two or three seconds. Here are its places:

h. m. s. R. A. Declination. Sept. 23, 12 0 14.6 M.T. 328 deg. 19' 16.0" -13 deg. 24' 8.2" Sept. 24, 8 54 40.9 M.T. 328 deg. 18' 14.3" -13 deg. 24' 29.7"

The planet is now retrograde, its motion amounting daily to four seconds of time.

"Yours most respectfully, BRUeNNOW."

"This discovery," Mr. Hind says, "may be justly considered one of the greatest triumphs of theoretical astronomy;" and he adds, in a postscript, that the planet was observed at Mr. Bishop's[802] Observatory, in the Regent's Park, {387} on Wednesday night, notwithstanding the moonlight and hazy sky. "It appears bright," he says, "and with a power of 320 I can see the disc. The following position is the result of instrumental comparisons with 33 Aquarii:

Sept. 30, at 8h. 16m. 21s. Greenwich mean time— Right ascension of planet 21h. 52m. 47.15s. South declination 13 deg. 27' 20"."



THE NEW PLANET.

"Cambridge Observatory, Oct. 15.

"The allusion made by Sir John Herschel, in his letter contained in the Athenaeum of October 3, to the theoretical researches of Mr. Adams, respecting the newly-discovered planet, has induced me to request that you would make the following communication public. It is right that I should first say that I have Mr. Adams's permission to make the statements that follow, so far as they relate to his labors. I do not propose to enter into a detail of the steps by which Mr. Adams was led, by his spontaneous and independent researches, to a conclusion that a planet must exist more distant than Uranus. The matter is of too great historical moment not to receive a more formal record than it would be proper to give here. My immediate object is to show, while the attention of the scientific public is more particularly directed to the subject, that, with respect to this remarkable discovery, English astronomers may lay claim to some merit.

"Mr. Adams formed the resolution of trying, by calculation, to account for the anomalies in the motion of Uranus on the hypothesis of a more distant planet, when he was an undergraduate in this university, and when his exertions for the academical distinction, which he obtained in January 1843, left him no time for pursuing the research. In the course of that year, he arrived at an approximation to the position of the supposed planet; which, however, he did not consider to be worthy of confidence, on account of his not {388} having employed a sufficient number of observations of Uranus. Accordingly, he requested my intervention to obtain for him the early Greenwich observations, then in course of reduction;—which the Astronomer Royal immediately supplied, in the kindest possible manner. This was in February, 1844. In September, 1845, Mr. Adams communicated to me values which he had obtained for the heliocentric longitude, excentricity of orbit, longitude of perihelion, and mass, of an assumed exterior planet,—deduced entirely from unaccounted-for perturbations of Uranus. The same results, somewhat corrected, he communicated, in October, to the Astronomer Royal. M. Le Verrier, in an investigation which was published in June of 1846, assigned very nearly the same heliocentric longitude for the probable position of the planet as Mr. Adams had arrived at, but gave no results respecting its mass and the form of its orbit. The coincidence as to position from two entirely independent investigations naturally inspired confidence; and the Astronomer Royal shortly after suggested the employing of the Northumberland telescope of this observatory in a systematic search after the hypothetical planet; recommending, at the same time, a definite plan of operations. I undertook to make the search,—and commenced observing on July 29. The observations were directed, in the first instance, to the part of the heavens which theory had pointed out as the most probable place of the planet; in selecting which I was guided by a paper drawn up for me by Mr. Adams. Not having hour xxi. of the Berlin star-maps—of the publication of which I was not aware—I had to proceed on the principle of comparison of observations made at intervals. On July 30, I went over a zone 9' broad, in such a manner as to include all stars to the eleventh magnitude. On August 4, I took a broader zone and recorded a place of the planet. My next observations were on August 12; when I met with a star of the eighth magnitude in the zone which I had gone over on July 30,—and which did not then {389} contain this star. Of course, this was the planet;—the place of which was, thus, recorded a second time in four days of observing. A comparison of the observations of July 30 and August 12 would, according to the principle of search which I employed, have shown me the planet. I did not make the comparison till after the detection of it at Berlin—partly because I had an impression that a much more extensive search was required to give any probability of discovery—and partly from the press of other occupation. The planet, however, was secured, and two positions of it recorded six weeks earlier here than in any other observatory,—and in a systematic search expressly undertaken for that purpose. I give now the positions of the planet on August 4 and August 12.

Greenwich mean time.

Aug. 4, 13h. 36m. 25s. {R.A. 21h. 58m. 14.70s. {N.P.D. 102 deg. 57' 32.2"

Aug. 12, 13h. 3m. 26s. {R.A. 21h. 57m. 26.13s. {N.P.D. 103 deg. 2' 0.2"

"From these places compared with recent observations Mr. Adams has obtained the following results:

Distance of the planet from the sun 30.05 Inclination of the orbit 1 deg. 45' Longitude of the descending node 309 deg. 43' Heliocentric longitude, Aug. 4 326 deg. 39'

"The present distance from the sun is, therefore, thirty times the earth's mean distance;—which is somewhat less than the theory had indicated. The other elements of the orbit cannot be approximated to till the observations shall have been continued for a longer period.

"The part taken by Mr. Adams in the theoretical search after this planet will, perhaps, be considered to justify the suggesting of a name. With his consent, I mention Oceanus as one which may possibly receive the votes of astronomers.—I {390} have authority to state that Mr. Adams's investigations will in a short time, be published in detail.

"J. CHALLIS."[803]



ASTRONOMICAL POLICE REPORT.

"An ill-looking kind of a body, who declined to give any name, was brought before the Academy of Sciences, charged with having assaulted a gentleman of the name of Uranus in the public highway. The prosecutor was a youngish looking person, wrapped up in two or three great coats; and looked chillier than anything imaginable, except the prisoner,—whose teeth absolutely shook, all the time.

Policeman Le Verrier[804] stated that he saw the prosecutor walking along the pavement,—and sometimes turning sideways, and sometimes running up to the railings and jerking about in a strange way. Calculated that somebody must be pulling his coat, or otherwise assaulting him. It was so dark that he could not see; but thought, if he watched the direction in which the next odd move was made, he might find out something. When the time came, he set Bruennow, a constable in another division of the same force, to watch where he told him; and Bruennow caught the prisoner lurking about in the very spot,—trying to look as if he was minding his own business. Had suspected for a long time that somebody was lurking about in the neighborhood. Bruennow was then called, and deposed to his catching the prisoner as described.

M. Arago.—Was the prosecutor sober?

Le Verrier.—Lord, yes, your worship; no man who had a drop in him ever looks so cold as he did.

M. Arago.—Did you see the assault?

Le Verrier.—I can't say I did; but I told Bruennow exactly how he'd be crouched down;—just as he was.

{391}

M. Arago (to Bruennow).—Did you see the assault?

Bruennow.—No, your worship; but I caught the prisoner.

M. Arago.—How did you know there was any assault at all?

Le Verrier.—I reckoned it couldn't be otherwise, when I saw the prosecutor making those odd turns on the pavement.

M. Arago.—You reckon and you calculate! Why, you'll tell me, next, that you policemen may sit at home and find out all that's going on in the streets by arithmetic. Did you ever bring a case of this kind before me till now?

Le Verrier.—Why, you see, your worship, the police are growing cleverer and cleverer every day. We can't help it:—it grows upon us.

M. Arago.—You're getting too clever for me. What does the prosecutor know about the matter?

The prosecutor said, all he knew was that he was pulled behind by somebody several times. On being further examined, he said that he had seen the prisoner often, but did not know his name, nor how he got his living; but had understood he was called Neptune. He himself had paid rates and taxes a good many years now. Had a family of six,—two of whom got their own living.

The prisoner being called on for his defence, said that it was a quarrel. He had pushed the prosecutor—and the prosecutor had pushed him. They had known each other a long time, and were always quarreling;—he did not know why. It was their nature, he supposed. He further said, that the prosecutor had given a false account of himself;—that he went about under different names. Sometimes he was called Uranus, sometimes Herschel, and sometimes Georgium Sidus; and he had no character for regularity in the neighborhood. Indeed, he was sometimes not to be seen for a long time at once.

The prosecutor, on being asked, admitted, after a little hesitation, that he had pushed and pulled the prisoner too. {392} In the altercation which followed, it was found very difficult to make out which began:—and the worthy magistrate seemed to think they must have begun together.

M. Arago.—Prisoner, have you any family?

The prisoner declined answering that question at present. He said he thought the police might as well reckon it out whether he had or not.

M. Arago said he didn't much differ from that opinion.—He then addressed both prosecutor and prisoner; and told them that if they couldn't settle their differences without quarreling in the streets, he should certainly commit them both next time. In the meantime, he called upon both to enter into their own recognizances; and directed the police to have an eye upon both,—observing that the prisoner would be likely to want it a long time, and the prosecutor would be not a hair the worse for it."



This quib was written by a person who was among the astronomers: and it illustrates the fact that Le Verrier had sole possession of the field until Mr. Challis's letter appeared. Sir John Herschel's previous communication should have paved the way: but the wonder of the discovery drove it out of many heads. There is an excellent account of the whole matter in Professor Grant's[805] History of Physical Astronomy. The squib scandalized some grave people, who wrote severe admonitions to the editor. There are formalists who spend much time in writing propriety to journals, to which they serve as foolometers. In a letter to the Athenaeum, speaking of the way in which people hawk fine terms for common things, I said that these people ought to have a new translation of the Bible, which should contain the verse "gentleman and lady, created He them." The editor was handsomely fired and brimstoned!

{393}



A NEW THEORY OF TIDES.

A new theory of the tides: in which the errors of the usual theory are demonstrated; and proof shewn that the full moon is not the cause of a concomitant spring tide, but actually the cause of the neaps.... By Comm^r. Debenham,[806] R.N. London, 1846, 8vo.

The author replied to a criticism in the Athenaeum, and I remember how, in a very few words, he showed that he had read nothing on the subject. The reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr. Critic." Had he read any of the actual investigations on the usual theory, he would have known that to this day the sun and moon continue to be called planets—though the phrase is disappearing—in speaking of the tides; the sense, of course, being the old one, wandering bodies.

A large class of the paradoxers, when they meet with something which taken in their sense is absurd, do not take the trouble to find out the intended meaning, but walk off with the words laden with their own first construction. Such men are hardly fit to walk the streets without an interpreter. I was startled for a moment, at the time when a recent happy—and more recently happier—marriage occupied the public thoughts, by seeing in a haberdasher's window, in staring large letters, an unpunctuated sentence which read itself to me as "Princess Alexandra! collar and cuff!" It immediately occurred to me that had I been any one of some scores of my paradoxers, I should, no doubt, have proceeded to raise the mob against the unscrupulous person who dared to hint to a young bride such maleficent—or at least immellificent—conduct towards her new lord. But, as it was, certain material contexts in the shop window suggested a less {394} savage explanation. A paradoxer should not stop at reading the advertisements of Newton or Laplace; he should learn to look at the stock of goods.

I think I must have an eye for double readings, when presented: though I never guess riddles. On the day on which I first walked into the Panizzi reading room[807]—as it ought to be called—at the Museum, I began my circuit of the wall-shelves at the ladies' end: and perfectly coincided in the propriety of the Bibles and theological works being placed there. But the very first book I looked on the back of had, in flaming gold letters, the following inscription—"Blast the Antinomians!"[808] If a line had been drawn below the first word, Dr. Blast's history of the Antinomians would not have been so fearfully misinterpreted. It seems that neither the binder nor the arranger of the room had caught my reading. The book was removed before the catalogue of books of reference was printed.



AN ASTRONOMICAL PARADOXER.

Two systems of astronomy: first, the Newtonian system, showing the rise and progress thereof, with a short historical account; the general theory with a variety of remarks thereon: second, the system in accordance with the Holy Scriptures, showing the rise and progress from Enoch, the seventh from Adam, the prophets, Moses, and others, in the first Testament; our Lord Jesus Christ, and his apostles, in the new or second Testament; Reeve and Muggleton, in the third and last Testament; with a variety of remarks thereon. By Isaac Frost.[809] London, 1846, 4to.

{395}

A very handsomely printed volume, with beautiful plates. Many readers who have heard of Muggletonians have never had any distinct idea of Lodowick Muggleton,[810] the inspired tailor, (1608-1698) who about 1650 received his commission from heaven, wrote a Testament, founded a sect, and descended to posterity. Of Reeve[811] less is usually said; according to Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself with one specimen of Mr. Frost's science:

"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when the reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs in support of his theory of the earth revolving round the sun: all the rest is assertion without any proofs.'—'What are they?' inquired the Doctor.—'Well,' I said, 'they are, first, the power of {396} attraction to keep the earth to the sun; the second is the power of repulsion, by virtue of the centrifugal motion of the earth: all the rest appears to me assertion without proof.' The Doctor considered a short time and then said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the credit of completing the system, but really he has only half done his work.'—'How is that,' inquired my friend the Doctor. My reply was this: 'You will observe his system shows the earth traverses round the sun on an inclined plane; the consequence is, there are four powers required to make his system complete:

1st. The power of attraction. 2ndly. The power of repulsion. 3rdly. The power of ascending the inclined plane. 4thly. The power of descending the inclined plane.

You will thus easily see the four powers required, and Newton has only accounted for two; the work is therefore only half done.' Upon due reflection the Doctor said, 'It certainly was necessary to have these four points cleared up before the system could be said to be complete.'"



I have no doubt that Mr. Frost, and many others on my list, have really encountered doctors who could be puzzled by such stuff as this, or nearly as bad, among the votaries of existing systems, and have been encouraged thereby to print their objections. But justice requires me to say that from the words "power of repulsion by virtue of the centrifugal motion of the earth," Mr. Frost may be suspected of having something more like a notion of the much-mistaken term "centrifugal force" than many paradoxers of greater fame. The Muggletonian sect is not altogether friendless: over and above this handsome volume, the works of Reeve and Muggleton were printed, in 1832, in three quarto volumes. See Notes and Queries, 1st Series, v, 80; 3d Series, iii, 303. {397}

[The system laid down by Mr. Frost, though intended to be substantially that of Lodowick Muggleton, is not so vagarious. It is worthy of note how very different have been the fates of two contemporary paradoxers, Muggleton and George Fox.[813] They were friends and associates,[814] and commenced their careers about the same time, 1647-1650. The followers of Fox have made their sect an institution, and deserve to be called the pioneers of philanthropy. But though there must still be Muggletonians, since expensive books are published by men who take the name, no sect of that name is known to the world. Nevertheless, Fox and Muggleton are men of one type, developed by the same circumstances: it is for those who investigate such men to point out why their teachings have had fates so different. Macaulay says it was because Fox found followers of more sense than himself. True enough: but why did Fox find such followers and not Muggleton? The two were equally crazy, to all appearance: and the difference required must be sought in the doctrines themselves.

Fox was not a rational man: but the success of his sect and doctrines entitles him to a letter of alteration of the phrase which I am surprised has not become current. When Conduitt,[815] the husband of Newton's half-niece, wrote a circular to Newton's friends, just after his death, inviting them to bear their parts in a proper biography, he said, "As Sir I. Newton was a national man, I think every one ought to contribute to a work intended to do him justice." Here is the very phrase which is often wanted to signify that {398} celebrity which puts its mark, good or bad, on the national history, in a manner which cannot be asserted of many notorious or famous historical characters. Thus George Fox and Newton are both national men. Dr. Roget's[816] Thesaurus gives more than fifty synonyms—colleagues would be the better word—of "celebrated," any one of which might be applied, either in prose or poetry, to Newton or to his works, no one of which comes near to the meaning which Conduitt's adjective immediately suggests.

The truth is, that we are too monarchical to be national. We have the Queen's army, the Queen's navy, the Queen's highway, the Queen's English, etc.; nothing is national except the debt. That this remark is not new is an addition to its force; it has hardly been repeated since it was first made. It is some excuse that nation is not vernacular English: the country is our word, and country man is appropriated.]



Astronomical Aphorisms, or Theory of Nature; founded on the immutable basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.

This is by the framer of the Weather Almanac, who appeals to that work as corroborative of his theory of planetary temperature, years after all the world knew by experience that this meteorological theory was just as good as the others.

{399}



The conspiracy of the Bullionists as it affects the present system of the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).

This pamphlet is one of a class of which I know very little, in which the effects of the laws relating to this or that political bone of contention are imputed to deliberate conspiracy of one class to rob another of what the one knew ought to belong to the other. The success of such writers in believing what they have a bias to believe, would, if they knew themselves, make them think it equally likely that the inculpated classes might really believe what it is their interest to believe. The idea of a guilty understanding existing among fundholders, or landholders, or any holders, all the country over, and never detected except by bouncing pamphleteers, is a theory which should have been left for Cobbett[818] to propose, and for Apella to believe.[819]

[August, 1866. A pamphlet shows how to pay the National Debt. Advance paper to railways, etc., receivable in payment of taxes. The railways pay interest and principal in money, with which you pay your national debt, and redeem your notes. Twenty-five years of interest redeems the notes, and then the principal pays the debt. Notes to be kept up to value by penalties.]



THEISM INDEPENDENT OF REVELATION.

The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price 2d. Is there sufficient proof of the existence of God? 8vo. 1847.

This acorn of the holy oak was forwarded to me with a manuscript note, signed by the editor, on the part of the {400} "London Society of Theological Utilitarians," who say, "they trust you may be induced to give this momentous subject your consideration." The supposition that a middle-aged person, known as a student of thought on more subjects than one, had that particular subject yet to begin, is a specimen of what I will call the assumption-trick of controversy, a habit which pervades all sides of all subjects. The tract is a proof of the good policy of letting opinions find their level, without any assistance from the Court of Queen's Bench. Twenty years earlier the thesis would have been positive, "There is sufficient proof of the non-existence of God," and bitter in its tone. As it stands, we have a moderate and respectful treatment—wrong only in making the opponent argue absurdly, as usually happens when one side invents the other—of a question in which a great many Christians have agreed with the atheist: that question being—Can the existence of God be proved independently of revelation? Many very religious persons answer this question in the negative, as well as Mr. Holyoake. And, this point being settled, all who agree in the negative separate into those who can endure scepticism, and those who cannot: the second class find their way to Christianity. This very number of The Reasoner announces the secession of one of its correspondents, and his adoption of the Christian faith. This would not have happened twenty years before: nor, had it happened, would it have been respectfully announced.

There are people who are very unfortunate in the expression of their meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded a pamphlet on the existence of God, and said that the Society trusted I "may be induced to give" the subject my "consideration." How could I know the Society was one person, who supposed I had arrived at a conclusion and wanted a "guiding word"? But so it seems it was: Mr. Holyoake, in the English {401} Leader of October 15, 1864, and in a private letter to me, writes as follows:

"The gentleman who was the author of the argument, and who asked me to send it to Mr. De Morgan, never assumed that that gentleman had 'that particular subject to begin'—on the contrary, he supposed that one whom we all knew to be eminent as a thinker had come to a conclusion upon it, and would perhaps vouchsafe a guiding word to one who was, as yet, seeking the solution of the Great Problem of Theology. I told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he must be content to wait. On some day of courtesy and leisure he might have the kindness to write.' Nor was I wrong—the answer appears in your pages at the lapse of seventeen years."

I suppose Mr. Holyoake's way of putting his request was the stylus curiae of the Society. A worthy Quaker who was sued for debt in the King's Bench was horrified to find himself charged in the declaration with detaining his creditor's money by force and arms, contrary to the peace of our Lord the King, etc. It's only the stylus curiae, said a friend: I don't know curiae, said the Quaker, but he shouldn't style us peace-breakers.

The notion that the non-existence of God can be proved, has died out under the light of discussion: had the only lights shone from the pulpit and the prison, so great a step would never have been made. The question now is as above. The dictum that Christianity is "part and parcel of the law of the land" is also abrogated: at the same time, and the coincidence is not an accident, it is becoming somewhat nearer the truth that the law of the land is part and parcel of Christianity. It must also be noticed that Christianity was part and parcel of the articles of war; and so was duelling. Any officer speaking against religion was to be cashiered; and any officer receiving an affront without, in the last resort, attempting to kill his opponent, was also to be cashiered. Though somewhat of a book-hunter, I {402} have never been able to ascertain the date of the collected remonstrances of the prelates in the House of Lords against this overt inculcation of murder, under the soft name of satisfaction: it is neither in Watt,[821] nor in Lowndes,[822] nor in any edition of Brunet;[823] and there is no copy in the British Museum. Was the collected edition really published?

[The publication of the above in the Athenaeum has not produced reference to a single copy. The collected edition seems to be doubted. I have even met one or two persons who doubt the fact of the Bishops having remonstrated at all: but their doubt was founded on an absurd supposition, namely, that it was no business of theirs; that it was not the business of the prelates of the church in union with the state to remonstrate against the Crown commanding murder! Some say that the edition was published, but under an irrelevant title, which prevented people from knowing what it was about. Such things have happened: for example, arranged extracts from Wellington's general orders, which would have attracted attention, fell dead under the title of "Principles of War." It is surmised that the book I am looking for also contains the protests of the Reverend bench against other things besides the Thou-shalt-do-murder of the Articles (of war), and is called "First Elements of Religion" or some similar title. Time clears up all things.]

* * * * *

Notes

[1] See Mrs. De Morgan's Memoir of Augustus De Morgan, London, 1882, p 61.

[2] In the first edition this reference was to page 11.

[3] In the first edition this read "at page 438," the work then appearing in a single volume.

[4] "Just as it would surely have been better not to have considered it (i.e., the trinity) as a mystery, and with Cl. Kleckermann to have investigated by the aid of philosophy according to the teaching of true logic what it might be, before they determined what it was; just so would it have been better to withdraw zealously and industriously into the deepest caverns and darkest recesses of metaphysical speculations and suppositions in order to establish their opinion beyond danger from the weapons of their adversaries.... Indeed that great man so explains and demonstrates this dogma (although to theologians the word has not much charm) from the immovable foundations of philosophy, that with but few changes and additions a mind sincerely devoted to truth can desire nothing more."

[5] Mrs. Wititterly, in Nicholas Nickleby.—A. De M.

[6] The brackets mean that the paragraph is substantially from some one of the Athenaeum Supplements.—S. E. De M.

[7] "It is annoying that this ingenious naturalist who has already given us more useful works and has still others in preparation, uses for this odious task, a pen dipped in gall and wormwood. It is true that many of his remarks have some foundation, and that to each error that he points out he at the same time adds its correction. But he is not always just and never fails to insult. After all, what does his book prove except that a forty-fifth part of a very useful review is not free from mistakes? Must we confuse him with those superficial writers whose liberty of body does not permit them to restrain their fruitfulness, that crowd of savants of the highest rank whose writings have adorned and still adorn the Transactions? Has he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill himself?"

[8] "Let no free man be seized or imprisoned or in any way harmed except by trial of his peers."

[9] "The master can rob, wreck and punish his slave according to his pleasure save only that he may not maim him."

[10] An Irish antiquary informs me that Virgil is mentioned in annals at A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of Saltzburg] died in Germany in the thirteenth year of his bishoprick." No allusion is made to his opinions; but it seems he was, by tradition, a mathematician. The Abbot of Aghabo (Queen's County) was canonized by Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be much damaged by the character given to the real bishop, if there were anything in it to dilapidate.—A. De M.

[11] "He performed many acts befitting the Papal dignity, and likewise many excellent (to be sure!) works."

[12] "After having been on the throne during ten years of pestilence."

[13] The work is the Questiones Joannis Buridani super X libros Aristotelis ad Nicomachum, curante Egidio Delfo ... Parisiis, 1489, folio. It also appeared at Paris in editions of 1499, 1513, and 1518, and at Oxford in 1637.

[14] Jean Buridan was born at Bethune about 1298, and died at Paris about 1358. He was professor of philosophy at the University of Paris and several times held the office of Rector. As a philosopher he was classed among the nominalists.

[15] So in the original.

[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the pantheistic philosopher, excommunicated from the Jewish faith for heresy, was born at Amsterdam in 1632 and died there in 1677.

[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire, Scotland, and died about 1291. He was one of the best known savants of the court of Emperor Frederick II, and wrote upon astrology, alchemy, and the occult sciences. He was looked upon as a great magician and is mentioned among the wizards in Dante's Inferno.

"That other, round the loins So slender of his shape, was Michael Scot, Practised in every slight of magic wile." Inferno, XX.

Boccaccio also speaks of him: "It is not long since there was in this city (Florence) a great master in necromancy, who was called Michele Scotto, because he was a Scot." Decameron, Dec. Giorno.

Scott's mention of him in Canto Second of his Lay of the Last Minstrel, is well known:

"In these fair climes, it was my lot To meet the wondrous Michael Scott; A wizard of such dreaded fame, That when, in Salamanca's cave, Him listed his magic wand to wave, The bells would ring in Notre Dame!"

Sir Walter's notes upon him are of interest.

[18] These were some of the forgeries which Michel Chasles (1793-1880) was duped into buying. They purported to be a correspondence between Pascal and Newton and to show that the former had anticipated some of the discoveries of the great English physicist and mathematician. That they were forgeries was shown by Sir David Brewster in 1855.

[19] "Let the serpent also break from its appointed path."

[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at Florence in 1803; died at Fiesole in 1869. His Histoire des Sciences Mathematiques appeared at Paris in 1838, the entire first edition of volume I, save some half dozen that he had carried home, being burned on the day that the printing was completed. He was a great collector of early printed works on mathematics, and was accused of having stolen large numbers of them from other libraries. This accusation took him to London, where he bitterly attacked his accusers. There were two auction sales of his library, and a number of his books found their way into De Morgan's collection.

[21] Philo of Gadara lived in the second century B.C. He was a pupil of Sporus, who worked on the problem of the two mean proportionals.

[22] In his Histoire des Mathematiques, the first edition of which appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died at Versailles in 1799. He was therefore only thirty-three years old when his great work appeared. The second edition, with additions by D'Alembert, appeared in 1799-1802. He also wrote a work on the quadrature of the circle, Histoire des recherches sur la Quadrature du Cercle, which appeared in 1754.

[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the first four books of the conics of Apollonius of Perga (247-222 B.C.). He also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and on the two books on Equilibrium of Archimedes (287-212 B.C.)

[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His famous arithmetic appeared in 1677 and went through many editions. It was written in a style that appealed to teachers, and was so popular that the expression "According to Cocker" became a household phrase. Early in the nineteenth century there was a similar saying in America, "According to Daboll," whose arithmetic had some points of analogy to that of Cocker. Each had a well-known prototype in the ancient saying, "He reckons like Nicomachus of Gerasa."

[25] So in the original, for Barreme. Francois Barreme was to France what Cocker was to England. He was born at Lyons in 1640, and died at Paris in 1703. He published several arithmetics, dedicating them to his patron, Colbert. One of the best known of his works is L'arithmetique, ou le livre facile pour apprendre l'arithmetique soi-meme, 1677. The French word bareme or barreme, a ready-reckoner, is derived from his name.

[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom Cato or Tully could have acknowledged for their countryman." His works on arithmetic, music, and geometry were classics in the medieval schools.

[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV (1261-1264). He was one of the early medieval translators of Euclid from the Arabic into Latin, and the first printed edition of the Elements (Venice, 1482) was from his translation. In this work he probably depended not a little upon at least two or three earlier scholars. He also wrote De computo ecclesiastico Calendarium, and De quadratura circuli.

[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the circumference to the diameter of a circle.

[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in 1853. His Bibliotheca Mathematica, Leipsic, 1797-1805, is ill arranged and inaccurate, but it is still a helpful bibliography. De Morgan speaks somewhere of his indebtedness to it.

[30] Abraham Gotthelf Kaestner was born at Leipsic in 1719, and died at Goettingen in 1800. He was professor of mathematics and physics at Goettingen. His Geschichte der Mathematik (1796-1800) was a work of considerable merit. In the text of the Budget of Paradoxes the name appears throughout as Kastner instead of Kaestner.

[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in 1476; died at Rome in 1558. He was an astrologer and mathematician, and was professor of mathematics at Ferrara in 1531. In 1545 he became bishop of Civita Ducale.

[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in 1892. He and Leverrier predicted the discovery of Neptune from the perturbations in Uranus.

[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811, and died at Paris in 1877. It was his data respecting the perturbations of Uranus that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in 1540, and died at Leyden in 1609. His Cyclometrica elementa, to which De Morgan refers, appeared at Leyden in 1594.

[35] The title is: In hoc libra contenta.... Introductio i geometriā.... Liber de quadratura circuli. Liber de cubicatione sphere. Perspectiva introductio. Carolus Bovillus, or Charles Bouvelles (Boueelles, Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He was canon and professor of theology at Noyon. His Introductio contains considerable work on star polygons, a favorite study in the Middle Ages and early Renaissance. His work Que hoc volumine continētur. Liber de intellectu. Liber de sensu, etc., appeared at Paris in 1509-10.

[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions of honor in the church, including the bishopric of Brescia. He was made a cardinal in 1448. He wrote several works on mathematics, his Opuscula varia appearing about 1490, probably at Strasburg, but published without date or place. His Opera appeared at Paris in 1511 and again in 1514, and at Basel in 1565.

[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was one of the most successful printers of his day. He was known as Typographus Parisiensis, and to his press we owe some of the best works of the period.

[38] Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was born at Estaples, near Amiens, in 1455, and died at Nerac in 1536. He was a priest, vicar of the bishop of Meaux, lecturer on philosophy at the College Lemoine in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy, theology, and mathematics.