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oblige your constant and much ad- a square, in the Constellation of the miring reader,

M. P. Fishes. Mars rises on the 1st about Lincolnshire, Oct. 14, 1819.

eight in the evening, and on the 31st CASUALLY taking up Dr. Ilutton's about six. His stay above the horiTreatise on Mensuration, I opened to zon is therefore so long, that the ashis definition of an Ellipsis, and found tronomer may pursue at leisure his obit to be as follows:-“ The section is servations on him. He is first seen called an Ellipsis when the cone is cut between the third and fourth of the obliquely through both sides.” Which Crab, the rmer star above, and the immediately struck me with the idea of latter below him, the intervening nea figure in the shape of an egg, having bula being near to him to the west. ordinates, drawn from points on the His motion is very slow to the east till axes equally distant from the centre, of the 7th, when he is stationary, and he unequal length. Yet on looking a lit- does not pass the fourth, receding back tle further, I found the Ellipsis de- after this day, and directing his course cribed as an oval whose two segments, to the third, passing between this star occasioned by the cutting of its conju- and the nebula, but nearest to the star. gate diameter, would be exactly similar and equal. Not satisfied with the the Doctor, I had recourse to Bonnycastle ; and finding that he treats the THESE curious phænomena, which are subject in precisely the same manner, but of rare occurrence, liave been obI am at a loss to account for what must served by astronomers of the two last be an error somewhere. In hope of centuries with very great care; and, seeing something further on the sub- from their observations preserved in ject, these observations are submitted the Transactions of the Royal Society to the public.

of London, and the scientific works of other nations, tables of the motions

of Mercury have been rendered as acCelestial Phænomena.

curate as those of the other planets in

the Solar System. Dr. Halley was MR. EDITOR,

the first who gave us tables, by means If you think the following Astronomi- of which the times of the transits of cal Occurrences worthy of publication, Mercury over the solar disk could be your insertion of them will much oblige readily calculated. These have been Your's, &c.

corrected by the late celebrated De la AN OBSERVER. Lande, from more recent observations

made by himself and others. From Astronomical Occurrences for December.

the corrected tables just referred to, it The sun enters Capricorn on the 22d, appears that the transits of Mercury at four minutes past three in the after- over the disk of the sun return in stated noon, when the Winter quarter com- periods of six, seven, thirteen, thirty

The Moon is full on the 1st; three, forty-six, two hundred and sevenenters her last quarter on the 9th ; she teen, and two hundred and sixty-three is new on the 17th ; enters her first years, as follows:quarter on the 230; and she is again

Transits of Mercury at the ascending full on the 31st. She will pass Mars on the 5th, the Georgian Planet on

node, in November, the 16th, Mercury on the 17th, Venus Period 1.—6 years, 8 days, 18 hours, on the 18th, Jupiter on the 20th, and and 39 minutes, with two intercalaSaturn on the 22d. Jupiter sets on the tions; and one day more, if the year 1st, at one minute past nine in the even- of the preceding transit be bissextile, ing; and on the 31st, about a quarter or the one following it. Mercury at before eight. He is therefore on the the end of this period, moves along the western side of the meridian, and will solar disk in a track 31' 26" to the easily be distinguished by his superior north of his preceding one at the same brightness. Saturn is on the meridian node. This period is of very rare ocon the 1st, about a quarter past seven in currence. the evening, and about half past five on PERIOD II.—7 years all but 7 days the 31st. He is seen at a considerable and 57 minutes, with two intercaladistance to the east of Jupiter, and tions; otherwise 6 days 57 minutes below four stars nearly in the form of only must be substracted. Mercury's



Transits of Mercury.


track at the end of this period will be the time and circumstances of the next 23' 12' to the south of that at its com- transit of this planet at the descending mencement. This period occurs twice node?—By a single glance at Period or thrice in a century.

I. we find that its addition to May 7, Period III.-13 years, 2 days, 17 1799, will not produce a transit at the hours, 42 minutes, with three interca- descending node; for the planet's south lations ; but, when there are four, 1 latitude at its inferior conjunction will day, 17 hours, 42 minutes, must only be 22' 38", i. e. several minutes greater be added. Mercury's track is 8' 14" than the solar semidiameter. By adding more to the north at the end of this Period II. to May 7, 1799, we find period.

there will be a transit, as below:PERIOD IV.-46 years, 4 hours, 42 To the transit of 1799 add Period minutes, with twelve intercalations; II. 33 years; and the sum will be 1832 but, when there are only eleven, a day for the year of the next transit. From more must be added. Mercury's track May 7 days, 1 hour, 4 minutes, sub1' 35" more to the south.

tract 2 days, 52 minutes, (there being PERIOD V.–217 years, 6 hours, 11 eight intercalations) and the difference, minutes, with 54 intercalations. Mer- 5 days, 0 hours, 12 minutes, will be the cury's track 6' more to the south. In time in the month of May of Mercury's the transits of the nineteenth century inferior conjunction. The nearest apMercury will be about 5" more to the proach of the centres will be found by north.

subtracting 5' 31" from 13' 46"; the Period VI.—263 years, 1 day, 11 difference 8' 15" being the nearest aphours, with 66 intercalations. Mer- proach of the centres of the Sun and cury's track 1' 40" more to the north. Mercury in the transit of 1832, the Transits of Mercury at the descending

planet being to the north. node, in May.

Example 2. The same transit calcu

lated by the one which happened in Period I.-13 Julian years, 3 days, 1786; the time of the conjunction being 7 hours, 53 minutes, with three inter- May 3 days, 17 hours, 2 minutes, and calations. Mercury more to the south the nearest approach of the centres 17' 7".

11'21", the planet being to the north.PERIOD II.-33 years, all but 2 days, To the transit of 1786 add 46 years, 52 minutes, with eight intercalations. and the sum 1832 will be the year of Mercury 13' 46" more to the north. the transit. To May 3 days, 17 hours,

Period III.—46 years, 6 hours, 40 2 minutes, add 1 day, 6 hours, 40 minutes, with twelve intercalations. minutes, (there being only eleven inMercury 3' 30' more to the south. tercalations,) and the sum May 5 days,

Period IV.-217 years, 2 hours, 0 hours, 42 minutes, will be the time with 54 intercalations. Mercury 13" of the inferior conjunction. If we submore to the north.

tract 3' 30' from 11' 21", the difference PERIOD V.—263 years, 1 day, 9 7' 51" will be the nearest approach of hours, with 66 intercalations. Mercury the centres, the planet being to the 3 more to the south.

north. N. B. If there should be fewer in- Example 3. The same transit calcutercalations in any of the above periods lated by the one which happened in than what are specified, as will fre- 1615; the time of the conjunction being quently happen in the longer ones ac- May 2 days, 21 hours, 39 min. and the cording to the Gregorian calendar ; an nearest approach of the centres 7' 37", additional day must be added for every the planet being to the north.—To the one which is wanting to make up the transit of 1615 add 217 years, and the specified number. Three examples sum 1832 will be the year of the transit; will be sufficient to shew how the and 2 days 2 hours added to May 2 transists of Mercury are to be calcu- days, 21 hours, 39 minutes, (there being lated by the above periods.

52 intercalations) will give May 5, at 39 Example 1. A transit of Mercury minutes past eleven in the forenoon happened at the descending node on the for the time of the conjunction. To 7th of May, 1799; the time of the con- 7' 37" add 13'; and the sum 7' 50" will junction being at 4 minutes past one be the nearest approach of the centres. in the afternoon at Greenwich, and the It will be observed that there is a nearest approach of the centres 5' 31" considerable difference in the circumthe planet being to the south.—Query, stances of the transit of 1832, as ob


For the 3364

25X 169—40


and ?



tained by the three periods of 33, 46, In the example proposed, taking the and 217 years : but the method is exact numbers in order as given, a=2,6=4, enough in the great majority of in

22 and d =

and if we assume stances, to obtain the time of the infe


5' rior conjunction to the nearest hour; p=2and q=3, then we shall obtain for and the nearest approach of the centres | the answer these square numbers. viz. to within about 20" or 30'.

16 80656 3844 information of the curious, the follow


+ ing are the particulars of the transitof if in the two first terms p= 4, q=1,

169 169 25 x 169 1832, as obtained by direct calculation

14 from De la Lande's Tables of Mercury. and in the two last terms p = Time of the inferior conjunction (at

5 Greenwich) May 5 days, Oh. 34 minutes.


-5 Nearest approach of the centres

the answer given by the author 8' 16", the planet being to the north. will come out, and thus an indefinite

number of answers may be obtained.

From this solution, it is evident, that if a given number consist of any even

number of given square numbers, it Sir,

may variously be resolved into as many In answer to the problem in the Impe- other square numbers. rial Magazine for August, respecting square numbers, I transmit you the following general solution.

Review—The History of Dublin,2 Thos. ExLEY. Bristol, Sept. 16, 1819.

vols. quarto, pp. 1348, with an Appendix, pp. 104. Cadel and Davies,

London. In Mr. Bonnycastle's Algebra, and several other works, we have a general The late J. Warburton, deputy keeper solution of the following Problem, of the Records in Dublin Castle, Esq

. viz.: To divide a given number con- supplied the annals, antiquities, charsisting of two known square numbers, ters, and ecclesiastical history, which into two other square numbers. If the is contained in the first volume : and roots of the given square numbers be this was prepared for the press, by the denoted by a and b, and if p and q be late Rev. James Whitelaw, author of any two numbers not in the proportion the Census of the population of Dubof a to b, or a + b to ab, then the given lin. The second volume, after his numbera? +v=2bpq+a[gp>) + 2bpq+alq?-p>) + death, was written by the Rev. Robert

Walsh, M. R. S. A. completing the work (apq+b(p=0)). See Bonnycas- public buildings, schools, institutions,

by the present state of the City, its tle’s Algebra, octavo edition, p. 276. canals, analysis of mineral springs From this, it is evident, that if the and lead mines; biography of eminent roots of the four given square numbers natives, population, revenue, combe a, b, c, and d, the given number, or,

merce, and literature; botany of the m*+b++=(26pq+ali-r*);+ neighbouring coast; ancient Irish MSS.

county of Dublin, conchology of the pta

in the libraries; rents of the corporablp?¢¢¢?


&c. &c. *+(3epq+ d(p-1)), which is a This volume displays, along with p + q*

extraordinary industry, an uncommon general expression for the answer; extent of multifarious learning, arts, where a’ and b’ may be any two of the sciences, and belles lettres, in the ingiven square numbers, and c, d the defatigable author. remaining two, and p. and q may be In so voluminous a work, it may any numbers, not having the propor- be expected that much information is tion above mentioned ; also the values given, and that some inaccuracies and of p and q may be assumed for the want of systematic arrangement may, first two terms, and different values appear, as there has been no history of may be taken, if it be thought proper, this second city in the empire, except for the two last terms.

its Antiquities by Harris. But in ge

History of Dublin.--- American Slavery.

814 neral, the facts are most accurately | titutes; thirteen houses for desolate stated, and the information is copious widows; two houses of refuge, for and minute.

young female servants out of employThere are prints of 19 public build- ment; an asylum for old female serings, among which are the Castle ; vants past work; the same for old rePatrick's Cathedral, in three views ; duced tradesmen; a university, and St. George's Church; the Custom- an observatory ; two botanic gardens, House; Exchange; Four Courts; and conservatories of foreign plants. Bank of Ireland; the late Tholsel ; There are in Dublin, about 3000 College; Provost's House ; Foundling presbyterians, 1700 independents, 1400 Hospital, and others.

methodists, 250 moravians, 150 bapThis work should be particularly tists, 650 quakers, 50,000 of the estainteresting to Liverpool ; Dublin being blished church, and 140,000 romanists ; situated on the opposite side of the 67 charity schools, educating 13,000 Irish channel, supplies provisions by children; of these 11 are of the church, two great canals, from the interior of 15 dissenters, 8 mixed, having the Ireland, to the Liverpool provision- scripture only for religious instruction, ships; and the situation of Liverpool without note or comment, these are on near the heart of England, convenient a large scale ; and 32 romanist schools: to the principal manufacturing places, 5 societies for education, 18 charitable is adapted to supply the wants of Ire- associations, 3 literary institutes, 4 land, through Dublin, with British ma- public libraries, 2 agricultural socienufactures, while the extensive foreign ties, 7 prisons, of which two are subtrade to Liverpool, forms the most stitutes for transportation, by confineconvenient depository to supply a ment to work. The total population large portion of Ireland, through Dub- is about 200,000, who dwell in 15,000 lin, with colonial produce. Its docks houses, besides barracks for 3000 horse are spacious, and the harbour is im- and 8000 foot, leaving 1200 houses proved by the piers, which form its waste, and standing on 1300 acres, inthree harbours, which are among the cluding waste ground, five

squares, and grandest specimens of marine archi- the river Liffey, which flows through tecture.

the centre of the city. The first volume is of least general A cheap edition in 8vo. of this excelinterest, although the ancient annals lent Work, is extremely desirable. of Dublin, produced now from the most unquestionable sources, throw a considerable light on the history of Ireland. It contains the charters, I borrow from a pleasing little work, lists of lord lieutenants, bishops, lord written by a Virginian, and entitled, mayors, and sheriffs: the house of “ Letters from Virginia,” the followeducation and maintenance, for the ing description, which he gives in the sons of reduced citizens; a foundling character of a foreigner, newly landed hospital for all Ireland; a house for at Norfolk. educating, clothing, and maintaining “ I took the boat this morning, and soldiers' children; another on the same crossed the ferry over to Portsmouth, plan, for sailors' children; house of the small town which I told you is opindustry, embracing every class of dis- posite to this place; it was court-day, tressed poor, requiring assistance; and and a large crowd of people was gaa male penitentiary.

In the second thered about the court-house. I had volume other hospitals are described, hardly got upon the steps to look in, viz. : a lying-in hospital ; one for mad- when my ears were assailed by the ness; one for the cure of syphilis and voice of singing, and turning round ruptures; four for the sick and hurt, to discover from what quarter it came, wounds, and fractures; four for fever; I saw a group of about thirty negroes, one for sick soldiers ; one for incurable of different sizes and ages, following complaints ; six dispensaries of medi- a rough-looking white man, who sat cine and advice; institutions for the carelessly lolling in his sulky. They had eye, for vaccination, and for cutaneous just turned round the corner, and were complaints; colleges of physicians, and coming up the main street, to pass by of surgeons; an apothecaries' hall; the spot where I stood, on their way four asylums for the blind, male and out of town. As they came nearer, I female ; five asylums for penitent pros- saw some of them loaded with chains


to prevent their escape; while others To develop the hidden principles of had hold of each other's hands strongly human action, is not always placed grasped, as if to support themselves in within the power of man.. Neverthetheir affliction. I particularly noticed less, when we behold persons of taa poor mother, with an infant sucking lent and respectability, voluntarily reat her breast as she walked along, nouncing all the comforts of civilized while two small children had hold of and social life, and encountering the her apron on either side, almost run- most formidable danger, that they may ning to keep up with the rest. They take up their abode among savages, came along singing a little wild hymn, cut off from nearly all intercourse with of sweet and mournful melody ; tlying the companions of their childhood and by a divine instinct of the heart, to riper years, without the least prospect the consolation of religion, the last re- of obtaining any remuneration in this fuge of the unhappy, to support them life for the sacrifices they make, we in their distress. The sulky now stop- cannot but conclude, that something ped before the tavern, at a little dis- more powerful than either gold or tance beyond the court-house, and the honours, communicates the vigorous driver got out. My dear Sir,' (said I impulse under which they act. In the to a person who stood near me,) can missionary department, characters of you tell me what these poor people this description constantly appear; have been doing? what is their crime? but in no case have they shone with and what is to be their punishment? such undeviating and undiminished -0, (said he) its nothing at all, but a lustre, as among the Moravian Breparcel of negroes sold to Carolina, and thren. Of the perils which some of that man is their driver, who has these faithful servants of their Lord bought them.'—. But what have they are called to endure, some knowledge done, that they should be sold into ba- may be obtained from the following nishment?— Done, (said he,) nothing article. at all that I know of; their masters

Extract of the Journal of the Voyage of wanted money, I suppose, and these drivers give good prices. Here the

the Brother G. Kmoch and his wife, driver having supplied himself with

and the single Brethren Körner and brandy, and his horse with water, (the

Beck, in the brig Jemima to Labrador,

in 1817.- Written by Brother G. poor negroes, of course, wanted no

Kmoch.) thing,) stepped into his chair again, cracked his whip, and drove on, while After describing the circumstances the miserable exiles followed in fune- alluding to their departure from Lonral procession behind him.”

don on the 2d of June, and the voyage From Hall's Travels in Canada. to the Orkneys, as having been re

markably favourable, he proceeds-,

“ We arrived at Stromness on the

12th of June. Our abode in that place It has frequently been said, that the was rendered very pleasant, by the hope of acquiring wealth or fame ope- kindness we experienced from many rates with more influence upon the hu- friends, among whom was the minister man mind than any other motive. This of the town. seems to have been laid down as a po- “ On the 14th, we set sail, and had sition not to be disputed. It has been pleasant weather, with variable winds admitted as a fact, by men of talent, and calms. On the 24th, we were halfand, having derived sanction from the way between Great Britain and Lageneral conduct of mankind, age and brador, and pleased ourselves with custom have conspired together to the prospect of an expeditious voyage. mature it into an axiom.

Many sword-fishes and porpoises playFrom individuals who look no far- ed about the ship. Of the latter the ther than the present state of things, shoals were so numerous, that the sea such conclusions may very naturally seemed to swarm with them in all dibe expected. But on minds that are rections. enlightened to behold the realities of “ Between the 4th and 5th of July, the invisible world, there are motives we heard and saw many icebirds. This which operate with a more command- bird is about the size of a starling, ing stimulus than fame or fortune can black, with white and yellow spots, possibly bestow.

and is met with about 200 English


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