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TO THE EDITOR OF THE IMPERIAL

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- 4

and d =

em stances, to obtain the time of the infe

23, and if we assume

5' rior conjunction to the nearest hour ; p=2 and 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

+ +

+

169 169 25 x 169 ing are the particulars of the transit of 1832, as obtained by direct calculation If in the two first terms p= 4, q=1,

14 from De la Lande's Tables of Mercury. and in the two last terms p= and

2 Time of the inferior conjunction (at

5

23 Greenwich) May5days, 0h. 34 minutes.

the answer given by the author

-5 Nearest approach of the centres 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 MAGAZINE.

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 a-6, then the given lin. The second volume, after his numbera?+6=(26pq+ a[9*—p*)* + death, was written by the Rev. Robert

p+q

+ Walsh, M.R.S.A.completing the work (2a pq+b(p-1). See Bonnycas- public buildings

, schools, institutions, + 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

of the «°++&+d=(26pq+ (1+r)+ neighbouring coast;ancient Irish MSS. (2a pq+b(p=0))+(2dpq+¢¢? —po)) tion, ancient ecclesiastical revenue, p> + q

p2 + q &c. &c. 2+(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 bmay be any two of the sciences, and belles lettres, in the ingiven square numbers, and c», do 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 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 general, 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

AMERICAN SLAVERY.

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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; flying 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, poor negroes, of course, wanted no

in 1817.-/Written by Brother G. thing,) stepped into his chair again,

Kmoch.) 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

VOYAGE TO LABRADOR.

miles from the Labrador coast. When | wind was in a direction, that it apthe sailors hear it, they know that they peared scarcely possible to keep clear are not far from the ice. It flies about a of it, the ship being likewise beset on ship chiefly in the night, and is known all sides with fields of ice. In about by its singular voice, which resembles an hour's time the fog dispersed, and a loud laugh.

we perceived, that we had just passed “ On the 6th, the weather was re- by at a short distance; which excited markably fine. In the afternoon, the us to praise our almighty Saviour for wind shifted to the south-east, and our preservation. during the night brought us into the “ 14th. Land was discovered a-head. ice. We tacked, and stood off and on. It was the coast of Labrador, sixty or

7th, the morning was cold and eighty miles south of Hopedale. We rainy. In all directions drift-ice was were close to the ice, and as a small to be seen. In the afternoon it cleared opening presented itself, the captain up a little, and we entered an opening ventured to push in, hoping, if he could in the ice, looking like a bay. The penetrate, to find open water between continual rustling and rvaring of the the ice and the coast. For some time ice reminded us of the noise made by we got nearer to the land, but were the carriages in the streets of London, obliged at night to fasten the ship with when one is standing in the golden two grapnels to a large field. This was gallery of St. Paul's cathedral. The elevated between five and six feet mountains and large flakes of ice take above the water's edge, and between all manner of singular forms, some re- fifty and sixty feet in thickness below sembling castles, others churches,wag- it. It might be 300 feet in diameter, gons, and even creatures of various flat at the top, and as smooth as a meadescriptions. As we or they changed dow covered with snow. The wind positions, the same objects acquired has but little power over such huge a quite different appearance; and masses, and they move very slowly what had before appeared like a with the current. There are small church, looked like a huge floating streams and pools of fresh water found monster. Sitting on deck, and con- on all those large pieces. Our situatemplating these wonderful works of tion now defended us against the God, I almost lost myself in endea- smaller flakes, which rushed by and vouring to solve the question,—“For were turned off by the large field, what purpose these exhibitions are without reaching the ship. We were made, when so few can behold them, all well pleased with our place of as they so soon vanish by returning to refuge, and lay here three whole days, their former fluid and undefined state ?" | with the brightest weather, and as safe But surely every thing is done with as in the most commodious haven; design, though short-sighted man can- but I cannot say that I felt easy, though not comprehend it. Having in vain I hid my anxiety from the party. "I exerted ourselves to penetrate through feared that a gale of wind might overthe ice, we returned at night into the take us in this situation, and carry open sea.

fields larger than that at which we lay, 8th, the wind was north and strong, when the most dreadful consequences and we hoped that it would open a might ensue; and the sequel proved, way for us to Hopedale, for we were that I was not much mistaken. in the latitude of that place.

“ On the 17th, the wind came round “ From the 9th to the 13th we were to the south, and we conceived fresh continually on different tacks, 'some- hopes of the way being rendered open times on the outside, and again among for us. the ice, with various kinds of weather, “18th, the weather was clear, and and often prayed to the Lord to grant the wind in our favour; we thereforo us soon to reach the end of our voyage. took up our grapnel, got clear of our

13th, towards evening, we disco- floating haven, and again endeavoured vered an ice-mountain of immense to penetrate through some small openheight and length, flat at its top. As ings. Both we and the ship's comwe approached it

, we were enveloped pany were peculiarly impressed with in a thick fog, and could not see a yard gratitude for the proteotion and rest from the ship, which increased the we bad enjoyed, and the warmth of a danger we were in of running foul of summer's sun felt very comfortable it and being lost, especially as the among these masses of ice. The clearNo. 9,- VOL. I.

3 G

66

ness of the atmosphere to-day caused a distance, towards which we were them to appear singularly picturesque. driving, without the power of turning It seemed as if we were surrounded by aside. Between six and seven, we immense white walls and towers. In were again roused by a great outcry the afternoon we had penetrated to the on deck.

We ran up, and saw our open water, between the ice and the ship, with the field to which we were land, but we durst not venture nearer, fast, with great swiftness approaching as the sea is here full of sunken rocks, towards the mountain; nor did there and the captain knew of no harbour on appear the smallest hope of escaping this part of the coast. Having found being crushed to atoms between it and another large piece of ice convenient the field. However, by veering out as for the purpose, we fastened the ship much cable as we could, the ship got to it. In the evening a thick fog over- to such a distance, that the mountain spread us from the north-east, and we passed through between us and the were again quite surrounded by ice, field. We all cried fervently to the which, however, was soon after dis- Lord for speedy help in this most pepersed by a strong north-west wind. rilous situation; for if we had but

“ In the night between the 19th and touched the mountain, we must have 20th we were driven back by a strong been instantly destroyed. One of our current to nearly the same situation we cables was broken, and we lost a graphad left on the 17th, only somewhat nel. The ship also sustained some danearer to the coast. On the 20th the mage. But we were now left to the morning was fine, and we vainly en- mercy of the storm and current, both deavoured to get clear, but towards of which were violent; and exposed evening the sky lowred, and it grew likewise to the large fields of ice, very dark. The air also felt so very which floated all around us, being oppressive, that we all went to bed, from ten to twenty feet in thickness. and every one of us was troubled with The following night was dreadfully uneasy dreams. At midnight we heard dark, the heavens covered with the a great noise on deck. We hastened blackest clouds, driven by a furious thither to know the cause, and found wind; the roaring and the howling of the ship driving fast towards a huge the ice, as it moved along, the fields ice-mountain, on which we expected shoving and dashing against each every moment to suffer shipwreck. other, was truly terrible. A fender The sailors exerted themselves to the was made of a large beam, suspended utmost, but it was by God's merciful by ropes to the ship's sides, to secure providence alone that we were saved. her in some measure from the ice; but The night was excessively cold with the ropes were soon cut by its sharp rain, and the poor people suffered edges, and we lost the fender. Remuch. We were now driven to and peated attempts were now made to fro, at the mercy of the ice, till one in make the ship again fast to some large the morning, when we succeeded in field; and the second mate, a clever fastening the ship again to a large young man, full of spirit and willingfield. But all this was only the pre- ness, swung himself several times off

, lude to greater terrors. Deliverance and upon such fields as approached from danger is so gratifying, that it us, endeavouring to fix a grapnel to raises one's spirits above the common them, but in vain, and we even lost level. We made a hearty breakfast, another grapnel on this occasion. The and retired again into our cabins. At storm indeed dispersed the ice, and one, the cook, in his usual boisterous made openings in several places; but way, roused us by announcing dinner, our situation was thereby rendered and putting a large piece of pork, and only still more alarming, for when the a huge pudding upon the table, of ship got into open water, her motion which we partook with a good appe- became more rapid by the power of tite, but in silence, every one seem- the wind, and consequently the blows ingly buried in thought, or only half she received from the ice more violent. awake. Shortly after, the wind changed Whenever therefore we perceived a to north-east and north, increasing field of ice through the gloom, towards gradually, till it turned into a furious which we were hurried, nothing apstorm. Topmasts were lowered, and peared more probable, than that the every thing done to ease the ship. We violence of the shock would determine now saw an immense ice-mountain at our fate, and be attended with imme

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