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could assume, whether all the poor Indians of this country were converted? Whether the soul

of a Pottawottomy was not as well worth saving

as that of a Hottentot? And whether their duty to God and their country would not be quite as well fulfilled, by converting dangerous and bloody savages at our doors, into mild and peaceable Christian neighbours, as by going to the East for that purpose? Lord, Sir, replied the lady, nobody thinks of matters so near at home. Besides, the Missionary Magazines, and Reviews, don't say half as much about our Indians as they do about the Hottentots and Hindoos.' This was conclusive; so I paid my contribution for the conversion of the poor Hottentots, in hopes of getting into the Missionary Magazine.

"After this rencontre I went out, leaving directions with the servant to note if any suspicious persons knocked in my absence. On my return he informed me that six ladies, with subscription-books, had called during the remainder of the morning.

"I hope by this time you begin to comprehend what I mean; to wit, that the distribution of public charities ought to be in the hands of public officers, acquainted with the world, and able to detect imposture of every kind. It will then be bestowed with a wariness and circumspection, which, while it operates as far as is possible to the relief of virtuous distress, does not encourage and pamper idleness and debauchery. I can hardly believe these good ladies, to whose desire to do good I give every due praise, do really benefit mankind by taking from the pockets of the good to bestow on the worth

The sentiments of these letters, with which we least accord, are those in regard to the cultivation of the physical sciences. On this subject the author has allowed his satire to flow too freely, and in his reprehension of the follies of philosophers, has indulged a contemptuous manner toward some of the greatest and most deserving men of the age, entirely unjust to them, and altogether unworthy the general liberality of his views and magnanimity of his feelings.

Our author's account of the papermoney system of this country, contains a great deal of mournful and momentous truth, and cannot be too effectual in exciting our citizens to ponder upon the consequences of that rabid spirit of speculation, which has already commenced its devastations, and is going on to shake our social fabric to its deepest foundations.

The genius of our author is not a little versatile; he can, with much ease and grace, pass from the sarcastic and indignant reprehension of vice, or the sprightly and cutting raillery of folly, to the most deep-felt enjoyment and poetical description of the retired and tranquil scenes of nature, or the delineation of the mild, benignant, and placid features of domestic life. As a beautiful spe

cimen of his power in the pathetic, we following short account of the life, chacannot resist the temptation to quote the racter, and death of a Quaker lady. After some excellent, racy remarks on the manners and character so frequently assumed by young clergymen, the author thus indulges his contemplative mood.

"Having two or three hours to spare till dinner, we rainbled about the church-yard, reading the records of mortality, which, though every where confined to a few simple items, concerning a few insignificant people, are always interesting. They are the history of high and low; and none can read them without being im pressed with a conviction that all are his brothers at last for all die. He who moulders below was born, and died; and whether rich, or a beggar, his short history is that of kings. The struggles of restless ambition, the reverses of the great, and the story of the wreck of lofty pride, we read as an interesting romance, addressing itself solely to the imagination: but when a monarch or a hero dies, he becomes our equal; his death is an example equally with that of the meanest mortal; and we here realize our common nature, and common end.

tion was attracted by a long cavalcade, on foot, "While poring over these tombstones, our attenon horseback, and in carriages of various kinds, winding slowly over one of the hills at a distance. It came towards the church-yard, entered it, and stopt at a large oak, under which was a newly dug grave we had not noticed before. The people of the village were attracted by it, and came up, one after another, until there were, I suppose, two hundred, men, women, and chil dren, gathered together. Without a whisper, except that of the oaks around, the coffin was taken from the wagon, lowered into the grave, and covered with earth. I never witnessed a silence more solemn and affecting; and beautiful as is our church funeral service, I will venand awful devotion than that which impressed ture to say it never raised a feeling of more deep the dead silence around. There was no need of saying "dust to dust:" every clod of earth, as it fell hollowly on the coffin, proclaimed that; neither was any proof wanting that "man who is born of a woman, must die, for a thousand fact. When the mound over the grave was little hillocks around gave silent testimony to the smoothed with pious care, a little buzzing ran through the crowd-and as it slowly separated, some ventured to talk about the deceased perdied-as others die, of some common malady or Son, who was, I found, a Quaker lady, who other. She was neither a belle nor a beauty ;no crowd ever followed her at a ball, nor could I learn that she had ever received a single offer of marriage, except from the person we had left still standing by her grave. Yet there was something in the story I learned of her, that affected me, I can hardly tell why, for it was not the least romantic.

"It seems that her husband, in consequence of

imprudence or misfortune, had several years be

fore been confined in a prison for debt, leaving a family of eight children destitute. By the rare magic of industry and economy united, this woman, by her own labours, kept the little ones together,-fed, clothed, and sent them to school, until the gaol accidentally took fire, and the prisoner walked home. Here he afterward remained unmolested, for the

virtue of his wife had sanctified his person. There is a species of calm, persevering, courageous, and unconquerabl, industry, that gets the better even of fate. Such, it seenis, was the industry of this valuable woman, and it was rewarded even in this world. She lived, God bless her,—to see her husband independent, and to share many years of independence with him. She reared all her children, saw them honourably settled, and heard the old people say, that whatever had been her sacrifices for them, they had repaid her, by their dutiful at fection, and exemplary conduct. Then when she at last died, neither poet made her an angel, nor newspaper eulogy a saint; but the neighbours-the neighbours, followed her to the grave without itering a word,--and the husband and children stoed round it with their faces co

vered.

"Now, if this little true story wants a moral, I think it will easily be found. For my part, I cannot help believing this simple Quaker woman was a more valuable being, and fulfilled her duties far more to the benefit of society, than if she had been a member of as many charitable societies as aunt Kate-and had refused as many fools as a lady I once heard of in Virginia. I must own too, that I consider her silent, unob

trusive, suffering, fire-side virtue, as far preferable to the public and ostentatious newspa per charity, which, in the present time, stalks bravely forth, and beckons every worthiess vagabond to its shrine from Europe, Asia, Africa,

and America."

There are numerous grammatical errors, which we are surprised should have escaped the notice of the author, and an occasional slovenliness of style that looks like affectation; still, we think the "Let ters from the South," well calculated to strengthen the bonds of our union by weakening sectional prejudice, and rendering all parts of our country mutually amiable in the eyes of Americans; and we cordially recommend it to general perusal. L.

The Balance of Comfort; or, the Old Maid and Married Woman. A Novel. By Mrs. Ross, author of the Marchioness, &c. &c. 2 vols. New-York, 1917.

us.

Something superior to the mass of similar publications, our readers must not expect to meet with many traits of superlative excellence in the volumes before Indications of a tolerably extensive, if not very delicate and discriminating, acquaintance with the ordinary varieties of every-day life, are by no means unfrequent; and the facility and liveliness with which they are touched off, would be amusing enough, were the outlines more gracefully sketched, and the tints deeper and more determinate. With the dignified incident and diction of the higher class of modern novels, it would be ridiculous to compare a production, which the authoress evidently intended to occupy its unambitious station by the side of her

former publications. Her representations of low character are drawn with a vigour and facetiousness that evince her familiarity with the species; but in her delineations from the polished world, she is often and obviously at fault, continually mistaking vulgar grossness and rough raillery for elegant wit and refined humour: throughout her attempts of this description, there is too much horseplay; while occasionally, she rushes into scenes, and ventures upon allusions very suitable indeed to the pages of Tom Jones and Roderick Random, but altogether inconsistent with that chasteness of sentiment, and delicacy of language, which ought to characterize the the works of female writers.

G.

The Essence of English Grammar, by Samuel Houston, A, B. Principal of Rural Valley Seminary in Rockbridge, Virginia. Harrisonburg, Lawrence Wart

mann. 12 mo. pp. 49.

This essence of English Grammar, as distilled through the alembic of Mr. Houston's brain, is a product as different from the material, as whiskey is from rye. After whose prescription "it was composed," (to borrow an expression of the author, when speaking of elegant composition,) we know not, but imagine that the diligent and exclusive study of Hannah Glasse's recipes might enable one to produce something very like it.

E.

A Grammar of Moral Philosophy, and Natural Theology, with a summary of the Evidences of Christianity, abstracted chiefly from the works of Dr. Paley. To which are subjoined Questions and Tables, adapted to the study of the sacred scriptures. By the Rev. J. W. Baker, New-York, David Longworth, 12mo. 248 pp.

This is a judicious abstract, bringing into small compass and in a discreet arrangement, much of the most important matter on the subjects treated, and would form a good text-book for the older and more advanced scholars in our principal schools. L.

Longworth's Pocket Almanack, and New-York and United States Kalendar, for 1818. New-York, David Longworth, 32mo.

This is a very convenient Register, comprising much information of everyday use.

THE TOUCHSTONE, or WORLD AS IT

1818.

GOES; a Comedy in four acts, as per-
formed at the Theatre Royal, Drury-
Lane. By James Kenny, New-York,
DAVID LONGWORTH, 12mo. pp. 77.

THE MERRY WIVES OF WINDSOR, a Comedy, in five acts, as performed at the Theatres Royal, Drury-Lane and Covent-Garden. By William Shak. speare. New-York, DAVID LONGWORTH, 12mo. pp. 75.

ELPHI BEY, OF THE ARAB'S FAITH, a

Musical Drama, in three acts, as per-
formed at the Theatre Royal, Drury
Lane. By R. Hamilton. New-York,
DAVID LONGWORTH, 12mo. pp. 53.

THE DEVIL'S BRIDGE, an Opera, in three acts. By Samuel James Arnold. New-York, DAVID LONGWORTH, 12mo. pp. 57.

LOVE IN A VILLAGE, a Comic Opera, in three acts. By Isaac Bickerstaff. NewYork, DAVID LONGWORTH, 12mo. pp. 64.

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Solution to the same, by X. of New-Haven.
If a and b be the roots of the equation
uxy+y2 =0, x—a and r-b are the
factors required; since whatever be the
value of the given expression, their pro-
duct must always be equal to it. To find
these roots, we have, by completing the
square, auxy+ 4 u2 y3 = (4 u2 −1)
y; from which the roots are found,
uy+y√ { u2 −1 and buy-y√4u2-1.
Hence the required factors are x-y.
‡u+ √ \ u2 −1, & x-yu-√4u-1;
which multiplied together will be found
to re-produce the given expression.
When u<2, these factors are necessarily
imaginary, although the imaginary parts
disappear in the product.

Solution to Ques. 6, by M. O'Connor, New-
York.

Let x, y and z denote the absciss, ordinate, and curve respective, and x, y and z their respective fluxions-put a=7854, and c=3-1416. Then 4ay3x=cyx= the fluxion of the solid, and 2cyz= the fluxion of the superficies. Now these fluxions, in every position of the generating circle 2cy will be in the constant ratio of m to n, because by the question their fluents must be in that ratio; therefore m:n::cy3x: 2cyż :: yx: 2ż; hence 2m

myx but z=√12+y3. Hence by sub

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myt

stitution and division √2+y2 2m

By involution, transposition and division, This equation by evo2=

4m2 y2 n2y2+4m2

lution will be x=

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2my √n2y2+4m2

of which the fluents, by notation and form 9th of EMERSON'S table of fluents, are x=

2m

n

> hyper. log. of y+ √y2+4m2 which

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is the required equation of the curve.

Solution to the same, by a disciple of

Newton.

To find the equation of a curve such, that the contents of the solid, formed by the curve, and ordinate about a variable absciss, shall be in a constant ratio to its curve superficies-Let x be the absciss, and y the ordinate, and let z represent the length of the curve to the absciss x, let p=3.1416; then it is well known that 2pydz expresses the differential of the curve superficies, and py2 dr expresses the differential of the solid contents; suppose that the solid is to its curve superficies as m to n, then since this proportion is constant, it follows that py2dx: 2pydz ::m:n·.·ydxn=2dzm, whence ydxx

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Solution to Question 8, by M. O'Connor, New-York.

Since the sun's declination, July 4th, 1817, is 220 55', it is plain that the sun's central ray on that day describes a cone of which the vertex is at the earth's centre, whose axis is coincident with that of the earth, and whose side forms with its axis at said vertex an 4 of 67° 05'. Taking the lat. of N. York 400 43', its comp. 49° 17' the the horizon of N. York makes with the cone's base, and this being greater than 22° 55′ (= sun's declination) the which the cone's side makes with its base, the intersection of the cone and said horizon must be an hyperbola; and all cones described by

Solution to Question 7, by a disciple of the same ray must evidently be similar,

Let D E

be the given

circle, and A B the right line given in position. At the point B, in the right line A B, let the angle A BN be made equal to the given angle, through the centre, C, draw CF rallel to B'N, and draw C A perpendicular to C F, meeting A B in A', divide C F into two parts in L, so that it may be FL:CL::n:

pa

Newton.

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then join AL, intersecting the circle in K, through K draw HMKG parallel to CF, then HM KG will be the line required; for since MG is parallel to CF, one side of the triangle AFC, and is cut by A'L, we shall have FL: CL::GK:KM...GK:

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and cut by the same horizon, must produce like curves. Now the which the sun's meridional ray makes with the horizon in a meridional direction is = the supplement of half the cone's vertical added to the lat. of N. York = 72° 12′

the sun's altitude at noon. And since the earth's radius is very small compared with its distance from the sun, the solar ray, which by means of the summit of the edifice marks the vertex of the given transverse axis, may be regarded as coincident with and equal to the said meri. dional central ray, the former and latter necessarily make one and the same of 72° 12' with said horizon. Now this ray, during the time it describes the curve of which the axis is given, describes portions of two opposite cones, which have their common vertex at the summit of the edifice, and it is the intersection of the horizon with the northern cone that forms the curve in question, which, as we have shown, must be an hyperbola; also, these cones are similar to the first cone, and the horizon cuts them at the same angles as the first. And the distance on the plane of the horizon in the direction of the meridian between the points when said plane meets the cones, is the given transverse axis. Imagine a vertical plane through the axis of these cones, and its intersection with both and the horizon forms a of which two sides are between the horizon and their common vertex; and the 3d, the given axis upon the horizon; in which we have given, besides the axis, the A at the vertex = twice the sun's declination = 45° 50', and one of the angles at the horizon = the supplement of 720 12 the sun's altitude 107.48, to find by trigonometry

=

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B

D

curve a whose vertical shall equal 2X sun's declination, and one of the angles at the base sum of latitude, and sun's polar distance, the perpendicular let fall from vertical angle upon the base (produced if necessary) shall be the height of the tower.

Calculation, As sine 220 55' x Rads. 19 855711.

: 49° 18'-22° 55′ X sine 49° 18' X 220 15'. 19 626486.

:: Transverse axes, 250 feet, 2 397940 : Height required, 147 5 feet.

PRIZE QUESTION

TO BE ANSWERED IN THE APRIL NUMBER.

By Michael Ward, near Sligo, Ireland. It is required to determine geometrically an arc of a given circle, such that its sine may be equal to the excess of

Upon a base transverse axes, of the its secant above the radius.

ART. 16. REPORT OF DISEASES TREATED AT THE PUBLIC DISPENSARY, NEW-YORK, DURING THE MONTH OF NOV. 1817.

FE

ACUTE DISEASES.

EBRIS Intermittens, (Intermittent Fever,) 1; Febris Remittens, (Remittent Fever,) 6; Febris Continua, (Continued Fever,) 8; Febris Ephemera, (Ephemeral Fever,) 1; Febris Infantum Remittens, (Infantile Remittent Fever,)7; Hernia Humoralis, 1; Ophthalmia, (Inflammation of the Eyes,)2; Cynanche Tonsillaris, (Inflammation of the Throat,) 4; Catarrhus, (Catarrh,) 4; Bronchitis, (Inflammation of the Bronchia) 1; Pneumonia, (Inflammation of the Chest,) 8; Enteritis, (Inflammation of the Intestines,) 4; Rheumatismus Acutus, (Acute Rheumatism,) 1; Urticaria, (Nettle Rash,) 1; Erysipelas, (St. Anthony's Fire,) 1; Variola, (Small Pox,) &; Vaccinia, (Kine Pock,) 18; Convulsio, (Convulsions,) 1.

CHRONIC AND LOCAL DISEASES.

Asthenia, (Debility,) 1; Vertigo, S; Cephalalgia, (Head-Ach,) 7; Dyspepsia, (Indigestion,) 7; Gastrodynia, (Pain in the Stomach,) 2; Obstipatio, 4; Colica, (Colic,) 2; Hysteria, (Hysterics,) 1; Palpitatio, 1; Hypochondriasis, 1; Ophthalmia Chronica, (Chronic Inflammation of the Eyes,) 3; Pharyngitis Chronica, (Chronic Inflammation of the Throat,) 2; Catarrhus Chronicus, (Chronic Catarrh,) 2; Bronchitis Chronica, 4; Phthisis Pulmonalis, (Pulmonary Consumption,) 1; Rheumatismus Chronicus, (Chronic Rheumatism,) 0; Pleurodynia, 4; Lumbago, 3; Hæ

moptysis, (Spitting of Blood,) 1; Menorrhagia, 1; Hæmorrhois, (Piles,) 1; Dysenteria Chronica, (Chronic Disentery,) 4; Diarrhoea, 7; Leucorrhoea, 1; Amenorrhea, 3; Dysuria, (Difficulty of Urine,) 1; Lithiasis, (Gravel,) 1; Anasarca, (Dropsy,) 1; Ascites, (Dropsy of the Abdomen,) 1; Hydarthrus, (White Swelling,) 1; Vermes, (Worms,); Syphilis, 11; Urithritis, 4; Phymosis, 1; Hernia Congenita, (Congenital Hernia,) 1; Luxatio (Dislocation,) 1; Contusio, (Bruise,) 12; Ustio, (Burn,) 1: Abscessus, (Abscess,) 2; Ulcus, (Ulcer,) 10; Psoriasis, 1; Urticaria, (Nettle Rash,) 1; Erythema, 2; Porrigo, (Scalled Head,) 6; Impetigo, 1; Scabies et Prurigo, 18; Eczema Mercuriale, 1; Aphthæ, 1; Eruptiones Variæ, 3.

The temperature of this month has been generally uniform, and exceedingly mild. The winds have been part of the time from N. E. and N. W, but more commonly between S. E. and S. W. There have been some foggy evenings and mornings:-a few inconsiderable rains, and heavy ones on the 1st and 2nd, and on the 17th and 18th; the whole quantity that has fallen nearly 6 inches on a level. The highest temperature of the morning has been 60°, lowest 29°, mean 420 ;— highest temperature of the afternoon 59o, lowest 32°, mean 490.6 :-highest temperature of the evening 640, lowest 30°, mean 470.6-greatest diurnal variation

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