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same with day-light) is to the density at the earth (reflected from the moon); as the square of 219 to 1, or as 47961 to 1. But since in reality, there is not so much light tails on the moon, being no more than what falls on her disk, and her disk being only her enlightned hemisphere, the density of light at her surface upon each hemisphere will be but half as much. And it matters not whether any falls upon the opposite disk or not ; for (by the rule of proportion) that would all be reflected to the opposite hemisphere, and does not concern us, who are opposed to the full moon. Therefors it will now be, as day light, to moon-light, so is 47961 to, or as 95922 to i, or in round numbers as 96000 to 1...

Cor. I. Moon-light is to day-light; as half ibe Squart of the moon's radius, to the Square of the moon's distance, wben she is full. And in the quadratures, as the Square of obe moon's radius, to the Square of the moon's diftance.

After the same manner may be found the light of any other celestial body, compared with day-light; let it be Ve. nus. Let d = sun's distance from the earth, v = Venus's distance from the sun, a = her distance from the earth," = her radius. Then if Venus and the earth were equally illuminated by the sun, then is her light to day-light :rirr: a . But Venus being nearer the sun, is more enlightened in the ratio of — to 1; therefore her light is to day-light ::

dd Tax :a a ::: jordd: vwa a. But since in her quadratures d = a nearly, therefore Venus's light is to daylight; as rr to vv. And that is as ito 804.000000 nearly. Hence

•Corol. II. The light of Venus in ber quadratures, is to day-lig'i, as I to 800 millions.

• This is supposing the radius of Venus, to her distance frori the fun, to be as 1 to 14200.

Cor. III. Hence the light of the moon is 8000 times as great as the light of Venus. Supposing they botb of them reflect all ibe light . tbat falls on them."

Subjoined to this treatise on optics, we have, in two seations, the principles of perspe&tive, and practical rules for operation, illustrated by a great variety of examples, all executed in the Lame masterly manner with the other parcs of this very valuable performance.

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IX. Letters between an Englith Lady, and ber Friend at Paris,

in which are contained the Memoirs of Mrs. Williams. · By a Lady. In Two Vols. 8vo. Pr. 6s. Becket.

W E are so seldom rewarded by the contents of a novel for

the time which we allot to the perufal of it, that we receive the greater pleasure from the volumes before us.

In the Preface to this little work, the authoress informs the reader, that' she is the least calculated to shine in the novelstile, as she never could draw any amusement from that species of writing ;' and declares, that though the believes the following memoirs to be true, they bear so strong a resemblance to many others, which have owed their birth only to the ima. gination of their authors, that she fears they will not be esteemed so but by the few, who may have had some know. ledge of the facts related in them.' She then relates a plausible anecdote, to induce us to believe that she has not been sporting in the fields of fiction.

The history opens with a letter from Mrs. Williams, to a Mademoiselle D'Angeville, in which she mentions her arrival at Dover, and the regret she feels on being separated from her dear friend Adelaide. She discovers also not a little uneasiness at her landing in her native country, as she cannot help reflecting upon the ill-treatment she met with in it, and promises to return to France when her business to England is finished. Her friend, in answer tells her, that she has disco. vered her brother the marquis D’Aise to be in love with her, by his unhappiness at her absence, and by his anxiety, left he should not be capable of gaining a return of affection. Mrs. Williams, in reply, confesses that she has observed the mar. quis's passion for her, but pronounces herself dead to every idea of love; adding, that her heart, hardened by a series of uninterrupted disappointments and misfortunes, is reduced to a state of apathy, not to be removed, as it has felt till it can feel ng more. She avers, at the same time, that friendfhip, and the highest esteem, are tributes which the cannot, without revolting against reason, withhold from him." Adelaide, in re. turn, puts her in mind of the promise Me had made with regard to her history, and infifts upon her conveying it to her ; acquainting her also with her brother's ill state of health on her account. When a few more letters have been exchanged between them, Mademoiselle D'Angeville, in consequence of her brother's being in the most imminent danger, intreats her friend, in the strongest terms, to write to the marquis, and to save his life. Mrs. Williams expresses her grief, pity, and

friends friendship for the marquis. She writes to him ; tells him how much disquietude me feels by thinking on the uneasiness the has occasioned to him and his lifter, and begs him to use all possible means for his recovery. She also desires he would read her story to his sister, assuring him, that if, after the perusal of it, he thinks it possible for her heart to be again susceptible of a tenderer sentiment than that of friendship, and could inspire that heart with love, she would give him her hand.

The memoir-part opens with an account of Mrs. Williams's family. The characters of her father and mother are described. The former are pofseffed of 3000l. per annum in the West of England, where he resided, and educated his daughter Charlotte according to his own plan, leaving her sister Sophia under the direction of his wife : The teaches Charlotte history, and makes her study the different modes of government in different nations, and what he called the Science of

Thinking. He had masters to instruct her in French, writing, music, drawing, &c. She, on the contrary asserts, that girls without a learned education are more rational than their masters, and dislikes her daughter Charlotte because she is her father's favourite, Charlotte is very uneasy as she is the cause of continual disputes between her parents. Her father, on account of those disputes, sends her to a fifter of his, whose husband's nephew and heir is a Sir Charles Stanly, Sir Charles becomes enamoured with her: he is a young man of good nature and good sense : Charlotte esteems him very much, but cannot bring herself to love him. On her return to her fa. ther's he congratulates her upon the conquest which she has made in such a manner, and speaks so highly in Sir Charles's favour, that her looks prompt him to believe he has no objection to him for a husband : but as she is thought to be too young then, no time is fixed for the celebration of their puptials. She continues wishing, for two years, to love Sir Charles, but is not, from an unaccountable caprice, able to feel the least tenderness for him. A lady Betty Ruffel makes a visit to her aunt's, while she is in this situation, and desires to take her into the North for a couple of months. Her aunt consents, but with reluctance. At an assembly, occasioned by the races, Charlotte dances with a Mr. Williams, who appears so much the gentleman, that lady Betty, being much pleased with him, enquires about him, and finds him to be the son of an old acquaintance of hers. Upon his expressing a wish to pay his respects to her ladyship, the invites him to spend a few days with her at her seat, concluding that as Miss Rutland's affections were fixed upon Sir Charles Stanly The would run no risque by being acquainted with Mr. Williams. The youth U 4

and

and innocence, however, of Miss Rutland soon make Mr. Williams sensible that if he likes her, she also prefers him in her heart, though fhe declares that she has too much honour to fwerve from the engagements into which she has entered voJuntarily with Sir Charles. When lady Betty carries her back to her uncle's, Sir Charles receives her with raptures. She soon afterwards goes home to her father's to prepare for her marriage, the thoughts of which plunge her into despair : but being ashamed and indeed afraid to complain, the only looks uncommonly serious; her seriousness is supposed to arise from a becoming modesty. Her lister having more penetration than the rest of the family, dives into the secrets of her bosom, and plainly taxes her with not loving Sir Charles, adding, “ how capricious is fortune ! why don't you see him with my eyes, then would you both be happy.” This discovery of her sister's inclination for Sir Charles added to her own aversion, induces her to wish to break off the match rather than to render both her sister and herself miserable. Yet she has not courage suf. ficient to undertake so arduous a talk. She wishes for Mr. Williams to give her advice, as be only knows the real situation of her heart. In a short time after their arrival in London for the speedy conclusion of the marriage, Charlotte, crossing the Park, meets Mr. Williams. He persuades her—nothing loth--to resign Sir Charles, and to marry him, telling her that he is heir to five thousand a year. He confefles also that his father is covetous, but encourages her to believe that when the affair is finished he will be reconciled. At her return home the sight of the lawyers and Sir Charles's declaration stagger her resolution so much that she thinks she ought not on many accounts to give him her hand. She declares indeed that the does not chuse to be married to any body; but standing in need of a protector to defend her against her incensed relations The imagines there is a necessity for her running away with Mr. Williams, and prevails on her fister to go along with her. Sophia knows nothing of Williams till the attends them at May-fair. When the ceremony is over Mrs. Williams writes to her uncle, her aunt, and to Sir Charles : Sophia, at her request, dispatches a letter to her father. Mr. and Mrs. Rutland send for Sophia, and forbid her sister to appear be. fore them again, Mrs. Williams is informed by her aunt that the has married a libertine deeply in debt; by the treatment which she meets with from her relations upon this occasion, and the intelligence she receives, she is both astonished and afflicted. Sir Charles writes a very handsome letter to her, but takes no notice, at that time, of the friend who, according to a hint in one of hers, had conceived a violent pasion

for for him : the detection of which passion greatly contributed to her desertion. Mrs. Williams soon finds the strongest reacon to repent of her conduct-she discovers her husband to be too vicious to make any woman happy. She is first visited by a female, sent by one of her husband's kept mistresses, who tells her he has left Fanny without paying for her lodgings or advancing a farthing; she gives this perfon ten guineas. Soon af. terwards Mr. Williams brings a Mr. Smith to see her, who had offered to be a mediator between her and her father, and who behaves in a very friendly manner to her. She is determined not to mention Fanny to her husband, in hopes of making him virtuous by persuading him to imagine she is convinced of his goodness. Mr. Smith introduces her to her husband's father and mother. She in a little while discovers that he is upon ill terms with them upon account of his extravagance. She receives a letter with a bill of 500l. in an unknown hand : The is, at the same time, admonished not to give it Mr. Williams. She determines not to conceal any thing from him, but says nothing about it just then : as his father and mother continued to exhibit him in the most unfavourable light, telling her that if she was Venus herself he would grow tired of her, and reduce her to beggary. After a thousand different modes of disti. mulation, ill-treatment, and prodigality, she is too thoroughly convinced of the turpitude of his chara&er to hope for amendment. She is brought to bed of a fon : her uncle Boldly stands god. father. This event produces a reconciliation with her father and mother ; but the indifference with which her father be. haves upon the occasion, cuts her to the soul. Mr. Williams then informs her that he has bought a house fourteen miles out of town. It is so much out of repair, that he intends to rebuild it. This intention alarms her. He desires, that if his father and mother should blame him for having made the purchase, she would say it was bought to oblige her. She excuses herself from telling so palpable a lie, and only consents to give them room to suppose it was purchased to please her. They charge her with want of æconomy, and the quite forfeits their esteem. In the mean while, she thinks to surprize Mr. Williams very agreeably, by presenting the goo 1. to him. She perfuades him to let the old front remain. When she has leffened his intended expences, and brought them within that fum, she hears that he is arrested. On going to see him, with her purse, in order to release him, he finds him with a pretty girl sitting on his lap. This girl proves to be Fanny, and he confesses that she had drawn him in to give her a promissory note for a sum of money. Mrs. Williams pays the girl a hunGred pounds, and gives the husband the remaining four. Mr.

Wil.

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