fame with day-light) is to the denfity at the earth (reflected from the moon); as the fquare of 219 to 1, or as 47951 to 1. But fince in reality, there is not fo much light falls on the moon, being no more than what fal's on her disk, and her disk being only her enlightned hemisphere, the density of light at her furface upon each hemifphere will be but half as much. And it matters not whether any falls upon the oppofite difk or not; for (by the rule of proportion) that would all be reflected to the oppofite hemifphere, and does not concern us, who are opposed to the full moon. Therefore it will now be, as day light, to moon-light, fo is 47961 to, or as 95922 to 1, or in round numbers as 96000 to 1.

Cor. I. Moon-light is to day-light; as half the fquare of the moon's radius, to the Square of the moon's distance, when she is full. And in the quadratures, as the fquare of the moon's radius, to the Square of the moon's distance.

After the fame manner may be found the light of any other celeftial body, compared with day-light; let it be Venus. Let d = fun's diftance from the earth, Venus's

distance from the fun, a her distance from the earth, = her radius. Then if Venus and the earth were equally illuminated by the fun, then is her light to day-light: a a. But Venus being nearer the fun, is more enlightened d d

in the ratio of

d d

to 1; therefore her light is to day-light ::

# TT X -:aa :: ¦ rr dd: vva a. But fince in her

quadratures da nearly, therefore Venus's light is to daylight; asr to v v. And that is as 1 to 804.000000 nearly. Hence

'Corol. II. The light of Venus in her quadratures, is to day-light, as 1 to 800 millions.

This is fuppofing the radius of Venus, to her diftance from 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. Suppofing they both of them reflect all the light that falls on them.'

Subjoined to this treatife on optics, we have, in two fections, the principles of perfpective, and practical rules for operation, illuftrated by a great variety of examples, all executed in the fame masterly manner with the other parts of this very valuable performance.

IX. Letters between an English Lady, and ber Friend at Paris, in which are contained the Memoirs of Mrs. Williams. By a Lady. In Two Vels. 8vo. Pr. 6s. Becket.

WE

VE 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 novelftile, as she never could draw any amusement from that species of writing;' and declares, that though fhe believes the following memoirs to be true, they bear fo ftrong a resemblance to many others, which have owed their birth only to the imagination of their authors, that the fears they will not be efteemed fo 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 fporting in the fields of fiction.

The history opens with a letter from Mrs. Williams, to a Mademoiselle D'Angeville, in which the mentions her arrival at Dover, and the regret the feels on being feparated from her dear friend Adelaide. She discovers also not a little uneasiness at her landing in her native country, as the cannot help reflecting upon the ill-treatment she met with in it, and promises to return to France when her bufinefs to England is finished. Her friend, in answer tells her, that she has difcovered her brother the marquis D'Aife to be in love with her, by his unhappiness at her abfence, and by his anxiety, left he fhould not be capable of gaining a return of affection. Mrs. Williams, in reply, confeffes that she has obferved the marquis's paffion for her, but pronounces herself dead to every idea of love; adding, that her heart, hardened by a series of uninterrupted difappointments and misfortunes, is reduced to a ftate of apathy, not to be removed, as it has felt till it can feel no more. She avers, at the fame time, that friendship, and the highest esteem, are tributes which fhe cannot, without revolting against reason, withhold from him. Adelaide, in return, puts her in mind of the promise the had made with regard to her hiftory, and infifts upon her conveying it to her; acquainting her alfo with her brother's ill ftate of health on her account. When a few more letters have been exchanged between them, Mademoiselle D'Angeville, in confequence of her brother's being in the most imminent danger, intreats her friend, in the strongest terms, to write to the marquis, and to fave his life. Mrs. Williams expreffes her grief, pity, and

friend

friendship for the marquis. She writes to him; tells him how much difquietude the feels by thinking on the uneafiness she has occafioned to him and his fifter, and begs him to use all poffible means for his recovery. She alfo defires he would read her story to his fifter, affuring him, that if, after the perufal of it, he thinks it poffible for her heart to be again fufceptible of a tenderer fentiment than that of friendship, and could infpire that heart with love, fhe 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 defcribed. The former are poffeffed of 3000l. per annum in the Weft of England, where he refided, and educated his daughter Charlotte according to his own plan, leaving her fifter Sophia under the direction of his wife: fhe teaches Charlotte hiftory, and makes her ftudy the different modes of government in different nations, and what he called the Science of Thinking. He had masters to inftru&t her in French, writing, mufic, drawing, &c. She, on the contrary afferts, that girls without a learned education are more rational than their mafters, and diflikes her daughter Charlotte because she is her father's favourite, Charlotte is very uneafy as the is the caufe of continual difputes between her parents. Her father, on account of those disputes, fends her to a fifter of his, whofe 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 fenfe: Charlotte efteems him very much, but cannot bring herself to love him. On her return to her father's he congratulates her upon the conqueft which she has made in such a manner, and speaks fo highly in Sir Charles's favour, that her looks prompt him to believe he has no objection to him for a husband: but as fhe is thought to be too young then, no time is fixed for the celebration of their nuptials. She continues wifhing, 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 vifit to her aunt's, while fhe is in this fituation, and defires to take her into the North for a couple of months, Her aunt confents, but with reluctance. At an affembly, occafioned by the races, Charlotte dances with a Mr. Williams, who appears fo much the gentleman, that lady Betty, being much pleafed with him, enquires about him, and finds him to be the fon of an old acquaintance of hers. Upon his expreffing a wish to pay his refpects to her ladyship, the invites him to spend a few days with her at her feat, concluding that as Mifs Rutland's affections were fixed upon Sir Charles Stanly fhe would run no rifque by being acquainted with Mr. Williams. The youth

and innocence, however, of Mifs Rutland foon make Mr. Williams fenfible that if he likes her, she also prefers him in her heart, though fhe declares that he has too much honour to fwerve from the engagements into which he has entered voluntarily with Sir Charles. When lady Betty carries her back to her uncle's, Sir Charles receives her with raptures. She foon afterwards goes home to her father's to prepare for her marriage, the thoughts of which plunge her into defpair: but being afhamed and indeed afraid to complain, the only looks uncommonly ferious; her seriousness is fuppofed to arise from a becoming modefty. Her fifter having more penetration than the rest of the family, dives into the fecrets of her bosom, and plainly taxes her with not loving Sir Charles, adding, “how capricious is fortune! why don't you fee him with my eyes, then would you both be happy." This discovery of her filter's inclination for Sir Charles added to her own averfion, induces her to wish to break off the match rather than to render both her fifter and herself miferable. Yet he has not courage sufficient to undertake fo arduous a task. She wishes for Mr. Williams to give her advice, as be only knows the real fituation of her heart. In a fhort time after their arrival in London for the speedy conclufion of the marriage, Charlotte, croffing the Park, meets Mr. Williams. He perfuades her-nothing loth-to refign Sir Charles, and to marry him, telling her that he is heir to five thousand a year. He confeffes 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 fight of the lawyers and Sir Charles's declaration stagger her refolution fo much that she thinks he ought not on many accounts to give him her hand. She declares indeed that the does not chufe to be married to any body; but standing in need of a protector to defend her against her incenfed relations fhe imagines there is a neceffity for her running away with Mr. Williams, and prevails on her fifter to go along with her. Sophia knows nothing of Williams till fhe 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 fend for Sophia, and forbid her fifter to appear before them again. Mrs, Williams is informed by her aunt that the has married a libertine deeply in debt: by the treatment which the meets with from her relations upon this occafion, and the intelligence the receives, fhe is both astonished and afflicted. Sir Charles writes a very handfome 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 paffion

for

for him: the detection of which paffion greatly contributed to her defertion. Mrs. Williams foon finds the strongest reason 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, fent by one of her husband's kept miftreffes, who tells her he has left Fanny without paying for her lodgings or advancing a farthing; the gives this perfon ten guineas. Soon afterwards Mr. Williams brings a Mr. Smith to fee 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 perfuading him to imagine fhe is convinced of hist 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 5001. in an unknown hand: she is, at the fame time, admonished not to give it Mr. Williams. She determines not to conceal any thing from him, but fays 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 diffimulation, ill-treatment, and prodigality, he is too thoroughly convinced of the turpitude of his character to hope for amendment. She is brought to bed of a fon: her uncle Boldly ftands godfather. This event produces a reconciliation with her father and mother; but the indifference with which her father behaves upon the occafion, cuts her to the foul. Mr. Williams then informs her that he has bought a house fourteen miles out of town. It is fo much out of repair, that he intends to rebuild it. This intention alarms her. He defires, that if his father and mother should blame him for having made the purchase, fhe would fay it was bought to oblige her. She excufes herself from telling fo palpable a lie, and only confents to give them room to fuppofe it was purchased to please her. They charge her with want of œconomy, and the quite forfeits their esteem. In the mean while, fhe thinks to furprize Mr. Williams very agreeably, by prefenting the 500l. 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 arrefted. On going to see him, with her purfe, in order to release him, he finds him with a pretty girl fitting on his lap. This girl proves to be Fanny, and The confeffes that she had drawn him in to give her a promiffory note for a fum of money. Mrs. Williams pays the girl a hundred pounds, and gives the husband the remaining four, Mr.

Wil