of surrendering my money, as if a pistol was held at my breast. Every idea of charity is equally out of the question in both cases; though in the one the money is demanded for God's sake, and in the other for my own sake." "I remember," rejoined the second, "being once singled out by a terrible woman with an enormous belly, who stuck to me brawling for charity the whole length of Piccadilly. Being determined not to give her a farthing, I was quickening my pace to shake her off, when unluckily I met a lady of my acquaintance, and stopped to speak to her. The hideous wretch with the belly, taking advantage of the incident, renewed her clamour so loud and so woefully, that I was afraid she would have been delivered in the open street; and so I was obliged to throw her a shilling, which put an end to her labour, and my pangs, at once." THE PRINCESSES. (With Portraits.) AMONG the illustrious females who have adorned the Royal Families of this country, few have been more beloved than the present, and few we presume have ever rendered themselves more deserving of national affection. Charlotte Augusta Matilda, Princess Royal of England, was born on the 29th of September, 1766. Her amiable character endeared her to the nation during the earlier part of her life, and her illustrious virtues, rather more than her exalted rank, rendered her an object of affection to a foreign prince, to whom she was afterwards united. She was married to Frederick Charles William, Elector of Wirtemberg, May 18, 1797, who was created king in 1805. This prince died in 1816, leaving her in a state of disconsolate widowhood, to mourn over those common calamities from which no station can exempt the human race. Springing from a monarch remarkable for his benevolence, we have no doubt, that she still continues to display thosc charitable virtues in a foreign land, which, in her native country, from her earliest infancy she was taught to venerate and cherish. Her Hoyal Highness the Princess Augusta, was born November 8, 1768, 1054 and she continued to live under her Majesty's paternal care in Windsor Castle, until her royal mother's death. In this castle she had private apartments fitted up in a style of simplicity and elegance, suited to her refined taste, with an extensive collection of books and paintings. Her visits to the surrounding nobility, accompanied by her sisters, were frequent; and whenever the weather was fair, she rarely omitted either to walk or ride daily through the beautifully romantic scenery of the parks. She had a horse that was a particular favourite, which, always on her return from riding, partook from her Royal Highness' own hand, a dainty repast which was ready at the palace door. She usually made presents of select publications on particular occasions, and generally on New Year's Day, to most of her domestic servants. Her purchases were frequently made by herself, visiting the shops personally; on which occasions her conduct and manner were so humble and unassuming, as to endear her to all to whom she was known. The charitable institutions in Windsor are very extensive, all of which received an annual bounty from her royal hand; and every object of distress coming to her knowledge, received immediate relief. Her Royal Highness, with her sisters, added much to the beautiful walks round the palace. On the north side of the castle formerly was a piece of land forming a plantation, called the Slopes, running in extent from west to east, about three-quarters of a mile, which had continued a rough uncultivated spot for many years. It is now tastefully laid out, affording one of the most interesting walks about the Royal residence, and has a private communication with Frogmore Lodge. Both inhabitants and strangers have free access to this delightful spot, where every accommodation is offered to the weary, by several alcoves, or thatched cottages, with seats. Her Royal Highness is displaying great taste in the present alterations now making at Frogmore. The whole mansion has undergone considerable alterations; and the improvements made through the gardens, are well worthy the admiration of every stranger; to whom Her Royal Highness frequently grants permission to take a | Many of the rural spots in Frogmore a few hours' walk. We would recommend none to take this rural ramble without joining the retired hermit, who will always be found with his cross and bible in devout meditation. The following lines, said to be the composition of Her Royal Highness Princess Elizabeth, are descriptive of this interesting scene. YE whom variety delights, What though the sun's meridian light Her Royal Highness the Princess Elizabeth, was born May 22, 1770. Literature, the Arts,-Charitable Institutions, the Widow,-the Orphan, and the Friendless, have reason to hail with unspeakable joy this happy event. She was the patroness of every laudable undertaking. Her bountiful hand, which on all occasions was united with her sympathizing heart, rendered her departure an irreconcileable loss to the needful, who had so long partaken of her charity. She wrote many pieces of poetry, and prose; acquired a considerable knowledge of drawing; and is said to have engraved or etched a series of plates. Most of her own productions she had printed at Frogmore, at the press of Her Majesty, who had fitted up a small private printing-office. She established a school of girls, at Old Windsor Cottage, the country residence of Her Royal Highness, which was supported entirely by herself. gardens, and other parts, were laid out after her own taste. An exquisitely beautiful grotto, forming an interesting feature in the Frogmore gardens, is said to have been completed by her. The Princess Mary was born April 25, 1776. She was married to William Frederick, Duke of Gloucester. This princess has always supported an amiable character, following the steps, and copying the example, of her elder sisters. She was the constant attendant upon the late Princess Amelia, during the long period she was confined to her bed, watching her with unceasing affection till she expired. To assist in works of charity she was ever ready; and many benevolent institutions enjoyed the benefits of her influence and liberality. The Princess Sophia, was born Nov. 3, 1777. The same amiable spirit by which her sisters have been distinguished, breathes in her conduct, and dignifies her actions. Charmed with domestic life, her retiring virtues shun the eye of popular observation, on which account her real worth is less generally known; but it is rendered the more valuable, because it is not obtrusive. Affable, charitable, and sympathetic, she has an ear that attentively listens to tales of woe, and a hand that is always ready, by administering to the necessities of the indigent, to soothe them in affliction, and alleviate their distress. In these respects, the Princesses of England appear to be actuated by one common spirit. Our benevolent institutions have acquired respectability and vigour under their fostering patronage; and among the poor who have been relieved by their bounty, their munificence will be long remembered with grateful affection, when they shall be gathered to the sleep of their fathers. Destitute of that haughtiness which too frequently associates with royalty, they have rendered themselves beloved in their respective neighbourhoods, by their dignified condescenson, without compromising their illustrious descent, or degrading themselves in the eyes of the most exalted, who cannot but admire in their conduct, a lovely feature which pride will not permit them to imitate. They have taught ambition a lesson by their own humility; and in 1057 Literary Notices.-Solutions of Mathematical Queries. 1058 stances, assumed the garb of disinterested charity. structed avarice by their genuine liberality. The nation has long experienced the effects of their benevolence; and the consequences of their influence among those who have been honoured with titles, wealth, and station, will in all probability extend beyond the present generation of ed in a size for the pocket; with entirely new Embellish mankind. Their example has operated among many, who have been strangers to their motives; so that even ostentation has, in several in- | Literary Notices. A new Edition of Walton and Cotton's Complete Angler, is preparing for the Press, by Mr. Bagster. It will be print ments. In the course of November will be published, in One Vol. 8vo. "Augustus; or, The Ambitious Student." On the 1st November was published, the whole of the Rev. G. C. Smith's Works, (Author of the Boatswain's Mate,) in 24 Parts, illustrated with a Portrait of the Author, half-bound, 5s. SOLUTIONS OF MATHEMATICAL QUERIES. MR. EDITOR,-Your correspondent P. in col. 734, of your valuable Magazine, proposes three Queries, and requests a Solution to the 4th Mathematical Query in No. 15, col 387, which I have given below. The first of P.'s Queries, if I rightly understand its meaning, is included in that Solution: for it is there proved, that we shall obtain the same value of x in the Biquadratic, whichever root of y we make use of. With respect to the second Query, in the instances alluded to, by your correspondent, Bonnycastle must certainly have intended the cubic to be solved by the method of divisors, or by a table of Co.sines or by the converging series, (though he has neglected to mention this point) in which cases there is no necessity that any of the roots of the Biquad. should be impossible: but, if the cubic is to be solved by Cardan's method, that of Des Cartes will certainly not apply, except two of the roots are impossible or imaginary. Your correspondent P. says, that " three of the roots, frequently all the four, are rational;" he should recollect, that there cannot be three roots rational, and one irrational, or impossible, because the latter always enter equations by pairs, (when the coefficients thereof are rational.) Upon the whole, Des Cartes' method is exceedingly laborious, and must yield, as well as every other, to that of approximation, both with respect to accuracy and expedition. By inserting this communication, you will very much oblige, your's &c. Lynn Regis, Sept. 11, 1820. Solution to the 4th Question of No. 15, col. 387. PETRARCH. The equation for determining (a), found by Des Cartes' method, is aa + 2 p a* + p2—4r. a3 — q2 — o for a substitute y y3 +2py' + p2 - 4 r. y — q2 = o Let m2, n' and be the values of y or a'; then, since the coefficient of the second term is equal to the sum of all the roots, with their signs changed, &c. .. 2pm2 — n23 — i̇2 and — q' (— m2) × (— n2) × ( — t3) — — m2 n2 t2 whence q = mnt. Now let us use the first value of y (m2) and the value of a, (m) then, if the component quadratics are x2 + ax + b = 0 and x2 - ax + c = 0, we have |