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XIII. On wheel-carriuges. By T. Estcourt, Esq:

XIV. An essay on the cultivation of potatoes. By the Rev. Edmund Cartwright. Too much encouragement cannot be given to the cultivation of this most excellent root. It affords a wholesome and abundant nutriment for map and beast. Il is the best fallow or preparation for wheat; and will grow in almost any soil or situation; its seed time extends through five months, and it possesses powers of propagation superior to those of any other esculent.' This ingenious essay does not indeed throw inuch new light on the subject, but it is comprehensive and instructive.

The potatoe is a plant remarkably tenacious of life, and Dr. Cartwright mentions its possessing a principle of vitality or self-propagation, which few persons, it is believed, suspect.

• In looking over some potatoes,' he says, which were going to be planted, I observed on several of them small buds breaking out where there was no appearance of an eye ; these I cut out and planted, all of which grew and produced potatoes, Willing to trace this principle of vitality to the source, I took a number of potatoes, which, after pating off the rind, I cut into cubes of about an inch square. These cubes being kept in a dry place for a day or two, that they might heal over, were planted in the same manner as common cuttings. Of these, two thirds at least produced healthy vigorous plants, and came to maturity. How is this to be accounted for? Do the embryo-plants extend themselves in all directions from the eyes through the whole paren.chymatous substance of the potatoe, converting it, as it were, into a vegetable polypus? There is nothing obvious to the eye at least, that leads to any such hypothesis.'

XV. On the subject of wceding; or the improvements to be effected in agriculture by the extirpation of weeds. By Mr. W. Pitt of Wolverhampton. No less than 55 sorts of weeds are described in this paper, as infesting corn lands, and a great number of others are mentioned that ought to be extirpated from meadows and leys. It is worthy of observation that fifteen or sixteen of the commonest weeds are pointed out, as having beneficial uses either in husbandry or domestic econoniy, Mr. Pitt coincides with the President in thinking, “ that some regulatio!1 of police for fiving those, who harbour weeds the seeds of which might be blown into their neighbour's ground, has no injustice in its principle.”

XVI. An essay on the production and consumption of corn in Great Britain ; its population at different periods ; the means of increasing human subsistence ; and of preventing future scarcities. By Mr. W. Pitt of Wolverhampton. We think Mr. Pitt has gone much out of his element in the statistical subjects of this essay His statements seem deficient, and his deductions inconclusive. He estimates the number of horses in England at one million. Mr. Curwen, in No. V. makes an estimate VOL IV.

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grounded on the returns of the tax office, that they amount to 1,430,000.; of these Mr. C. calculates that one million are employed in husbandry and for draught, (900,000 and upwards being actually entered) while Mr. Ř. considers 600,000 as a liberal estimate. The conclusions deduced from these and other deficient data, cannot therefore be correct. In his sixth chapter, when treating of the improved agricultural and grazing systems, of fallow crops, and feeding heavy stock within doors, Mr. P.'s remarks are more worthy of regard. He is miserably wrong, however, where he attempts to prove that little advantage would be derived from the more general substitution of oxen for horses in agriculture. This error principally arises from his assumption of erroneous data; one of which is, that the horses used in agriculture are in a great measure a nursery for those wanted for other purposes, the teverse we beliere is quite as commonly true. His eighth, On gardens, and potatoe and cow ground for labourers, contams nayy useful and judicious observations.

The Second Part of this Volume will probably come under our notice in the next Number. Ar VIII. Mathematics Simplified and practically Illustrated, by the

Adaptation of the principal Problems to the ordinary Purposes of Life, Los and, by a progressive Arrangement, applied to the most familiar Objects z in the plainest Terms: together with a complete Essay on the Art of

Surveying Lands, &c. by such Simple Inventions, as may for ever banish the Necessity of costly and complex Instruments. By Capt. Thomas Williamson, Author of the Wild Sports of India. 8vo. pp. v.

224. Price 9s. Longman and Co. 1808. INSTEAD of “ Mathematics Simplified,” the valiant author

would have shewn more wisdom and honesty if he had pitched on some appropriate title, such as Mathematics perplexed, or Mathematics misrepresented, or Mathematics misunderstood, or Mathematics degraded; and we would seriously recommend One or other of these to his adoption, should any of his friends advise a new edition of the tille page.

We should conjecture that Capt. W. designed to give, in this book, a few problems in Practical Geometry, and to make these preparatory to a treatise on land-surveying, on levelling, mining, and timber measuring: but the nature of his production makes it quite certain that the contents of his cranium were woefully confused, while he was employed in executing his intention. He begins, secundum artem, with definitions, or rather with censuring the definitions of Euclid and oiher bunglers of early times, which he says are too vague for the uninstructed, and are contrary to the conviction of the proficient:" and then, to shew how far his own definitions are from every thing “ vague,” and how consistent with “ the conviction of the proficient,” he presents a few specimens : e. g. 1. “A true cone is created by the revolving or spinning of a triangle on its centre, supposing the point to serve as a pivot, and another point to be in the centre of the opposite side !" 2." A sphere or globe is a solid figure, which, however taken, always gives the same girth and the same diameter !” After these, he proceeds to his problems, which are such as a child stumbles upon at the very threshold of mathematical science, and scarcely two of which the captain attempts to demonstrate: the poor, despised, inaccurate Euclid, however, helps him to a demonstration of one " problem,for such our author, unfortunately for his reputation, denominates the theorem, which stands as the 47th proposition of the first book of the Elements.“ This famous problemn,says the scientific Captain," seems to centre in itself the greater part of what is contained in the preceding; for there are few, matters hitherto treated of, which do not come into either its formation or its solution; hence it has been designated “ the pons asinorum,” or the “ ass's bridge." Now as all our readers know that the 5th proposition, and not the 47th, is the celebrated bridge in question, they will naturally suppose that the warlike author had bathed in the stream that runs underneath it; and there, unhappily for himself and the public, washed

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bis brains, a loss, of which the volume before us furnishes so many striking indications. He does not forget, however, though“ dipped in Lethe's lake," to shew very minutely huw to draw a squarc: he then adds “ Here we have one of the most difñcult operations in mathematics [drawing hyperbolas, or parabolas, or finding the fluents to elliptic transcendentals, we suppose, is nothing to it]; it requires the utmost nicety to describe this figure, which is the parent, or the proof of at least half the problems in use :" Again, “A square, or its derivative, the parallelogram (vulgarly termed the oblong square), is either the basis, or is connected with almost every thing in use among us :"--a boiled plum-pudding, for example, between which and a square there is a remarkably close connection. Capt. Williamson, after exhibiting a few more

a few more " problems," such, as that “ Parallellograms of equa! base and altitude are equal to each other,”. &c. proceeds to treat of ellipses; and soon convinces us that he does not know the difference between an ellipse and an oval, though he gives a rule by which a dextrous handler of a pair of compasses may

“ describe an ellipsis of a true egg form.Then he “ introduces 26 axioms to the student's notice ;" from which it is obvious that this simplifying mathematician knows no more of the difference between an axion and a proposition susceptible of demonstration, than of that between a problem and a theorem: among his self-evident truths, he classes many such as the following: Angles that are in the same segment of a circle must be equal to each other." “ Every cone is a third part of a cylinder, having the same base and equal altitude." 6 Cones and cylinders being upon equal bases, are to one another as their altitudes.” Should the valiant Captain ever favour the world with a treatise on Astronomy, we would recommend him to assume as axioms, that the sun is a hundred millions of miles from the earth, that the squares of the periodic times of the planets are as the cubes of their distances from the central body, and that the force of attraction varies inversely as the squares of the distances from such body : which would amazingly simplify that interesting science.

Our author's treatise on surveying we do not profess to understand : for his directions are very obscure, and the illustrative etchings are execrably bad and incorrect. We cannot help observing, however, that he is rather un philosophically enraged against a brother pioneer among the thickets and furze bushes of science, a Mr. William Davis, of whom we know no crime or folly except that he has been adventurous enough to dive under the same pons asinorum, where we fancied we spied Captain Williamson bathing a short time ago.

Toward the end of his volume, our simplifier of mathematics gives directions for preparing colours, &c. telling us, for instance, that " white is a body colour, generally made of white lead, which turns ultimately to a dirty black.** In an appendix to a new edition, we think he might enrich the mathematical sciences, by giving a lecture upon blacking boots, and cutting out pantaloons according to the equidistant ordinate method. Then indeed his performance would " sufficiently display its utility and importance, especially among those who are born gentlemen," and " mean to follow up the study to the fountain head."

But we must dwell no longer on such trash. We blame not the Captain for his ignorance ; in itself it would be an object of compassion, and especially if connected with docility and modesty ; but the arrogant airs and pretensions to author. ship of an ignorant man, are just objects of condemnation. To have expressed our opinion less distinctly would have been a breach of our public duty, and a departure from the maxim of the excellent Judge Hale; “ When I find myself inclined,” says he, to pity a criminal, let me remember that there is likewise a pity due to the country:

Art. IX. Fragments in Prose and Verse : by a young Lady, lately de

ceased. With some Account of her Life and Character, by the Author of “ Sermons on the Doctrines and Duties of Christianity.” Second

Edition. 8vo. pp. 220. Price 6s. Cruttwell and Co. Hatchard, 1808. BEFORE we had time to notice this very interesting little

work, the first edition was sold off; and those who have had the pleasure of perusing it, will be at no loss to account for the earliness and extent of the demand, or to decide whether its immediate success may be reckoned on as the pledge of its extensive circulation and celebrity. It describes a character which few will be able to contemplate without the most tender and salutary emotions ;--a character of juvenile and female loveliness, animated with the most amiable sensibilities, adorned with the richest accomplishments, ennobled by a signal success in literary and scientific pursuits, sanctified by a zealous attachment to the cause of virtue and piety, endeared by adversity and languishing illness, and finally invested with the perfection of beauty and brightness as it is caught up from the earth to a premature inmortality. Hopeless must be the condition of that heart; in which such an object can fail to excite a higher reverence for female worth, a pungent sense of inferiority and defect, and a solemn resolve, at least, to withdraw' every faculty from dissipation and indolence, and stimulate it to the most active prosecution of the most worthy purposes. Indeed we have seldom met with a publication, of which the indirect influence seemed likely to be so effectual and beneficent;, and we shall be happy if our recommendation should avail to extend the sphere of that probable influence tu every school and juvenile library iv the kingdom.

An excess of delicacy, we think, has induced the fair editor to designate her amiable friend by the initial only of a name which should rank with the Agnesis and the Carters. For this little breach of duty to the reputation of her sex, it would be an appropriate punishment to disclose her own riame, and those of several respectable friends, who are also distinguished in the course of the publication by single letters. We shall content ourselves with stating, that the name of the lamented author of these fragments was Elizabeth Smith. She was born of opulent parents, December, 1776; and her family resided, for a considerable time, at the beautiful seat, called Piercefield. Her father was engaged in a banking concern, and shared in the misfortune which befel many establishments of that nature, at the commencement of the war in 1793. He then entered the army ; and his daughter, after enjoying the instructions of Mrs. Bowdler, at Bath, accompanied her parents with the regiment to Ireland. The family afterwards moved to Conway, and other stations, which it is unnecessary

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