MONTHLY CATALOGUE, For FEBRUARY, 1799. MATHEMATICS. Art. 17. A Treatise on Spherical Geometry, containing its fundamental Properties; the Doctrine of its Loci; the Maxima and Minima of Spherical Lines and Areas: with an Application of these Elements to a Variety of Problems. By John Howard. 8vo. pp. 170. 6s. Boards. Longman. 1798. THE object of this treatise is to advance the doctrine of the sphere, which has made but small progress since the time of the antient Geometricians.-The distribution of the work is as follows: Book I. contains the fundamental principles of spherical angles and triangles, including not only those composed of great circles of the sphere; but, in general, such as are composed of circles of less radii. A subject that I do not know has before been attempted. Book II. contains the fundamental principles of spherical qua. drangles, with some added properties of spherical quadrangles, and determines the measurement of solid angles. Book III. contains a great many curious properties of straight lines, and circles drawn from given points within and without the surface of the sphere, and terminating in the circumference of given spherical circles; also, some curious LOCI of spherical angles and triangles, and of lines drawn to spherical and cylindrical surfaces, analogous to some of the plane LOCI of Apollonius. And here the reader will find many beautiful analogies between the properties of lines drawn to meet in the surface of the sphere, and of those drawn to meet in the circle in plano. Book IV. includes the doctrine of spherical maxima and minima ; and here, I believe, will be found a variety of new and useful pro perties relative to triangles, polygons, &c. not confined to figures composed of great circles of the sphere; but, in general, extending to such as are composed of circles of less radii, including the remarkable problem which determines the curve, that under a given perimeter, includes the greatest spherical surface, as also an extensive theorem of solid maxima and minima. Book V. (or I. of the application) contains the construction of spherical problems deduced from the foregoing principles; many of which will, I trust, be found useful in astronomical researches; and here is included, a series of curious problems, analogous to those which VIETA has constructed in plano, and that FERMAT has extended to planes and spheres; beginning with determining a circle on the sphere that shall pass through two given points, and touch a circle given in magnitude and position, and ending with finding a circle on the sphere that shall touch three other circles given in magnitude and position. Book VI. (or II. of the application) contains a variety of prob lems relating to triangles,' This publication deserves the notice of Philomaths. HISTORY, HISTORY, ANTIQUITIES, &c. Art. 18. Specimens and Parts; containing a History of the County of Kent, and a Dissertation on the Laws, from the Reign of Edward the Confessor to Edward the First; of a Topographical, Commercial, Civil, and Nautical History of South Britain, with its gradual and comparative Progress in Trade, Arts, Population, and Shipping, from authentic Documents. By Samuel Henshall, Clerk, M.A. Fellow of Brazen-Nose College, Oxford. 4to. pp. 175. Ios. 6d. Boards. Faulder. 1798. This ample title-page is followed by a prospectus, from which we learn that it is Mr. H.'s intention to continue a similar investigation in every county, up to the present reign; and that his whole design will be completed in ten fasciculi, of the same size and plan as that before us. The undertaking is arduous, in proportion to the difficulty of its execution, the extent of the subjects, and their importance in forming a genuine history of the early reigns. This specimen gives a map of Kent from Domesday-book, and a new arrangement of its contents in summary tables, which are digested with diligence and perspicuity. In describing the early feudal tenures, and ascertaining the rank and privileges of the tenants, an uncommon acquaintance with the Norman law, and its influence in England during the first centuries, after the conquest, is displayed in almost every page. We refer our readers to the specimen itself, which would suffer by an analysis, cordially wishing that the attempt may meet with its merited encouragement and success. Art. 19. Miscellaneous Antiquities (in Continuation of the Bibliotheca Topographica Britannica). No. 6. containing the History and Antiquities of Twickenham, being the First Part of Parochial Collec tions for the County of Middlesex, begun in 1780. By Edward Ironside, Esq. 4to. pp. 156. 10s. 6d. sewed. Nichols. 1797. On this specimen of the parochial survey of the county of Middle. sex, and as the sixth No. of the continuation of Mr. Nichols's additional antiquities, we would beg to hazard one or two observations. Are extracts of the mere names of obscure individuals from the register, and epitaphs given verbatim, of sufficient importance to any class of readers, to occupy fifty-one pages out of 156, largely and loosely printed? Are a comparative statement of the price of provisions from 1730 to 1780, and a list of principal inhabitants in 1739 relating to a popu lous village near the capital, worthy of forming a part of a general county history? Our opinion is in the negative;-and we hoped to have found some little relief in the description of a place which is rendered classical by the long residence of Pope and Walpole, and highly embellished by the resort of the opulent and the polished: but we have discovered no valuable supplement to the judicious account given by Mr. Lysons in his Environs of London (vol. iii. p. 538), which Mr. Ironside has very freely adopted, as far as the facts. The memoirs of the learned Viear, II George George Costard, are the most interesting: but his portrait, and the other plates, are positively below criticism; especially at a time like the present, when able artists abound, whose employment is very limited. Art. 20. The History and Antiquities of Tewkesbury. By W. Dyde, 2d Edition, with considerable Additions and Corrections. 8vo. pp. 213. 6s. Boards. Printed at Tewkesbury, by the Editor. London, Wilkie. 1798.. The first edition of this work has been already noticed with approbation in our annals*. It now appears in an enlarged and improved form, and may be considered as a pretty performance, at once instructive and entertaining. It is accompanied with a View of the Town, and some other additional engravings, very well executed. IRELAND. Art. 21. Necessity of an Incorporate Union between Great Britain and Ireland, proved from the Situation of both Kingdoms. With a Sketch of the Principles on which it ought to be formed. 8vo. pp. 132. 2s. 6d. Wright. 1799. Not one of the many tracts which we have seen, in favour of the proposed Union between Great Britain and Ireland, has taken a more comprehensive view of the subject than that which is now before us. The author supposes that the first idea, that an union was to take place between Great Britain and Ireland, originated with the public; whence he infers a general conviction, that some arrangement must be formed between the countries, to ensure their joint prosperity and mutual good understanding.' The manner in which the idea originated does not affect its merits: but our belief is, that it first came to the public in the shape of a rumour that such a plan was in the contemplation of ministry, independently of any public or general consideration respecting its necessity. 6 The points which the author attempts to establish are, first, 'that the present system is insufficient to promote the prosperity and ensure the tranquillity of the empire;' and 2dly, that an incorporating union, forming the two nations into one kingdom, subject to the same laws, and governed by the same legislature, is the only means to accomplish these salutary effects.' After a short but clear state. ment of the situation of Ireland previously to 1782, he observes that, By the final recognition of her legislative independence, Ireland then took a new station, in respect to this country, from that in which she had previously stood. Two consequences necessarily folkowed, from her Parliament having gained the exclusive right to regulate her national interests; both materially affecting her connection with Great Britain. First, it left no common bond of union between the kingdoms, except what arose from their acknowledgment of a common sovereign. Secondly, it reduced their commercial intercourse to a mere matter of convention. It left each at liberty, unless where bound by positive compact, to consider the other as a foreign nation; to disregard its maritime regulations; to exclude its * See Rev. for May 1791, N. S. p. 111. commodities commodities from the home market, or even to give a decided preference to those of a rival staple.' Sister kingdoms, being portions of the same empire, he insists, must admit of some common supremacy to regulate their mutual intercourse, and to improve and apply their physical strength to their joint advantage.' If the present system supplies such an authority, he adds, it must be, that a principle of empire sufficient to regulate the conduct of these islands to their mutual advantage is created by the unity of the executive government, or that it exists somewhere else. After having shewn that the prerogatives of the crown do not furnish power adequate to this purpose, he demands,' where else, then, can this imperial principle be said to exist? Surely not in two legislatures, by their constitution wholly distinct and independ-ent; possessing neither means nor forms, nor even a painted chamber to communicate or hold a conference with each other.' It must be obvious that a principle, sufficiently powerful to direct the affairs of Ireland according to the views of the executive government of this country, has existed, notwithstanding the recent instance of the legislature of that kingdom rejecting the proposed plan of an union; which is only to be regarded as an exception to a rule, otherwise almost without exception. The writer allows that the Irish Parliament, notwithstanding the giddy wishes of the people, have wisely avoided all subjects of contest with this country, and prudently submitted to such regulations as her laws prescribe to the empire: but (adds he) a new malady, dangerous to the connection of the countries, has arisen out of this very practice, by which it has been hitherto preserved. Artful, innovating men, have ascribed this acquiescence to servile and shameless corruption. They have painted the Parliament of Ireland as more attentive to the nod of a British Minister, than to the interests or the will of that people by whom they are chosen.' The author asserts, (we hope, erroneously,) that many well-affected Irishmen are of opinion that a separation of the two countries would produce no ill consequences to Ireland. Many of the probable evils, which Ireland would have to sustain in consequence of a separation, are pointed out, and by no means exaggerated :—indeed, we are of opinion that it is scarcely possible to exaggerate the description of the mischiefs which a separation would bring on both countries; and that it would be to each an event more fatal than any which has befallen either, since the Norman conquest. As a separate country, the au thor justly remarks, the very limited strength of Ireland must keep her in a state of relative insignificance, when compared with those empires which predominate in Europe.' Diminutive states have neither means nor power to command the tranquillity, or ensure the prosperity of their people. They exist rather by the sufferance and jealousy of more powerful neighbours, than by their own inherent vigour. Many such have been created, and all those which have existed since the time of the Emperor Charles V. have been favoured and protected by the balance of power in Europe. Their destruction was the first consequence of its fall. Those rough republican storms, which which shook little more than leafy and deciduous honours from the great monarchies of Europe, have torn the lesser states from their foundations, and laid them prostrate.' Ireland may share greatness with others, but, by herself, she cannot hope even for that tranquillity which is essential to happiness. The author has happily described the temper and abilities necessary for the examination of a question so important as a scheme of perpetual union: Those who consider an object which extends infinitely beyond our petty space of time upon the earth, should cautiously purge the mind of such little anxieties for aggrandisement as center in ourselves, and must terminate with us. We must disencumber and lighten the understanding of these selfish passions, which cannot flutter above the narrow spot on which they are used to grovel, if we would rise to that degree of elevation from whence, as from the true point of perspective, the mind's eye may wander over the entire plan; survey its proportions; examine its ends; compare its beauty with its use; and contrast its durability with both. To frame or judge of the plans of a statesman, with the wisdom of a statesman, requires a statistical knowledge of the country upon which they are to operate; profound views of human nature; a laborious and patient comparison of all that the wise and the disinterested have accomplished, and all in which they have failed, to assuage the evils and augment the happiness of human life.' Having remarked on the inconveniences of the different kinds of federal union, and on the advantages of an incorporate union, as the only one suited to the present occasion, the writer states the following objections, which are most likely to be urged: 1. That it would destroy the very name of Ireland as a nation. 2. It would annihilate her Government and her independence. 3. It would greatly increase the preponderance of English influence: every place, worth having, would be conferred on Englishmen; the retainers of ministers, peers, or persons otherwise of great English in terest. 4. The number of absentees would be greatly augmented. 5. Dublin, the capital and present seat of the legislature, would be reduced to the state of an inconsiderable village. 6. It would bring that country into partnership as to the debts, as well as the prosperity of England, and her taxes would be increased to an enormous extent." Of these, the 2d and last are perhaps the most important. The establishment of a new government necessarily annihilates the old: the only question worth consideration is, whether the new be preferable to that which it has superseded. Independence, likewise, cannot belong to any separate portion of a state; and this will apply to both countries. The share of political importance which Ireland would enjoy, if she were fairly represented in an united parliament, would probably be more than she at present possesses; and we are willing to believe, with the writer, that the objection built upon the supposition that a narrow principle of rivalship and jealousy must continue to exist between the two countries, although an union should take place,' is void of foundation; and that an united legislature would 1 3 A |