accuracy. Since that time, Mr. Nicholson has procured the volume to which this specimen of early skill is attached, and there can be little doubt, that, hereafter, this drawing will greatly enhance its value among collectors of curiosities, antiquaries, and connoisseurs. The writer of this memoir has been favoured with a sight of this curious specimen of ingenuity, and thinks it well worthy of the preservation it has experienced. In nore modern editions of Euclid, the figures cut on wood are embodied in the same page that contains the letter-press, so that their fate cannot be separated, but in the translation by Cunn, all the figures were on distinct plates.

About the age of twelve, Mr. Nicholson was taken from school, to assist his father in his business; but this was an occupation to which he felt no attachment. He discovered nothing in it that coincided with his genius, so that it was viewed with indifference, if not with aversion. This did not escape the observation of his father, who, instead of compelling him to submit to an employment which he disapproved, at the end of one year bound him an apprentice to a cabinetmaker, in the neighbouring village of Linton, this being an occupation more congenial with his taste. In Scotland, three years are as usually the period of an apprenticeship, as seven are in England, but, for reasons we have not heard, young Nicholson was indentured for four years.

During his apprenticeship, he studied Algebra with unremitting assiduity, from Maclaurin, and employed every spare moment in improving his mind. In the summer mornings, from daylight until six, when he went to work, and also in the evenings, when the business of the day was over, he practised drawing from" Salmon's London Art of Building," and by occasionally measuring heights and distances in the fields, he became familiar with trigonometry, as applicable to real business, which, in all his exertions, he invariably kept in view.

In addition to these prosecutions of his studies in theory, every day furnished him with an opportunity, while working with his hands, of reducing his speculations to practice. This has always been considered as of great advantage to men of science. There is a species of knowledge conveyed to

the mind by the tools, through the fingers, that hypothesis never can impart.

It is not indeed often that men of science labour with their hands, but when this happens to be the case, in all future inquiries their ideas are more accurate, and there is a greater probability that they will become inventors. So far as observation can extend, it is an unquestionable fact, that the greatest inventors in me chanics have, at one time or other, laboured with their hands. This, to Mr. Nicholson, has been an advantage, that has more than compensated for the scantiness of his education. He was not ignorant of its value, and he has turned it to good account, for there are few men to whose genius the art of building is more indebted, than to the subject of this memoir.

On the termination of his apprenticeship, Mr. Nicholson repaired to Edinburgh, in the character of a journeyman, where, while working with his hands, he prosecuted his studies with unabating vigour, extending his knowledge of mathematics more generally, from "Ward's Introduction." Having, in some books which fell into his hands, found several references to the fluxionary calculus, a strong desire was excited in his mind, to obtain an additional acquaintance with this branch of science. Full of this desire, he went to the shop of a Mr. Bell, a noted bookseller in Parliament-square, and after examining the titles, prefaces, and contents of several works, he fixed on the Introduction to Emerson's Fluxions. But here, unfortunately, a new obstacle presented itself. His wages being scanty and his resources low, the price of the book amounted to more money than he could spare. With this fact Mr. Bell was soon made acquainted, when, with a generosity that deserves to be handed to posterity, on seeing a young man eager in the pursuit of knowledge, but retarded through pecuniary deficiencies, he resolved to give him encouragement, by directing him to take the book, although an entire stranger, and pay for it when more convenient. This was accordingly done, and Mr. Nicholson now mentions the circumstance with feelings of gratitude.

Although Emerson's treatise on fluxions has been generally considered as peculiarly difficult, on this branch

of analytical science, it was not long before Mr. Nicholson became master of its first principles; and the pleasure which resulted from their application to many sublime problems, at once rewarded his industry and stimulated him to renewed exertions. In all his advances, he saw difficulties in his way, but he encountered them with courage, and surmounted them with such success, that, to whatever part of the work he turned his attention, new conquests crowned his exertions.

At the age of twenty, Mr. Nicholson first made his appearance in London, where, in addition to his regular labour, he still devoted his leisure hours to the study of mathematical science. After some time, however, he discontinued his pursuit of analytical subjects, confining his researches to Geometry alone, as being more congenial with his views in life. He was attracted to the British metropolis by an uncle, named Hastie, who then carried on an extensive business as a builder. The patronage, however, which he expected from this relative, only served to delude his hopes. The uncle was willing to employ him as a working mechanic, and to receive him as an assistant, but as a mathematician he gave him every discouragement. But, notwithstanding these partial oppositions, Mr. Nicholson still pursued his mathematical studies, and such was his knowledge in the geometrical construction of carpentry and joinery, that the fame of his acquirements soon spread among his fellow-workmen, who, anxious to improve themselves, solicited to become his pupils. At this time he was with a Mr. Wyat, in Berwick-street, where be announced his intention of delivering some lectures on those branches of science which he had made his particular study. The number that first made their application was about ten. They, however, frankly declared that they could not afford to give any thing by way of entrance, but expressed their wish to pay for his lectures whatever they could spare from their wages.

Mr. Nicholson made a beginning; the fame of his teaching soon brought an influx of pupils; and his success being more than equal to his expecta tions, the plane was soon dropped. Being thus raised above a common journeyman, he obtained more leisure

than he had been accustomed to enjoy. This he devoted to the invention and arrangement of materials for a new and original treatise, in quarto, on carpentry and joinery, which was published in 1792, under the title of "The Carpenter's New Guide." Of this work the plates were engraven by himself. In addition to the improvements in various kinds of groins which are to be found in this production, he introduced the construction of spherical niches, both upon straight and circular planes. Before this vo lume made its appearance, no work on the practical parts of building had shewn, generally, how the sections and coverings of solids were obtainable from their definitions. The principles went only to find the section of a right cylinder perpendicular to a given plane, parallel to its axis, and to the covering of such a cylinder, and that of the frustum of a right cone. Some attempts had, indeed, been previously made to obtain the same result, but they proved on trial to be erroneous and abortive; and, as they had not succeeded with the plane sections and coverings of simple solids, they could scarcely be expected to give rules for the construction of the intersection of any two surfaces or curves of double curvature, of which the variety is almost infinite.

Mr. Nicholson, in this work, besides his own inventions, has both simplified and generalized the old methods, which before were only applicable to particular circumstances. His rules for finding the section of a prism, cylinder, or cylindroid, through any three given points, whether in or out of the body to be cut, enable workmen to execute hand-rails without difficulty, and from the least quantity of stuff. His principles on the intersection of solids extend to groins and arches of almost every description. The covering of polygonal and circular domes had been exhibited in several prior publications on carpentry and building, but no author had ever shewn how these coverings were to be formed, without the actual plan, the drawing of which might be attended with some inconvenience, on account of the great space it required; neither had any method for covering domes upon an elliptic plan been given. "The Carpenter's New Guide" has passed through nine editions. It is still in as

much request as ever, and, though his first publication, may be ranked among his most useful works.

"The Carpenter's New Guide" was immediately followed by "The Student's Instructor," in octavo, which has passed through several editions. This was succeeded by "The Joiner's Assistant," in quarto, a work abounding with useful information, both to those who are employed to make working drawings, and to such as are engaged in the superintendence of buildings. In this work, several of the articles which were but slightly touched in the "Carpenter's New Guide," are more fully explained and extended. Besides the designs of roofs actually executed, which it contains, it was the first work that treated on the methods of forming the joints, and of hinging and hanging doors and shutters. The utility of The Joiner's Assistant," and the high estimation in which it is held, may be inferred from its having passed through five editions.

In 1799, Mr. Nicholson published, in three volumes octavo, a work entitled, "The Principles of Architecture." Prior to the appearance of this publication, all the works that had been known on this subject, were greatly deficient in mathematical principles, which this production of our author happily supplied. It also contains a system of practical geometry, including many new problems of great utility to builders. Mr. Nicholson, in this work, was the first who noticed that Grecian mouldings are conic sections; and that the volutes of the Ionic capital ought to be composed of logarithmic spirals, for which he gave rules for the describing of arches, mouldings, and spirals, of so general a nature, as to be applicable in all cases. It is also understood, that he was the first to shew how to describe any number of revolutions, between any two given points in a given radius, in which the centre of the spiral was given. By these means he generalized the principles of De l'Orme and Goldman, whose methods were limited to three revolutions, and the eye of each of their volutes to one-eighth part of the whole height.

But, above all the methods which have hitherto been invented for describing volutes, his application of the logarithmic spiral to this purpose, approximates most nearly to perfection.

He has not only shewn how points in the curves of volutes are to be found by means of proportional compasses, and by calculation, but also the most easy and practical methods of describing them with compasses, from the most minute scale, to that of the greatest magnitude. His method of forming the logarithmic spiral with compasses is so far perfect, that every two adjacent arcs not only join each other, but have the same tangent at the point of junction; that all the points of junction are in the true curve of the proposed spiral; and, lastly, that the centres of the arcs are in the curve of another proportional or logarithmic spiral, which is the evolute of the curve of the spiral required. These methods were first published in Rees's Cyclopedia, in the Edinburgh Encyclopedia, and recently in the "Builder's Director."

"The Principles of Architecture" was the first book in this country, in which the projection of planes and solids, and the orthographical forms of the shadows of objects, were clearly ascertained from principles purely geometrical. These subjects were treated of, by Mr. Nicholson, without the least knowledge of any publication from which he received the slightest hint, although, nearly about the same time that his work appeared in England, a treatise somewhat similar was published in France by M. Monge, but the methods pursued by these two authors are widely different. Another work on the projection of shadows, translated from the French, has also lately appeared; but the author has not so explained the subject as to be clearly understood, nor are the delineations of the shadow intelligibly defined.

Mr. N. has not only treated of the shadows of objects, but he has given a most luminous view of projections in general. He has shewn how every object may be projected by means of an intersecting line, which is not only more simple and uniform, but more useful, than the French method by means of traces. This general method was first published in Rees's Cyclopedia, since which, it has got into general practice, and its principles have appeared in several recent publications; but, we understand, of late he has greatly improved the principles and extended the application of

their extensive circulation, a minute analysis of their particular merits is rendered almost unnecessary. Their worth was acknowledged on their first appearance, in the reviews and periodical journals of the day; and particularly in the Monthly Review for December 1820, there is a perspicuous and luminous examination of his analytical tracts.

66

In the month of February 1822, Mr. Nicholson published a Popular Course of Mathematics," consisting of Algebra, Euclid's Elements, Differential Calculus, Fluxions, Conic Sections, Doctrine of Curves, Trigonometry, Mensuration, Land- Surveying, Gauging, Perspective, Dialing, Spherics, Mechanics, Dynamics, Hydrostatics, Optics, Physics, and Astronomy, with tables of Logarithms, and numerous questions for exercise, illustrated by several hundred engravings.

He also furnished the materials for the higher branches of a practical system of Algebra, lately published by Baldwin and Co. In these departments of abstruse science, Mr. Nicholson appears to be quite at home; and the works enumerated in this memoir, will serve to shew what may be accomplished by industry and unwearied perseverance.

To connect science with industry, and to improve their union, has been the great object of this celebrated architect, and both by the lectures he has delivered, the lessons of instruction he has given, and the volumes he has published, these important objects have been essentially promoted. In our present day, lectures are delivered, and institutions are established, in many cities and large towns; from which the rising generations of genius may derive incalculable advantages. Of such assistants Mr. Nicholson, in early life, knew nothing. Like Columbus, he had to navigate | the ocean for himself, and, like that celebrated adventurer, his laborious researches have immortalized his

name.

If such institutions as now facilitate the acquirement of science, had existed in his early days, his advancement would, in all probability, have been still much greater than it now appears. But we must not forget, that in such a case, Mr. Nicholson would not have been what he now is,

the child of genius, indebted chiefly to application for that renown by which his elevation is distinguished.

On reviewing this memoir, it will be seen, that, as an individual, Mr. Nicholson has done much, and from the numerous editions through which his works have passed, that the public are not insensible to his merit. The advantage also to be derived from his publications, is as fully verified by the constant demand in which they are held, as by the legal contention, still undecided, respecting the copy-right of one of his valuable works.

To

The productions of this author will present to posterity a lasting monument of what may be accomplished by the efforts of original talents, under the most disadvantageous circumstances. supineness and imbecility, mountains may appear formidable, but instinctive activity will always find means, either to scale their acclivities, or to wind round their base. The honourable niche which his name has obtained in the temple of Fame, will operate as a powerful incentive to future aspirants, while the path that marks his career, by inviting them to imitation, will furnish a presage and promise of success.

Mr. Nicholson still resides in London, and, although sixty years of age, his mental faculties remain unimpaired, and his bodily energies shew but little of the effects of time. It is not, therefore, unreasonable for the scientific public to expect something more from his pen, nor at all improbable that such an expectation will be gratified.

For many leading facts in the preceding article, we acknowledge ourselves indebted to the biographical sketch of Mr. Nicholson, written by Mr. William Playfair, brother to the late celebrated professor of that name; the other parts have been derived from equally authentic sources.

THE BIBLE.

A NATION must be truly blessed if it were governed by no other laws than those of this blessed book; it is so complete a system, that nothing can be added to it, or taken from it; it contains every thing needful to be known or done; it affords a copy for a king, and a rule for a subject; it gives instruction and counsel to a senate, authority and direction to a magistrate;