day in future, or in esse, as the lawyers say-become the humble instrument to instruct my and his fellow citizens in the "meaning of words" and the "application of principles." Speaking of my younger days, I can remember when I put on my first pair of breeches, and I remember I thought my father had made a man of me by the act. But "Warren's Blacking,"-I had really lost sight of that, when thinking about Hartford Convention-men -Bull's Consuls-pattern-card gentry-British agents-and my own breeches!! I hope that I shall not fly off again, but there are some "natural associations of ideas" that " puzzle the will," and require more discipline than I aspire to, to keep one's pen in its course. Now, here a dissertation on the propriety of giving utterance to a man's thoughts just as they occur to him, might be seasonably introduced-but I'll leave it for another opportunity.-It cannot but be a matter of knowledge to all the candid and intelligent subscribers to my Register-that I am happy to say are in general pretty punctual as the "times go"-otherwise I could not get along-since "what is often used must be often greased" as poor Richard says I say it must be a thing notorious to all that Warren has a competitor in the market-two Richards in the field," as my worthy friend the constitution-expounding and Shakespeare-quoting senior editor of the Richmond Inquirer would say. Messers Day and Martin are also venders of blacking, competing thereby in the market with Warren. But I shall not pretend to indicate the preference that my mind induces me to lean to, for indeed I have none about the matter. "Measures and not men" has always been the "pole-star" that guides my editorial career. I detest the mumbo-jumbo of man-worship that is only fit for the enslaved mind of a legitimate. I have often said, with regard to the Presidential question, about the great men who are now in the public eye for the most dignified position in the people's gift, that it is of less importance to me than a ray of moonshine when I am asleep, which succeeds, and I may say as much of the conflicting and contending claims of the two rivals whose wares now struggle which can outvie the other in the market. Each of the candidates have polished many a boot by means of their Blacking, and the nation's reputation demands that they should be treated decently. The wishes of the people in many of the states is far from being settled for or against any particular individual. One may every where, especially in the middle states, meet with five persons, (all "democrats" or all "federalists,") and find as many various preferences for the supremacy! But, lately in an oyster cellar, I accidentally fell in with seven dandys from New York, very finished dressers, all favourable to large cravats and polished boots, with gilt chains, and they were all, to a man, in favour of Warren.-To conclude-it is probable that as editor of the Register I shall not take any part in favour of this man against that, for manufacturer of Blacking. But I am opposed to

any caucus, which would multiply divisions among the people, and not unite them in any one sentiment. Some may have been working behind the scenes, BUT THE PEOPLE HAVE NOT ACTED ON THE SUBJECT. To them I leave it, because it is their business, and they know how to black for themselves (without any of the ifs, buts, and ands of my friends the Editors of the National Intelligencer, who thereby often put construction at defiance.)-I shall resume the subject on a future occasion, when I shall treat it more exactly than I find I done in the above desultory and hasty suggestions, which I merely place on record for future reference.

For the Port Folio.

ON THE STUDY OF MATHEMATICS.

LETTER TO A CLERGYMAN IN PHILADELPHIA.

SIR,

Some days ago you told me that the young ladies at a certain school were studying the elements of geometry from a popular treatise of Navigation, compiled by one of our most eminent mathematicians. From the interest which I have always taken in the education of youth, I am inclined to communicate to you my sentiments on such books of geometry, as seem best adapted to the use of the higher schools in this country. Good, concise, elementary treatises of Algebra and Geometry, for the use of schools, are much wanted in the United States. The proper object of geometry is the development of the abstract properties and relations of space. In this science it cannot be expected that females will make much proficiency. Nor ought geometrical knowledge to be considered as a necessary object of their pursuit. By the Grecian philosophers in general, mathematical studies were regarded as an essential part of a liberal education, and as the best model and exercise for the judgment of youth. Pythagoras, to whom the discovery of the solar system has been erroneously ascribed, instructed his pupils in mathematics; and Plato, one of the most learned men of antiquity, made the previous knowledge of geometry a condition of admission into his seminary. Geometry has been recommended by Mr. Locke, and other eminent authors, for its tendency to strengthen the reasoning faculties. The main object of this branch of academical education is not so much to make geometricians, as to initiate youth in the art of reasoning in a clear, correct, and methodical manner. From the time of the ancient Greeks to the present day this kind of instruction has been found most successful in practice. No study has been proposed, by men of learning, as preferable for youth: none has been attempt

ed with greater efficacy in the attainment of the object. I will quote one authority, which claims the respect and reverence of all men of literature. Quinctilian says, "In geometria partem fatentur esse utilem teneris ætatibus; agitari namque animos, atque acui ingenia, et celeritatem percipiendi venire inde, concedunt:"-which may be thus translated,-The study of geometry is useful to youth, for it excites and exercises their mind, and sharpens their faculties, and thereby gives quickness of percep tion. For arguments in favour of the propriety of mathematical studies, as mental discipline, in the higher places of education, I refer to the works of Reid, Stewart, and other writers on metaphysics.

Bonnycastle's Geometry, in 8vo, is probably the best work of the kind, when we consider it in the double sense of a complete introduction to mathematics, and an excellent system of practical logic. The latter quality was a principal object of the author's attention when he composed his book. Our publishers have an interest in the sale of other books of the same kind, and would not be willing to reprint it, lest it should retard the sale of those which are now in use. Some propositions, which are not absolutely necessary in a course of mathematics, might be omitted by students both in schools and colleges.

The treatises of geometry of Bezout, Bossut, and of the professors in the college of St. Cyr, in Paris, are good introductions to mathematics; but they are not good systems of practical logic, which I deem an essential quality in a treatise of geometry designed for youth. There are many larger works of the kind than these, both in French and English; but they are not fit for young ladies, who cannot devote much time to the study of abstract science without the neglect of other acquirements, which are considered of primary importance.

Concise systems of geometry, in connection with other mathematical subjects, may be found in several works, as Ingram's Mensuration, (a recent book, and unknown here,) Young's Syllabus of a course of Lectures on Natural Philosophy, Young's Lectures on Natural Philosophy, vol. II, and Young's Illustrations of La Place's Celestial Mechanics, and in Mackay's Navigation. All these, with some additions, and extensions of some of the short demonstrations of Young and Ingram, would be fit for the use of youth, and might be transcribed without much loss of time. The expense of preparing and printing any of these three tracts would be little. The authors are excellent mathematicians, and have been engaged in public or private education. I would recommend a large collection of useful problems to follow the elements.*

Ingram's Mensuration contains 35 theorems, with many corol

* See Keith's Euclid, Pasley's Practical Geometry, Landman's Practical Geometry.

laries, in plane geometry. These are all the propositions which he uses in the theory of Plane Trigonometry, Mensuration of Superficies and Solids, Surveying, Gauging, &c. With the addition of a few elementary propositions in planes and solids this short treatise of geometry would be a sufficient introduction to all the branches of mixed mathematics, as Mechanics, Optics, &c.

Each of the three books of Dr. Young contains about 60 propositions in plane and solid geometry, which are all that he employs in his demonstrations of the mathematical principles of Mechanics, Hydrostatics, Optics, and Astronomy. To these a few theorems might be added, either on account of their elegance, or convenient application in certain geometrical subjects of the higher kind.

Mackay's Navigation contains 19 theorems in plane geometry, which are sufficient for the theory of Plane Trigonometry and Navigation. It would be necessary to add ten or more theorems, to render the tract fit for other purposes. Mackay's demonstrations are fuller than those of Young and Ingram, and are therefore easier to beginners. I should prefer Mackay's geometry to the other two tracts if it were more extensive.

The doctrine of proportion is not included in any of those tracts. Young and Ingram give the principal properties of proportion in the algebraical part of their books. These properties must be prefixed to the geometry, because they are required in the demonstrations of some propositions, and in all parts of mixed mathematics.

Though any of the above tracts on geometry may suffice for the use of schools, yet I should prefer a larger book, like Bonnycastle's, which would answer the double purpose of a system of practical logic, and of a complete introduction to all the synthetical parts of mathematics. The recent and improved editions of Euclid's Elements of Geometry by Playfair, Ingram, and Keith, are excellent systems of practical logic, and good introductions to mathematics in general; but certain parts of Euclid's Geometry are more difficult to learners than some of the latest and best treatises of geometry which have been published in Europe. Of the recent treatises of geometry, Cresswell's is undoubtedly the most systematical, and is founded upon the most legitimate principles. But the very circumstance of the accuracy of its fundamental principles, and the metaphysical nature of a few of them, render the first 39 pages somewhat intricate, and not so intelligible to young students as might be desired. But after these have been established, and some of the most elementary propositions demonstrated, the rest of the volume is clear and satisfactory. This treatise constitutes a complete course of elementary geometry; but it is too large and too expensive to be adopted in this

country.

There is an excellent treatise of plane geometry by professor Leslie of Edinburgh; but the geometry of planes and solids is not

to be published soon, so that the work is not complete. We do not, however, want such extensive books as the last two in our schools and colleges, where the pupils are young, and the more useful and practical branches of literature and science are generally taught. The present state and circumstances of America seem to exclude, with propriety, from our public seminaries the cultivation of recondite and abstract studies. Hence perhaps it is that we are inferior to some other nations in profound and abstruse learning; while we rival, or even surpass, them in the more useful and popular kinds of knowledge. Cui Bono? is the question, and the principle which directs our conduct on most occasions. It is certainly an excellent rule in all cases of profit and temporal interest; but in all other respects it is pernicious, and checks the progress and mental improvement of the human species. It is, in general, a selfish maxim, and militates against benevolence, morality, and religion.

To Geometry should be annexed the common elements of Plane Trigonometry, with its application to practice. Trigonometry is a branch of geometry, and is applicable to a variety of measurements, and mathematical investigations. As much of the theory and practice of Plane Trigonometry as can be taught in schools may be extracted from several books, as Hutton's or Davidson's Mathematics, Ingram's Mensuration, the larger treatises of Trigonometry by Keith, Bonnycastle, and Gregory. A neat and concise separate treatise is wanted in schools. The tracts in certain books cannot be recommended to learners, for some of them consist of theory alone, others contain only practical rules and numerical examples, and others are destitute of simplicity, perspicuity, and accuracy in the demonstrations of the propositions. The deficiency of good elemementary books in the higher places of education, indicates the neglect of certain studies, or the superficial manner in which they have been generally prosecuted.

In my account of certain books of geometry I have forgotten to mention Legendre's; part of which has been translated from the French for the use of the University of Cambridge, in Massachusetts. In the method of demonstration it has a greater resemblance to Euclid's Elements than any one of the kind which has been published on the continent of Europe. But it is too large for the use of schools, and is exceptionable, both in its arrangement and execution. The problems and theorems are detached, though they have a mutual connection with, and dependence on one another. To evade the difficulties which all authors have encountered in laying the foundation of the science of geometry, M. Legendre has made certain gratuitous assumptions, which the ancient geometricians would not have granted. He assumes first principles as true which are not evident, and need demonstration; and he demonstrates, indirectly, the equality of right angles, though this property is an immediate and obvious consequence from two