conscience never fails to inflict, a wound which time | ON THE CULTIVATION OF MATHEMATICS DURING cannot assuage, which art cannot cicatrize.*

Veritas odium parit.

THE EIGHTEENTH CENTURY, AND THEIR IN.
FLUENCE UPON THE PROGRESS OF THE HUMAN
MIND DURING THIS PERIOD.

In every age of the history of the Sciences, some,

It may be deemed by those who reflect little, and who are unacquainted with the manner in which scholas tic business is, in general, conducted, that this, as well which are the most rapid in their growth are obser as some of our former strictures are rather too severe.tists and citizens to establish on a firm basis, an instituBut, when they exercise their reason and come to a knowl-ion in which the former may exhibit their specimens and edge of facts, we believe their doubts will waver and derive additional improvement in their art, from the best give way, and a consequent conviction be the result.models of ancient and modern times. Among the artists From the days of the illustrious Quintillian to the present of our city, and who deserve from their intimate acquaintime, men of splendid genius have pointed out in glowing tance with their profession, every encouragement which eloquence, the evil consequences, that must ultimately genius should receive, are Messrs. Jarvis, Dunlap, Walflow from the practice of employing low, iguorant, vicious do, E. Metcalf, and Mr. N. Rogers, miniature painter, and illiterate instructers in the education of our youth &c. &c. &c &c. The three first of these are already To doubt the consequences, would be the height of folly known, and we will venture to say, that Mr. Metcalf, In the scholastic as in all other professions, there are though a young artist, from the excellency of some of his those who deserve the severest censure. In this country portraits which we have seen, will rise to a very exalted as well as in Europe, there are thousands of this cast ;-standing in the estimation of the public. Of Mr. Rogers, and it was, with peculiar pleasure, that we saw the em we predict much; he is possessed of talents which have ployment of such men, noticed by our enlightened gover-drawn the attention of our citizens towards him, and nour, Dewitt Clinton, in his message to the legislature of which place him among the first miniature painters of our this state We hope the subject, will be deeply consider-country.-Relative to his painting, we present the foled by our representatives, and that they will not disap❘lowing very able remarks, written by one of the profes point the hopes and earnest wishes of those who are the sion. The portrait of which he speaks, is that of a lady, friends of literature and science. and was exhibited in the Academy of the Fine Arts Although, our remarks may not be palatable to many "This picture deservedly attracts the attention of every of the profession, yet we are well acquainted with a num-visiter. Its harmony, rotundity, softness, delicacy of her in various parts of our country, who by their respec-pencilling, constitute it one of the best miniatures we tability, talents and acquisitions, reflect honour on their have ever seen in this institution. If not highly coloured. avocation. To arouse the public to a sense of their duty it is a fault on the right side, which will inevitably cor is, in part, the object of the above observations. rect itself by practice. The artist, who commences with Although we have thus freely expressed our opinions a gaudy stile, loses al! knowledge of the delicate tints, in which we are not single, and of the literary and scien-whose harmonies constitute the painting's greatest charm. tific institutions and improvements in our country, yet we hope, that they will not be considered derogatory to the American character. Far be it from us to injure her reputation; we ardently wish to see it extended, aud we are convinced, that nothing will do this more than eminence in literature, which depends in a great measure, on the state and character of our places of learning. This gentleman, we understand, was a pupil of Mr. Notwithstanding our wishes for her greatness, we shall Wood; and public approbation to the works is a proof not with one party enlogize America, ` if undeserving it; that the master's principles were good, and were imparnor with another endeavour to degrade her in the esti-ted with fidelity, to have produced such specimens of mation of other nations. We are no party men, but zeal-talents, so creditable to both.

If, like a skilful musician, you begin low, you can raise your tone, as he his voice, to the pitch required; on the other hand, by dashing into the glare of colour, or din of sound, you may astonish the multitude by your poners, but can never hope to please the ear of harmony or the eye of good taste.

ous advocates for all such measures as may tend to en- We cannot dismiss the miniatures without expressing hance her glory, which she has obtained both by arins, our regret at not finding any productions of Mr Dickiaand the progress he has already made in literature and son or Mr. Brown, whose variety of styles, with the one science. As to statesmen, and military and naval com- before us, would have formed so useful a lesson by analo manders, the pages of our history exhibit numbers that gy We want no old masters in miniature; the aspiring will bear comparison with those of ancient or modern na-artists we now possess would constitute a school in this tions. As to scholars, we cannot indeed vaunt of a sure- department of the art, and though it occupies not the first riority to Europe at present But though Europe surpass walk in the realms of virtue, yet, in an infant institution, us in her catalogue of learned men, we confidently it is the first to arrive at maturity,” assert, that there is in existence no nation which has made so rapid progress in the arts and sciences as America, since she has become an independent nation.-In the art of painting, America stands pre-eminent. She has a West, a Trumbull, a Vandelyne, a Leslie, a Stewart, whose glory, it will be the duty of future historians to record.

Touching the art of painting, we remark with peculiar pleasure, the great exertions that are making by our ar

But closing these remarks- After these observations, we hope we shall not be charged with having written any thing derogatory to the American character or her insti tutions. We repeat it, we think that the inhabitants of our country possess as great and versatile genius, as those of Britain, France or Germany; and it only needs that something be done, to arouse into action the powers of their minds, to produce statesmen, philosophers, orators, poets and artists of the highest excellence.

ved to array themselves in greater brilliance, to nity, remained at first concentrated in the country attract universal attention, to become the ruling which had witnessed their birth; so great was the passion of the time, and to give to the age in which they thus flourish an impulse and a character which exercise a powerful controul over the progress of intelligence. The nature of this control, whether beneficial or baneful, must be determined by examining whether the mind has attached itself to substantial objects, or has been engaged in the pursuit of phantoms.

zeal with which the followers of Descartes attempted to prevent their dissemination. Men know so little how to renounce those notions, however false, with which they have been imbued at the age from which they date the most delightful of their remembrances, that, with but few exceptions, in a whole nation, new opinions are embraced and new facts propagated by the youth alone. Thus, it required The Scholastic Philosophy, originating in a half all that ardour to signalize themselves in the field barbarous age, with ignorant and superstitious of science, which is natural to those who are servmen, who carried into the cultivation of letters the ing their first campaign in it, to introduce into bad taste of that, has been remarked on the monu- France the philosophy of Newton, against an opments they have left us, retarded for a long time position from the ancient universities almost simithe happy influence that was to be exercised upon lar to that which the opinions of Descartes experithe mind by the study of the poets, the historians, enced. and the philosophers of antiquity.

The philosophy of Newton was indeed supported Overturned by the Cartesian Philosophy, which by the powerful aid of calculation, the result of gave a better hold to reason, which spoke a new, which not only agreed with observation, but even intelligible, and more precise language, and which anticipated it in the delicate circumstances which was cotemporary with the most important discove-it had not yet developed. It was no longer, as by ries in mathematics and in physics, the Scholastic the vortices of subtile matter, a vague explanation Philosophy at length left a field free to the medita- of the manner in which it was possible that the phetions of more exalted minds; the steps of reason nomena of nature might be produced: their quanwere then marked by the progress of language tities as well as their forms were susceptible of a which becomes pure only when judgment presides precise determination; but this theory, such as it over the choice and connection of words, and which had presented itself to its inventor, was within the is enriched only by new ideas springing from an at-reach of but few men, even among those who at tentive observation of moral and physical nature; that time took to themselves the title of geometribut this was hardly the dawning of that perfect day cians. which the mathematical discoveries of Newton, of Yielding to the established usage, of considering Leibnitz and of their school, were preparing for a no other propositions than those demonstrated afgeneration destined to complete what the great ter the manner of the ancients as worthy of seeing men had but begun, and to re-establish reason in its rights, after it had been bound down so long beneath the burden of prejudices.

the light, Newton, rather for the ornament of his work than for the concealment of the course he had followed, suppressed the method which he had The homage which I here render to mathemat employed in his researches; and the mass of the ies, in attributing to them, at least, a great part of men of science of his time, unable to rebuild the the honour of having directed the march of the edifice he bad demolished, exclaimed that the dochuman mind during the eighteenth century, is far trine of attraction was but a revival of that of occult from being one of those exaggerations so often dic-cause, which had been justly banished from philosotated by the interest naturally attached to the ob-phy by Descartes. Mankind were yet to be conject which may have chiefly occupied our thoughts. vinced, that facts carefully observed must form the No man who has not devoted his whole life to the commencement of every science; that they must mere arranging of words, to support with commonplace arguments, refuted as often as raised, the worst of causes, when it happens to be that of his interest or of his prejudices, can have failed to ob serve, how rapid has been the enlargement of the human mind, since, with the aid of the new mode of calculation, and of the fruitful and admirable law of gravitation, it achieved the conquest of heaven, by penetrating into its immensity, to trace there the course of those bodies by whose brilliance it is adorned.

These sublime discoveries, the most imposing title upon which the genius of man can found its dig

then be combined together, either to discover what they have in common, and how they respectively produce each other or to shew what must result from their succession, and to have the wisdom to pronounce nothing in relation to the causes from which they spring. The course, that the mind should follow to arrive at truth, consists in the collection of facts, the deduction of results from them, and the application of them to the circumstances in which they may reproduce themselves; it is the course nature follows in the developement of mind from our earliest infancy. If it was necessary to explain the immortal book of "the mathematical principles

of natural philosophy," it was no less so to perfect important results, those productions, equally va its details, and to investigate some questions of rious and delightful, which he annually poured up which its illustrious author had given but a glimpse. on the public. The schools of Descartes and of Leibnitz having Who can deny, that his "Elements of the Phi shown in all its brightness, the superiority of the losophy of Newton," imperfect as they are when algebraical analysis over the analysis and synthesis scientifically considerd, that bis Epistle to Maof geometry, exclusively known and cultivated by dame Duchâlelet, in which the System of the World the ancients, it became desirable to apply it to the is described in verses that will bear to be compared problems of the "higher mechanics" to which New- with the finest passages of Lucretius, and that a ton had reduced the determination of the circum-multitude of touches scattered through his poetical stances of the motion of the heavenly bodies, and of compositions, have rendered popular both the fruits which he had given a general resolution only in the of the vigils of geometricians, and the able opera most simple case; but the means of calculation were tions that were executed in the voyages, undertaken first to be enlarged. to verify the figure which Newton had assigned to To hasten the triumph of the new methods, that the earth, from his theory alone. But, if the Machance which so rarely accumulates in the same pe-thematical sciences owed much to Voltaire, it is riod talents of the same class, gave birth to men but just to suggest, that his reputation received a who soon put them in a condition to lend themselves great encrease from his observation upon the riches, to the necessities of physical astronomy. Claviant, they were acquiring before his eyes, and from the D'Alembert and Euler, as if by one impulse, leaping attention with which he cultivated the society of into the career, left far behind the rivals who had the most distinguished geometricians. struggled to keep pace with them. La Grange, La What judicious mind would dare, for example, Place, Legendre, who were their disciples and who to affirm, that it was to the education, received by succeeded them, without an interval, carried to Voltaire, at the College of the Jesuits, that he owed the highest degree of perfection, the monuments the various as well as the frequent successes, which that had been raised to science by their masters. he deserved and obtained during his long career. This is not the place, for displaying the means by I leave it to the critics to discuss the rank that he which they opened to themselves, the route that they have traversed with such triumphant success, or for disclosing those labours which were the prelude to their brilliant discoveries and the happy coincidences that occurred among them in their researches. These details belong to the complete history of mathematics during the eighteenth century, and my purpose is simply to review the causes and the cir-to posterity, is the astonishing variety with which he cumstances which have advanced these sciences to has been able to diversify his works, as well as the the state they have reached in our own time. The ease with which he has taken every tone to please eyes of mankind would hardly have been turned to and to instruct. Is it from the cold lessons and the the new improvements of analysis by a small num- turgid declamations of his instructers, or from that ber of truths which although striking in themselves, cloud of modern manufactures of Latin Verse, who lay buried in calculations and in formulas, far be- are unable to produce a decent line in their native yond the elementary knowledge, scattered in public tongue, that he has drawn the means of supporting instruction, and which received their confirmation this enchanting variety? or, is it rather from the solely from the results of those labours which occu- multitude of acquisitions which he had made by pied a few astronomers in the silence of their obser- himself, in the course of his immense readings? is vations. But the men who cultivated these pur- it from having learned much, from baving observed suits, united themselves with one of those geniuses, much, from having reflected much, that he has be amazing for their facility and fruitfulness, who come the writer who of all his age is re-read with seem to have been formed by nature to send into the most frequency and profit? His peculiar genius minds even of the lowest class, every thing fair that was doubtless required to put into operation the ma has been fashioned, and every thing great or useful terials that be had accumulated in his head: the bes that has been conceived among the small number has need of her organs to work up the essences of those who live retired in the sanctuary of the sci- which she gathers from the flowers; but the ancient Clothed as they were in technical forms, system of education was as far from being fit to supthe earliest works on the bigher analysis and me-ply these materials, as a parched desert is incapable chanics, would have long remained unknown in the of furnishing the means of an abundant barvest of possession of a very limited number of readers, if honey.

ences.

Voltaire had not hastened to adorn with their most

ought to hold among the men who have rendered themselves illustrious by the charms of verse, and who have retrodden the footsteps of the ancients with greater or less felicity; but, none surely will contest, that the distinctive character of Voltaire, which attaches to him the greatest number of read. ers, and which forms his greatest recommendation

PHILOLOGICAL DEPARTMENT.

GRAMMAR. Continued from page 203.
SECT VII.

Regimen of the Active Verb.

adjectives, though participles in etymology and

in form.

The infinitive mood has the same similarity to the substantive norn as the participle has to the adjective. It may become a nominative to a verb, as "to enjoy is to obey;" or an accusative, as "men generally wish to live long;" but, when introductory to other words, it has a more powerful and ready regimen than the noun. In Latin, it

clusively the genitive, like the noun. We shall af terwards consider more particularly the participle and the infinitive mood. At present we have merely accounted for the fact, that grammarians have reckoned them real parts of the verb.

SOME actions are of such a nature that the object affected by them is always interesting, and, in the earliest use of language, such actions are never re-like the verb governs the accusative, and not exJated without immediate mention of au object thus affected. It also happens on such occasions, that the manner in which the object is affected is evident from the nature of the action. Of this nature are the actions expressed by the verbs to make," "to build,” “to cut," "to strike," "to kill." Such It must always have been obvious that this office verbs in the Latin language generally govern the of the active verb is not common to all verbs, and accusative case, intimating the most rapid transition therefore is not characteristic of this part of speech; from the idea conveyed in the governing verb to and, if the participle and the infinitive mood are to that conveyed in the noun. The noun governed be reckoned parts of the verb, the problem still remay, in consequence of its own regimen, be ren-mains unsolved, what is the true characteristic of dered introductory to further additions both to the the verb? Mr. Tooke intimated that he was prepaform and meaning of a sentence. The verb thus be- red with some doctrine which appeared to himself comes a hinge on which the greater part of the satisfactory as a description of the verb, including meaning of a sentence turns. The large proportion its infinitive mood. Every philologist must regret of verbs which govern nouns in this manner has that this acute writer did not communicate his conferred a conspicuous rank on this part of speech. views more fully to the world. On this part of the It is in this respect more powerful than the adjec-subject, it is possible that they may have been both tive. Even when adjectives are used as predicates well founded and original. We are certain that they in affirmation, the meaning which they introduce generally terminates in themselves, or leads to sub. ordinate ideas only throngh the medium of prepositions. We say "this man is good," "that man is just" also, "this man is good at heart," "that man is just in all his conduct." It is seldom that adjectives in Latin can be admitted to govern the our own most matured reflections, we naturally accusative; and even the phrases in which this might appear to take place, such as Os húmerosque similis, are commonly explained by the subaudition of the preposition quoad. These differences betwixt the active verb and the other parts of speech have had a secret influence in leading grammarians to attach great importance to the verb. Its full power seems to reside in this form of it. Verbs of other kinds have appeared to be exceptions, or words to which convenience has assigned a verbal form, though they are not originally entitled to it.

would have been at least worthy of attention. They appear to have been valuable in his own eyes; they would have been exhibited in a forcible manner, if he had chosen to publish them, and might have led the way to a more satisfactory account of the subject. But, as no explanation of this sort occurs on

suspect (however presumptuous the declaration may appear,) that his theory would have either turned out eventually inconsistent with some of the opinions which he has published, or would have been in itself unsatisfactory.

A precise answer to the question in the form now proposed is not of great importance. We have pointed out assertion as one office which is perform. ed by verbs alone. We have pointed out the quality of an active regimen, as belonging to an exten. sive department of verbs, and bave shown that this The governing powers of the active verb are re-quality is possessed by parts of speech closely allied tained by the active participle and the infinitive to the verb in etymology, and generally numbered mood. This act seems to have led grammarians to among its parts, though not possessing an asserting consider these forms of words as parts of the verbs power. We have shown in what words assertion properly so called. The participle is distinguished and a transitive regimen are separate, and in what from the adjective by regimen alone. Hence those they are combined. Assertion is separate in the ingrammarians who call participles real adjectives have dicative mood of substantive and neuter verbs; the always been most fully satisfied with the apellation transitive regimen, in the infinitive mood and acwhen applied to the participles of verbs destitute of tive participle of active verbs. We have endeav regimen, such as "thriving," "charming," "sur-oured to investigate the connection betwixt these prising," words which are in all respects used as parts of speech and the indicative of the verb. In

so far as their character is inconstant or complica- events, that, even in describing the same sort of ted, we have stated the causes of these characteris-action, we should sometimes have a motive for mentics, and the shades of variation by which they are tioning an object affected, and sometimes not. For distinguished. We have shown in what respects this reason some verbs differ from each other only the intermediate kinds of words partake of the na-in their transitive or intransitive application, of ture of one part of speech, and in what respects which we have already given an instance in the they partake of the nature of another. If the par- difference betwixt the verbs "to speak" and "to ticulars on these subjects are impressed en our say." In other instances the same verb is used minds, our theories will be exempt from ambiguity either transitively or intransitively. We may say or confusion. at one time, "a miller grinds corn;" in this sentence, corn is the object affected by the act; at another time we may speak of the same act as char acteristic of the situation and employment of an individual; as in the sentence," two women were grinding at the mill, the one was taken and the other left." Here no occasion arises for mentioning any object on which the act of grinding is exerted. These however are not two different meanings given to the verb. In both cases it is used in its full meaning, that of describing a species of action. Whether we choose to introduce or omit

SECT. VIII. Intransitive Active Verbs.

may or may not be of use to add this circumstance to the description. It makes no more difference in the original meaning of the word, than the introduction of a second sentence in elucidation of the subject would affect the meaning of the words in the sentence first employed.

NEUTER Verbs have no such regimen as has been now described. Hence some have assumed this as a mark of distinction betwixt them and active verbs. It did not however escape observation, that some verbs which do not govern any noun signify action, and that therefore the term neuler, as implying the absence of active power, did not apply to them. For this reason these have been retained in the list of active verbs, but distinguished from verbs of re-the name of the thing acted on, depends on the degimen by the additional epithet intransitire. Their sign which we have in forming our discourse. It peculiar character has been generally represented as arising from this peculiarity in the nature of the actions signified, that they do not affect any ulterior object. But this is not true in point of fact. The transitive or intransitive nature of verbs of action depends solely on the occasions of mankind in making use of language. Transitive verbs are Sometimes verbs which are originally intransi those which express actions when we have occasion tive, and evidently not intended to have nouns subinstantly to mention an object acted on. Intransi- joined to them, except through the medium of pretive verbs describe actions when we are satisfied positons, are afterwards applied as active verbs with stating the connection betwixt the action and governing the accusative, in consequence of the the agent. Verbs which admit of no direct regimen, familiarity which the expression of particular kinds and therefore are termed intransitive, may intro- of connection acquires from habit. The verb "esduce other ideas, expressed by nouns, through the cape" originally required the preposition “from” medium of prepositions. The verb "to strike" is to express a certain sort of connection betwixt the transitive, while the verb “to walk" is intransitive; act and other objects. Yet we not only say "a and yet it is evident that in the act of walking one prisoner escaped from prison," but, speaking of our or more objects are acted on as much as in the act own memory, we may say that "names and dates of striking. Only it happens that when we speak escape us." Fugere, in Latin, is a verb of the same of striking, it is generally of importance to point kind, and the corresponding phrase me fugit is used out the object that is struck; but, when we speak in that language. Me latel is of a similar nature. of walking, our attention is chiefly directed to the Ardere is transitive, or perhaps ought rather to act as connected with the agent. In walking, how-be called neuter, yet it is made to govern the accuever, a man walks upon some object which supports sative: Formosum pastor Corydon ARDEBAT Alexin. him; he walks from some place, and to some other. Each of the phrases "I strike my horse," and "I walk upon the ground," expresses, in a manner equally explicit, a particular act, together with an object affected. The intervention of a preposition in the one case, and the absence of one in the other, imply no difference in the energy of the act related, but only the different degrees of interest excited in the passive voice. In Latin we have such words the connection of it with the object affected. It might naturally be expected, from the numerous and varied occasions which have for the relation of

In some instances an active verb, which we are in the habit of connecting with nouns by means of prepositions, is used to form a transitive verb, by being compounded with a preposition governing the accusative, and evidently derives its transitive power from the preposition. Such a verb, like others which govern the same case, may be used in

as initur, "it is entered on." In English the same thing takes place, though the two words continue separate. The phrase thus formed is treated