military commandant of Charleston, or that he had any actual "control" over Lord Moira, we cannot bring ourselves to believe. However this may be, we are sure that Lord Rawdon could have saved Colonel Hayne, and instead of doing so, that he gave his sanction to an execution which never would have taken place without it, and, therefore, whether that act entitles him to praise or to blame, he must bear it all. His theatrical display, in his dinner speech to the British officers, (as described by himself,) publicly announcing his concurrence with Colonel Balfour in the measure, must, forever, remove all doubts on this head. We have now performed, as well as we were able, what we conceived a duty to the memory of one of the most revered of our martyrs. It is due to the country, that not a single trophy of the Revolution should be suffered to be destroyed, and we should be sorry to see recorded on one of them, the memorable inscription on the beautiful naval monument in Washington, "mutilated by Britons." We would, if we could, preserve them all, in their simple majesty and beauty, to kindle in the bosom of our American youth, to the latest posterity, the sacred glow of patriotism. We have always considered the moral and political lessons, taught by the history of the Revolution, as the most precious inheritance derived from our fathers. The exploits of our heroes-the wisdom of our statesmen, constitute a portion of our national wealth, which, we had fondly hoped, would have withstood the assaults of time itself. If we were called upon to decide, by what measures, those who live in the present age, could confer the greatest blessings on posterity, we should say, without hesitation, by leaving behind them, those great examples of wisdom and of virtue, which are the most enduring monuments of national greatness. To the youth of any country, and especially of a free country, what incentive to noble actions can be offered, equal to the examples of the poets, orators, statesmen and warriors, who have immortalized the country which gave them birth, and adorned the age in which they lived. It is not, therefore, without feelings of mortification and regret, that we have witnessed, of late years, repeated attempts to strip from American history, some of the most brilliant trophies of the Revolution. It may be true, that our history, like all others, is "of a mingled yarn of truth and falsehood," but we fear, that any person who employs himself, at this day, in picking out the threads, will impair the beauty, if he does not destroy the strength of the fabric. It is too late now, to make a fresh distribution of the honors awarded by their contemporaries to the worthies of the Revolution. The partners of their toils-the very witnesses of their exploits, are lumbering in the dust, and we may be assured, that, if with the reeble and glimmering lights we now possess, we attempt to correct the supposed errors in our revolutionary history, we shall leave it much more imperfect than we found it. Let all Americans, therefore, unite in guarding the fair fame of the patriots and sages, whose names are embalmed in our history, as we would guard the bones of our fathers. Let the chaplet which gratitude has bound around their brows, be as enduring, as the blessings we owe to their exertions. Note.-We cannot close this article without bringing to the view of our readers, as affording an illustration of the truth of these remarks, the case of the gallant Colonel Campbell, who fell at the battle of the Eutaw Springs. The noble speech which Ramsay attributes to that distinguished soldier, who, after receiving a ball in his breast, asked, "which army is victorious?" and being answered, that of his country, exclaimed, “then I die contented," and expired-had placed him in public opinion, by the side of the proudest heroes of Greece and Rome. This distinction he continued to enjoy, until the publication of Lee's Memoirs, in 1813. In that work, General Lee says, "Colonel Campbell, highly respected and beloved, was killed. This excellent officer received a ball in his breast, in the decisive charge which broke the British line, while listening to an interogatory from Lieutenant Colonel Lee, then on the left of the legion infantry, adjoining the right of the Virginians, the post of Campbell. He dropped on the pommel of his saddle, and was borne in the rear by Lee's orderly dragoon, in whose charge he expired, the moment he was taken from his horse. Dr. Ramsay has represented the death of this highly respected officer differently, from information which, no doubt, the Doctor accredited. But as the writer was personally acquainted with the transaction, he cannot refrain from stating it, exactly as it happened. The Virginians had begun a fire, which was not only against orders, but put in danger Rudolph and his party, then turning the enemy's left. To stop this fire, Lieutenant Colonel Lee galloped down the line to Campbell, and while speaking to him on the subject, the Colonel received his wound, of which he soon expired, without uttering a word." Now, on reading this, who could doubt that the exclamation ascribed to the last moments of Campbell, had never proceeded from his lips? General Lee's authority on the subject, was deemed conclusive. And yet Judge Johnson has since given to the world, the testimony of Major Pendleton, who states, "I was not present when Colonel Campbell received his wound; but late in the afternoon, I met with Colonel Campbell, carried upon a litter by some soldiers. I got off my horse, and went to him. He perfectly retained his senses, but was in great pain, and seemed near his end. He asked me "who had gained the battle?" I told him we had completely defeated the enemy; "then," said he, "I die contented." I left him, and understood he died shortly after." Major Lee, in the work before us, acknowledges that his father was mistaken, and accounts for the mistake by saying, that Colonel Campbell, after being seen by General Lee to fall senseless on the pommel of the saddle, revived so far, as to express the noble sentiments heard by Major Pendleton. The explanation is satisfactory. But who, after this, will be disposed to rely, implicitly, on newly discovered testimony for the correction of errors in our revolutionary history? It is obvious, that but for the circumstance of Major Pendleton's having survived the publication of Lee's Memoirs, one of our distinguished heroes of the Revolution, would have been despoiled of the fairest portion of his fame-American history would have been robbed of one of its most interesting and romantic incidents-and the country deprived of one of the brightest jewels in the crown of its glory. ART. IV.-1. Elements of Analytical Trigonometry, Plane and Spherical. By F. R. HASSLER, F. A. P. S. New-York. Published by the Author. 8vo. 1826. 2. The American Quarterly Review, No. 1. March, 1827. 2d Edition. pp. 38-54. 3. On the Arithmetic of Impossible Quantities; from the Works of JOHN PLAYFAIR, Esq. Vol. III. Edinburgh, 1822. pp. 1-30. Published originally in the Philosophical Transactions, for 1779. 4. On the Necessary Truth of Certain Conclusions obtained by means of Imaginary Quantities. By ROBERT WOODHOUSE, A.M. Fellow of Caius College, Cambridge. Read January 8th, 1801. Philosophical Transactions. Vol. XIX. pp. 89-120. 5. On the Independence of the Analytical and Geometrical Methods of Investigation; and on the Advantages to be derived from their Separation. By ROBert Woodhouse, A. M. &c. Read January 14, 1802. Philosophical Transactions. Vol. XX. pp. 85-126. 6. Memoire Sur les Quantités Imaginaires. Par M. BUÉE. Read June 20, 1805. Philosophical Transactions. Vol. XXIV. pp. 23-89.* It is something very remarkable in the present advanced state of science, that, while its most abstruse and difficult branches are making rapid progress towards perfection, the very elements of those branches are neglected. There is scarcely a phenomenon in nature, which is not brought under the dominion of the modern analysis, technically termed the calculus. La Place, whose views of science are as extensive as they are profound, informs us, that, when a few more irregularities in the planetary motions, shall have been developed by time, "the geometrician will, at once, comprehend in his formulæ, both the past and future state of the system of the world." It is, however, an * The following essays have been also particularly referred to, and some of them partially reviewed: 1. On the Integration of certain differential Expressions, with which Problems in Physical Astronomy are connected, &c. By R WOODHOUSE, A. M. F.R.S. &c. Read April 12th, 1804. Philosphical Transactions. Vol. xxii. pp. 219–279. acknowledged fact, that notwithstanding all the sublime discoveries and improvements of the moderns, in the higher branches of the mathematics, its metaphysics, or that accurate knowledge of its elementary principles, in which the true philosophy of this science consists, were as well understood two thousand years ago, as at the present day. The state in which Euclid's Elements of Geometry are still suffered to remain, affords of itself, proof sufficient, to support this assertion-and yet these elements are more clearly and decidedly established, than any thing of a similar nature, which algebra or the modern analysis can exhibit. It would seem then, that these elementary principles are beneath the notice of men of genius, who, at a glance behold, and, as if by instinct, jump to their conclusions. If this be so, the human mind presents a strange, and, probably, an unaccountable phenomenon, viz. that in its inquiries, the simplest truths, and the easiest modes of arriving at them, are, generally, the last perceived. La Place, in writing to Lacroix, (“Traité du Calcul," &c. preface, p. 19) remarks this singularity, "Cette metaphysique est presque toujours la dernier chose que l'on decouvre L'homme de génié arrive comme par instinct aux resultats; ce n'est qu'en reflechissant sur le rout que lui et d'autres ont suivi, qu'il parvient a generaliser les methodes, et à en decouvrir la metaphysique." Men, with an instrument in their hands, so powerful as the calculus, which places them so far above the reach of ordinary 2. Philosophie Mathematique. Nouveaux Principes de Géométrie de Position, et Interpretation Geometrique des Symboles Imaginaires. Par M. J. F. FRANÇAIS, Professeur a l'ecole imperiale de l'artillerie et du genie. Annales des Mathematiques, &c. Rédigé par J. D GERGONNE. Vol. iv. pp. 61-72. Essai sur une Manière de Represénter les Quantités Imaginaires, dans les Con- Reflexions sur la Nouvelle Theorie des Imaginaires, suivies d'une application à la Demonstration d'une theoreme d'Analise. Par M. ARGAND. GERGONNE. Vol. v. pp. 197-210. 3. Theorie des Parallels. Essai par M. GERGONNE. Annales, vol. iii. pp. 353-357. Sur l'emploi de l'algorithme des Fonctions, dans la demonstration des theoremes de Geometrie. Par un ABONNE. Gergonne. Vol. x. pp. 161–184. Essai de Demonstration du Principe qui sert de fondement à la Theorie des Examen de Quelques Tentatives de Theorie des Parallèles. Par M. STEIN, Profes Suite de l'examen de Quelques Tentatives, &c. Par M. STEIN. Gergonne. Vol. Lettre au Rédacteur des Annales, sur la Theorie des Parallèles. Par M. SERVOIS, methods, are very apt to lose sight of the means, whereby that instrument was acquired—and while, apparently, erecting the most beautiful edifice, are too often building without a sure foundation. We cannot help being delighted when we perceive the advantages of a theorem, such as Newton's or Taylor's, at once presenting a whole science to our view; but we cannot be less delighted at the discovery of the steps which led to these results. We should, it is true, endeavour to generalize as we advance, but we should, at the same time, see our way distinctly, and not generalize too hastily-we should also endeavour to simplify as well as generalize, and to arrive, on every occasion, at the most elementary principles. Le Systême des connaissances, says La Place, (Cours de Sciences et Arts, v. iv. p. 49) liées entr'elles par une methode uniforme, peut mieux se conserver et s'étendre. Preferez donc dans l'enseignement les méthodes générales, attachez vous a les présenter de la manière la plus simple; et vous verrez, en même tems, qu'elles son presque toujours les plus faciles." Could we reduce all the complicated theories of the modern calculus to a simple elementary principle, such as that of multiplication or addition, as Newton has done, with respect to the various phenomena of the heavens, in reducing them to the single principle of gravitation, we should render an important service to science. And that this may, and will be effected, there can scarcely be a doubt-for, as we can ascend from the most evident elementary principles, such as the axioms in geometry, and the simple rules of addition and subtraction, or multiplication and division in algebra, to the most complicated investigations and formulæ by the synthetic process; so by the analytic process, from results the most complicated, we can descend to their elementary principles. In this research, the calculus is, as yet, extremely defective; and the more we cxamine it, the more we discover the weakness of its foundations, as depending on itself alone. These reflections have been elicited on perusing Hassler's Trigonometry, and the article which we have selected from the "American Quarterly Review," quoted above, and their truth, we have no doubt, will appear more evidently, as we proceed. The Reviewer prefaces his remarks on Mr. Hassler's Trigonometry, by a history of this science, the most interesting part of which, is taken from Delambre. And this history constitutes by far, the greatest portion of the article. In the remarks on trigonometrical tables, the Reviewer says, (p. 48) that "the best tables of a portable size, are those of Gardiner, Taylor and Callet; the first of which is out of print; the second, inconvenient in its shape and in its use; so that those of Callet, of much less |