mids and the temples of Yucatan, raised also the tumuli of Ohio, and that they really came over by Behring's straits; for on these points authorities are far from agreeing. We should not have passed over, in silence, the opinion of those who think that the mounds of Ohio were constructed by the Welsh, who came over in the twelfth century. If this fact is not yet proved to the satisfaction of every body, the same is true of almost every thing which relates to the history of America, prior to the arrival of the Europeans; if, for example, as Mr. Delafield seems inclined to believe, it can be proved that the builders of the tumuli were acquainted with the use of iron, this would be a fact, most of all, in favor of the Welsh colony; our author's opinion on this point may be inferred from the following extract:

"In Liberty township, Washington county, Ohio, are yet to be seen twenty or thirty rude furnaces, built of stone, with hearths of clay, containing pieces of stone, coal, and cinders, perhaps used in smelting ores. Large trees are still growing on them, and attest their age. They stand in the middle of a rich body of iron, and in a wild, hilly, and rough part of the country, better adapted to manufactures than to agriculture."

If we could conclude from this passage that, before the discovery of America by Columbus, iron was really smelted upon the banks of the Ohio, would it not necessarily follow, from what was said in the beginning of this article, that the Mexicans never had any connexion with the inhabitants of the borders of this river. For it is a fact, fully proved, that the former built their palaces and their temples, and worked their mines, without knowing the use of iron, although their country was very rich in the ores of this metal, as is known from the accounts of Cortes, who, immediately after his conquest of the country, directed the iron mines to be opened and worked. This fact, therefore, which Mr. Delafield himself has pointed out, would overturn his whole structure, and it would be almost proved that Europeans must have dwelt in the country bordering on the Ohio before 1492.

But thus far it does not seem to us proved, that these "rude furnaces were used to smelt ores," as our author thinks. It would be a difficult thing to smelt iron and extract the metal from its ores, with no better means of keeping a furnace in blast than the bamboo-bellows of the Mexicans. Until slags and scoriæ, or metallic iron, should be found near these furnaces, thousands of them will prove nothing. The presence of stone

coal in them, far from being an argument in favor of the use of iron, is fairly against it, inasmuch as nothing but the increasing scarcity of wood led Europeans to make use of coke for smelting iron.

These reflections have, involuntarily, arisen in our minds in pursuing this subject. They show, at least, how difficult it still is to frame an hypothesis in all respects satisfactory, and at the same time, point out the necessity of basing every explanation upon facts first established.

It has given us great pleasure to find nothing in Mr. Delafield's work to object to, except that part to which he seems to have attached the least importance; its principal object being to discover from what quarter of the ancient continent, and by what route, the first inhabitants of our own came. In pursuing this inquiry, the author has exhibited no less talent than courage, and has followed, with great skill, through the obscurities of ancient history, the microscopic thread which connects the primitive settlers of this continent, with that in which they had their origin. The course which he adopts to establish the resemblances between the Mexicans and the Peruvians, as well as between the Americans and certain nations of Asia, and of the valley of the Nile, is equally satisfactory, although this is only, in reality, a preliminary proposition, preparatory to the demonstration of his main one, which we have given above. It is, by a comparison of languages, crania, mythology, hieroglyphic writings, astronomical knowledge, architecture, and ornaments, in fine of manners and customs, that the author first establishes the necessity of a community of origin between the people in question. Afterwards, in the subsequent part of the book, he endeavors to determine at what time the nation which came to America separated from its sister nations of the ancient continent. The volume concludes with the explanation of Boturini's chart, and surely the author need not fear to repeat, in finishing his highly interesting and learned work, the question proposed in the beginning,

"Do THESE INCIDENTS FORM A WELL CONNECTED CHAIN ?”

ART. VIII. — CRITICAL NOTICES.

1. Elements of Trigonometry, Plane and Spherical, adapted to the present state of analysis, with Logarithmic, Trigonometrical, and Nautical Tables, for the use of Colleges and Academies. By the REV. C. W. HACKLEY, Professor of Mathematics in the University of the City of New York. New York: 1838. Wiley & Putnam. 8vo. pp. 307.

THIS work seems to us to be admirably well adapted to the purpose for which it has been prepared. Without being unduly extended, it is a more complete treatise on Trigonometry than those generally used as text books in our colleges. The attention of the student is first directed to the methods of resolving triangles by construction, and, in immediate connexion, to the use of scales of equal parts and protractors, for laying off right lines and angles. Examples are given which serve to show the utility of trigonometry in the measurement of heights and distances. The evident inaccuracy of the solution of triangles by construction, leads the student to perceive the necessity of resolving them by some method of calculation. He is thus conducted, by a natural and easy transition, from geometry to analytical trigonometry, without being, as is commonly the case, ushered at once into this new department of mathematical science, before he has obtained a sufficiently distinct conception of its objects, or become persuaded of its practical utility. He is, also, at the same time, taught approximate methods of resolving triangles, which there may be frequent occasion to employ in practice. The subject of analytical trigonometry is treated of under the two divisions of Plane Trigonometry and Spherical Trigonometry. Under the head of Plane Trigonometry are found, the theory of the trigonometrical lines, the derivation of formulæ for the solution of right angled plane triangles, the theory and use of logarithms, and the solution of triangles with the aid of logarithms. The nature and properties of the trigonometrical lines are explained more minutely and systematically than in most other treatises on trigonometry. The theory of logarithms is a subject so intimately connected with trigonometrical processes of resolving triangles, that the exposition of it in this work, in immediate connexion with that of these processes, together with a detailed explanation and exemplification of the use of logarithmic tables in arithmetical computations, cannot but be regarded as an improvement. Another excellence, as it seems to us, as peculiar to this work, is the application of each of the

formulæ, as they are successively investigated, to the solution of a practical example. The student is thus made to see a practical utility in every analytical investigation, as he proceeds, and thus cannot fail to take more interest in the study, than if the evidence of such utility should be kept out of view until all the formulæ have been derived. The examples are well selected. Those of spherical trigonometry are astronomical. They are resolved by the aid of logarithmic tables appended to the work. The work also contains a treatise on the application of plane and spherical trigonometry to the principles of navigation and nautical astronomy, of sufficient extent to meet the wants of the college student. It is chiefly taken from Young's deservedly popular treatise on trigonometry. On the whole, from the examination that we have been able to give this work, we are decidedly of the opinion that it is a more simple and interesting, as well as a more complete and practical exposition of this important science, than any other treatise on the subject, designed for a college text book, with which we are acquainted.

2. The Reformation of Medical Science demanded by Inductive Philosophy: a Discourse delivered before the " New York Physicians' Society," at their Anniversary, November 21, 1838. By WILLIAM CHANNING, M. D. New York: 1839. Wiley & Putnam. 8vo. pp. 58.

THE introductory part of this performance exhibits an able view of the inductive philosophy, and a spirited recommendation of the application of its principles to the practice of the healing art. The author's views of Homoeopathia, the more immediate object of the discourse, will be received with less decided approbation. He is a strenuous advocate for the new doctrines, and seems equally disposed with Hahnemann himself, to extend its laws to the treatment of every mode and variety of disease. Dr. Channing accordingly claims for homœopathy the honor to rank in medicine as the science of therapeutics; and from the certainty of its deductions, hesitates not to place it in the class of the positive sciences. Few of our medical readers, we believe, will be disposed to adopt, with the enthusiasm of Dr. C., the theory of the erudite and fanciful German. At present, homoeopathy is viewed with little approbation by the most intelligent and experienced members of the profession.

It appears from a note by Dr. Channing himself, that the doctrines of the discourse are at variance with the prevailing opinions of the "New York Physicians' Society," before whom it was delivered.

3. A Review of Edwards's " Inquiry into the Freedom of the Will," etc. By HENRY PHILIP TAPPAN. New-York: 1839. John S. Taylor. 12mo. pp. 300.

We can do little more at present than announce this volume to our readers. We name it, however, as one of the most note-worthy publications of the quarter. It is a work which, from its subject, and the manner in which it is handled, is entitled to the respectful attention of every person who makes any pretension to be a thinking man, and to have an opinion about the celebrated treatise here reviewed. To speak more particularly, this work is entitled to notice, because, in the first place, it is the most regular, systematic, and complete attempt at an exposition and criticism of Edwards's treatise; secondly, it is characterized by a tone of remarkable candor and fairness; and thirdly, it is, written with great clearness, excellent method, and distinguished ability.

Whatever may be thought of the accuracy of the author's analysis, or of the justness of his conclusions, every person must be struck with the genuine philosophical spirit, the pure love of truth, which pervades the work. Perfectly free from subjection to the force of authority, and undeterred by any dread of the odium theologicum, he boldly exposes what he considers the pernicious and destructive logical consequences of the system of Edwards, yet with perfect love and reverence for the intellectual and moral greatness and worth of the man. Such a mode of conducting the discussion of questions connected with theology, is unhappily too rare in this country. Mr. Tappan's book is a perfect model in this respect, and we could wish that it might be imitated by all who profess to be lovers of truth and righteousness.

The following passage from the Introduction will explain the author's plan, and indicate how far, in the present volume, it is carried out. We hope, soon, to see the completion of the task he has proposed to himself; and shall then go into a more extended examination of his labors:

"I am aware, however, that the doctrine of the will is so intimately associated with great and venerable names, and has so long worn a theological complexion, that it is well nigh impossible to disintegrate it. The authority of great and good men, and theological interests, even when we are disposed to be candid, impartial, and independent, do often insensibly influence our reasonings.

It is out of respect to these old associations and prejudices, and from the wish to avoid all unnecessary strangeness of manner in handling an old subject, and more than all, to meet what are regarded by many as the weightiest and most conclusive reasonings on this subject, that I open this discussion with a review of Edwards's Inquiry into the Freedom of the Will.' There is no work of higher authority among those who deny the self-determining power of the will; and none which on this subject has called forth more general admiration for acuteness of thought and logical subtlety. I believe there is a prevailing impression that Edwards must be fairly met in order to make any advance in an opposite argu29

NO. IX.- VOL. V.