science, would, by that mere collection, introduce system into a line of investigation which has thus far been singularly unsystematic. But we are confident that, under Mr. Haven's auspices, such a journal would become much more than a mere compend of observations published elsewhere.

We copy some of his suggestions from his own recent report:

"It may, perhaps, be reasonable to expect that such an undertaking would, at its commencement, be comparatively humble and imperfect; and possibly doubts may be entertained whether sufficient materials to fill the pages and sustain their interest would present themselves. But a journal printed in a style of moderate expense, that would admit of a proportionately extensive circulation, might develop resources now dormant or unrecognized. There is a taste for investigation already prevalent, which it would be calculated to encourage and direct, as the appetite for such pursuits seldom fails to grow by what it feeds on. There are many claims of discoveries, more or less remarkable, that deserve so much attention as may be necessary to determine their reality and importance; or that should be recorded, where they can be readily referred to, should circumstances at any time give them additional significance. Of this nature are the frequent statements of the disinterment of coins, of an ancient and peculiar character, from considerable depths. beneath the soil. Such, too, are the supposed Runic inscriptions on the Island of Monhegan, now exciting considerable interest; the inscribed stone found in the interior of New York, with the date of 1520, and possessing marks supposed to be indicative of the presence in that region of some one of the early Spanish adventurers; and the manuscript, of which a fac-simile is before us, bearing the date of Nov. 29, 1564, said to have been taken from a leaden enclosure that came from the bank of a stream in Swanton, Vt., near Lake Champlain, deemed worthy of consideration by scientific gentlemen at Burlington. Indeed, there is no paucity of similar themes for passing notice or investigation.

"There is one object of great moment to ethnologists, whose accomplishment might be facilitated by an organ of archæological miscellany. A common feeling exists in regard to the desirableness of preserving the native names of lakes, mountains, rivers, and localities throughout the country, with their true interpretation. This cannot well be effected suddenly, or by any one compiler. If undertaken by an individual, as a single task, there would be great liability to misconception for want of accurate information, and on account of the different spelling and varied construction given to the same or similar words occur

ring in different localities. There are, however, many persons, in the various States and sections of the Union, who have given partial attention to the subject, and, by conference with intelligent Indians or other means, have collected and interpreted the traditionary appellations belonging to particular neighborhoods. It is also known that some gentlemen are attempting to form more general tables of these pregnant memorials of an expiring race; and it is probable, that, in the pages of a periodical open to such communications, and adapted to them in their elementary form, materials would accumulate, from whose number and variety a lexicon of aboriginal topography might ultimately be prepared with a reasonable degree of accuracy.

"It is not to be forgotten, that this institution is a continental one; and, although it may not be expected to organize explorations beyond the limits of the United States, it is under an implied obligation to be observant of whatever is transpiring relevant to its province in the Western hemisphere. The Mexican and the South American regions are fast losing their inaccessible character; and a systematic analysis of the reports of official surveyors, or the narratives of casual adventurers and travellers, that issue in various shapes from the press, might be fruitful of facts having an important ethnological bearing. It is well known that new views are being taken of both Mexican and Peruvian history. Strong suspicions are excited in regard to the trustworthiness of the Spanish chroniclers. Their observations and their representations are deemed to have been equally incorrect. What with pious frauds for religious objects, false or exaggerated bulletins for the enhancement of military achievements, and the application of the highsounding terms and titles of civilized countries to the rude arts and institutions of the natives, very untrue impressions are believed to have been given of the real condition of the people, their traditional history, and their degree of civilization. A revision of opinions, which had been, to a certain extent, established, is already commencing, and may be expected to make some demand on public attention. Whatever may appear in the publications of the day, whether directly or only incidentally applicable to these and other ethnological questions, has an interest, which would be much enhanced by prompt association and comparison.

"To these considerations are to be added the advantages attending the form of a current vehicle for the publication of proceedings, reports, lists of donations, minor papers, extracts from manuscripts, &c., which are not adapted to the character of substantial memoirs." *

*Report of Committee on Publication to the American Antiquarian Society at its Annual Meeting, Boston, October 21, 1856, pp. 61 – 64.

We cannot but hope that this plan may be carried out, and that the Antiquarian Society, to which our literature is largely indebted, will undertake such a journal. It would indeed take up the study of our antiquities exactly where Mr. Haven's book has left it, and we should have a trustworthy compilation and record of any new observations or theories.

ART. VIII. Lectures on Quaternions; containing a Systematic Statement of a New Mathematical Method; of which the Principles were communicated in 1843 to the Royal Irish Academy, and which has since formed the Subject of successive Courses of Lectures delivered in 1848 and subsequent Years, in the Halls of Trinity College, Dublin: with numerous Illustrative Diagrams, and with some Geometrical and Physical Applications. By Sir WILLIAM ROWAN HAMIL TON, LL. D., M. R. I. A. Dublin: Hodges and Smith. 1853. 8vo. pp. 64, lxxii, 736.

It is confidently predicted, by those best qualified to judge, that in the coming centuries Hamilton's Quaternions will stand out as the great discovery of our nineteenth century. Yet how silently has the book taken its place upon the shelves of the mathematician's library! Perhaps not fifty men on this side the Atlantic have seen it, certainly not five have read it.

There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy

of being mentioned in connection with his, - Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton's calculus, we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.

It may be true that really great men in any department are always rare. We have but one Plato and but one Homer, one Shakespeare, one Beethoven. But in other departments than that of mathematics, it is always easy to find competent judges. All men of a metaphysical turn of mind can appreciate the difference between Plato and Aristotle. Every man is ready to join in approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton's Quaternions, and show us wherein it is superior to Newton's Fluxions?

The great mathematician is a man peculiarly alone. Of all men, he most frequently treads

"The silent desert of a great new thought."

He is alone, and if others essay to join him, before they can possibly accomplish the long and toilsome ascent, he will probably have mounted higher. He is alone, so far as human companionship is concerned. But he ofttimes feels the sublime joy of knowing that to him only of mortal men has been revealed a thought of the Infinite Geometer who has created all things in number, weight, and measure. He stands in the council-chamber of Him who made the Seven Stars and Orion, and guides Arcturus and his sons.

The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of Mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we may explain a right angle to mean a square corner. But go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the simple phrase "functional exponent." How much more impossible,

if we may say so, would it be to explain a whole treatise like Hamilton's Quaternions, in such wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all possible modes of expression. It delivers the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University in England; or adopt the briefest and clearest forms, as under the pen of the geometer at our Cambridge; but it always reveals to us precisely the writer's thought. Hence the judgment which mathematicians, competent to judge at all, pronounce upon one another's work, is matter of certainty, of knowledge, not of mere opinion. There can never be the doubt which we sometimes feel in criticising a philosopher or essayist, whether the writer had any real thoughts, whether he was not skilfully using language to conceal his want of ideas.

Moreover, the nature of the subjects of which the analyst and geometer treats, is such that an almost equal degree of certainty belongs to the results of his study. It is a very rare thing for him to be mistaken in a matter to which he applies his tests. How often is Dr. Lardner's reported decision against the practicability of ocean steamers brought up to invalidate the decisions of science! The fact that this supposed mistake of a second-rate man is so continually quoted, shows that there are no real mistakes of first-class men to justify rebellion against scientific authority.

Popular sympathy is now-a-days on the side of the inventor, and the report of science adverse to his hopes is on that account unwillingly received. All the world wished Ericsson success in his new ocean motor, and we were therefore ready to hope that the inexorable decision of Professor Peirce against it would prove erroneous. But time certainly seems in this case inclined to confirm the analyst, rather than the inventor.

There is a popular sympathy also with rebellion, and lovers of freedom cheer on those who rebel against the rule of the mathematicians. It is not long since we heard one of the most acute and brilliant essayists of our country expressing his sympathy and hopes of success for one who was making an