We can now only refer to a single other topic-the remarkable bodily affections which characterized the great Kentucky revival at the beginning of this century-a topic of more than usual interest at the present time, from the re-appearance of similar manifestations in the recent remarkable revival in Ireland. The Kentucky revival broke out in the southern part of the state, in the year 1800, in connection with certain "union meetings," or sacramental meetings, in which Presbyterians and Methodists united their strength, and labored conjointly, to stem the prevailing torrent of infidelity and wickedness. At one of these meetings

"The people were seized as by a sort of superhuman power; their physical energy was lost; their senses refused to perform their functions; all forms of manifesting consciousness were for the time annulled. Strong men fell upon the ground, utterly helpless; women were taken with a strange spasmodic motion, so that they were heaved to and fro, sometimes falling at length upon the floor, their hair dishevelled, and throwing their heads about with a quickness and violence so great as to make their hair crack against the floor as if it were a teamster's whip. Then they would rise up again under this strange power, fall on their faces, and the same violent movements and cracking noise would ensue. Such peculiarities characterized the first meeting." p. 357.

Soon after there was a grand union camp-meeting held for several days at Crane Ridge, when people came sixty, seventy, a hundred, even three hundred miles to attend, and on one night not less than thirty thousand were supposed to be present. The preaching uttered from the brazen lungs of the Boanerges of the backwoods, was of the most exciting character. It was during a sermon of this kind, by William Burke, one of the most eloquent and powerful of the Methodist preachers, when there were present some ten thousand hearers, that the most remarkable physical manifestations were exhibited.

"It is said that all these people, the whole ten thousand of men and women standing about the preacher, were from time to time shaken as a forest by a tornado, and five hundred were at once prostrated to the earth, like the trees in a windfall,' by some invisible agency. Some were agitated by violent whirling motions, some by fearful contortions; and then came the jerks.' Scoffers, doubters, deniers, men who came to ridicule and sneer at the supernatural agency, were taken up in the air, whirled over upon their heads, coiled up so as to spin about like cart-wheels, catching hold, meantime, of saplings, endeavoring to clasp the trunks of trees in their arms, but still going headlong and helplessly on. These motions were called the 'jerks;' a name which was current in the West for many a year after; and many an old preacher has described these accurately to me. It was not the men who were already members of the church, but the scoffing, the blasphemous, the profane, who were taken in this way

Here is one example: A man rode into what was called the 'ring circle,' where five hundred people were standing in a ring, and another set inside. Those inside were on their knees, crying, shouting, praying, all mixed up in heterogeneous style. This man comes riding up at the top of his speed, yelling like a demon, cursing and blaspheming. On reaching the edge of the ring, he falls from his horse, seemingly lifeless, and lies in an apparently unconscious condition for thirty hours; his pulse at about forty, or less. When he opens his eyes and recovers his senses, he says he has retained his consciousness all the time-that he has been aware of what has been passing around-but was seized with some agency which he could not define. I fancy that neither physiology, nor psychol ogy, nor biology, nor any of the ologies or isms, have, thus far, given any satisfactory explanation of the singular manifestations that attended this great revival." pp. 359, 360.

SCIENCE.

POPULAR ASTRONOMY.*-This book is precisely what its title indicates, a popular presentation of the leading facts and principles of the science of astronomy, as far as possible in ordinary language, and without mathematical formulæ. It is not therefore a text-book for the student, nor a hand-book for the computer, but just such a book as any professional man, or other intelligent person, needs, who would revive his half-forgotten knowledge of the science, or acquire for the first time an understanding of the wonderful phenomena and laws which it reveals, and of the steps and processes by which the mind of man has been able to scale and span the heavens, and unravel and systematize the most intricate laws and relations of the material universe. It is just such a book as any one needs, who would post himself in a general way in reference to the recent progress and present state of this the oldest, yet, in these days, one of the most rapidly advancing, of the sciences. This work of Professor Mitchell's has many advantages over all others of the same scope. It has been prepared, not by a mere epitomizer, or book-maker, but by an astronomer-one who is an enthusiastic cultivator of the science, and who has a rare faculty of presenting its abstrusest points in such a manner as to interest and instruct the popular mind. Its arrangement is historical and inductive rather than systematic; and hence, it is calculated to stimulate rather than weary the mind, by leading it to contemplate, as far as possible, the actual steps by which original investigators have overcome the difficulties they

*

* Popular Astronomy. A concise elementary treatise on the Sun, Planets, Satellites, and Comets. By O. M. MITCHELL, LL. D., Director of the Cincinnati and Dudley Observatories. New York: Phinney, Blakeman & Mason. No. 61 Walker street. 1860. pp. 376.

encountered, and gradually developed the great facts and principles of the science. It is enriched occasionally by the results of the author's own observations and inventive genius, particularly in the portions which describe the telescopic appearances of celestial objects, and the most recent devices and methods in instrumental astronomy. The author has for years had at command one of the finest telescopes in the world, and is now bringing his peculiarly fertile inventive talents to bear upon his favorite science, as director of the observatories at Cincinnati and Albany. He has contributed much towards awakening a general interest in this science both by his attractive courses of lectures, and by the present and a preceding work which may be regarded as those lectures in print. The work before us treats specially of the Sun, Planets, Satellites, and Comets, and is illustrated with cuts and diagrams.

MATHEMATICS.

PROF. STRONG'S ALGEBRA.*-In our May number we gave a brief notice of this important work. We now proceed to indicate, somewhat more fully, the chief points wherein it may be distinguished from ordinary treatises of this kind.

In the first place, it is no compilation, it is the production of the author's own thoughts. Many of these, it is true, must have been derived from others: but from the first definition to the highest formula, all is presented exactly as things appear to the writer's own mind. This gives the whole a unity and concinnity of parts, which to the truly scientific reader is a charm of the highest character. Mere compilations, while for ordinary teaching they have their value, can never attain this excellence. Parts will be brought into juxtaposition, without sufficient re gard to their natural relations, and separated on the pages of a book, when in thought the one grows directly out of the other.

We observe, in the second place, this volume exhibits most completely the peculiar spirit of the Algebraic Calculus. This is the calculus of numerical fractions in a general way; or universal Arithmetic. Now this is by symbols, representing numbers, and indicating operations, and capable therefore of being submitted to the eye in all their processes. In strictly observing this, it seems to us, has consisted the special excellence of the French treatises upon the various topics and applica

* A Treatise on Elementary and Higher Algebra. By THEODORE STRONG, LL, D. New York: Pratt, Oakley & Co. 8vo. pp. 551.

tions of Algebra. Every thing, as far as possible, is submitted to the eye, and hence the conclusions have the evident validity of things seen.

Again as all the operations of Algebra have respect, ultimately, to numbers, Prof. Strong keeps this distinctly in view. Each conclusion, however high or abstract, is applied to some operation in numbers, and seen therefore, in its legitimate scope.

Beginners in Algebra are often not aware of the fact, that in this calculus different quantities are compared together merely in view of numerical relations. When, for example, we compare the cube of a with its square, it is not that a cube has any ratio to a square; but merely that the numbers expressing the peculiar units in the one, may be compared with those expressing the units of the other. We repeat-it is with general expressions of numbers that we have to do in Algebra, and with nothing else.

Once more; as we said in our May number, Prof. Strong has added to the before existing stock of knowledge in this department. To his treatise we may justly apply the words of Edward Burke, when speaking of "difficulty," he says of it: "This it has been the great glory of the great masters in all the arts to confront and overcome; and when they had overcome the first difficulty, to turn it to an instrument of new conquests over new difficulties; thus to enable them to extend the empire of science, and even to push forward beyond the reach of their original thoughts the land-marks of the human understanding itself." Prof. Strong has done this, as, in some particulars, we shall farther show; and hence he deserves a niche in the Temple of Fame, among the benefactors of

our race.

We proceed to designate some particulars, wherein we find either improvements upon the usual modes of treating the subjects, or actual additions to the science itself. Of the solution of the irreducible case of Cubic equations we have spoken before. The occurrence of this case under Cardan's formulæ was inevitable, on account of certain limitations of the auxiliary quantities employed in the general solution. Of this case, Bonnycastle says, (in his Alg., London, 1820,) "The solution of it, except by a table of series, or by infinite series, has hitherto baffled the united efforts of the most eminent mathematicians of Europe." So it has been to this day; and in virtue of this single achievement, Prof. Strong has earned himself the highest credit as a master in his art.

We find another equally ingenious extension of the science, in the method of extracting the roots of numbers of any degree, by a direct process, and without the aid of logarithms.

This depends primarily upon the proposition, that any quantity of the form one, plus b divided by a, can be resolved into any number of factors of the same form, as appears on p. 288, &c.

For the convenient application of this to all numbers, a resolution of the nine digits, as also the figure 10, into factors of the same form, is wanted, as appears in an Article by Prof. Strong in the April No. of the Mathematical Monthly. Altogether, this is one of the most curious feats that we know.

MISCELLANY.

HUMBOLDT'S LETTERS.*-When David Mallet, a native of Scotland, published the posthumous works of Bolingbroke, Johnson, speaking of the latter to Boswell, said, "Sir, he was a scoundrel and a coward; a scoundrel, for charging a blunderbuss against religion and morality; a coward, because he had no resolution to fire it off himself, but left half a crown to a beggarly Scotchman, to draw the trigger after his death!" An equally severe censure some may be disposed to pronounce upon Humboldt for the infidel remarks which for the first time see the light after his decease. But so hard terms are not, in this case, just; for though the remarks are, some of them, flippant, and none of them either new or profound, they disclose nothing concerning the writer, that was not known before. The pantheistic opinions of the author of Cosmos, are sufficiently patent to a discerning reader of that work, and he has been known in Germany to be a free-thinker if not an Atheist. Nor are we inclined to hold the famous naturalist responsible for the publication of these letters which, for many reasons, should never have been printed. They were written, and such of them as emanated from his distinguished correspondents, given, to his life-long friend, Varnhagen von Ense, and placed without reservation at his disposal. But the friend unexpectedly died first, and they fell into the hands of a female relative. who gives them to the world, professing that in so doing she is discharging a sacred duty, it being the express wish of Humboldt that they should be published at his death. We do not find sufficient proof of this statement in the evidence which she brings forward to support it. The principal passage cited in proof is from a letter of Humboldt to

*Letters of Alexander Von Humboldt to Varnhagen Von Ense, from 1827 to 1858. With extracts from Varnhagen's Diaries, and Letters of Varnhagen and others to Humboldt. Translated by FREDERICK KAPP. New York: Rudd & Carleton. 12mo. pp. 407.