will then vary in the opposite direction, and the obliquity will continually increase in like manner as it previously diminished. Finally, the in. clination of the equator and the ecliptic will attain a certain maximum value, and then the obliquity will again diminish. Thus the angle contained between the two planes will perpetually oscillate within certain limits. The extent of variation is inconsiderable. Laplace found that, in consequence of the spheroidal figure of the earth, it is even less than it would otherwise have been. This will be readily understood, when we state that the disturbing action of the sun and moon upon the terrestrial spheroid produces an oscillation of the earth's axis which occasions a periodic variation of the obliquity of the ecliptic. Now, as the plane of the ecliptic approaches the equator, the mean disturbing action of the sun and moon upon the redundant matter accumulated around the latter will undergo a corresponding variation, and hence will arise an inconceivably slow movement of the plane of the equator, which will necessarily affect the obliquity of the ecliptic. Laplace found that if it were not for this cause, the obliquity of the ecliptic would oscillate to the extent of 4° 53′ 33′′ on each side of a mean value, but that when the movements of both planes are taken into account, the extent of oscillation is reduced to 1° 33′ 45′′.

Variation of the length of the tropical year.-The disturbing action of the sun and moon upon the terrestrial spheroid occasions a continual regression of the equinoctial points, and hence arises the distinction between the sidereal and tropical year. The effect is modified in a small degree by the variation of the plane of the ecliptic, which tends to produce a progression of the equinoxes. If the movement of the equinoctial points arising from these combined causes was uniform, the length of the tropi cal year would be manifestly invariable. Theory, however, indicates that for ages past the rate of regression has been slowly increasing, and consequently the length of the tropical year has been gradually diminishing. The rate of diminution is exceedingly small. Laplace found that it amounts to somewhat less than half a second in a century. Consequently the length of the tropical year is now about ten seconds less than it was in the time of Hipparchus.

Limits of variation of the tropical year modified by the disturbing action of the sun and moon upon the terrestrial spheroid.—The tropical year will not continue indefinitely to diminish in length. When it has once attained a certain minimum value, it will then increase, until finally having attained an extreme value in the opposite direction, it will again begin to diminish, and thus it will perpetually oscillate between certain fixed limits. Laplace found that the extent to which the tropical year is liable to vary from this cause amounts to 38 seconds. If it were not for the effect produced upon the inclination of the equator to the ecliptic by the mean disturbing action of the sun and moon upon the terrestrial spheroid, the extent of variation would amount to 162 seconds. Motion of the perihelion of the terrestrial orbit. The major axis of

the orbit of each planet is in a state of continual movement from the disturbing action of the other planets. In some cases it makes the com plete tour of the heavens; in others it merely oscillates around a mean position. In the case of the earth's orbit, the perihelion is slowly advancing in the same direction as that in which all the planets are revolving around the sun. The alteration of its position with respect to the stars amounts to about 11" in a year, but since the equinox is regressing in the opposite direction at the rate of 50" in a year, the whole annual variation of the longitude of the terrestrial perihelion amounts to 61". Laplace has considered two remarkable epochs in connection with this fact, viz, the epoch at which the major axis of the earth's orbit co-incided with the line of the equinoxes, and the epoch at which it stood perpendicular to that line. By calculation he found the former of these epochs to be referable to the year 4107 B. C., and the latter to the year 1245 A. D. He accordingly suggested that the latter should be used as a universal epoch for the regulation of chronological occurrences.

EULOGY ON QUETELET.

ABSTRACT OF AN ESSAY UPON His Life and WORKS, BY ED. MAILLY.

[Translated for the Smithsonian Institution from the Annuaire de l'Academie royale of Belgium for 1875.] Lambert Adolphe Quetelet was born at Ghent on the 22d of February, 1796. He was educated at the lyceum of his native town, and early showed that nature had endowed him, not only with a vivid imagination and a mind of power, but also with the precious gift of indomitable perseverance. He carried away all the prizes of his school, and at the same time wrote poetry which attracted considerable attention. He also manifested a talent for art, and a drawing of his gained the first prize at the lyceum of Ghent in 1812.

Having lost his father when only seven years of age, and his family not being able to support him, he was obliged, as soon as he had completed his course at the lyceum, to enter, as a teacher, the institution for public instruction at Audenarde. Here he remained a year, teaching mathematics, drawing, and grammar; he was then given a mastership in his native town. In 1815 the lyceum at Ghent, by order of the municipal council, was converted into a university, and Quetelet was ap pointed professor of mathematics. He received his nomination on his nineteenth birthday. There was nothing brilliant in the lot which had thus far fallen to him, but it secured the means of existence, and left him at liberty to devote himself to art, literature, and science.

His most intimate companion, with whom he shared all his tastes, was G. Dandelin, who had been his fellow-pupil at the lyceum. The two friends at one time appear to have been seized with a dramatic furor, and, with the assistance of a distinguished musician, composed a grand prose opera in one act, called "John the Second, or Charles the Fifth, in the walls of Ghent." It was represented in the theater of Ghent, on the 18th of December, 1816. Its success appears to have been moderate, since it was only played twice, and was withdrawn on the plea that it excited the galleries too much. Be this as it may, with it ended the dramatic career of the authors. They had, however, in preparation, two other pieces, The Two Troubadours and The Jester, but before the completion of these Dandelin was appointed second lieutenant of engineers, and ordered to Namur, while Quetelet was won back to the pursuit of science through the influence of his associate, Professor Garnier.

In 1819 he passed his examination and received the degree of Doctor of Science, the first conferred by the new university. In honor of the event he gave a banquet, which was attended by many of the public functionaries, as well as the professors and pupils of the university.

His inaugural address gave brilliant promise of his future success. It was divided into two parts: In the first he showed that the locus of the centers of a series of circles, tangents to two given circles of position, is always a conic section; in the second he exhibited a new curve of the third degree, the focale, the locus of the foci of all the conic sections, determined by a transversal plane, revolving around a certain point, upon the surface of a vertical cone. The discovery of this curve was an important addition to mathematics, and the term focale is as inseparably connected with the name of Quetelet, as cycloid with that of his favorite author Pascal. Among the themes he submitted to the university in addition to his address, was a Latin essay upon the ques tion whether aerolites are projected from the moon.

On the occasion of the laying of the corner-stone of the university buildings, a banquet was given, preceded by a literary meeting, at which was read a poem by Quetelet upon the death of Grétry. This production, full of beautiful versification and expressions of exquisite sensibility, procured for him an introduction to M. Falk, minister of public instruction, who, with the interest excited by a young man at once a poet and a geometer, a man of letters and of science, caused him to be nominated to a professorship at the Athenæum of Brussels.

His first act on arriving at Brussels was to pay his respects to Commandant Nieuport, then in his seventy-third year, and who might be said to be the only representative of the exact sciences in Belgium. He had read the inaugural address of the young doctor, and appreciated, as it deserved, the discovery of the focale. Stimulated by the encouragement he received, Quetelet continued his labors in this direction, and published in 1819, in the Annales Belgique, an article under the title of Some new properties of the focale and of some other curves. This was favorably noticed by Garnier, his former preceptor at Ghent, and procured his election as a member of the Belgian Academy on the 1st of February, 1820. He was then twenty-four years of age.

He soon won the high regard of his associates in the academy, among whom were the talented Cornelissen and the renowned chemist Van Mons, whose niece he afterward married. The first use he made of his influence was to procure the election of his friend Dandelin and of Baron Reiffenberg, third regent of the athenæum, afterward professor of philosophy at the university of Louvain. The latter lodged in the same house with Quetelet, and soon became ardently attached to him. He was in intimate intercourse and a great favorite with the French refugees then in Brussels, and introduced to them his new friend. Among them were such men as David, Arnault, Bory de Saint Vincent, Berlier, Merlin, &c., who, if they had been won by the ready and bril liant wit of Reiffenberg, were equally attracted by the more solid quali ties of Quetelet. His relations with the refugees did not, however, prevent him from forming other associations; he sought out and made friends of the artists of the city, joined a literary society which had just

been formed, and became a member of the reading committee for the royal theaters. In the latter capacity he had free access to a stage which was favored each year by Talma, Mlle. Mars, and the principal French comedians of the day.

The literary society published annually a poetical almanac, the twentieth and last volume of which appeared in 1825, when the society quietly ceased to exist. Quetelet was a contributor, and, as his poetical life seems also to have ended about this time, it may be well to notice here some of the pieces published by him since the Eulogy on Grétry. The article entitled "The last moments" resembles somewhat, but is inferior to, the "Farewell of the poet to his lamp," one of his best pieces. "The 19th of January, or the night-watch of the ladies," contains some charming lines. An ode to Tollens is in the style of Horace, the favorite poet of Quetelet. An ode to Odevare, a painter, greatly admired in 1821, although now but little known, is much more elevated in character. The investiture of the principality of Orange, given by Charlemagne to William the Cornet, was also ably treated in verse by our associate. Works of the imagination, whether in prose or verse, greatly interested Quetelet. His "Essay upon Romance," published in 1823 in Belgic Annals, has lost none of its interest, and, with his poetry, ought to be reprinted. He studied the romances of different nations, translated into verse Schiller's tale called "The Knight of Toggenburg," and into prose various Spanish and English ballads.

He had no predilection for the classical, in literature or art, and says, of modern painting, "The pictures of antiquity, full of life and genius as they are, can never produce in our minds the illusive effect they had upon the Greeks and the Romans. Flora, Zephyr, Venus, so charming in their pictures, are seldom so in ours. It is no doubt good to be the echo of antiquity, but only those can understand the sounds repeated who can go back to past ages and assume for the moment their religion and national character. Let us imitate the Greeks in their simplicity and in their admirable portraiture of nature, but let us have, as they did, our own heroes, our groves, and our religion. What would the age of Pericles have said if Euripides and Sophocles had represented only Osirus or the mysterious fetes of the Egyptians?"

"The Lords of the Castle" and "The Countess Ida," (fables,) "My Lit tle Boat," an allegorical ballad, dedicated to M. Falk, an elegy upon the death of Adolph Delemer, an ode to Orion, translated from the Dutch of Nieuland, a translation of a portion of Byron's "Siege of Corinth," and the "Scald and Lysis," a romance, are among others of his poetical pieces worthy of mention. The latter was commended by the classic Raoul in the "Belgic Mercury." He says, in reference to it, "Quetelet, with whom poetry is only a relaxation, writes verse with great facility. He is of the number of those who illustrate the truth that the muses are sisters."

We have endeavored to give some idea of Quetelet as a poet, a man