instance, the parameters are the homogeneous co-ordinates of a point in a five-dimensional flat, one gets, by permuting them, seven hundred and twenty points, which correspond in twelves to the sixty Pascal lines. The analogy is precise; for the two figures have the same algebraic base, namely, the substitutions. In his former paper, Veronese forms, for convenience, out of the six fundamental points, fifteen triangles, and, out of the sixty Pascal lines and Kirkman points, six configurations II, consisting each of ten Pascal lines and ten Kirkman points, poles and polars with respect to a conic.

He finds, that, in a five-fold flat, to the triangles correspond fifteen surfaces of the second order in four dimensions; to the sixty Pascal lines, sixty surfaces of the fourth order in three dimensions; to the twenty Steiner points, twenty surfaces of the sixth order in two dimensions; and, to the six figures II, six configurations II, represented in the theory of groups by the six remarkable six-valued functions found by Serret (Liouville, 1850). As a sample of the vast multitude of propositions given concerning these figures and spaces, we may take the following: the seven hundred and twenty points obtained by permuting the six co-ordinates form a hundred and twenty cycles of six points on rational curves of the fifth order. They lie in sixes on conics in twenty-four hundred planes, which pass by hundred and twenties through the twenty intersections of the space unity with the faces of the fundamental pyramid. They are in twenty-fours in four hundred and fifty threefold spaces, which go by thirties through the intersections of the space unity with the fifteen threefold faces of the fundamental pyramid; and in hundred and twenties on thirty-six fourfold spaces, which go by sixes through the intersections of the space unity with the six fourfold faces of the fundamental pyramid. Such properties as these are simple and interesting in space of high degrees; but it is well to utilize them also for space of two and three dimensions, which Veronese does by means of his method of projection (Math. ann., xix.). Thus for every complete tetrahedron, pentagon, and hexagon, in space of three dimensions, he gets configurations of points, lines, and curves, like those of the Pascal hexagram, and so for every triangle, quadrilateral, pentagon, and hexagon of the plane; and he remarks that the same method might be applied to configurations determined by any value of n in a space of n 1 or less dimensions. other geometrical interpretation of the groups of substitutions of six letters is given by six

An

linear complexes of lines in involution two and two (Klein, math. ann., ii.). They determine fifteen surfaces of the second order, whose intersections are sixty curves of the fourth order corresponding to the sixty Pascal lines. There is also a theorem analogous to the Pascal theorem for a rational quartic in fourfold space.

M. Folie, in his report on this paper, complains that the contestant has refused to understand the question in the plain sense in which it was proposed; that he should have started out from the propositions which in M. Folie's book, Sur les fondements d'une géométrie supérieure Cartésienne,' are said to be analogous to the Pascal properties, namely, that in a plane cubic curve opposite sides of two quadrilaterals cut in a line, and that in a cubic surface opposite faces of two tetrahedrons cut in four lines in a plane; that, after having extended the question as far as possible in this direction, it was open to him to take another point of view, and even that which he has taken, though that is perhaps least of all susceptible of generalization. This work, he says, is remarkable and highly original, and would have deserved the prize had it been the aim of the academy simply to call forth a work of that description; but its object was to engage young geometers in the way already opened in his own memoirs, and to provoke them to researches which should complete those of the Belgian school of geometers, according to the expression of M. Chasles. This the author has not done: the question, hence, remains unattacked, and will continue to be retained upon the programme of the academy. Veronese, in reply, very pertinently inquires why it was not equally incumbent upon the contestant to follow in the way marked out by the Italian and the French schools, by Cremona and by Serret, and maintains that the prize is wrongly withheld on account of his having followed a new and original way instead of that which M. Folie professes to have pointed out to the geometers of the future. He admits that his results are not very susceptible of generalization, for the reason that they are already so extremely general. He complains that M. Folie has given no idea of the contents of his paper, - the usual task of a rapporteur, — and that, in each instance in which he refers to it, he fails to understand it. M. Folie says, for example, that Veronese has applied his method to cubics in space because he could, but not to plane curves or surfaces of order higher than the second, because his method was not there applicable; while, in fact, Veronese obtains

his results for curves in space not at all by application of his method, but by simple projection from the Pascal hexagram. M. Folie objects to Veronese's using the term 'involution' instead of cyclic homography;' but an examination of the table of contents might have shown him that Veronese devotes a section of his paper to cyclic homographies, and he gives simply a natural extension to the ordinary meaning of the term involution.' But, worst of all, M. Folie makes a singular slip in the enunciation of the original question, for there are no points or lines in the figure which are known as the points or lines of either Hesse or Bauer. At the end, Veronese turns the tables upon his opponent, and points out several striking inconsistencies in his memoirs, and several instances of his peculiar art of phrasing' as, "The greater part of these [M. Folie's] theorems had not yet been discovered, in spite of the depth and penetration of geometers; "'"To deduce the corollaries from them would be an enterprise which would require, perhaps, years of labor;" "It is a field which I have cleared, and in which those who follow will find an ample harvest of discoveries."

In conclusion, we can but share the regret expressed by the direction of the Annali, that academies should so frequently provide unwisely for the advancement of science, either by proposing subjects which are too special, or by compelling authors to follow in their solution a direction determined a priori. CHRISTINE LADD FRANKLIN.

OCCURRENCE OF AMBER NEAR TRENTON, N.J.

6

Ar the April meeting of the Trenton natural history society, the occurrence of amber in the bed of Crosswicks Creek was referred to, and no one of those present reported success in searching for it. The authority for its occurrence rests wholly, I believe, upon the statement in Comstock's Mineralogy (Boston, 1827), that it occurs near Trenton, N.J.,' and, again, "that found near Trenton occurs in small grains, and rests on lignite, or carbonated wood, or even penetrates it" (p. 297). I have several times met with small grains or pebbles of the mineral in the bed of Crosswicks Creek, and in 1860 found a mass as large as a pea, which I gave to the late W. S. Vaux, Esq., of Philadelphia. These small grains of amber, found in the bed of the creek, are undoubtedly derived from the beds of clay which are exposed in the bluff forming the southern bank of the

creek. Clays of the same character and age (cretaceous) occur nearer Trenton than Crosswicks Creek; and in them, also, occurs much fossil wood. In and on this, grains of amber are not uncommon. They are usually very small, and difficult to detect. The fossil wood in this cretaceous clay is soft and very recent' in appearance, and burns with an uncertain, flickering flame. The scanty traces of amber found with this- derived, I suppose, from it is the fossilized sap of the trees now found in these deposits of clay.

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CHARLES C. ABBOTT.

THE TOTAL SOLAR ECLIPSE OF MAY 6. THE U.S. S. Hartford, which sailed from Callao, Peru, March 22, with the American and English astronomers on board, arrived at Caroline Island April 20, sixteen days before the date of the eclipse. The island is in reality a chain of small islands of coral formation, encircling a lagoon; the length of the enclosure being about seven miles and a half, and the breadth one mile and a half. The land is low, but supports an excellent growth of grass and other vegetation, including a number of cocoanut-trees. There are no permanent inhabitants; but the island is leased by an English firm which deals in guano, cocoanuts, and other products of this and similar Pacific islands. An agent of this firm visits the island occasionally, and superintends the work of those employed. Seven persons were found living on the island for the time being, having been brought there from Tahiti two months before. These were four men, one woman, and two children. There were two large frame houses in excellent condition, besides several smaller houses, which furnished comfortable accommodations for the party, and also for the French astronomers, who arrived two days later in the L'Eclaireur. The latter party was composed of the following scientific men: M. Janssen of Meudon; M. Tacchini of Rome; M. Palisa of Vienna, formerly of Pola; M. Trouvelot of Meudon, formerly of Cambridge, Mass.; and M. Pasteur, photographer, also of Meudon.

The landing of the heavy cases containing the instruments was accomplished with difficulty, as even the small ship's boats could not come within several hundred feet of the shore, which was composed of rough coral rock. The cases were taken from the boats by men standing in about two feet of water, and carried to the shore, thence across several hundred feet of coral rock to the land, and about a quarter of a mile farther to the site selected for the ob

servations. After the completion of the landing, the men-of-war steamed away to Tahiti, leaving selected members of their companies to assist in the work. The American party was favored with the help of Messrs. Qualtrough, Dixon, Fletcher, and Doyle, officers of the Hartford, and of ten seamen.

The two weeks preceding the eclipse were occupied in mounting the instruments and in other preparations. Pendulum observations during this time were made by Messrs. Preston and Brown, under instructions from the U. S. coast and geodetic survey. The weather was in general pleasant; though there was one severe rain-storm, and nearly every day there were flying clouds with slight showers, as is not unusual in the region of the trade-winds. The wind was usually strong, and blew steadily from a direction varying from north to east, but never south of east, though the island is in the heart of the south-east trade region. Eight inches of rain fell during the seventeen days which the party spent on the island, more than half of this in one storm on May 4.

The weather on the morning of May 6 was cloudy and threatening; but after several showers the sky cleared shortly before the time of first contact. and remained clear the remainder of the day, with rapidly moving clouds. One of these partially concealed the corona for about twenty seconds in the first minute of totality, and the sun was wholly in a cloud soon after the close of totality; but the observations were not interfered with, though there was at all times haze in the atmosphere. Your readers have already been informed of the nature of the observations planned. All these were carried out successfully, with results which will be given in full detail in the official report of the expedition. A summary of these results can, however, be given at the present time. Professor Holden swept for intra-Mercurial planets, but discovered none. Spectroscopic observations were made by Dr. Hastings and Messrs. Rockwell, Brown, and Upton, with interesting results. Dr. Hastings had devised a spectroscope by which the spectra of two opposite sides of the sun were brought into juxtaposition, and could be examined simultaneously. This instrument, which was attached to a 64-inch equatorial, was used especially to note the changes in the appearance of the 1474 line on the preceding and following limbs of the sun as the eclipse progressed. At the beginning of totality the 1474 line extended to a height of about 12' on the eastern limb of the sun, while on the western limb it was faint, and not more than

4' in height. As the eclipse progressed, the lines changed relatively, becoming sensibly equal at mid-eclipse, and the conditions at the close of totality being the reverse of those at the beginning. This change was many times greater than any change due to the moon's motion, and is regarded by Dr. Hastings as conclusive proof that the outer corona is mainly due to diffraction. The dark D lines were seen in the corona, and the bright hydrogen and magnesium lines by several observers. The relative height and brightness of the coronal rings seen in an integrating spectroscope were estimated.

The duration of totality was five minutes twenty-five seconds. The corona was bright, and characterized by five well-defined streamers, a careful sketch of which was made by Dr. Dixon. The azimuths of the shadow-fringes at the beginning and end of totality were obtained, and their distances from each other estimated. The meteorological observations made by Mr. Upton showed a slight but welldefined rise in barometric pressure, a rise in humidity, and a fall in temperature. The temperature reached the values given at night, while the radiation thermometers indicated that the receipt of heat by the earth was almost wholly checked. The direction and velocity of the wind were unchanged during the time of the eclipse.

The photographs obtained by Messrs. Lawrance and Woods, the English members of the party, who were assisted by Mr. Qualtrough of the Hartford, include a series of negatives of the corona to its outer limits, and also of the coronal spectrum. The latter contains a few bright lines, but not as many as were obtained by the same observers in Egypt a year ago. The phenomenon of reversal of the Frauenhofer lines was also successfully photographed.

The French astronomers obtained many photographic negatives of the corona, and of the sky in the vicinity of the sun, to aid in the search for Vulcan. M. Palisa searched for intra-Mercurial planets without success. M. Janssen saw dark lines in the coronal spectrum, and M. Tacchini a faint spectrum resembling that of comets in one of the coronal streamers. M. Trouvelot made a sketch of the corona, and devoted also a portion of the time to the search for intra-Mercurial planets.

The Hartford returned to Caroline Island on the 8th of May, and on the 9th sailed for Honolulu, which was reached on the 30th; a stop of four days having been made at Hilo, Hawaii, to allow a visit to the volcano of

by side in a horizontal line. Before this plate is the diaphragm d, which can be turned on a vertical axis, and through which there is one hole. With this diaphragm the central opening in the end of r may be alone left open. In front is placed a kerosene lamp. From the flame of this lamp a fine pencil of rays passes through the hole in d, along the tubes r and r', and is reflected by a total reflecting-prism, p, which throws it on the mirror, G, of the galvanometer, which is connected in circuit with the line by the wires z. From the mirror G the light is reflected back through the lens l, which brings the rays to a focus on the photographic plate. This plate is put in a holder, k, in the slide S, before the beginning of the observation. There are spring clamps on S, so that, when the cover is drawn from in front of the plate, the holder will remain in S. In order that it may be possible to expose the plate after the box-cover is put down, there is a slit covered with rubber cloth in the box, through which the fingers may reach the top of the plate-holder and pull out the sliding front. The slide S travels on guides F, and on one side is furnished with two rollers, and on the other with one; so that the movement may be as straight as the guide against which the two rollers press. In the front side of F there is a horizontal slit at the height of the focus of the rays. The back side of S carries a rack which fits a pinion on the driving-axis of the clock U. The downward movement of S is therefore regulated by this clock, of which

For lesser changes the pendulum may be varied in length.

The wires leading to the galvanometer are connected with a commutator. When the needle is in its position of rest, a straight line will be marked on the plate by an upward movement of the slide. From this line the deflections caused when the earth-currents pass are measured. Time-signals may be made by turning back the diaphragm d, when marks will be made on each side of the neutral line. From time to time, currents of known strength may be sent through the apparatus, and will produce spots, as b.

Fig. 2 shows one of the diagrams obtained. The abscissa line was drawn through the portions a, which were marked by the light. The portions a are broken, and at these points occur the dots b, the result of the known currents. c, c are the time-signals.

A NEW CONDENSING-HYGROMETER.

EVERY one who has had occasion to use the common form of condensing-hygrometer for the determination of the dew-point of the air, as devised by Regnault, has found great difficulty in obtaining satisfactory results, especially if the air is in rapid motion, and there is a great difference between the dew-point and the air-temperature.

Professor Crova of Montpellier, France, recognizing these defects, has devised a new form of this apparatus which obviates many of the difficulties, and goes far toward making this justly important instrument one of precision.