to some other, founded in better ascertained laws of matter. The question is not one of pure mathematics, but of physics.

The material elements of all bodies of which we have any knowledge, are united by some conditions of aggregation, determined by the reciprocal action of molecular forces; and the circumstances of their relative motion will come from the equation d2y

Ση.
n.[(d2 z − x )8 x + ( 1 2 2 − Y )s y +(d2 2 − Z) 8 z]=0

0;

in which m is the mass of an element, xyz its coördinates of place, XYZ the sums of the components of impressed accelerations in the direction of the axes xyz, respectively.

The conditions of aggregation may be expressed in some functions of the coördinates of molecular places. As three coördinates determine the place of a single molecule, there will be three times as many coördinates as molecules; and if u be the number of molecules and the number of equations that give the conditions of aggregation, then will 3u-n be the number of coördinates which, if given, would reduce the number of unknown coördinates to the number of equations. These unknown coördinates could then be found, and the places of the molecules at the corresponding instant determined.

Denote the coördinates by xyz, x'y' z', &c., and the n coördinates by aßy, a'B'y', &c. The former of these coördinates, as also the forces, may be expressed in functions of the latter, and both eliminated from the general equation of motion. And if Ent, 'n'', &c., be the increments of a By, a' B'y', &c., at any instant and due to any transmitted initial disturbance, it is easily shown that

In which there are n terms comprehended by the sign, and in which will, in general, have different values from one term to another. When these values of ę are real and positive, the dif ferent terms in the values of 75, &c., will disappear periodically, the precise times of disappearance being given by

t.-ran; t'√√-r'=a'n; &c., &c.

in which a is any whole number. The intervals of disappearance will be

and if these intervals be commensurable, all the terms will dis

The vast atmosphere of ether which pervades all space is ever busy transmitting luminiferous waves from the sun and other heavenly bodies. Its molecules are ever on the move with velocities and in orbits determined by the relative places and intensities of existing wave sources. Any cause which will perturbate the etherial molecules of any limited volume of ether from these orbits, regarded as initial, and by the quantities § 75, '', &c., will make such volume self-luminous; and if the perturbation be great enough, it will be visible from all directions. Comets are known to exist in a state of great tenuity, their densities being almost insignificant in comparison with that of the fleecy clouds that float in the upper atmosphere. The luminiferous waves from the sun, entering such bodies with great ease, their intromitted greatly preponderate over their reflected components. The former of these components modify and determine the internal motions of comets, and make them self-luminous. The internal cometary elements become so many centres of disturbance. They throw their waves in all directions, and are simultaneously sources of molecular perturbations to the surrounding ether, each giving rise to a term R.N.Sm (t.√5—7), in the general value of the perturbating functions Ent, &c., and thus making the ether also self-luminous. The degree of illumination will vary with the maximum values of the perturbating functions. These will result, in any case, from the extent of the initial disturbance and the distance, at right angles thereto, over which the disturbance may have been propagated; decreasing, according to the principle of wave divergence, as the square of this distance increases. The components of the initial disturbance perpendicular to the line drawn from the comet to the sun, is, from the principle of wave propagation, much greater than in any other direction; and hence the much greater extent of the illumination on the side of the comet opposite the sun. The comet's head can have no phases, from its self-luminosity; neither can the coma and tail have sharply defined outlines, from the gradual degradation of molecular perturbations towards their borders.

This view denies the presence of cometary material in the coma and tail altogether, and regards these appendages but as phenomena due to the reciprocal action of the etherial and cometary molecular forces. According to it, the coma and tail become, as it were, a luminous shadow, a part of which is literally "cast before," and the dark cap which envelopes the head and

stretches away through the tail, a region of wave interference. No wonder, then, that comets turn their tails from the sun, and, at perihelion, whisk them, though of enormous lengths, through celestial arcs well nigh equal to a semi-circumference, in a few hours. This is no more surprising than that opaque bodies throw their shadows from the luminous sources whose light they intercept. The curvature, which is so remarkable a feature in the tail, is but the simple effect of the comet's orbital velocity, and the progressive motion of light.

If the principles here cited be well founded, then will the zodiacal light find an easy solution; and the great oblateness of its spheroidal figure must be taken as evidence that the component molecular motions in the sun are greater in the direction of the solar axis than in any other.

West Point, Oct. 25th, 1859.

ART. VIII.-On Sodalite and Eleolite from Salem, Massachusetts; by J. P. KIMBALL, Ph.D.

FOR a knowledge of this locality of the occurrence of the two rare silicates, sodalite and elæolite, we are greatly indebted to Gilbert L. Streeter, Esq., of Salem, as well as to several other gentlemen of the same city. Fortunately, Mr. Streeter very carefully observed their mode of occurrence, and, together with G. F. Cheever, Esq., and Rev. S. Johnson, Jr., collected choice specimens of them. The best of these are in the possession of the Essex Institute, Salem, to the curator of which, Dr. Henry Wheatland, I owe in a great measure the privilege of examining them.

The locality in which the minerals were found is "a pit or quarry, a short distance below the Almshouse upon the road passing along the northern side of the Neck, towards Hospital Point. They were first noticed in a "block of compact syenite resting upon the bank, the end of which presented a beauti ful coloring of blue and greenish white, with specks of black. Upon examination these conspicuous minerals were seen to be in a vein, a portion of which was connected with the block of syenite."+

Mr. Streeter subsequently discovered what undoubtedly was the continuation of the same vein. This traversed an erratic block of the same rock, imbedded in the drift, of which the small block, just mentioned, was a fragment. The vein is described to have been about six feet in width, and to have dimin

* G. L. Streeter: Essex Institute Proceedings, ii, 153.

SECOND SERIES, VOL. XXIX, No. 85.-JAN., 1860.

t Ib.

ished in thickness "wedge-like to a mere line at the termination." Although this vein-stone was identical in its character with that of the smaller block, its yield of fine specimens of sodalite and elæolite was less abundant than that of the latter. Unfor tunately enough, the discovery of the minerals was not made in time to rescue this precious vein-stone from the hands of the quarrymen. Large masses of it including, it is believed, the best specimens, had been carted away and buried deep beneath a littoral road along Collins' Cove. The quarry was opened in the autumn of 1855. I visited it last spring when it was not being worked, and found amongst the debris of the quarry very good specimens of both minerals. At that time a portion of the boulder which contained the vein was still left. This I identified as a syenitic porphyry (Quarzfreier Porphyr of Senft). It is characterized by remarkably entire crystals of oligoclase of a greenish color, which make up the base of the rock. Thickly disseminated through the base are minute grains of hornblende and scales of mica.

Besides the sodalite and elæolite, the vein-stone is composed of orthoclase for the greater part; biotite in black tabular prisms; small crystals of zircon in octahedral prisms; fine stellate brownish-yellow flakes of xanthosiderite; and (probably) albite in small, irregular, reddish, granular masses.

At Litchfield, Me.-the only other known locality in America where sodalite and elæolite occur together-these minerals are further associated with cancrinite and, as at Salem, with zircon; but instead of occupying a vein as in the Salem instance, exist as accidental constituents of a granitic rock composed of quartz, feldspar and black mica,* thus constituting a miascite analogous to that of the Ilmen mountains. The Litchfield rock, to be sure, is found only as erratic blocks; but the absence of cancrinite in the Salem boulder, and the dissimilarity between this and the Litchfield rock as to petrographic character, tend to preclude the possibility of the two having a common source.

Sodalite. The sodalite from Salem has quite the same charac ter as that from Litchfield and the Ilmen Mts., with specimens of which I have been able to compare it, excepting that the former in common with the elæolite, is contaminated with minute particles of what appears to be mica, thus rendering it very difficult to glean perfectly pure mineral for analysis. It is in crystalline, sub-translucent masses having an indistinct cleavage. Its lustre is greasy, and its color beautiful lavender blue.

Three separate determinations of its specific gravity were made with different portions of the mineral, giving the results as follows: 2.294, 2·303, 2·314.

J. D. Whitney: Poggendorff's Annalen, lxx, 434.

+ Senft: Classification und Beschreibung der Felsarten, 218.

Two portions of the mineral were used for the analysis. The one portion was treated with nitric acid, and the chlorine determined as chlorid of silver. The other portion was treated with diluted hydrochloric acid, whereby the silica, alumina, lime and soda were determined according to the customary methods.

Prof. J. D. Whitney,* in his analyses of the sodalite and its associated minerals from Litchfield, has so fully observed their chemical properties as to render superfluous here any remarks on the same subject.

Calculating all the sodium as soda, the following results are obtained:

But on the other hand, assigning to the percentage of chlorine enough of sodium to form chlorid of sodium in accordance with von Kobell's formula of this mineral (Na3Si+si+NaCl), we have 18-17 for the percentage of soda in combination with silica. Hence the analysis will stand thus:

These results are sufficiently in agreement with the established formula.

Eleolite. The elæolite from Salem possesses all the constant physical properties of this variety of nepheline. Its color is dull green, its lustre greasy, and its fracture sub-conchoidal. It is sub-translucent, and in structure massive. Its specific gravity is 2.629. Its chemical composition I find to be as follows: