ion of each belt into two pairs, the inner belt being denser than the outer, and the inner member of each pair being denser than its companion; Mercury being denser than Venus; Earth, than Mars; Jupiter, than Saturn; Uranus, than Neptune. This arrangement towards the Sun as a principal centre, appears, however, to be of more recent date than the tendency to condensation in the Telluric belt, for Earth is denser than Venus, and the great secular ellipticities of Mars and Mercury suggest the likelihood of a quasi-cometary origin. Similar tendencies would contribute to the chemical grouping of atoms by pairs, which is essential for polarity and for the already enumerated laws of chemical combination. 2 In the "nascent state," particles may be regarded either as parabolically perifocal, with the velocity of complete dissociation from a given centre, or as relatively at rest, and ready to obey the slightest impulses of central force. The mean vis viva of a system formed by two such particles would be m x (√2) 2 + m × 02 m × 1, representing a change from parabolic to circular orbits and a condensation of two volumes into one. At the parabolic limit between complete dissociation and incipient aggregation, if the focal abscissa 。 VF is taken as the unit of wave-length, the value of the successive ordinates, as well as the velocity communicated by uniform wave influence acting through the entire length of the ordinates, will be represented by V4; the resulting vis viva, and the consequent length of path, or VF ƒ2ƒ3 ƒ ƒ5 ƒ major axis, communicable against V uniform resistance, by 4 n; the successive differences of major axis, by 4. Each normal, V f equals +2' + 1fa the next ordinate, v + 1; there are, therefore, triple tendencies, both in the axis of abscissas, and on each branch of the curve, to suc cessive differences of 4 in the major axes of aggregation, in consequence of the meeting of abscissal, ordinal, and normal waves in the axis, and the meeting of tangential, normal, and abscissal waves upon the curve. At each node of aggregating collision two of the wave systems are due to normally alternating rectangular oscillations,* the third serving as a link between the axial and the peripheral waves. The bisection of the normals, by their equivalent ordinates, adds importance to the normal major axes, and increases the tendency to aggregation at their respective centres of gravity. "Fundamental Propositions," 13. Chemical molecules and atoms are so small that we are unable, at present, to show, so conclusively as in cosmical gravitation, that the "nascent" velocity, or the mean radial velocity at the limit between complete dissociation and incipient aggregation, is equivalent to the velocity of light. But the analogies, which are here presented, are strengthened by the frequent vivid, luminous and thermal accompaniments of chemical change, and by the electric polarity of combining elements. It seems, therefore, reasonably certain that the same limiting unity of velocity and vis vica, which can be easily traced in light, heat, electricity and gravitation, is also fundamentally efficient in chemical affinity. M. Aymonnet, in his communication of a "nouvelle méthode pour étudier les spectres calori fiques, "* says: "Je ferai remarquer, avant de terminer, que l'étude des spectres calorifiques d'absorption, faite avec des corps portés à diverses températures, peut et doit conduire à la connaissance de lois physiques reliant les phénomènes d'association et de dissociation des corps aux phénomènes calorifiques et lumineux." In another paper recently presented to the French Academy, "sur le rapport des deux chaleurs spécifiques d'un gaz," M. Ch. Simon deduces the theoretical ratio Cc:: 1.4 1. The first attempt at a solution of the problem upon a priori grounds, appears to have been Professor Newcomb's, who found from the hypothe sis of actual collisions, the ratio 5: 3 if the particles were hard and spheri cal, or 4 : 3 if they were hard and not spherical; the second, my own,§ based on the general consideration of all internal motions, which led to the ratio 1.4232: 1; the third, M. Simon's, which took account of rotations and neglected other internal vibrations. * Comptes Rendus, lxxxiii, 1102-4, Dec. 4, 1876. † Ib. 727, Oct. 16, 1876. Proc. A. A. S., v., 112. Ante, xiv, 651. CONTRIBUTIONS FROM THE LABORATORY OF THE UNIVERSITY OF PENNSYLVANIA. No. VII. On astrophyllite, arfvedsonite and zircon, from El Paso Co. Colorado, and a colorimetric estimation of titanium before the blow-pipe. BY GEORGE AUGUSTUS KÖNIG, PH. D. (Read before the American Philosophical Society January 19th, 1877.) General occurrence. The three minerals are imbedded in quartz. On the specimens which I examined no orthoclase, nor any other species could be found; yet the mother rock may be presumed to be a very coarse grained granite or syenite. Until satisfactory information is received on this point, it must, of course, remain doubtful. In stating that the three minerals occur together, it is but right to say, that I make a hearsay statement. For, the specimens of quartz in which astrophyllite and zircon abound, are destitute of arfvedsonite, and the specimen on which the latter is abundant, does not show either of the two other species. But the character of the quartz, as the common matrix, is strictly identical throughout, of grayish color, locally stained with iron ochre, and massive in structure. The co-occurrence of these three species, at once calls up the close similarity with that of Brevig in Norway, the only locality at which astrophyllite was known to exist. The only difference being that orthoclase forms the matrix at Brevig, and quartz in Colorado. To Dr. Foote, of this city, I am indebted for the material of this investigation. I. ASTROPHYLLITE. Geometrical properties. The crystals exhibit elongated prismatic forms, the cross section being nearly a rectangle on the majority of the individuals. I succeeded in finding some crystals, however, whose section is more complicated and with which I endeavored to establish the angular relations between the several faces. No terminal development of any kind could be observed; the crystals appear all broken across the direction of main extension. The measured edges are, therefore, all in one zone. The figure represents a cross section of the best developed crystal, and the faces are designated a, b, c, etc., solely in reference to their sequence. a is a cleavage face and reflects a sharp image, the other faces are true crystal faces, and, with the exception of c, reflect very imperfectly. The largest face (a) is not quite one-eighth of an inch wide. The measurement does not make any pretension of scientific accuracy for the reasons stated, yet the above angles are the means of repeated observations, which only differed by 10, for the edges a ^ e, c ^ e, and by less than 30′ for the other edges. Their approximate accuracy taken for granted, they clearly admit only an interpretation according to the laws of the monosymetric system, when c becomes the basal plane, e an orthopinakoid, band d hemidomes. Scheerer, who first described the species (B. H. Ztg. XIII 240, 1854) arrived at a different result. His measurements lead to an orthorhombic interpretation, and the optical investigations of Des Cloizeau (Dana, mineralogy) corroborate his view. But as none of the angles measured by me, find and analogon in those given by Scheerer, no comparison can be made, and future study must decide the truth. Structural properties. A very marked cleavage exists parallel to the face c, by which the structure becomes eminently micaceous. The cleavage is indicated on the lateral faces by a decided striation (very plainly visible on the quartz, after the removal of crystals), and re-entering angles. Unlike other micaceous minerals, the lamina are but very slightly elastic and tenacious, being easily reduced to a fine powder. That the crystals break easily across the main extension has already been mentioned. Hardness about 3. Optical properties. Color from brass yellow to deep bronze brown. Transmitted light deep yellow to reddish brown. Appearance of the powder at a certain degree of fineness like mosaic gold. I could not obtain an image of interference with a lamina, through which types of ordinary print were plainly visible But not possessing much experience in optical investigation, I have referred it to Professor P. Groth, of Strassburg. Specific gravity 3.375 at 15 Co. Pyrognostic properties. The mineral fuses very readily to a black globule in the flame of an oil lamp. With microcosmic salt the reactions for iron, manganese, titanium and silica are easily obtained. The mineral decomposes completely with sulphuric acid at ordinary pressure, and very readily in a sealed tube at 140 CO. The most rational approach to these figures will be represented by the by which all the affinities are satisfied. Note. In the above calculation zirconium is converted into its equiva Comparing my analytical results with those of Pisani, Scheerer, et. al. |