The ratio between the metallic acids and bases, exclusive of the water is, as 1:1·04 or Reb. The mineral occurs implanted in red feldspar in small irregular masses having an uneven fracture, but no distinct cleavage. Lustre, sub-metallic; color black, in thin splinters reddish-brown and translucent on the edges; streak reddishbrown; hardness that of apatite (5). Sp. gr. in coarse powder 5124 (16·6° C.). When hot water is poured upon fragments a crepitation or crackling takes place. B.B. with borax gives a reddish-yellow bead while hot, which on cooling be comes yellow; with salt of phosphorus is completely dissolved to a greenish-yellow bead while hot, becoming green on cooling. No reaction for manganese with soda. Treatment with concentrated sulphuric acid gave no reaction for fluorine. [This mineral corresponds in many of its physical and blowpipe characters with the bragite of Forbes (see Suppl. III). Possibly a thorough analysis of authentic specimens of bragite would show them to be very nearly related, if not identical. -G. J. B.]

Uranium, silicates of, see Hermann's paper in Jour. f. prakt. Chem., lxxvi, 320. URANONIOBITE (Hermann), see Pitchblende.

URANOCHALCITE, Hermann.—This name has been given by Hermann to a mineral from Joachimsthal (Jour. f. prakt. Chem., lxxvi, 321). It occurs in reniform amorphous masses having a metallic appearance. Fracture compact, and slightly conchoidal, with a feeble metallic lustre; brittle; opaque; color between steel-gray and pinchbeck-brown; streak black. H. 4. Sp. gr. 5.04. Heated in a closed tube the mineral at first gives off water, and then a sublimate of realgar, and finally metallic arsenic, leaving a black residue consisting chiefly of bismuth, uranium, copper, and iron. Treated with nitric acid the mineral is dissolved with separation of sulphur. On evaporation of the solution, silica separates in the gelatinous form. The analysis gave:

S As Cu Ni Fe Si Bi # Fe Fe й Ag

5.79 723 10.21 0.97 2:31 4:40 36:06 14:41 11.95 3.27 2:40 tr.=99.00* Hermann writes the formula 5(R4Si+4KSi+10H)+R(ASS). [It is quite improbable that this composition is that of a simple mineral, and until further investigation we may reasonably doubt the homogeneousness of the substance analyzed.—G. J. B.] VANADINITE [p. 362, II-IV].-Kokscharow considers the vanadinite crystals from Beresowsk to be pseudomorphs of pyromorphite. Struve found in the interior of each vanadinite crystal a portion of unaltered pyromorphite. The mean of two analyses gave: РЬСІ Pb Feër V P 0:43 2.92

G. 6.863. 9.60 .71.13

15.92

Struve represents this composition by the formula PbCl+Pb(P‡, V24) or (3Pb3ß +PbCl)+5(3Pb3V+PbCl)-(Kokscharow, Mat. Min. Russlands, iii, 44).

VIVIANITE[p. 415, III, IV].—For an article on the composition and formation of vivianite by Alphonse Gages, see L., E. and D. Phil. Mag., [4], xviii, 182.

WATER [p. 110]Analysis of water from the Dead Sea, by Dr. F. A. Genth.Ann. d. Chem. u. Pharm., cx, 240.

WOLFRAM [p. 351, I-IV]-F. A. Genth has published (this Jour., [2], xxviii, 253) an analysis of the wolfram which forms the nucleus of the peculiar tungstate of lime crystals alluded to under scheelite. One crystal showed the planes I, i-1, , and 1-. Sp. gr. 7-496 (at 25° C.). Composition:

corresponding to variety II. (Min., p. 352), having the formula 4Fe W+Mn W.

* The original gives 100, but owing to a typographical, or other error the analysis adds up only 99.

WULFENITE [p. 349, II, V]-The massive wulfenite from Garmisch, is a mixture of molybdate of lead, with carbonate of lead and other substances, as shown by Wittstein's analysis (Kopp's Jahresbericht, 1858, 721):

ZINO-BLOOM [p. 460, 513, VII]-Dr. Elderhorst has described a hydrous carbonate of zinc from Marion County, Arkansas, as a new species under the name marionite (First Geol. Rep. Arkansas, p. 153). The chemical composition he found:

[This is identical with analyses la, of zinc-bloom from Santander in Spain, by Peterson and Voit, published in the last supplement. This analysis gave Zn 731, Ĉ 151, 11-8. These analysts found that zinc-bloom undergoes a change on exposure to the air, thereby losing both carbonic acid and water. A specimen of la, exposed to the air for three months was found to contain Zn 74 73, Ĉ 13-81, H1145. Other analyses by Braun are quoted in the last supplement. Peterson and Voit (Ann. d. Chem. u. Pharm., cviii, 50) give the formula for zinc-bloom Žus, Ĉз, É6, which is the same as that given by Dr. Elderhorst for marionite ;—it is an interesting fact that this is also the composition of the precipitate, produced by adding an equivalent of carbonate of soda to a zinc salt at the boiling temperature. Marionite may be considered as zinc-bloom, and the earlier analyses of this species by Smithson and Berthier, are undoubtedly less correct than those of Karsten and the more recent ones by Peterson, Voit, Braun, and Elderhorst.-G. J. B.] Terreil mentions the occurrence of zinc-bloom at Santander in oolitic grains (L'Institut, No. 1847).

ART. XXXIV.-Theoretical Determination of the Dimensions of Donati's Comet; by Prof. W. A. NORTON.

It is proposed in the present article to investigate the dimensions of the great comet of 1858, at certain specified dates, upon the theory developed in this Journal, (vol. xxvi; No 79), and compare the theoretical determinations with the results of observation. Resuming the equation of the approximate orbit of a particle emitted from the nucleus, obtained in the investigation alluded to, viz.

in which the axis of z coincides with the original direction of motion, a denotes the angle of inclination of this initial line of direction to a line perpendicular to the radius-vector, r the radius of the nucleus, p the acceleration due to the repulsive force of the nucleus at its surface, and k the opposite acceleration produced by the sun's repulsion; let us pass to a new system of rectangular axes, x' and z', of which the axis of z' is coincident with the radius-vector of the orbit of the comet. Effecting the transformation of coördinates, reducing, and denot

ing by H the distance of the vertex of the cometary envelope

b

2

Let z'=0, and we obtain for the half-breadth of the envelope,

2K; and thence, for the coordinates of the vertex of the K

b

curve described by the particle, X==K, and Z=k=2.tanga. Transferring the coördinates to this point, we get for the equation of the curve, referred to its vertex,

This is the equation of a parabola, of which the parameter, 2p,=2K cot a=4h cot 2a; and the distance from the focus to the vertex = -cot a=h cot 2a.

K

2

It is also the equation of the curve that would be described by a particle if it were projected from the nucleus with a certain velocity, and subsequently repelled by the sun alone. From which it appears that the path pursued by a particle repelled from the nucleus is very nearly the same, and, for the purposes of the present investigation, may be regarded as the same, as that which would be followed if the particle were simply projected from the nucleus. If we had occasion to trace accurately the trajectory of the particle in the vicinity of the nucleus, another investigation would become necessary. It should also be observed, that in the case of any particle, which, on its return from its excursion toward the sun, comes into proximity to the nucleus, the parabolic projectory becomes materially modified by its repulsive action, and equations (3 and (4) are inapplicable.

We may conclude from the result just obtained that, so far as the form and dimensions of the nebulous envelope are concerned, the theory of a repulsion exerted by the mass of the nucleus does not differ materially from that of the projection of the cometary matter by an instantaneous force from its surface; which, it appears, has been advocated and discussed by

Bessel.

Other determinations relative to the envelope of the comet may be effected by the following formulas; in which Z= the greatest distance attained by a particle, in the initial direction of motion; Y the actual distance from the nucleus, of the particle when in this extreme position; the angle included between Z and Y; = the inclination of the tangent drawn to

=

ę =

any point of the curve followed by the particle, to the radiusvector of the orbit of the comet; v = the velocity of the particle at the vertex of its parabolic path; and v' its_velocity at any other point of the curve;

=

More accurately, we may obtain the velocity v" at right angles to the radius-vector, for any point of the actual curve, from the following equation :

x':

=

in which a distance of the point from the radius-vector. The distance from the nucleus to any point of the trajectory of the particle, whose coördinates are known, may be readily obtained from the polar equation of the curve.

Equs. (1) to (9) have been obtained on the supposition that the nucleus is at rest; or, in other words, they refer to the relative motion of the cometary particle and nucleus, on the supposition that the two have the saine velocity, and a constant direction of motion through space. Strictly speaking, there is not a perfect accordance between the two motions, even during the short interval of time that the particle remains within the limits of the envelope; but no material modifications of the theoretical results are required on this account, in investigating the form and dimensions of the envelope. But when we undertake to follow the cometary particle, after it has left the region of the envelope, and is receding from both the nucleus and the sun, under the influence of the solar repulsion, it will no longer answer to neglect the orbitual motion of the nucleus.

The general problem, to find the relative positions of a repelled cometary particle, and the nucleus of a comet, after any interval of time, appears to have been first effectually solved by Bessel. This important problem has recently been taken up independently, and solved anew by Prof. Peirce; who has shown. that the orbit of the repelled particle is a hyperbola convex towards the sun, and has verified the supposed law of variation of the sun's force of repulsion. In pursuing the line of investiga

SECOND SERIES, VOL. XXIX, No. 87.-MAY, 1660.

tion in hand, we are led to take a point of view somewhat dif ferent from that occupied by either of these eminent astronomers. It is now proposed to determine both the true and apparent positions of the receding particle, after the lapse of any interval of time, directly from the initial velocity and direction. of motion; in order to take account of the various circumstances of the original motion of the different particles supposed to proceed from the nucleus. The following formulas will serve for this purpose. Equs. (12) to (15) have been deduced from the general equations of motion of a body around a centre of attraction, by changing the sign of the force, and adapting them to convenient computation. Equ. (17) for calculating the true anomaly of the particle in its hyperbolic orbit, from the time, was independently investigated. It is sufficiently accurate for our purpose, and the calculation can be more readily effected with it than by the intervention of the eccentric anomaly. The constants which enter into the equation can be determined by very simple formulas, for any comet the elements of whose orbit are known, and for any position of the comet in its orbit; their values having been determined by other means for the perihelion of any one comet. They depend upon the initial circumstances of motion of the particle emitted from the nucleus. Equ. (16) was deduced from equ. (17).

If any particle, on leaving the sphere of influence of the nucleus, is subject to a diminished attraction from the sun, it will describe a hyperbola concave toward the centre of attraction, and will recede from the nucleus, though less rapidly than if it were effectively repelled by the sun. Equs. (22) to (25) serve for this case. There will be occasion to make use of them when we shall undertake to determine all possible particles that at any assumed date may go to make up the concave outline of the tail.

New Haven, March 28th, 1860.

(To be continued.)

ART. XXXV.-The Great Auroral Exhibition of Aug. 28th to Sept. 4th, 1859.-4TH ARTICLE.

IN the three preceding numbers of this Journal we have given observations of the Aurora of Aug. 28th to Sept. 4th, from almost every part of North America between the parallels of 13° and 48° north latitude. We now present a summary of observations of the same aurora in Europe, with some reports from Asia, and accounts of a simultaneous auroral exhibition in the southern hemisphere.