of the bundle broken parallel to the axis the subpermanent magnetism is contrary in direction to the permanent magnetism. It would be the same in direction in the case of a needle broken in a plane perpendicular to its axis, and of which the two fragments were separated or reunited end to end. This result has been verified by experiment.-Comptes Rendus de l'Acad. des Sciences, Feb. 23, 1874.

CONTRIBUTION TO THE THEORY OF THE MAGNETIC FORCES.

BY M. STEFAN.

66

The memoir consists of three parts. In the first, on the calculation of the magnetic forces of electric currents," it is pointed out that the equivalence between the forces emanating from magnets and those from electric currents is complete, not only, as is known, in the exterior, but also in the interior space, and that in this the action of a magnet on a point outside of its elements must be different from its action on a point within them. A simple rule is given for the calculation of the electromagnetic forces; and it is specially noted that the interior of a sphere round which currents run in parallel circles presents a homogeneous magnetic field, that the same property belongs to an ellipsoid, and that such systems of currents furnish galvanometer- and magnetizing spirals of constant force. In the second part, 66 on the action of a magnet on an internal point," this problem, already touched upon in the first part, is treated more in detail. It is shown that the action of a magnet on an internal point is not completely determined by the magnetic potential that other forces besides those given by that potential are operative, differing in direction and quantity according as the point affected is within or without a molecule of the magnet. These forces are dependent on the form and arrangement of the molecules, and so constituted that the sum of their works on a finite path is =0. Only when the magnetism of the molecules consists of electric currents is the latter generally not the case, and the principle of the conservation of energy requires the entrance of induction currents.

The third part has for its subject the "theory of magnetic induction." The basis of it is formed by the theorem, found in the second part, of the action of a magnet on a point in the interior of its molecules. On the foundation of this theorem the general equations of the theory of magnetic induction and of the theory, identical with it, of dielectric polarization can be immediately written, and, with the aid of some theorems found in the first part, some problems on the magnetizing of a sphere, an ellipsoid, a ring, be solved without further calculation. Several series of experiments are then discussed, from which it results that all sorts of iron and steel admit the same maximum of magnetization, that the resistance of iron and nickel to magnetizing is initially very great, then diminishes to a minimum, which is reached when the induced magnetic moment is one third of its maximum, and that thenceforward the resistance again increases till it reaches an infinite value. From these data and some general considerations is deduced a formula for

the magnetic molecular force, which accords well with experiment. -Sitzung der math.-naturw. Classe d. kaiserl. Akad. d. Wissensch. in Wien, February 12, 1874.

ON A PECULIAR OCCURRENCE OF CRYSTALLIZED SILICIC ACID.

BY THEODOR HÜBENER, OF ROSTOCK.

About a year since, I was treating some Gölitz browncoal for the purpose of exhibiting microscopic products with Schultze's maceration-fluid (a solution of chlorate of potass in nitric acid). After the coal had been sufficiently treated with the liquid, and then extracted with ammonia and alcohol, the microscopic examination showed in the residue a quantity of minute crystals the form of which (six-sided columns pointed at both) ends) left no doubt that they consisted of crystallized quartz. By repeated ignition of the residue and treatment with hydrochloric acid, they could be readily isolated. From, at the most, 1 kilogramme of the coal, I have in this way obtained about 3 grammes of the crystals. I have not at present found them in other browncoals. Unfortunately I have not yet succeeded in obtaining some of the sand which perhaps overlies the browncoal; but as the residue above mentioned contains scarcely any grains of ordinary quartz, it might be supposed that, by the influence of the products occurring in the gummifaction of coal (humic acid &c.), solution of siliceous salts infiltrated into it may be decomposed, whereupon the silicic acid is separated as crystals. My attempts (only on a small scale, it is true) to separate silicic acid in crystals by protracted digestion of humous substances with solutions of siliceous salts have been without result. I shall, however, continue these experiments during a longer time; and I have no doubt that in this way I shall succeed in separating crystallized silicic acid from solutions.--Poggendorff's Annalen, vol. cl. p. 643.

ON THE SPECTRUM OF THE LIGHT OF EXPLODING GUN-COTTON. BY O. LOHSE.

The yellowish flame produced when pyroxyline is ignited gives a very interesting spectrum. I first observed it, with a Browning miniature spectroscope, in January 1872, at a time when the frequently occurring phenomena of the aurora borealis induced me to investigate the origin of its spectrum. I thought then, on superficial consideration, that I could recognize a certain similarity between the latter and the spectrum of exploding gun-cotton-a sufficient reason for undertaking, in conjunction with Dr. Vogel, an accurate examination of this spectrum with a larger spectrum-apparatus which permitted the measurement of the lines and the determination of their wave-lengths. The result was that the lines of the two spectra did not coincide.

If I take leave to communicate in the following the details of the investigation, it is in view of the interesting experiments which have taken place in the Arsenal at Woolwich, on the velocity of propagation of the explosion of pyroxyline.

The brightest lines in the spectrum of this nitro-body are the two sodium-lines; they appear, however, not as in a quietly burning alcohol flame saturated with vapour of sodium, but strikingly widened, so that frequently the space between them vanishes. So far as the observations extend, this appears to be dependent on the violence of the explosion. Also the more refrangible sodium-line is always the most widened.

Characteristic of the spectrum are two brilliant lines in the green, which are indistinct on each side, and of which the more refrangible is the more intense. Further, there are two bright broad bands, striking in the red and orange, sharply defined towards the red end, and dying off towards the blue. Besides these lines and bands, we succeeded in measuring a faint streak in the red, another in the green, and a faint but sharp line in the green. Between the bright lines a continuous spectrum was present; but it could not be traced far beyond the green.

The instantaneousness of the explosion of the pyroxyline rendered extremely difficult the fixing upon the lines; yet I believe that a fair degree of certainty may be attributed to the following numbers, as numerous and repeated measurements were effected:Wave-length.

millionths of a millim.

644-6 A faint streak.

554.8

A very bright, broad but ill-defined line (aurora borealis 557.1).

550-4. A bright, broad, ill-defined line.

Poggendorff's Annalen, 1873, No. 12, p. 641.

DR. J. H. VON MÄDLER.

On the 14th of March, 1874, one of the first of European astronomers, Dr. Mädler, Professor and Director of the Dorpat Observatory, entered into rest. His life had been one of ceaseless and untiring activity, and he was well known for his general astronomical labours; but the work that will carry his name to posterity perhaps more than any other is the Mappa Selenographica, bearing his name conjointly with that of Beer. From the announcement of his death sent by his widow, Minna v. Mädler, to his friends, we learn that during the last sixteen months his sufferings were very great from frequent attacks on his brain, to which he ultimately succumbed when about completing his eightieth year. His works were numerous; and we fully enter into the feelings of the widow in desiring, according to her own expression, "a blessing on his works and peace to his ashes."