Such is the brief account of our researches which we wished to present to-day to the Academy. It is probable that our experiments, which give, in considerable masses, substances whose hardness is comparable to that of the natural ruby, will be utilized from time to time by the watchmaker, and even by the jeweller. We will say, in conclusion, that in this labour the aim we pursue is exclusively scientific; consequently we put into the possession of the public the facts we have discovered, and shall be very happy to learn that they have found useful industrial applications. VIII. On a Variety of the Mineral Cronstedite. By FREDERICK FIELD, F.R.S., Vice-President of the Chemical Society*. THE HE various analyses of the interesting mineral Cronstedite, named after the Swedish mineralogist Cronstedt and hitherto found only in two localities (Przibram in Bohemia and Wheal Maudlin in Cornwall), are rather conflicting, since the amounts of ferrous and ferric oxide differ considerably, as the following results will show. Nevertheless all examinations tend to prove that Cronstedite is essentially a hydrous silicate of ferrous and ferric oxide. From four specimens from Przibram we have:— This was corrected by Von Kobell, after a determination of the degree of the oxidation of the iron, which gave: And in two more analyses, one by Steinmann and one by Damour, the ferrous oxide varied more than 2 per cent.: * Communicated by the Author. SiO2. Fe, 03. Fe 0. MnO. MgO. H2O. Steinmann... 22.83 29-08 31.44 3.43 3.25 10.70 Damour...... 21.39 29.08 33.52 1.01 4.02 9.76 Messrs. Maskelyne and Flight, in a valuable paper upon certain Cornish and other minerals (vide 'Journal of the Chemical Society,' new series, vol. ix. p. 9), gave the results of some analyses of specimens of Cronstedite from Cornwall, handed them by Mr. Talling; but these, again, are not very concordant. The first analysis of this mineral gave the following numbers: Iron protoxide 36.307 36.762 ...... 17.468 10.087 •087 100.711 Water Calcium oxide A second analysis, with a fresh and more carefully selected material, gave the following percentages: Mr. Talling called my attention to an amorphous, dark leekgreen mineral, at times associated with Cronstedite, which struck me as interesting, inasmuch as, although differing so widely at first sight from the brilliant black of the latter, yet had exactly the appearance and colour of the streak of Cronstedite after abrasion with a file or some hard mineral. Qualitative examination proved it to consist entirely of ferric and ferrous oxides, silicic acid, and water. Its specific gravity was 3, hardness about 2·5. On heating, water was evolved, and the green powder rapidly passed into yellowish brown. No traces of either magnesium- or manganic oxide could be detected (as in the case of the Bohemian mineral); and there was no evolution of carbonic acid on the addition of weak hydrochloric acid, by which it is instantly decomposed with separation of silica and solution of the two iron oxides. A quantitative analysis yielded: It would be useless perhaps to attempt to give a formula to the above; and the entire absence of crystallization deprives it of much of the interest it should otherwise possess. The following, perhaps, would give the best idea of its constitution : It may be merely a coincidence; but it is worthy of remark that the water in the mineral just described and that in the Cronstedite examined by Messrs. Maskelyne and Flight* is much about the same, which can also be said of the ferrous oxide, neither of them varying 1 per cent., while the silicic acid and ferric oxide seem, so to speak, to have changed places. It has already been remarked that, on heating the green mineral, its colour is changed to yellowish brown; and on examination of the residue, no trace of ferrous oxide could be detected. When the water has been drawn off, at the lowest possible temperature, and the mineral further heated, it rapidly gains in weight from absorption of oxygen. IX. On the Distribution of Electricity on two Spherical N the two memoirs "Sur la Distribution de l'Electricité à la Surface des Corps Conducteurs," Mém. de l'Inst. 1811, Poisson considers the question of the distribution of electricity upon two spheres: viz. if the radii be a, b, and the distance of the centres be c (where c> a+b, the spheres being exterior to each other), and the potentials within the two spheres respectively have the constant values h and g, then for Poisson's f) writing $(~), and for his F F() writing a * From the most carefully selected specimen. (x)-the question depends on the solution of the functional equations ap(x)+ Φ where of course the x of either equation may be replaced by a different variable. It is proper to consider the meaning of these equations: for a point on the axis, at the distance from the centre of the first sphere, or say from the point A, the potential of the electricity on this spherical surface is ax or x X $(2), accord ing as the point is interior or exterior; and, similarly, if now denote the distance from the centre of the second sphere (or, say, from the point B), then the potential of the electricity b2 on this spherical surface is be or (2), according as the point is interior or exterior; (x) is thus the same function of (x, a, b) that P(x) is of (x, b, a). Hence, first, for a point interior to the sphere A, if x denote the distance from A, and therefore c-a the distance of the same point from B, the potential of the point in question is X and, secondly, for a point interior to the sphere B, if x denote the distance from B and therefore c-x the distance of the same point from A, the potential of the point is The two equations thus express that the potentials of a point interior to A and of a point interior to B are = h and g respectively. It is to be added that the potential of an exterior point, distances from the points A and B =a and c-a respectively, is and that by the known properties of Legendre's coefficients, when the potential upon an axial point is given, it is possible to pass at once to the expression for the potential of a point not on the axis, and also to the expression for the electrical density at a point on the two spherical surfaces respectively. The determination of the functions 4(x) and Þ(x) gives thus the complete solution of the question. I obtain Poisson's solution by a different process as follows:-Consider the two functions respectively. Ynx + En Observing that the values of the coefficients are (a, b)=(-a2, a2c), and (a, B)=(—b2, b2c ), so that we have (γ, δί \-c', c2-a2 ( a+d=a+d, =c2—a2—b2, ad—bc=ad—ßy, =a2b2, and consequently that the two equations (x+1)2 _ (a + d)2 (x+1)2 _ (a +8)2 λ = = ad-be' λ аб-BY are in fact one and the same equation (x+1)2 _ (c2 — a2 — b2)2 = λ a2b2 for the determination of λ, then (by a theorem which I have recently obtained) we have the following equations for the anx c_x+d2= 1 n-1 a+ x2 = 1 (a + d)" ̄ { (x2 + 1 − 1 ) (ax+b)+(\"−X)(−dæ+b)}, and similarly {(x2+1−1)(cx+d)+(λ”—λ)( ca—a)}; -1 +1 {(λn+'—1)(yx+8)+(x”—x)( yx−α)}. |