same property; because the line drawn from the upper extremity of the edge, on which their base originates, to the lower extremity of the opposite edge, is perpendicular to both, as I have explained in my Memoir on the Law of Symmetry.

The ratios of which we are speaking appear at intervals in the series of those which the different angles give that divide the circumference...They take place at the parts in which their component parts are susceptible of division by a common factor, which reduces their value, and frees them from the complication in which they were enveloped. The intervals which separate these ratios answer to the differences in the corresponding angles, which vary more or less, sometimes the fourth of a degree, sometimes half a degree, or more. When the crystals on which we operate have a form not very determinate, it is possible that an approaching ratio may be taken for the true one. This of necessity happened to me more than once when I was composing the geometrical part of my Treatise, I have corrected, as I have already said, a part of my old determinations, among which there are some that relate to the angles taken by Mr. Phillips, to which they approach much more nearly at present than they did formerly.

t

Admitting then that I have obtained, with respect to all the other species, ratios in which accuracy agrees as nearly as possi ble with simplicity, as, I think, has been the case in particular with regard to quartz, oxide of tin, and sulphate of lead, I consider myself as entitled to say, that these ratios are sufficient to determine without any ambiguity the laws of decrement, on which depend the secondary forms belonging to each species; for the difference in the inclination of the faces that would be. produced by mistaking one law for another, would be much greater than what could exist between the angles as given by my ratio and by the reflecting goniometer. There is even in the results derived from both a convergence worthy of being remarked and very favourable to the theory. It consists in this, that the differences between the primitive angles become much less in the inclinations of the secondary faces; so that sometimes they approach so near that all difference vanishes. I shall take as an example the angles of the primitive rhomboid of calcareous spar. According to the measures of Wollaston and Malus, the angle which any face of the rhomboid forms with a parallel to the axis is 134, 37' instead of 135° which I had indicated, from the condition that when the axis of the rhomboid was situated vertically, each of its faces was equally inclined to a vertical and a horizontal plane. If we set out from the two preceding measures, we find for the great angle which the faces of the rhomboid make with each other on the one side 105° 5′, on the other 104° 28', which is a difference of 37'. But this difference diminishes in passing into the results of the decrements which produce the secondary forms; so that in the metas

tatic dodecahedron it is only 10 and 4' for the two respective inclinations of the faces situated towards the same summit. In another dodecahedron, which results from a decrement whose exponent is on the same edges of the primitive rhomboid, it is reduced to 2' and 1'2"; and in a third dodecahedron, produced by an intermediate decrement on the lower angle, and which belongs to the variety which I have called euthetic, it falls between 1' 50" and 26".

Now it is evident that the ordinary goniometer employed to verify ify these different results, is of a precision which may be considered as rigorous. The angles of the crystals of quartz, of oxide of tin, and of sulphate of lead, have presented convergences of the same nature, though rather less sensible."

I add that the forms of the integrant molecule, being the geometrical types of the species, the ratios which I have, adopted have, în consequence of their simplicity, the advantage of offering neat conceptions, and easy to take up from that which characterizes these types, and the lines of demarcation between the different species deduced from them, while the mind perceives only through a mist, as it were, these distinguishing characters obscured by the great numbers in which they are enveloped.

We perceive at once and we remember the result which informs us that the cosine of the smallest incidence of the faces in the primitive rhomboid of quartz is the thirteenth of the radius. But the other result, according to which it is only the, is not easily understood, and cannot be remembered.

I have advanced above, that the ratios between the dimensions of the primitive solids, such as I have chosen them, are sufficient to determine without ambiguity the laws of decrement from which the secondary forms are derived. This I shall render sensible by an example drawn from the forms produced by decre ments on the inferior edges, D, D (fig. 11), of the primitive rhom boid of calcareous spar. This decrement produces dodecahedrons with scalene triangular faces, more or less elongated, which I represent in general by that represented in fig. 12. When two ranges are abstracted, we obtain the metastatic variety in which the incidence of N on N is 144° 20′ 26′′, that of Non N 104° 28' 40", and that of N on N 133° 26'. Among the other known dodecahedrons, that which approaches most nearly to the

This law gives

139° 52′ 50′′.

Diff. 4° 27' 36".

preceding has for its sign D.
For the incidence of N on N,
of N on N', 106 13 30.
. 1224
of N on N", 141 12 24.

Diff. 1 44 50
Diff. 7 46 24

Hence it is obvious that we can easily avoid mistaking this last dodecahedron for the metastatic. POT radto

Let us suppose a dodecahedron much nearer than the last,

Far;

15

the sign of which would be Ď; ; we shall have for the incidence

of N on N, 142° 13′ 22′′, which differs from the corresponding angles of the two preceding dodecahedrons 274 and 2° 20' 32".

For the incidence of N on N′ 105° 15′ 14′′ Die 36, 8434 Diff. 36 34" and

58' 16".

For that of N on N′′, 137° 5′ 56′′. Diff. 6° 14′ 30′′ and 4° 6' 28".

from We see that there remains still a certain latitude for the appre ciable differences of other dodecahedrons approaching still more and more to the metastatic; but which can only be regarded as hypothetic; because the law on which they would depend would deviate more and more from the simplicity of the ordinary laws,

15

than that represented by D, the possibility even of which may be questioned.

entre ei and I return to the measurements of angles taken by the reflecting goniometer. Mr. Phillips acknowledges that this instrument is very delicate, and requires great attention in the choice of the crystals to be measured. He mentions one which gave him successively for the inclination of two of its faces 92° 55′ and 93° 20′, or even 93° 25′, which makes a difference of 30. He speaks of another kind of difficulty which comes from the inequalities of reflexion on the different faces. Having undertaken to deter mine the angles of the crystals of oxide of tin, he no doubt had at his disposal the most perfect which the county of Cornwall could furnish; and he has himself furnished the touchstone of his results, by indicating the measures, which may be considered as given à priori, or which depend geometrically on each other, We have seen that some of the differences which had prevented him from being of accord with himself, were equal to those which exist between the primitive angles indicated by his goniometer, and those which correspond with the limits which I have adopted, and that there is even one which goes a great deal further; namely, to 26'..

Without venturing to pretend that the simple ratios on which these limits depend are the true ratios of nature, as seems is to me to have been the conclusion of philosophers of distinguished merit, I think at least that the results just stated are insufficient to demonstrate the contrary. But I will suppose, if you please, that the reflecting goniometer, employed with all the requisite skill on crystals possessed of the greatest perfection, gives appreciable differences from the angles deduced from the ratios of which I have spoken, and that these differences may amount to half a degree, too.

To render the new angles obtained in this way capable of being employed in the applications of the theory, we must deduce

a fixed ra

terminat dat we must

a their sines and cosines. But in the first place can gles can only be approximations; the measures from which they have been deduced having but an indefinite degree of precision. Further, suppose in the valuation of these we neglect every thing beyond a certain quantity, such neglect every thing beers meas second, the as the minute numbers representing the sines and cosines will always exhibit a series of decimals, which has no so still neglect something in order to submit them to calculation. In my mode of operating the occurence of a simple ratio, which presents itself to our view, points out the term at which we ought to stop; so that if different observers are directed by the same rule, they will agree about the w of the point in on the other hand, we Boxed from. If, measures taken with different instruments in their possession, they will necessarily vary in the choice of the limit at which they ought to remain.

suppose

if

Thus the measures of the angles, which have been published, though valuable in themselves, are hitherto nothing more than isolated observations, which nobody has attempted to bring under the requisite form to make suitable to the theory. It is the business of the philosophers who have given us these measures to complete their work by giving us the manner of deducing from them the fixed data for the solution of problems relative to of crystals. But I think I can affirm, that these data will do nothing more than displace a little the term from Which the theory must set out, and that without any other assistance than that of the ordinary goniometer, it has at present all that is requisite to arrive at its principal object, by a route equally certain and easy.

the etry

6978

betnovanq bad deeds rosacralih sil la amos sdt 1992 over 9W 920dt of laupe now oemid diw biocon lo quisd mort mid -oinog aid ya botes bni rolgas villany cat noon tod dene dorda eved i donlw and ARTICLE III. a szoftbas, poJAUZ inch 35979 $ 2oog noida ong ngva madt & My bas „pesgob. Memoir on Cyanogen and Hydrocyanic Acid. By M. Vauquelin daidw no aciter slam ori ind' baster of pada w odw

PRUSSIC acid, in consequence of its singular nature, may be reckoned among the number of bodies which more particularly captivated the attention of the most celebrated chemists. The annals of the science recall the numerous experiments tried in vain by Geoffroy, Macquer, and Bergmann, to separate the

t

cmake theple of prussian blue. It was reserved for Scheela

to make that important discovery, which afterwards received, from Berthollet all the development, consistent with the then state of chemical science. However, the continual progress. which chemistry made from day to day soon enabled us to perceive great blanks in our knowledge of the properties of prussic

* Translated from the Journal de Pharmacie, Nov. 1818, p. 435.

17

acid. This produced a desire to see some skilful chemist undertake this difficult task, and give it all the perfection which the great improvements in the means of analysis induced chemists to wish for and expect. This task was accordingly undertaken by M. Gay-Lussac, and the results to which he arrived would have been astonishing had they not been produced by a philosopher possessed of very uncommon sagacity; yet he acknowledged that experiments were still wanting to complete the subject. This confession occasioned the memoir of M. Vauquelin, of which we propose to give an abridgment in the present article. Even M. Vauquelin himself still admits that his own labours are far from completing our knowledge of this intricate subject. "Though I found the road struck out, and easily followed," says he, "I am yet far from pretending that I have traversed the whole of it. Many lateral paths issuing from that road still remain to be discovered. But these routs will gradually be laid open." Sad now lo sbrze doriw Of the Alteration which Cyanogen dissolved in Water gradually undergoes, ealt moft tusb;ve ei t

The phenomena presented by the decomposition of cyanogen dissolved in water are very important to be known. Upon them depend the explanation of a multitude of changes observed in the reaction of this body, and of hydrocyanic acid on other bodies. This is the reason why M. Vauquelin begins with it in his

memoir.

The fresh solution of cyanogen in water is quite colourless; but after an interval of some days it becomes yellow, then brown, and allows a matter of the same colour to precipitate. Then the liquor has lost the penetrating odour of cyanogen, and possesses the peculiar odour of hydrocyanic acid. If iron filings do not occasion the formation of prussian blue, as would happen if they were brought in contact with pure hydrocyanic acid, this depends upon a cause which will be understood immediately. We may, however, produce prussian blue in the liquor separated from the iron filings, by adding to it a slight excess of sulphuric acid. When, on the contrary, the iron is superabundant, the sulphuric acid combines with it by little and little, and the blue colour, which was at first manifest, disappears; but it always appears again when a new dose of acid is added.

Water seems to be the sole efficient cause of the alteration of cyanogen in the present case. M. Vauquelin has ascertained that the solution of this body in ether, though quickly and easily made, does not become coloured, and that alcohol alters it so much the less the stronger it is,

The aqueous solution of cyanogen, altered by standing, yields, when distilled, a liquid, having a strong odour of hydrocyanic acid, which contains hydriodate of ammonia and subcarbonate of ammonia. The residue of this distillation is a liquid, holding