The formation of phorone takes place according to the equation C24 H24 024-C18 H14 O2+6C02+10HO.

Grape-sugar. Phorone.

By treating phorone with pentachloride of phosphorus, the chloride of phoryle, C18 H13 Cl, is formed; it is an oil lighter than water, boiling at 175°. By distilling phorone with anhydrous phosphoric acid, there passes over a limpid, highly refracting oil, of an agreeable odour, and boiling at 150°-160°. This is probably cumole, C18 H12, or a substance isomeric with it.

M. Bodart suggests that the formula of Fremy's metacetone should be C18 H15 03 instead of C6H5O. Its formation from grape-sugar would then be thus expressed :

C24 H24 024-C18 H15 03+6CO2+9HO.

Grape-sugar. Metacetone.

In support of this view, M. Bodart found that by distilling this metacetone with anhydrous phosphoric acid, phorone is produced,

C18 H15 09+ PO5=C18 H14 O2 + PO3 HO.

From its reactions, phorone must be considered as an alcohol to which cumole stands in the same relation as olefiant gas does to common alcohol. The transformation of phorone into cumole connects sugar with the cuminic acid series, and consequently with the benzoic acid series, for cumole has been converted into benzoic acid by Abel.

The same chemist* has investigated the action of pentachloride of phosphorus on some fixed acids, which give rise to pyrogenous acids. With mucic acid he obtained a chlorinated acid. With pyromucic acid, he found that the action was the same as with monobasic acids in general. Chloride of pyromucyle is formed, a very highly refracting liquid boiling at 170° C., of a similar odour to chloride of benzoyle, and which strongly excites

Chloride of pyromucyle gives with water, pyromucic acid; and with ammonia, pyromucamide,

C10 H3 CIO4 + NH3 = HCI +

Chloride of pyromucyle.

C10 H5 NO4.

Pyromucamide.

With malic acid Bodart obtained an acid not containing chlorine, and which appeared to be maleic or fumaric acid.

* Comptes Rendus, August 18, 1856.

XXXI. On the Problem of the In-and-circumscribed Triangle. By the Rev. GEORGE SALMON, Trinity College, Dublin*.

THE

HE following was suggested by Mr. Cayley's paper in the January Number of the Philosophical Magazine, which I have just met with.

Let it be required to find the envelope of the third side of a triangle inscribed in a conic U, and two of whose sides touch a conic V.

Let the condition that AU+V should represent two right lines be

then since the value of λ plainly cannot depend on the particular axes to which the equations are referred, it follows, that, no matter how the equations are transformed, the ratios of the coefficients of the powers of λ in the equation just written remain unaltered.

Let now the sides of the triangle in any position be x, y, z, then the equations of the conics admit of being transformed into U=2xy+2yz+2xz=0,

V=l2x2+m2y2+n2z2 — 2lmxy —2mnyz―2nlzx-2Axy=0; and it is plain that the equation

AU+V=0

represents a conic touched by the third side z. But in this case we find, if l+m+n=p, lmn=r, ▼=2, O=—p2—2A, O'=2p(2r+An), ▼'=−(2r+An)3,

whence

40▼′-0′′2=8A (2r+An)2;

and the equation AU+V=0 may be written

{40V'~O'}U—4VV'V=0.

The coefficients in this equation being invariants, it follows that the conic which we have proved is touched by the third side is a fixed conic.

We can in like manner find the locus of the vertex of a triangle circumscribed about V, and two of whose vertices move along U. In this case the equations may be transformed into

U=2xy+2yz+2zx+Az2,

V=l2x2+m2y2+n2x2— 2lmxy — 2mnyx-2nlzx,

and we have

V=2-A, O=-p2+2lmA, O'=4pr, '=-4.p2.

* Communicated by the Author.

Again, let F=0 be the equation of the covariant conic which passes through the points of contact of common tangents to U and V (see my 'Conics,' pp. 268, 288), then the coefficient of 2 in its equation will be

-4rn(1-A).

Hence it can be seen that the coefficient of 22 vanishes identically in the equation

16U-4{40V'-0"}V'F+ {40 ▼'—O"}2V=0, which is therefore the equation of the locus required. Its form shows that it represents a conic touching the four tangents common to U and V.

If 40'-'2=0, the envelope reduces to V, and the locus to U, in conformity to Mr. Cayley's theorem. It does not seem impracticable to obtain the equation of the locus by the same method when the two sides touch different conics.

Trinity College, Dublin,
February 16, 1857.

XXXII. On certain Double Compounds of Ammonia and Chromium. By CHARLES W. VINCENT, Assist. Lib. Royal Institution*.

THE

HE solubility of freshly precipitated hydrate of sesquioxide of chromium in ammonia has long been known. In endeavouring to discover the amount of this solubility and the circumstances which modify it, I met with many difficulties. Operating with solutions of sesquioxide of chromium, obtained by deoxidizing bichromate of potassa by treatment with alcohol, on addition of ammonia I obtained results which did not at all coincide with one another; in some cases the precipitated chromic oxide was readily dissolved, in others it was quite insoluble. The tints of the solutions, when produced, also oftentimes differed very much; and altogether I met with such apparently contradictory effects, that I was led to make the experiments which form the subject of the present note with a view to their reconciliation.

In order to exclude all other compounds from taking any part in whatever action might occur between the chrome and ammonia, I prepared a precipitate of the green hydrate of chromic oxide from a solution of the sesquichloride of chromium, washed this thoroughly with distilled water, digested it for half an hour with concentrated ammonia, and then filtered it. The ammonia passed through the filter perfectly clear and colourless, without a trace of the red tint which denotes the solution of the chrome. This experiment I repeated many times, with every precaution, and

* Communicated by the Author.

uniformly found that when a well-washed precipitate was used, it was perfectly insoluble in ammonia. I now passed a small quantity of hydrochloric acid through the filter containing the sesquioxide of chromium, so as to moisten it with the acid, and then again submitted it to treatment with concentrated ammonia, heating the mixture for a few minutes. The precipitate during this time changed its colour from green to a greyish-blue; and on filtering, I found the ammonia had acquired a distinctly red hue. I then added a rather larger quantity of hydrochloric acid to the precipitate than was sufficient for its complete solution, reprecipitated with ammonia, and filtered. The bulk of the precipitate I observed to be much less, and the colour more intense than previously. By continuing this kind of treatment with hydrochloric acid and ammonia alternately, I at length reached a point where the ammonia no longer produced a precipitate, but changed the colour of the liquid from a dingy green to a beautiful crimson colour. When I substituted nitric or sulphuric acid for the hydrochloric acid in the foregoing experiment, I obtained precisely similar effects; but the respective tints of the solutions produced were different.

From the behaviour of the chromic oxide in the preceding experiment, I was led to infer the existence of a double salt of ammonia and chromium in the solution, to which the colour is due, and not, as has been supposed, to the mere solution of the chromic oxide in ammonia.

The following is a more convenient method of producing these compounds*:-A concentrated solution of ammonia is gently heated; to this a solution of the sesquichloride of chromium, acidulated with a small quantity of hydrochloric acid, is added drop by drop. A green precipitate immediately falls down, which on standing gradually changes to a blue, violet, and lastly indigo colour. On the addition of hydrochloric acid to this precipitate, it readily dissolves, with the formation of the beautiful crimson colour above adverted to.

In this last experiment I have used an acid as a direct means for the production of the coloured solutions. By this plan the colours are much more intense than when prepared by the first method; in other respects, however, they are perfectly identical with them. It appears to me, therefore, a strong corroboration of the idea, that it is to the formation of a double salt that the colour is due.

In an elaborate paper by Hertwig (Annalen der Pharmacie,

* I have used the chloride of chromium and hydrochloric acid as an example; but with the nitrate of chromic oxide and nitric acid, or with the sulphate and sulphuric acid, the same course is pursued when it is desired to produce the compounds corresponding to these several acids,

vol. xlv. p. 299), he gives a full account of the deportment of chromium with ammonia, and mentions the sulphuric acid compound I have above alluded to, but ascribes its production to a totally different cause from that which I have assigned.

His mode of proceeding was as follows:-1. He evaporated a solution of chrome-alum with a small quantity of oil of vitriol to a small bulk, and dropped this mixture into an excess of concentrated ammonia. ("By this means," he says, "less than 0.2 per cent. of chromic oxide remains undissolved.") 2. He dropped a solution of chrome-alum into ammonia (producing a greyish-violet precipitate), and dissolved this unwashed precipitate in sulphuric acid.

These solutions have a wine-red colour, and are the same as the acid and alkaline modifications I have mentioned above. Hertwig, however, does not recognize that the coloured solution of the chromic oxide by both the first and second method is owing to the same cause, viz. the formation of a double salt of sesquioxide of chromium and ammonia with sulphuric acid, but believes that the first instance is a simple case of the solution of the chromic oxide by the concentrated alkali. Of the second case he gives no explanation. He points out also the necessity of a purple modification of the green hydrate of chromic oxide being formed previous to any solution in ammonia, but overlooks entirely the fact, that without the presence of an acid this modification is never produced, and when obtained is as insoluble as the green variety.

I have mentioned above that different tints are produced according to the acids used for the solution of the chromic oxide in ammonia; they are as follow:-With nitric acid, rosepink; with hydrochloric acid, crimson; with sulphuric acid, a rich port-wine colour.

Of the ultimate composition of these compounds I have no means of judging, since every attempt to obtain them in the solid state has hitherto failed. If exposed to the air for any length of time, they decompose into the nitrates and sulphates of chromic oxide and ammonia respectively; the hydrochloric acid compound into chloride of ammonia and chloride of chromium: to a mixture of this kind the addition of ammonia and hydrochloric acid will restore the colour. When heated, ammonia is given off and a violet powder precipitated; this also is redissolved by ammonia with restoration of the colour. None of these compounds are affected by concentrated solutions of potassa or soda in the cold; but when heated they are readily decomposed, and on cooling, the green sesquioxide of chromium is precipitated.