68. Diphosphate of Soda.-4 ounces of spring water and 100 grains of diphosphate of soda; hot metal positive. Retried with distilled water and the liquid pre-boiled; same result, but in a less degree. Liquid exhibited weak alkaline reaction with testpaper.

69. Hyposulphite of Soda.-4 ounces of distilled water and 100 grains of hyposulphite of soda, pre-boiled; hot metal positive. Retried after absorption of some atmospheric air; same result, but in a greater degree. Liquid neutral to test-paper. 70. Sulphate of Soda.-4 ounces of distilled water and 100 grains of sulphate of soda, solution pre-boiled; hot metal negative. Retried after absorption of a little air; same result. Neutral to test-paper.

71. Chloride of Sodium.-4 ounces of distilled water and 100 grains of chloride of sodium, pre-boiled; hot metal positive. Retried after absorption of air; same result. Neutral reaction with test-paper.

72. Nitrate of Soda.-4 ounces of distilled water and 100 grains of nitrate of soda, pre-boiled; hot metal positive. Retried liquid after it absorbed some air; same result. Neutral to test

paper.

73. Microcosmic Salt.-4 ounces of distilled water and 100 grains of microcosmic salt, pre-boiled; hot metal positive. Retried after absorption of air; same result. Liquid exhibited alkaline reaction.

74. Bitartrate of Soda.-4 ounces of distilled water and 100 grains of bitartrate of soda, pre-boiled; hot metal very feebly positive. Retried several times with similar results. Acid reaction.

75. Solutions of chloride of barium, nitrate of baryta, chloride of strontium, nitrate of strontia, chloride of calcium, sulphate of magnesia, and chloride of magnesium, were also similarly prepared, and each examined several times; and the results obtained, although uniform, and confirmatory of all previous ones, were so mninute in degree, and affected by such slight circumstances, that I have thought it unadvisable to publish them.

76. Sulphate of Alumina.-4 ounces of distilled water and 50 grains of sulphate of alumina, pre-boiled; hot metal negative. Retried after exposure to air; same result. Liquid acid to

litmus-paper.

77. Sulphate of Zinc.-5 ounces of spring water and 100 grains of sulphate of zinc; hot metal negative. Acid reaction with litmus-paper. Retried with distilled water, and the solution pre-boiled; same result. Weak acid reaction.

78. Sulphate of Copper.-5 ounces of spring water and 110 grains of sulphate of copper; hot metal negative. Retried

with the liquid pre-boiled; same result. Added 1 drachm of pure sulphuric acid to this solution and retried; same result, but in a very much greater degree. Same solution pre-boiled gave similar results. Tried again with 4 ounces of distilled water and 100 grains of the salt pre-boiled; same result.

79. Nitrate of Copper.-5 ounces of spring water and 110 grains of nitrate of copper; hot metal negative. Retried with the liquid pre-boiled; same result. Acid reaction.

80. According to these results, hot platinum is negative to cold platinum in the following liquids :-moderately dilute aqueous solutions of boracic, phosphoric, sulphuric, hydrochloric, nitric, oxalic, acetic, tartaric, and citric acids. Also in aqueous solutions of the following salts:-sulphate, hydrochlorate, and nitrate of ammonia, sulphate of soda, sulphate of alumina, sulphate of zinc, sulphate of copper, sulphate of copper acidulated with sulphuric acid, and nitrate of copper. And hot platinum is positive to cold platinum in aqueous solutions of ammonia, carbonate of ammonia, potash, carbonate, sulphite, sulphate, chlorate, and nitrate of potash, cyanide of potassium, soda, carbonate, biborate, diphosphate, and hyposulphite of soda, chloride of sodium, nitrate of soda, and microcosmic salt.

81. In every case (provided chemical action was completely or sufficiently excluded) where the liquid was strongly acid to testpaper, hot platinum was decidedly negative to cold platinum; and in every case where the solution was strongly alkaline, it was as decidedly positive. Also in every case where the liquid was neutral, or exhibited but feeble acid or alkaline reaction with test-paper, the current obtained was very feeble, and was affected by very slight circumstances, so that the results in such cases are necessarily less certain and less to be relied upon than in the more definite ones. We may select from amongst those examined the following solutions as being of the less certain character:-hydrochlorate of ammonia, sulphite, sulphate, chlorate, nitrate, and tartrate of potash (bitartrate of potash was also feeble), diphosphate, hyposulphite, sulphate, and nitrate of soda, chloride of sodium (bitartrate of soda was also feeble), and sulphate of zinc.

82. Thus, speaking in general terms, liable, as we have seen, to some slight exceptions, we may say that hot platinum is negative to cold platinum in acid liquids, and positive to it in alkaline ones; the only exceptions to this statement amongst the instances given are aqua-regia and dilute hydrocyanie acid, in which the hot plate was positive; sulphate of soda, which exhibited neutral reaction, and yet in which the hot metal was negative, though very feebly; and bitartrate of soda, in which, although of acid reaction, the hot metal was feebly positive. On account of the Phil. Mag. S. 4. Vol. 13. No. 83. Jan. 1857.

C

feeble action of neutral solutions, or those of weak acid or alkaline properties, it is probable that by further experiment with substances of greater purity, several exceptions will be found amongst those examined.

DELICACY OF THE APPARATUS.

83. To test the degree of delicacy of the foregoing apparatus and method for detecting those supposed new properties of acid and alkaline liquids, I made the following experiments :-Took 4 ounces of distilled water and of a drachm of a mixture of 1 measure of pure and strong nitric acid and 16 measures of distilled water, and mixed them together a mixture of 1 measure of strong nitric acid and 2192 measures of water; pre-boiled the liquid; hot platinum (i. e. at 208° F.) was decidedly negative to cold platinum (i. e. at 60° F.) in it. Distinct acid reaction with litmus-paper. Retried; same result. Now took a drachm of the liquid of this experiment and added to it 4 ounces of distilled water a mixture of 1 measure of strong nitric acid and 142480 measures of water; pre-boiled the liquid; the hot platinum was still negative, but in an extremely feeble degree. The liquid gave very faint acid reaction with test-paper. I now increased the proportion of acid by adding a second half drachm of the liquid of the previous experiment and retried; the hot metal was now negative in a greater degree, and the liquid gave distinct acid reaction with litmus-paper.

84. To test its delicacy with alkaline liquids, I took a drachm of a solution consisting of 4 ounces of water and 100 grains of anhydrous potash, and added to it 4 ounces of pre-boiled distilled water to a mixture of 1 part of potash and 2914-4 parts of water; hot platinum was decidedly positive to cold platinum in it, and test-paper exhibited weak alkalinity. I now added a drachm of the liquid of this experiment to 4 ounces of pre-boiled distilled water a mixture of 1 part of potash and 189500 parts of water, and retried; the hot metal was still decidedly positive, though in a very feeble degree, and exhibited a more distinct result than the weakest mixture of nitric acid. The liquid gave no perceptible reaction with litmus-paper. It appears to me quite likely, that, with an apparatus containing much larger plates, these supposed new properties might be detected in water containing much smaller proportions of acid or alkali than those mentioned. I propose for the present to call the apparatus a thermo-electro-liquid-examiner.

GENERAL INFERENCES.

85. Having eliminated the various sources of interference, and determined the influence of a number of circumstances upon the

currents, I may now sum up the chief points ascertained. The currents under consideration are not due to thermo-electric properties of the liquids, nor are they influenced in any material degree by the simple thermo-electric properties of the metals. They arise from a differential action of heat at the surface of liquid contact of the two plates, and not from any action in the body of the liquid, the latter functioning merely as a conductor of the current. Hot platinum is almost invariably positive to cold platinum in alkaline liquids, and as often negative in acid liquids; and as far as I have examined other metals, they are the same, provided chemical action is completely or sufficiently excluded. The currents obtained with platinum plates are not. due (except with a very few liquids, such as aqua-regia) to chemical action, but to some cause which I have not yet completely determined; whilst with base metals, both this cause and chemical affinity are in most cases operating; the one tending to produce a current in one direction, and the other in an opposite one.

86. As the currents obtained with platinum are extremely minute, it is necessary to use a very sensitive galvanometer; and it would be an advantage to have an examiner with larger plates than the one described, say of 4 inches diameter.

Birmingham.

II. Supplementary Remarks on the Porism of the In-and-circumscribed Triangle. By A. CAYLEY, Esq.*

IN

my former papers (see Phil. Mag. August and November 1853) I established (as part of a more general one) the following theorem, viz. the condition that there may be inscribed in the conic U=0 an infinity of triangles circumscribed about the conic V=0, is, that if we develope in ascending powers of k the square root of the discriminant of kU+V, the coefficient of k* in this development must vanish. Thus writing

disct. (kV+U) = (K‚©‚©',K'Xk, 1)3,

the condition in question is found to be

302-4KO'=0.

The following investigations, although relating only to particular cases of the theorem, are, I think, not without interest. If the equation of the conic containing the angles is

U=2ayz+2bzx+2cxy=0,

and the equation of the conic touched by the sides is V=x2+ y2+z2-2yz-2xx-2xy=0,

* Communicated by the Author.

we have

disct. (k, k, k, a―k, b—k, c—k(x, y, z)2 = (K, ©, ©', K'Xk, 1)3,

which is satisfied identically. This is as it should be; for it is plain that there exists a triangle, viz. the triangle (x=0, y=0, z=0), inscribed in the conic U=0, and circumscribed about the conic V=0.

Suppose that the equation of the conic containing the is

y2-4zx=0,

and the equation of the conic touched by the sides is

ax2+by2+ cz2=0.

Then the tangential equation of the last-mentioned conic is bc2+can2+abg2=0.

And if we take for the angles of the triangle x:y:2=1:2λ 1λ2, or 1: 2μ: μ2, or 1: 2v: v2, then the equation of the line joining the angles (u), (v) is

2μvx-(u+v)y+z=0,

which will touch the conic ax2+by2+cz2=0 if

bc4μ2v2+ca (μ+v)2+ab.4=0.

And it is required to find under what circumstances the equations bc. 4μ22+ca(u+v)2+ab.4=0

bc. 4v2x2+ca(v+λ)2 +ab.4=0

bc. 4λ2μ2+ca(λ+μ)2+ab.4=0

become equivalent to two equations only. The condition is of course included in the general formula; and putting

disct. (ka, kb+1, kc, 0, −2, 0X x, y, z)2= (K, ©, &', K'Xk, 1)3,

we must have

302-4KO'=0.

The discriminant in question is

k3abc+k2ac-k.4b-4=0,

or K=1, 0= ac, ' = — b, K'=-4; the required condition