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Salts of the Alkalis. Salts of the alkalis (and, so far as I have examined them, of the alkaline earths), when introduced into the separator by means of the spray, impart their characteristic tint and spectrum to each cone, but as the inner cone has a much higher average temperature than the outer one it acquires by far the brighter tint.

These facts may be exhibited in a very striking way as follows :- A mixed solution of cupric chloride and lithium chloride is introduced into the sprayer feeding a separator with air; if the gas-supply be in excess, the undivided flame shows a mixed colour due to the copper and lithium salts ; but if now the gas-supply be diminished and the cones allowed to separate, the inner cone appears bright crimson and the outer one only green. The explanation of this is very simple: the colour proper to the copper salt is, as we have seen, developed only in the outer cone, that due to the lithium salt in both cones; but in the upper one it is so faint as to be entirely masked by the green of the copper salt.

Conclusions. The experiments recorded in this paper afford some evidence as to the validity of the view of the origin of flamespectra advocated by Pringsheim. If, as he concludes, the flame-spectra commonly attributed to the alkali metals are a direct consequence of chemical processes occurring in the flame, the same is presumably true for the spectra of chemical compounds such as those of copper and gold. As a matter of fact chemical changes do accompany the production of the spectra dealt with in this paper. Thus when cupric chloride is introduced into the flame, we have the formation of cuprous chloride and of cuprous oxide. The case of gold chloride is more important. In the case of this salt the spectrum is only developed when a large excess of chlorine or of hydrochloric acid and air are present ; in their absence a considerable quantity of a spray or dust of the salt may be passed through the flame without giving any spectrum. The gold chloride, in fact, can only be maintained at a temperature sufficient to develop its spectrum when it is surrounded by an atmosphere either of chlorine or of an equivalent mixture of hydrochloric acid and oxygen. The gold-chloride molecules, however, must not be regarded as remaining intact under these circumstances, for where a dissociable salt appears to be maintained in the undissociated state, through t? presence of an excess of one of the products of dissocia:

a

we ascribe it to the fact that, if momentarily dissociated, there is instantly a reunion. Whilst, therefore, on the one hand,

, the high temperature at which the gold-chloride spectrum is developed compels the separation of the gold and chlorine, the large excess of chlorine on the other hand, by the action of mass, compels a recombination. Though this in a sense is tantamount to saying that the gold-chloride molecules remain undissociated, the dynamical view of dissociation obliges us to picture a constant interchange between atoms of gold and atoms of chlorine.

We are obliged to conclude, therefore, that the experiments recorded above are quite in harmony with the view advocated by Pringsheim.

In a previous part of this paper I have offered some criticisms of the experiments on which Pringsheim based his conclusions. Notwithstanding this I have never considered his view to be disproved : on the contrary, it seems prima facie to be a reasonable explanation of many phenomena occurring in Aames. The facts I have now brought forward are in harmony with it, but I believe the evidence is still far from complete, and that further experiments are necessary to establish the doctrine that the light-emission from coloured flames is a direct consequence of chemical processes.

I have to express my grateful acknowledgments to Sir G. G. Stokes, Bart., for the interest he has taken in the work recorded in this paper and for his invaluable and ever ready counsel. I have received much assistance from Mr. Frankland Dent, B.Sc., who especially has devoted the most patient labour to the drawing of the spectra.

The chief conclusions arrived at in this part of the paper

I. When cupric chloride is introduced into a flame, three substances are formed : metallic copper, cuprous chloride, and cuprous oxide. The first of these give a bright yellow flame and a continuous spectrum ; the second a bright blue tint and brilliant spectrum of bands and lines; the last a green tint and spectrum of not very strongly developed banas. Under certain circumstances cupric chloride may exist in a fame, when it gives a feeble ruddy tint and a continuous spectrum.

II. Gold chloride gives a flame-spectrum only in presence of an excess of chlorine or of hydrochloric acid and oxygen.

III. In the above cases the development of a spectrum is concomitant with chemical changes affecting the substance concerned ; a fact in harmony with the view as to the origin of flame-spectra advocated by Pringsheim.

are :

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IX. Specific Inductive Capacities of Water, Alcohol, &c.

By J. HOPKINSON*. N the December number of the Philosophical Magazine Measurement of the Specific Inductive Capacities of Water, Alcohol, &c. In this article he states that the high values found by Cohn and Arons and others for water, alcohol, &c. are not correct, but that the true values are in every one of these substances very nearly equal to that called for by Maxwell's theory. He also states that all the determinations of such substances as sulphur, &c. are incorrect. The observations said to be incorrect are not those of a single observer, but of many whose results are in good accord.

Taking solids first, it has been shown that the capacity of light flint-glass at ordinary temperatures is the same whether the time of charge is 20.000 second, or } second, that it is

: independent of the potential of the charge, and that its value is about 6:7t. It is also well known that this glass insulates so well that it will hold its charge for months f. Is it suggested that these results are vitiated by electrolytic polarization or by a hypothetical laminated structure of the material? The specific inductive capacity of ice has been determined by Bonty ş. He finds 78, practically the same value as Cohn and Arons find for water. But the resistance is from 105 to 106 times as great as that of water, which quite precludes the suggestion of electrolytic polarization.

Turning to liquids, we have a large number of determinations which also deviate from Maxwell's law. Take, for example, castor-oil and ether. Both insulate well enough to make certain that electrolytic polarization does not affect the result. Quincke determined the capacity of ether || by three very different methods and found it in each case about 4:7; my result by a fourth method was 4•75. For castor-oil I obtained by two very different methods 4:78 and 4:821. All these results deviate much from Maxwell's law making use of refractive indices for visible rays, and render the results of Cohn and Arons and the independent results of Tereschin for water not improbable à priori. Indeed, I think much more evidence will be needed than Prof. Fessenden has given before they are doubted. Prof. Fessenden also states that pure

• Communicated by the Author.

+ Phil. Trans. vol. clxxii. p. 372, and Gray's 'Absolute Measurement in Electricity and Magnetism,' vol. i. p. 473. I Phil. Trans. vol. clxvii. p.

610. § Comptes Rendus, p. 533, March 7, 1892. || Gray, p. 483.

Phil. Trans. (loc. cit.), and Proc. Roy. Soc. October 1887.

water insulates as well as indiarubber! The highest recorded resistance for water is far below that of indiarubber.

I would not have troubled you with this note were it not that any thing appearing in the Philosophical Magazine carries authority, and if inaccurate is calculated to mislead.

X. On Colonel Hime's Outlines of Quaternions.'

To the Editors of the Philosophical Magazine,

GENTLEMEN,

I

CANNOT agree with your reviewer in holding that

paragraph 11 of the 'Outlines' is not quaternions. The equation

i=j=k=V-1=-i=-jr-k, as your reviewer says, may be nonsense ; nevertheless it follows from the fundamental principles of quaternions as laid down by Hamilton and Tait. It is said that i=-1 and j=-1; therefore it follows that i2=j?, unless in quaternions the axiom does not hold which says that things which are equal to the same thing are equal to one another. But from i=it follows that i = +j or –j, for we are told that it is only the commutative law of all the laws of algebra which breaks down, and here that peculiarity does not enter. By extending the same reasoning to the other two pairs, we obtain

i=j=k=V-1=-i=-j=-k. How does your reviewer demonstrate that it is nonsense ? He says that i, j, k have already been defined as co-perpendicular unit-vectors, and to say that they are equal is to rob them arbitrarily of their most characteristic feature, so that they are no longer what they were defined to be. Yet a few sentences before this same writer defends Hamilton's no less arbitrary violation of the definition of a vector, which does not indeed rob it of any of its meaning, but piles on it what does not belong to it. That which in Hamilton is an "outburst of genius” is in Colonel Hime “contrary to the whole genius of common sense.

The manner in which the author founds the calculus is not satisfactory to your reviewer. This is not surprising ; on examination I find that it is based on a collection of definitions. The fundamental rules are explained as follows :-In i j the former symbol is a quadrantal versor and the latter a vector, the effect of the former on the latter is to change it into k. Logically, we expect that in ii the former symbol is a quadrantal versor and the latter a vector, giving i as the result; but it is not so: both symbols are now to be considered quadrantal versors, giving i = - 1. These two inconsistent theories are simultaneously applied to find the product of two vectors,

mji+maj + mzk and n;i+ naj +nzk. The product consists of two kinds of terms; minii is a type of the one, and m, n, ij of the other. We are asked to believe that in minii both unit-vectors become quadrantal versors, while in my naij it is only the former of the two. The operator and operand theory is applied to one set of terms, and a double operator theory to the other set of terms; while in the vectors themselves there is no operator at all.

In my papers on Space-analysis I have attempted to lay down the fundamental principles in a logical manner. When that is done, the meaning of every expression and equation becomes clear, and there is no need for a special chapter such as we find in the Outlines,' on the “Interpretation of Quaternion Expressions.” The best proof of the correctness of my principles is that they have enabled me to carry the analysis beyond the point where Hamilton left it.

In conclusion I wish to say that I yield to no one in admiration of the works of Hamilton and Tait. The attitudo of mind of your reviewer appears to be that of “wondering awe.” In that I cannot follow him ; I stand in awe of the truth only.

ALEXANDER MACFARLANE. Ithaca, N. Y.

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