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stance p m being by hypothesis small (two or three radii of the planet suppose), it follows that the angle peq is extremely small, and may be neglected. Hence a planet will appear to be displaced from the position which it had when the light left it, just as a star in the same direction is displaced. But besides this, the planet has moved from P while the light has been travelling to E, These two considerations combined lead to the formula for aberration, which is applicable to the planets, as is shown in treatises on astronomy. The same reasoning which applies to a planet will apply equally to the sun, the moon, or a comet.
To give an idea of the sort of magnitudes neglected in neglecting p q, suppose pm equal to the diameter of P, and suppose the curvature from p to m uniform. Let r be the radius of P, v its velocity, and R the distance P E. The greatest possible value of the angle between the tangents at p and m is
v v r v
In this case we should have JLpeq = y-y^ = y ®
being the semidiameter of P as seen from E. Hence the angle peq must be very much greater for the moon than for any other body of the solar system; for in the case of the planets the value of v is in no instance double its value for the earth or moon, while their discs are very small compared with that of the moon ; and in the case of the sun, although its disc is about as large as that of the moon, its velocity round the centre of gravity of the solar system is very small. It would indeed be more correct to suppose the sun’s centre absolutely at rest, since all our measurements are referred to it, and not to the centre of gravity of the solar system. Taking then the
case of the moon, and supposing y = - 7r, D = 15', we
find that the angle peq is about yTth of a second, an insensible quantity.
If we suppose the whole solar system to be moving in space with a velocity comparable with that of the earth round the sun, it follows from the linearity of the equations employed, that we may consider this motion separately. It is easy to show, that as far as regards this motion, the sun, moon, and planets will come into the positions in which they are seen just at the instant that the light from them reaches the earth. With respect to the stars also, that part of the aberration which varies with the time of year, the only part which can be observed, will not be affected. If we suppose the aether which* fills the portion of space occupied by the solar system to be moving in a current, with a velocity comparable with that of the earth in its oibit, the result will still be the same. For if
On the Structure of Electro-precipitated Metals
we suppose a velocity equal and opposite to that of the aetlte^ to be impressed, both on the aether and 011 the bodies of the solar system, the case is reduced to that of the solar system moving through the aether supposed to be at rest.
IV. On the Structure of Electro-precipitated Metals.
By Warren JDe la Rue, Esq.*
rr,HE following observations, being the result of an exten-sive series of experiments on the practical application of the processes of electro-metallurgy, will, I am induced to believe, be acceptable to the Chemical Society.
The various appearances of the metallic deposit (ire familiar to all manipulators in electro-metallurgy, and are distinguished by the names crystalline, lesser crystalline, malleable, sandy and spongy ; the latter being produced by an excess of power in the battery, the first by too small a power in relation to the strength of the solution operated on. All these deposits are however merely modifications of each other, they are essentially crystalline, and even the malleable, or in other words the most cohesive, is very inferior.in strength to metals wrought by the processes in ordinary use.
The malleable is that deposit usually required ; yet, even with all the art of a practised electro-metallurgist, it is difficult for a lengthened period to obtain it, inasmuch as the power of the battery, the temperature of the air, and consequently the conducting power of the fluids composing the circuit are constantly changing their relation to the strength of the electrolyte to be decomposed. There are other causes presently to be considered which also play an important part in producing these difficulties, and which we shall better understand by considering what effect the form of the matrix and the nature of its original surface have on the resulting precipitate.
It is well known to persons conversant with the precipitation of metals from their respective solutions by means of voltaic electricity, that these solutions become exhausted of the metal at the cathode to such an extent, that if we place the cathode on the surface of the liquid all action after a short time ceases: the exhausted liquid being specifically lighter, no mechanical transfer of fresh liquid takes placet) and conse-
* Communicated by the Chemical Socicty; having been read February 17, 1845.
f Professor Daniell and Dr. Miller, in a paper on the electrolysis of secondary compounds, have entered into the investigation of these phenomena.