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· First. The force of double refraction and polarisation extends without the surface of crystals, and within the sphere of the force which produces partial reflection.
Second. The change in the angle of polarisation produced by the interior force, depends on the inclination of the reflecting surface to the axis of the crystal, and also on the azimuthal angle which the plane of reflection forms with the principal section.
• In any given surface, where A and A" are the minimum and maximum polarising angles, viz. in the azimuth of o° and 90°, the polarising angle Al at any intermediate azimuth a, may be found by the formula
A- A+ Sin. (A-A).
A"-A=138'. • Third. The change in the direction of the polarisation must be produced after the ray has suffered reflection ; for if the change preceded reflection, the reflecting force would have po. larised it in the plane of reflection, whatever had been the direction of its previous polarisation.
· Fourth. The change in the direction of the polarisation depends upon the angle which the incident ray forms with the axis of the crystal, and takes place in such a manner that if
o = angle of incident ray with the axis; and 'C=change in the direction of the polarisation, we shall have
Sin. $C=Sin. Q. If we make
• A = complement of the inclination of the reflecting plane to the axis ;
a = azimuth of the plane of incidence with the principal section; and
*i= angle of incidence reckoned from the perpendicular, we shall have
Cos. a X Tang. A = Tang. z, and
Cos. A x cos. (i + x)
Cos. %. • In one of the ordinary rhomboidal surfaces where the incli. nation to the axis is 45° 23', A=44° 36'; and with oil of cassia į or the incidence of the mean ray, when the polarisation is completo, is about 45° 17'. I have assumed it at 45° 23' (which will be more correct for the mean luminous ray than 45o 17'), for the purpose of making the change of polarisation commence with zero in oo of azimuth.'
Remarks on the Probabilities of Error in Physical Observations; and on the Density of the Earth, considered especially with regard to the Reduction of Experiments on the Pendulum. By Thomas Young, M. D. &c.
We have in this memoir a very miscellaneous composition, touching first on the dead letters in the Post-Office; then on the probability of Spain having been formerly a colony of Egypt;
thirdly, on the credibility of Diodorus Siculus as an historian; and, fourthly, furnishing an examination of La Place's opinion relative to the original fluid state of the terrestrial globe, pendulum experiments, and atmospherical refraction.
We have frequently had occasion to notice, in our reviews of the volumes of the French Institute, the sort of mania which has of late seized some of our continental neighbours with respect to the doctrine of probabilities : all questions, whether of ethics, politics, or science, being alike submitted to the test of this universal principle. The being of a God is made to depend on the inclination of the planetary orbits: the truth or fallacy of the verdict of a jury is computed and exhibited in certain functions of x and y; and, as to the orbits of comets, the internal structure of the earth, the height of tides, &c., these questions are as commonly now computed according to the laws of chance, as the value of a lottery-ticket or that of a particular contingency at whist. Against this perversion of mathematical science we have always entered our feeble protest; and we are glad to find that the author of the present memoir is of the way
of thinking, at least in part: for he observes:
• It has been a favourite object of research and speculation, among the authors of the most modern refinements of mathematical analysis, to determine the laws, by which the probability of occurrences, and the accuracy of experimental results, may be reduced to a numerical form. It is indeed true, that this calcu. lation has sometimes vainly endeavoured to substitute arithmetic for common sense, and at other times has exhibited an inclination to employ the doctrine of chances as a sort of auxiliary in the pursuit of a political object, not otherwise so easily attainable; but we must recollect, that at least as much good sense is required in applying our mathematics to objects of a moral nature, as would be sufficient to enable us to judge of all their relations without any mathematics at all; and that a wise government and a brave people may rely with much more confidence on the permanent sources of their prosperity, than the most expert calculators have any right to repose in the most ingenious combinations of accidental causes.'
This oblique hint at the quackery of certain modern analysts by no means displeases us, because it looks something like a disposition (considering the quarter whence it comes) to shake off an absurd fondness for imitating French mathematical fashions, and to return to the less imposing but more profitable method of investigation, in which truth, and not chance, is the object of research.
In making this remark, we must beg to be understood not as objecting to the principles on which the doctrine of probabilities is founded : for, on the contrary, we have always considered it, abstractedly, as a highly interesting branch of analysis, and even as of great utility when directed to proper subjects of inquiry; it is only to the abuse of it that we object, when, to use the words of Dr. Young, an endeavour is made to substitute arithmetic for common sense.'
We have stated that Dr. Young, by way of illustrating his arguments, has referred to various questions to which he conceives probabilities have occasionally been improperly applied; at the same time alluding to those in which we may actually derive some advantage from considering them under this point of view. Among others, he refers to the inquiry whether Spain was ever a colony of Egypt; his data being, that there are six words in the Biscayan language, analogous to the same number of Egyptian words, meaning the same things; whence he argues that the chances are more than one thousand to one that, at some very remote period, an Egyptian colony established itself in Spain: the actual probability being ro's: This, it is to be observed, is one of those questions which the writer seems to think come fairly within the
of this doctrine: how far our readers may be disposed to adopt the same mode of reasoning, we are unable to say: but, for our own part, we are not prepared to admit the infallibility of the conclusion.
The author next proceeds to examine questions of a scientific nature; and to shew that, the greater is the number of observations made in any case, each equally liable to a certain limited error in excess and defect, the more nearly will the mean result approach towards the truth: but here, again, it is very properly remarked that, in computing the probable degree of approximation due to a given number of observations, we are still open to a degree of fallacy not contemplated in fixing the data of the problem; namely, that in all likelihood some circumstance, with which we are unacquainted, will determine the greater number of errors to a particular side of zero : . consequently, the assumption of our being equally liable to err in excess or in defect is erroneous, and must lead to an erroneous conclusion.
Dr. Young now arrives at the question of the earth's density, which he thus introduces :
• It has been observed by some philosophers, that the excess of the density of the central parts of the earth, above that of the superficial parts, is so great as to render it probable that the whole was once in a state of fluidity, since this is the only condition that would enable the heaviest substances to sink towards the centre. But before we admit this inference, we ought to inquire, how N 4
great would be the effect of pressure only in augmenting the mean density, as far as we can judge of the compressibility of the substances, which are the most likely to be abundant, throughout the internal parts of the structure.'
He then goes on to shew that pressure alone would be sufficient to account for the greater internal density, without any reference to the original state of fluidity: -- but a question here occurs to us;
we conceive pressure to be exerted through such a mass as the terrestrial globe, if it had never existed in any other than in its solid state ? Let us imagine, for instance, that this globe, instead of being solid, were merely a shell of granite, 100 or 200 miles in thickness, would not this substance be sufficient to sustain it in its present form; and would not this relieve all the internal matter, if any existed, from the superincumbent pressure? We cannot foresee what mechanical objection can be urged against this supposition; and, if the possibility of it be admitted, it seems to destroy entirely the doctrine of pressure producing an increase of density independent of fluidity.
On the Anomaly in the Variation of the Magnetic Needle, as observed on Ship-board. By William Scoresby, jun. Esq.
On Irregularities observed in the Direction of the CompassNeedles of his Majesty's Ships Isabella and Alexander, in their late Voyage of Discovery, and caused by the Attraction of the Iron contained in the Ships. By Captain Edward Sabine, Royal Artillery, F. R. S.
Observations on the Dip and Variation of the Magnetic Needle, and on the Intensity of the Magnetic Force ; made during the late Voyage in search of a North-west Passage. By the Same.
The intimate relation which subsists between these three articles induces us to place them thus in combination; and the real importance of the subject, to which they refer, will be a sufficient apology for extending our remarks to rather a greater length than we usually allow in reporting the detached memoirs published in the Philosophical Transactions.
Two years ago, we called the attention of our readers to the valuable little treatise on the variation of the compass, by Mr. Bain (see M. R. vol. Ixxxiv. p. 301.), and particularly to that part of it which treated of the local attraction of a ship’s guns, &c. on her compass. The effect of local attraction was first clearly pointed out to the attention of navigators by Captain Flinders: but the remarks of that excellent seaman seem to have been too much disregarded, and would in all probability have been entirely forgotten, had not the author above mentioned again pressed them on the notice of the
public, public, with various additional observations of his own, respecting both the quantity and the consequences of this source of error. Such being, we believe, indisputably the case, we cannot but consider it as a deficiency of liberality, that the name of this modest and ingenious writer is only once mentioned in the three articles under review; and then rather with a view of detracting from the originality of his observations in certain cases, than for the purpose of bestowing on him that meed of praise to which he is justly intitled.
The two ships sent out on a voyage of discovery in 1818 (the Isabella and Alexander) were specifically charged to make as many
observations as were consistent with the other purposes of the voyage, on the disturbance of the needle as caused by local attraction; and, besides the statements on this subject in Captain Ross's narrative, and those of different officers in the expedition, we have the present memoir by Captain Sabine, who accompanied Captain Ross in the capacity of astronomer and naturalist
. The object of inquiry, however, was not simply to observe the quantity of the deviation produced by the cause above mentioned, but at the same time to compare the several results with certain deductions of Captain Flinders; and to ascertain how far the rules laid down by that officer were applicable to cases in which the dip of the needle was considerable. That they could not always be trusted had already been pointed out by Mr. Bain, and the accuracy of his conjectures has been confirmed in a great degree by Captain Sabine: but one point of difference yet remains between Captain Flinders and Mr. Bain; since the rule of the former implies that the deviation caused by the iron vanishes when the dip vanishes, a principle which Mr. Bain is disposed (and, we think, with great reason,) to doubt. The determination of this point must, therefore, be left to future observation.
Another principle laid down by Captain Flinders was that, with the ship’s .head on the magnetic north or south points, the deviation was nothing, and that it was greatest when the head was east or west. The attraction being nothing at north or south obviously depended on the uniform distribution of the iron, and would probably obtain in most ships of war; but that the case will not be the same in vessels in which the same uniformity is not observed was by no means doubtful. It even appears from Captain Sabine's statement that, in the Alexander in particular, the direction of the line of no error was nearly at right angles to the magnetic meridian; a fact which induces Captain Sabine to change the words magnetic meridian, in Captain Flinders's rule, into those of line of no attraction, which expression is certainly more appropriate :