| Whittaker | |||||||||
 |
|||||||||
| History of theories of Aether and Electricity | |||||||||
|
The Theory of Aether in the seventeenth Century
|
|
of velocity parallel to the cloth must be unaffected by the
impact; and therefore the projection BE of the refracted ray
must be k times as long as the projection BC of the incident
ray. So if i and r denote the angles of incidence and refraction, we have
\sin{r} = \frac{BE}{BI} = K; \frac{BC}{BA} = K\sin{i}
or the sines of the angles of incidence and refraction are in a constant ratio ; this is the law of refraction. Desiring to include all known phenomena in his system, Descartes devoted some attention to a class of effects which were at that time little thought of, but which were destined to play a great part in the subsequent development of Physics. The ancients were acquainted with the curious properties possessed by two minerals, amber and magnetic iron ore. The former, when rubbed, attracts light bodies : the latter has the power of attracting iron. The use of the magnet for the purpose of indicating direction at sea does not seem to have been derived from classical antiquity ; but it was certainly known in the time of the Crusades. Indeed, magnetism was one of the few sciences which progressed during the Middle Ages ; for in the thirteenth century Petrus Peregrinus,[1] a native of Maricourt in Picardy, made a discovery of fundamental importance. Taking a natural magnet or lodestone, which had been rounded into a globular form, he laid it on a needle, and marked the line along which the needle set itself. Then laying the needle on other parts of the stone, he obtained more lines in the same way. When the entire surface of the stone had been covered with such lines, their general disposition became evident; they formed circles, which girdled the stone in exactly the same way as meridians of longitude girdle the earth ; and there were two points at opposite ends of the stone through which all the circles passed, just as all the meridians pass through the Arctic and Antarctic poles of the earth.[2] Struck by the analogy, Peregrinus proposed to call these two points the poles of the magnet : and he observed that the way in which magnets set themselves and attract each other depends solely on the position of their poles, as if these were the seat of the magnetic power. Such was the origin of those theories of poles and polarization which in later ages have played so great a part in Natural Philosophy. The observations of Peregrinus were greatly extended not long before the time of Descartes by William Gilberd or Gilbert[3] (6. 1540, d. 1603). Gilbert was born at Colchester: after studying at Cambridge, he took up medical practice in London, and had the honour of being appointed physician to Queen Elizabeth. In 1600 he published a work[4] on Magnetism and Electricity, with which the modern history of both subjects begins. Of Gilbert's electrical researches we shall speak later : in magnetism he made the capital discovery of the reason why magnets set in definite orientations with respect to the earth ; which is, that the earth is itself a great magnet, having one of its poles in high northern and the other in high southern latitudes. Thus the property of the compass was seen to be included in the general principle, that the north-seeking pole of every magnet attracts the south-seeking pole of every other magnet, and repels its north-seeking pole. Descartes attempted[5] to account for magnetic phenomena by his theory of vortices. A vortex of fluid matter was postulated round each magnet, the matter of the vortex entering by one pole and leaving by the other : this matter was supposed to act on iron and steel by virtue of a special resistance to its motion afforded by the molecules of those substances. Crude though the Cartesian system was in this and many other features, there is no doubt that by presenting definite conceptions of molecular activity, and applying them to so wide a range of phenomena, it stimulated the spirit of inquiry, and prepared the way for the more accurate theories that came after. In its own day it met with great acceptance: the confusion which had resulted from the destruction of the old order was now, as it seemed, ended by a reconstruction of knowledge in a system at once credible and complete. Nor did its influence quickly wane ; for even at Cambridge it was studied long after Newton had published his theory of gravitation ;[6] and in the middle of the eighteenth century Euler and two of the Bernoullis based the explanation of magnetism on the hypothesis of vertices.[7] Descartes' theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of refraction was, however, called in question by his fellow-countryman Pierre de Ferinat (b. 1601, d. 1665)[8], and a controversy ensued, which was kept up by the Cartesians long after the death of their master. Fermat eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated [9] in the form, " Nature always acts by the shortest course." From it the law of reflexion can readily be derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the con dition of meeting the reflecting surfaces.[10] In order to obtain the law of refraction, Fermat assumed that " the resistance of the media is different", and applied his "method of maxima and minima " to find the path which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution.[11] "The result of my work", he writes, " has been the most extraordinary, the most unforeseen, and the happiest, that ever was ; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established." His surprise was all the greater, as he had supposed light to move more slowly in dense than in rare media, whereas Descartes had (as will be evident from the demonstration given above) been obliged to make the contrary supposition. Although Fermat's result was correct, and, indeed, of high permanent interest, the principles from which it was derived were metaphysical rather than physical in character, and con sequently were of little use for the purpose of framing a mechanical explanation of light. Descartes' theory therefore held the field until the publication in 1667 [12] of the Micrographia of Robert Hooke (b. 1635, d. 1703), one of the founders of the Royal Society, and at one time its Secretary. Hooke, who was both an observer and a theorist, made two experimental discoveries which concern our present subject ; but in both of these, as it appeared, he had been anticipated. The first [13] was the observation of the iridescent colours which are seen when light falls on a thin layer of air between two glass plates or lenses, or on a thin film of any transparent substance. These are generally known as the " colours of thin plates," or " Newton's rings " ; they had been previously observed by Boyle. [14] Hooke's second experimental discovery,[15] made after the date of the Micrographia, was that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shadow of an opaque body. This observation had been published in 1665 in a posthumous work [16] of Francesco Maria Grimaldi (b. 1618, d. 1663), who had given to the phenomenon the name diffraction. Hooke's theoretical investigations on light were of great importance, representing as they do the transition from the Cartesian system to the fully developed theory of undulations. He begins by attacking Descartes' proposition, that light is a tendency to motion rather than an actual motion. " There is", he observes, [17] " no luminous Body but has the parts of it in motion more or less " ; and this motion is " exceeding quick." Moreover, since some bodies (e.g. the diamond when rubbed or heated in the dark) shine for a considerable time without being wasted away, it follows that whatever is in motion is not permanently lost to the body, and therefore that the motion must be of a to-and-fro or vibratory character. The amplitude of the vibrations must be exceedingly small, since some luminous bodies (e.g. the diamond again) are very hard, and so cannot yield or bend to any sensible extent. Concluding, then, that the condition associated with the emission of light by a luminous body is a rapid vibratory motion of very small amplitude, Hooke next inquires how light travels through space. " The next thing we are to consider", he says, " is the way or manner of the trajection of this motion through the interpos'd pellucid body to the eye : And here it will be easily granted " First, that it must be a body susceptible and impartible of this motion that will deserve the name of a Transparent ; and next, that the parts of such a body must be homogeneous, or of the same kind. " Thirdly, that the constitution and motion of the parts must be such that the appulse of the luminous body may be communicated or propagated through it to the greatest imaginable distance in the least imaginable time, though I see no reason to affirm that it must be in an instant. " Fourthly, that the motion is propagated every way through an Homogeneous medium by direct or straight lines extended every way like Rays from the centre of a Sphere. " Fifthly, in an Homogeneous medium this motion is propagated every way with equal velocity, whence necessarily every pulse or vibration of the luminous body will generate a Sphere, which will continually increase, and grow bigger, just after the same manner (though indefinitely swifter) as the waves or rings on the surface of the water do swell into bigger and bigger circles about a point of it, where by the sinking of a Stone the motion was begun, whence it necessarily follows, that all the parts of these Spheres undulated through an Homogeneous medium cut the Rays at right angles." Here we have a fairly definite mechanical conception. It resembles that of Descartes in postulating a medium as the vehicle of light ; but according to the Cartesian hypothesis the disturbance is a statical pressure in this medium, while in Hooke's theory it is a rapid vibratory motion of small amplitude. In the above extract Hooke introduces, moreover, the idea of the wave-surface, or locus at any instant of a disturbance gene- rated originally at a point, and affirms that it is a sphere, whose centre is the point in question, and whose radii are the rays of light issuing from the point. Hooke's next effort was to produce a mechanical theory of refraction, to replace that given by Descartes. " Because", he says, "all transparent mediums are not Homogeneous to one another, therefore we will next examine how this pulse or motion will be propagated through differingly transparent mediums. And here, according to the most acute and excellent Philosopher Des Cartes, I suppose the sine of the angle of inclination in the first medium to be to the sine of refraction in the second, as the density of the first to the density of the second. By density, I mean not the density in respect of gravity (with which the refractions or transparency of mediums hold no proportion), but in respect only to the trajection of the Rays of light, in which respect they only differ in this, that the one propagates the pulse more easily and weakly, the other more slowly, but more strongly. But as for the pulses themselves, they will by the refraction acquire another property, which we shall now endeavour to explicate. "We will suppose, therefore, in the first Figure, ACFD to be 
a physical Ray, or ABC and DEF to be two mathematical Rays trajected from a very remote point of a luminous body through an Homogeneous transparent medium LL, and DA, EB, FC, to be small portions of the orbicular impulses which must therefore cut the Rays at right angles : these Rays meeting with the plain surface NO of a medium that yields an easier transitus to the propagation of light, and falling obliquely on it, they will in the medium MM be refracted towards the perpendicular of the surface. And because this medium is more easily trajected than the former by a third, therefore the point C of the orbicular pulse FC will be moved to H four spaces in the same time that F, the other end of it, is moved to three spaces, therefore the whole refracted pulse to H shall be oblique to the refracted Rays GHK and GI" Although this is not in all respects successful, it represents a decided advance on the treatment of the same problem by Descartes, which rested on a mere analogy. Hooke tries to determine what happens to the wave-front when it meets the interface between two media ; and for this end he introduces the correct principle that the side of the wave-front which first meets the interface will go forward in the second medium with the velocity proper to that medium, while the other side of the wave-front which is still in the first medium is still moving with the old velocity : so that the wave-front will be deflected in the transition from one medium to the other. This deflection of the wave-front was supposed by Hooke to be the origin of the prismatic colours. He regarded natural or white light as the simplest type of disturbance, being constituted by a simple and uniform pulse at right angles to the direction of propagation, and inferred that colour is generated by the distortion to which this disturbance is subjected in the process of refraction. "The Ray",[18] he says, " is dispersed, split, and opened by its Refraction at the Superficies of a second medium, and from a line is opened into a diverging Superficies, and so obliquated, whereby the appearances of Colours are produced." "Colour" he says in another place, [19] " is nothing but the disturbance of light by the communication of the pulse to other transparent mediums, that is by the refraction thereof." His precise hypothesis regarding the different colours was[20] "that Blue is an impression on the Retina of an oblique and confus'd pulse of light, whose weakest part precedes, and whose strongest follows. And, that red is an impression on the Retina of an oblique and confus'd pulse of light, whose strongest part precedes, and whose weakest follows." Hooke's theory of colour was completely overthrown, within a few years of its publication, by one of the earliest discoveries of Isaac Newton (b. 1642, d. 1727). Newton, who was elected a Fellow of Trinity College, Cambridge, in 1667, had in the beginning of 1666 obtained a triangular prism, " to try therewith the celebrated Phaenomena of Colours." For this purpose, " having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Sun's light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby ; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form, which, according to the received laws of Refraction, I expected should have been circular" The length of the coloured spectrum was in fact about five times as great as its breadth. This puzzling fact he set himself to study ; and after more experiments the true explanation was discovered - namely, that ordinary white light is really a mixture of rays of every variety of colour, and that the elongation of the spectrum is due to the differences in the refractive power of the glass for these different rays. " Amidst these thoughts," he tells us, [21] " I was forced from [1] His Epistola was written in 1269 [2] "Procul dubio oranes lineae hujusmodi in duo puncta concurrent sicut omnes orbes meridian! in duo concurrunt polos mundi oppositos." [3] The form in the Colchester records is Gilberd. [4] Gulielmi Gilberti de Magnete, Magneticisque corporibus, et de magno magnete tellure : London, 1600. An English translation by P. F. Mottelay was published in 1893. [5] Principia, Part iv, 133 sqq. [6] Winston has recorded that, having returned to Cambridge after his ordination in 1693, he resumed his studies there, " particularly the Mathematicks, and the Cartesian Philosophy : which was alone in Vogue with us at that Time. But it was not long before I, with immense Pains, but no Assistance, set myself with the utmost Zeal to the study of Sir Isaac Newton's Wonderful Discoveries." Whiston's Memoirs (1749), i, p. 36. [7] Their memoirs shared a prize of the French Academy in 1743, and were printed in 1752 in the Recueil des pieces qui ount remporte les prix de l'Acad., tome v. [8] Renati Descartes Epistolae, Pars tertia ; Amstelodami, 1683. The Fermat correspondence is comprised in letters XXIX to XLVI. [9] Epist. XLII, written at Toulouse in August, 1657, to Monsieur de la Chambre ; reprinted in (AEuvres de Fermat (ed. 1891), ii, p. 354. [10] That reflected light follows the shortest path was no new result, for it had been affirmed (and attributed to Hero of Alexandria) in the "book" of Heliodorus of Larissa, a work of which several editions were published in the seventeenth century. [11] Epist. XLIII, written at Toulouse on Jan. 1, 1662 ; reprinted in (Euvres de Fermat, ii, p. 457 ; i, pp. 170, 173. [12] The imprimatur of Viscount Brouncker, P.R.S., is dated Nov. 23, 1664. [13] Micrographia, p. 47 [14] Boyle's Works (ed. 1772), i, p. 742. [15] Hooke's Posthumous Works, p. 186. [16] Physico- Mathesis de lumine, coloribus, et iride. Bologna, 1665 ; book i, prop. i. [17] Micrographia, p. 55. [18] Hooke, Posthumous Works, p. 82. [19] To the Royal Society, February 15, 1671-2. [20] Micrographia, p. 64. [21] Phil. Trans., No. 80, February 19, 1671-2. |