On the 10th of Nov. 1828, its distance from the sun will be the same as at the time of its discovery in 1818, and it will be considerably nearer to the earth; and on the 21st of December, its position with respect to the sun will be the same as at its last observation in 1819; and with respect to earth, its situation will be more advantageous. The 1st of January, 1829, it will set with the sun.
It follows, that the most advantageous time for seeing it will be during the whole of November, and the first 25 days of December. It will scarcely be seen before the end of September, as it has heretofore never been observed more than two months before the time of its perihelion, and even in the dark winter nights will scarcely be visible more than 14 or 15 weeks before that period. After the perihelion it will not be visible in these parts of the world.
ii. Elementary View of the UNDULATORY Theory of Light. By Mr. FRESNEL. [◊] [Continued from the last Number.]
IN order to complete the explanation of the conditions necessary for the formation of the fringes, it remains to show why a small luminous point must be employed in experiments on diffraction, and not an object of any considerable dimensions. If we resume the case of the interior fringes of the shadow of [p432] a narrow body, it will be easy to apply similar arguments to other cases of diffraction.
The middle of the central band, which is always formed by the simultaneous arrival of rays, which depart at the same instant from the luminous point, must be found in the plane drawn through this point, and the line bisecting the narrow body: because, since every thing is symmetrical on each side of this plane, the rays which unite in it must have passed through equal routes on each side, and must consequently arrive at the same instant, unless they have passed through different media, which is not the case to be considered at present. The situation of the middle stripe being determined, that of every other stripe must also be determined accordingly. Now it is evident that if the luminous point should change its situation a little, and be moved to the right, for example, the plane, which has been supposed, would incline to the left, and would carry with it all the fringes which accompany the middle stripe. And if, instead of supposing motion, we suppose the luminous point to become of sensible dimensions; the integral points of which it is composed will each produce a group of fringes, and their situations will be so much the more remote as the luminous object is larger; and ultimately, if its size is sufficiently increased, they will extinguish each other and disappear. This is the reason that, when the rays cross each other at sensible angles, as in all the phenomena of diffraction, it becomes necessary to employ a very fine luminous point, in order to discover their mutual influence: and the point must be so much the finer as the angle formed by the rays is greater.
However minute the luminous point may be, it is always composed, in reality, of an infinite number of centres of oscillations, and it is of each of these centres that we must understand what has been said of a luminous point. But as long as they are very near to each other in comparison with the breadth of the fringes, it is obvious that the different groups of fringes which they produce, instead of mixing with each other in a confused manner, will be superposed almost exactly, and instead of extinguishing, will co-operate with each other. [p433]
When the two systems of waves which interfere are parallel, the interval which separates their corresponding points must remain the same for a great portion of the surface of the waves, that is to say, in other words, the fringes will become almost infinite in breadth, so that a very considerable displacement of the centre of undulation will cause very little difference in the agreement or disagreement of their vibrations. And in this case it is no longer necessary to employ so small an object in order to perceive the effects of their mutual influence.
If the coloured rings, which are produced by the interference of two systems of undulations nearly parallel, exhibit, like the fringes, and often within a very short distance, alternations of dark and bright stripes; this circumstance depends entirely on the want of uniformity in the thickness of the plate of air interposed between the glasses, which causes a variation of the difference of the routes of the rays reflected at the first and at the second surface of this plate, of which the mutual interference produces the bright and dark rings.
We shall readily be able, to understand why the luminous rays, although they always exert a certain influence on each other, exhibit it to the eye so seldom, and in cases so much limited, if we consider that it is necessary, for such an exhibition, first, that the rays concerned shall have been derived from a common source; secondly, that the difference between their paths shall amount to a limited number of undulations only, even when the light is as homogeneous as possible; thirdly, that they shall not intersect each other at too great an angle, because the fringes would become so small as to be invisible even with the assistance of a strong magnifier; and fourthly, unless the rays are nearly parallel, that the luminous object should be of very small dimensions, and the smaller in proportion as the inclination of the rays is greater.
It has been thought necessary to insist so much at length on the theory of interferences, because of its numerous applications to the calculation of the most interesting of the laws of optical phenomena. These considerations may perhaps appear at first somewhat delicate and difficult of comprehension, notwithstanding the minuteness of the [p434] explanation; but with some reflection it will be found that nothing can be simpler than the principles on which they are founded, and their application will soon become familiar to the imagination.