Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/835

simply because his light, by illuminating our air, veils the stars from view, we can nevertheless ascertain exactly along what path on the star-sphere he seems to move, at what rate,

and whether the rate is uniform or variable.

But before we examine the results of observations carried out for this purpose, it will be well to consider a circumstance affecting observations made in this manner. We refer to the refractive action of the earth s atmosphere, by which the apparent positions of the celestial bodies are to some degree affected. This is the proper place to mention the effects of refraction, because there can be little doubt that it was during observations of the sun that the refractive action of the atmosphere was first discovered. However, in explaining this action reference will be made to the stars as heretofore, in order that the inquiry into the sun s apparent motions may be referred solely to the sphere of the fixed stars.

By a well-known optical law, a ray of light in passing obliquely from one medium to another of greater density is refracted or bent towards the normal to their common surface. We may regard our atmosphere as composed of ^n infinity of concentric spherical shells, whose densities increase the nearer they are to the earth s surface. When a ray of light from a star enters the atmosphere, therefore, it is inflected towards the earth, and the inflection is increased by every successive stratum of the atmosphere through which the light passes. In fig. 10, let AA , BB , CC ,

Fig. 10.

represent the boundaries of successive strata, supposed for convenience to have a finite thickness. A ray of light from S, reaching the highest stratum at a, leaves its original direction Sax, and travels in the direction aby; reaching the next stratum at b it is further bent, viz., from direction aby to the direction bz ; and at c it is deflected in the direction cO. In its progress from a to O, it has therefore succes sively moved in the direction of the sides of the polygon abcO; and to the spectator at O, the star from which it pro ceeded, instead of appearing in its true place at S, will appear to be at S , or in the last direction of the visual ray. ]S ov if A A is the most elevated stratum of the atmosphere into which the ray enters in the direction Sa, it is clear that the whole effect is produced by the atmospherical strata tsituated below AA, and that the length of Sa is perfectly indifferent; hence the refraction is entirely independent of the distance of the stars, provided they are beyond the limits of the earth s atmosphere.

The decrease of the density of the atmosphere, from the surface of the earth upwards, follows the law of continuity, or takes place by insensible degrees ; so that the luminous ray, in traversing the atmosphere, enters at every instant into a denser medium, and is therefore continually brought nearer and nearer to the vertical direction. Hence the true path of the ray is curvilinear, and concave towards the earth, as represented in fig. 11. This is equivalent to the supposition that the thickness of the different concentric strata of uniform density is infinitely small, and that the light, as it successively penetrates each, deviates from its former path by an infinitely small angle, which may be considered as the differential of the refraction, the total amount of which will therefore be obtained by integration. The direction of the ray, when it reaches the eye of the observer, is the tangent to the last portion of its curvilinear path ; and the apparent zenith distance of the star will be ZOS , while the real zenith dis tance is ZOS. The difference of these two angles, namely S OS, is what is denominated the Astronomical Refraction. It is evident that the whole path of the ray is confined to the vertical plane in which the star and the eye of the observer are situated ; for the earth and its atmosphere being very nearly spherical, that plane will divide the strata symmetrically ; there will, therefore, be no displacement in a lateral direction, i.e., no refraction out of the vertical plane. When the observed star is due north or south, the vertical plane is the plane of the meridian; hence, in meridional observations, the whole of the refraction takes place in declination, while the right ascension remains unaltered.

Fig. 11.

It is evident that the amount of the refraction is greater

in proportion as the observed star is nearer to the horizon ; for in this case the luminous rays strike the tangent planes of the atmospherical strata more obliquely, and have besides to traverse a greater extent of atmosphere before they arrive at the eye of the observer. On determining by experiment the refraction at every altitude from zero to 90, tables of Refraction may be constructed, which will furnish the means of discovering the law of its diminution ; but as such a process would be exceedingly tedious, and likewise apt to lead to erroneous results on account of the inevitable errors of observation, it is found more convenient to assume some hypothesis for a basis of calculation, and to verify the results which it leads to by comparing them with observation. In regard to media which may be said to be permanent, such, for instance, as water and glass, the determination of the refraction is not attended with great difficulty ; but the circumstances are greatly altered when we come to make experiments on the atmosphere. In this case the difficulty arises from the incessant changes which the atmosphere is undergoing relatively to its refractive power, changes which it is impossible for the observer fully to appreciate, inasmuch as he can only determine its physical state within a short distance of the earth, while that of the upper strata remains wholly unknown to him. The refractive power of the atmosphere is affected by its density and temperature. The effects of the humidity are insensible ; for the most accurate experiments seem to prove that the watery vapours diminish the density of the air in the same ratio as their refractive power is greater. It is therefore only necessary, even in delicate experiments, to have regard to the state of the barometer and thermo meter at the time the observation is made. At a medium density, and at the temperature of melting ice, it was found by Biot and Arago, from a great number of exact experi ments, that at any altitude between 10 and the zenith the refraction is very nearly represented by the formula r _ 60" 6 tan. (Z - 3 25 x ?), in which r is the refrac tion corresponding to a given zenith distance Z. With the exception of the numerical coefficients, this formula was first given by Bradley ; but whether it was deduced

from theory by that astronomer, or was only empirical, is