Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/836

770 uncertain. Bradley s formula was r&#61;57&quot; tan. (Z 3 x r). When the direction of the luminous rays makes a smaller angle than 10 with the horizon, it becomes indispensable to take into account, in the calculation of the refraction, the law of the variation of the density of the atmosphere at different altitudes, a law which is subject to incessant variation, from the operation of winds and other causes which agitate the atmosphere, as well as the decrease of temperature in the superior regions. For this reason all astronomical observations which have not refraction directly for their object, or which are not by their nature inde pendent of its influence, are made at an elevation exceed ing 10. For lower altitudes it is to be feared that no theory will ever be found sufficiently exact to entitle the observations to much confidence.

[It may be explained here in passing that the refraction of the rays of light in traversing the earth s atmosphere is the cause of Twilight, which sensibly lengthens the duration of the day, and prevents a sudden transition from light to darkness on the disappearance of the sun. When the sun is more than 33 below the horizon, the refraction is not powerful enough to bring his rays sufficiently near the earth to reach our eyes ; they pass over our heads, and are irregularly reflected by the molecules of the atmosphere. By this means a portion of the celestial vault is enlightened, while the sun is invisible. This illumination of the upper regions is called the twilight. It commences as soon as objects can be distinguished before sunrise, and terminates when they cease to be visible after the sun has set. The time, however, at which the twilight commences and ter minates cannot be assigned with any degree of precision. It is generally supposed to be limited by the depression of the sun 18 below the horizon. Lacaille found the limit in the torrid zone to be between 16 and 17. According to Lemonnier, it varies in France between 17 and 21. The duration of the twilight will evidently be longer or shorter according as the inclination of the sun s motion to the horizon is more or less oblique.

Fig. 12. The apparent enlargement of the sun and moon near the horizon is an optical illusion, connected in some measure with the atmosphere, of which various explanations have been given since the time of Ptolemy. According to the ordinary laws of vision, the celestial bodies, particularly the moon, which is nearest to the earth, ought to appear largest in the meridian, because their distance is then less than when they are near the horizon ; yet daily experience proves that the contrary takes place. To an observer placed at E (fig. 12), the visual angle subtended by the moon, in the horizon at M, is somewhat less than that under which she appears in the zenith at ; and this fact, a consequence in deed of her circular motion, is proved by accurate measurement of her diameters in those circumstances by the micrometer. The mean apparent diameter of the moon, at her greatest height, is 31 in round numbers, but in the horizon she seems to the eye two or three times larger. The commonly received ex planation of this phenomenon was first given by Descartes, and after him by Dr Wallis, James Gregory, Malebranche, Huyghens, and others, and may be stated as follows: The opinion which we form of the magnitude of a distant body does not depend exclusively on the visual angle under which it appears, but also on its distance ; and we judge of the distance by a comparison with other bodies. When the moon is near the zenith there is no interposing object with which we can compare her, the matter of the atmos phere being scarcely visible. Deceived by the absence of intermediate objects, we suppose her to be very near. On the other hand, we are used to observe a large extent of land lying between us and objects near the horizon, at the extremity of which the sky begins to appear ; we there fore suppose the sky, with all the objects which are visible in it, to be at a great distance. The illusion is also greatly aided by the comparative feebleness of the light of the moon in the horizon, which renders us in a manner sensible of the interposition of the atmosphere. Hence the moon, though seen under nearly the same angle, alternately ap pears very large and very small. Desaguliers illustrated the doctrine of the horizontal moon by the supposition of our imagining the visible heavens to be only a small por tion of a spherical surface, as mnop (fig. 12), in which case the moon, at different altitudes, will appear to be at dif ferent distances, and will therefore seem to vary in magni tude, as at m, n, o.] Correction being made for refraction, the true position of the sun on the star-sphere can be ascertained day after day ; and thus his apparent motions, as we have said, can be determined.

The result of such observations is to show that in a period of about 365 days the sun traverses a great circle of the star-sphere inclined to the equator. This period is ie B called a year, and is familiar to all as the period in which the sun s varying positions, alternately north and south of the equator, bring about the circuit of the seasons. For we have already seen that a star to the north of the equator is above the horizon more than half the sidereal day, and at its meridian culmination has an altitude exceeding that of the south point of the equator. When the sun is north of the equator he has a daily arc like that of a star similarly placed, so that day lasts longer than night, and at mid-day the sun pours his heat more directly on the earth than if he were on the equator. In like manner it is shown that, when the sun is south of the equator, night lasts longer than day, and the sun at mid-day has a smaller altitude than if he were on the equator. The result of constant experience shows, that the sun s declination reaches its maximum on the south side of the equator about the 22d of December, when it amounts to 2 3 465. From this time it gradually diminishes till about the 21st of March, when the sun reaches the plane of the equator. At this time the days and nights are of equal length all over the earth, and the instant of time at which the sun s centre is in the equatorial plane is called the instant of the equinox. The sun then passes to the northern side of the equator, and his declina tion or meridional altitude continues to increase till about the 22d of June, when he becomes stationary, and then again shapes his course towards the equator. His maxi mum declination on the north side of the equator is exactly equal to that on the south, amounting to 23 4G5. The sun now continues to approach the equator till about the 24th of September, when he again reaches that plane, and a second equinox succeeds. Continuing still to move in the same direction, he declines from the equator south ward, till he reaches his former limit about the 22d of December; and so on continually.

The two small circles of the sphere, parallel to the equator, which pass through the two points where the declination is greatest, are called the Solstices or the Tropics; that on the northern hemisphere is called the Tropic of Cancer, and the other is called the Tropic of Capricorn. These two parallels, which mark the extreme limits of the sun s declination, are, as has just been stated, equally