CHAPTER V.

REFRACTION AND TWILIGHT.

Refraction. Its nature.—Importance of a correct knowledge of its amount.—Table of the correction for Refraction.-Effect of Refraction on the position of objects in the horizon.-History of its discovery.-Twilight-How caused.—Its duration.

R

EFRACTION.—Besides the change of place to which the heavenly bodies are subjected by the effects of parallax, atmospheric refraction gives rise to a considerable displacement; and it is this power which the air, in common with all transparent media, possesses, which renders a knowledge of the constitution of the atmosphere a matter of importance to the astronomer. "In order to understand the nature of refraction we must consider that an object always appears in the direction in which the last ray of light comes to the eye. If the light which comes from a star were bent into 50 directions before it reached the eye, the star would nevertheless appear in a line described by the ray nearest the eye. The operation of this principle is seen when an oar, or any stick, is thrust into the water. As the rays of light by which the oar is seen have their direction changed as they pass out of water into air, the apparent direction in which the body is seen is changed in the same degree, giving it a bent appearance-the part below the water having apparently a different direction from the part above a."

a Olmsted, Mechanism of the Heavens, p. 94. Edinburgh edition. In Sir J. Herschel's Outlines of Ast. (pp. 27 et

seq.) there will be found a useful summary of information concerning refraction.

The direction of this refraction is determined by a general law in optics, that when a ray of light passes out of a rarer into a denser medium-e.g. out of air into water, or out of space into the Earth's atmosphere-it is bent towards a perpendicular to the surface of the medium; but when it passes out of a denser into a rarer medium, it is bent from the perpendicular. Inasmuch then as we see any object in the direction in which the rays emanating from it reach the eye, it follows that the effect of refraction is to make the apparent altitude of a heavenly body appear greater than the true altitude; so

that for example any object situated actually in the horizon will appear above it. Indeed, some objects that are actually below the horizon, and which would be otherwise invisible were it not for refraction, are thus brought into sight. It was in consequence of this that on April 20, 1837, the Moon rose eclipsed before the Sun had set; and other like instances may be conceived.

In Fig. 177, Z is the zenith, CD the visible horizon, A B a parallel of latitude, A E B the boundary of the Earth's atmosphere. Then the light of the star Q will, to the observer at O, seem to come from the point P.

A correct determination of the exact amount of atmospheric refraction, or the angular displacement of a celestial object at any altitude, is a very important, but a very difficult subject of inquiry, owing to the fact that the density of any stratum of air (on which its refractive power depends) is affected by the operation of meteorological phenomena with which we are at present but very imperfectly acquainted. Thus, the amount of refraction at any given altitude depends not only on the density but also on the thermometric and hygrometric conditions of the air through which the visual ray passes. And although we know the general fact that the barometric pressure and the temperature constantly diminish as we rise from the Earth's surface, yet, the law of this diminution is not fully ascertained. In consequence of our ignorance on these points, some degree of uncertainty is introduced into the determination of the amount of refraction, which affects astronomical observations involving extremely minute quantities. Nevertheless it must be remembered that inasmuch as the total amount of refraction is never considerable, and in most cases very small, it can be so nearly estimated as to offer no serious impediment to the

astronomer.

Tables are in use, constructed partly from observation and partly from theory, by means of which we can ascertain approximately the mean refraction at any given altitude; additional rules being given by which this average refraction may be corrected according to the state of the air at the time of observation. At the zenith, or at an altitude of 90°, there is no refraction whatever, objects being seen in the position which they would

b Since the barometer rises with an increase in the weight and density of the air, its rise is coincident with an augmentation, and its fall with a decrease, of refraction. It will be tolerably near the truth if we assume that the refraction at any given altitude is increased or diminished by of its mean amount for every 10th of an inch by which the barometer exceeds or falls short of 30 inches. e Also as an increase of temperature

causes a decrease of density, it follows that the rise of the thermometer diminishes the effect of refraction, the barometer remaining stationary. We may assume that the refraction at any given altitude is increased or diminished by of its mean amount for each degree by which the thermometer exceeds or falls short of the mean temperature of 55° Fahr.

d See Vol. II, post.

have were the Earth devoid of any atmosphere at all. In descending from the zenith towards the horizon, the refraction constantly increases, objects near the horizon being displaced in a greater degree than those at high altitudes. Thus the refraction, which at an altitude of 45° is only equal to 57′′, at the horizon increases to nearly 35'. The rate of the increase at high altitudes is nearly in proportion to the tangent of the apparent angular distance of the object from the zenith; but in the vicinity of the horizon this rule ceases to hold good, and the law becomes much more complicated in its expression. Since the mean diameter both of the Sun and Moon is about 32', it follows that, when we see the lower edge of either of these luminaries apparently just touching the horizon, in reality its whole disc is completely below it, and would be altogether hidden by the convexity of the Earth were it not for refraction.

It is under these circumstances that one of the most curious effects resulting from atmospheric refraction may often be noticed, namely the somewhat oval outline presented by the Sun and Moon when near the horizon. This arises from the unequal refraction of the upper and lower limbs. The lower limb being nearer the horizon, is more affected by refraction, and consequently is raised in a greater degree than the upper limb, "the effect being to bring the two limbs apparently closer together by the difference of the two refractions. The form of the disc is therefore affected as if it were pressed between two forces, one acting above and the other below, tending to compress its vertical diameter, and to give it the form of an ellipse, the lesser axis of which is vertical and the greater horizontal."

The dim and hazy appearance of objects in the horizon is not only occasioned by the rays of light having to traverse a greater thickness of atmosphere (because their direction is oblique), but also from their having to pass through the lower and denser part. "It is estimated that the solar light is diminished 1300 times in passing through these lower strata, and we are thereby

enabled to gaze upon the Sun, when setting, without being dazzled by his beams." Or, as Bouguer put it, the Sun's brilliancy at 40° above the horizon is 1000 times greater than it is at 1°.

"The dilated size (generally) of the Sun or Moon when seen near the horizon beyond what they appear to have when high up in the sky, has nothing to do with refraction. It is an illusion of the judgment, arising from the terrestrial objects interposed, or placed in close comparison with them. In that situation we view and judge of them as we do of terrestrial objects-in detail, and with an acquired habit of attention to parts. Aloft we have no associations to guide us, and their insulation in the expanse of the sky leads us rather to undervalue than to over-rate their apparent magnitudes. Actual measurement with a proper instrument corrects our error, without however dispelling our illusion. By this we learn that the Sun, when just on the horizon, subtends at our eyes almost exactly the same, and the Moon a materially less angle than when seen at a great altitude in the sky, owing to its greater distance from us in the former situation as compared with the latter." Guillemin remarks that if the Moon, when in the horizon, be looked at through a tube, the illusion will disappear.

Claudius Ptolemy was the first who remarked that a ray of light proceeding from a star to the Earth undergoes a change of direction in passing through the atmosphere 8. He moreover stated that the displacement is greatest at the horizon, diminishes as the altitude increases, and finally vanishes altogether

• This explanation of Sir J. Herschel's has been disputed, but its general correctness is rendered highly probable by the fact that the apparent size of a balloon varies in precisely the same way, according as it is high up in the air or near the horizon. See some remarks by Stroobant quoted in Observatory, vol. viii. p. 130, April, 1885. This writer thinks that the loss of brilliancy suffered by the Sun and

Moon when low down towards the horizon has much to do with the phenomenon, but that it is mainly due to some physiological cause, connected with the direction of vision, which is worthy of further and special study.

Sir J. Herschel, Outlines of Ast., P. 35.

Almag., lib. vii. cap. 6.