CHAPTER IV. ON REFRACTION AND TWILIGHT. 46. As connected with the earth, we may here consider its atmosphere, and how it affects the apparent places of the heavenly bodies. We know, from the science of pneumatics, that the air surrounding the earth is an elastic fluid, the density of which is nearly proportional to the compressing force, or the weight of the incumbent air. Whence it follows that the density continually decreases, and at a few miles high becomes very small. Now a ray of light passing out of a rarer medium into a denser, is always bent out of its course toward the perpendicular to the surface, on which the ray is incident. It follows therefore that a ray of light must be continually bent in its course through the atmosphere, and describe a curve, the tangent to which curve, at the surface of the earth, is the direction in which the celestial object appears. Consequently the apparent altitude is always greater than the true. 47. The refraction or deviation is greater, the greater the angle of incidence, and therefore greatest when the object is in the horizon. The horizontal refraction is about 32'. At 45o altitude, in its mean quantity it is 571". 48. The refraction is affected by the variation of the quantity or weight of the superincumbent atmosphere at a given place, and also by its temperature. In computing the quantity of refraction, the height of the barometer and thermometer must be noted. The quantity of refraction at the same zenith distance varies nearly as the height of the barometer, the temperature remaining constant. The effect of a variation of temperature is to diminish the quantity of refraction about part for every increase of one degree in the height of the thermometer. Therefore, in all accurate observations of altitude or zenith distance, the height of the barometer and thermometer must be attended to.a 49. The refraction may be found by observing the greatest and least altitude of a circumpolar star. The sum of these altitudes diminished by the sum of the refractions corresponding to each altitude, is equal to twice the altitude of the pole: from whence, (if the altitude of the pole be otherwise known), the sum of the refractions will be had; and from the law of variation of refraction, known by theory, the proper refraction to each altitude may be assigned. 50. Otherwise, when the height of the pole is not known, the ingenious method of Dr. Bradley may be followed, who observed the zenith distances of the sun at its greatest declinations, and the zenith distances of the pole star above and below the pole. The sum of these four quantities must be 180° diminished by the sum of the four refractions; hence he obtained the sum of the four refractions, and then by theory apportioned the proper quantity of refraction to each zenith distance. In this manner he constructed his table of refractions.b a Theory shews that, whatever be the law of change of density, the variation of refraction is as the tangent of the zenith distance, between the zenith and about 74° zenith distance. At greater zenith distances we cannot apply theory to obtain the variation of refraction, because there the variation of the density of the air at different heights will sensibly affect the quantity of refraction, and the law of this variation is unknown. b The object of the observations in this and the preceding article is to ascertain the coefficients of refraction. If we suppose the refraction to vary as the tangent of the zenith distance there is but one coefficient, which can be thus accurately de 51. The ancients made no allowance for refraction, although it was in some measure known to Ptolemy, who lived in the second century. He remarks a difference in the times of rising and setting of the stars in different states of the atmosphere.This however only shews that he was acquainted with a variation of refraction, and not with the quantity of refraction itself. Alhazen, a Saracen astronomer of Spain, in the ninth century, first observed the different effects of refraction on the height of the same star above and below the pole.-Tycho Brahe, in the sixteenth century, first constructed a table of refractions. This was a very imperfect one. 52. As the atmosphere refracts light, it also reflects it, which is the cause of a considerable portion of the day-light we enjoy. After sun-set also the atmosphere reflects to us the light of the sun, and prevents us from being plunged into instant darkness, upon the first absence of the sun. Repeated observations shew that we enjoy some twilight, till the sun has descended 18° below the horizon. From whence it has been attempted to compute the height of the atmosphere, capable of reflecting rays of the sun sufficient to reach us; but there is much uncertainty in the matter. If the rays come to us after one reflection, they are reflected from a height of about 40 miles: if after two, or three, or four, the heights will be twelve, five, and three miles. The computation requires the assistance of termined. Let the zenith distances of the sun be S, S'; and of the star Z, Z', then by Bradley's method we have 180°=S+ S'+Z + Z' + A. (tan. S+tan. S' + tan. 2+tan. Z'), if the refraction be represented by A. tan. zen. dist. in general; hence A can be determined exactly. See Delambre Abregé d'Astronomie, p. 136. Ed. The investigation of the law of variation of refraction from theory, is much too difficult to find a place in an elementary book. Reference may be had to Simpson's Mathematical Dissertations; Vince's Astronomy, chap. 7, p. 76; Laplace's Mecanique celeste, tom. iv. p. 267, &c., Trans. R. Irish Academy, vol. xii. the theory of terrestrial refractions. Astronomy, Art. 206.) (See Professor Vince's 53. The duration of twilight depends upon the latitude of The sun's depression behave the three sides of a the place and declination of the sun. 54. Refraction is the cause of the oval figures which the sun and moon exhibit, when near the horizon. The upper limb is less refracted than the lower, by nearly five minutes, or of the 'whole diameter, while the diameter parallel to the horizon remains the same. The rays from objects in the horizon pass through a greater space of a denser atmosphere than those in the zenith, hence they must appear less bright. According to Bougier, who made many experiments on light, they are 1300 times fainter, whence it is not surprising that we can look upon the sun in the horizon without injuring the sight. फ 55. Another striking phenomenon respecting the sun and moon in the horizon, must not be entirely passed over, although rather belonging to the science of optics, viz. their great apparent magnitudes. The cause of this undoubtedly is the wrong judgment we form of their distances then, compared with their a Or when the sun's polar distance exceeds the latitude by a quantity less than 18.-Ed. distances when their altitudes are greater. In estimating their distances when in the horizon, we are led to judge them greater than when considerably elevated, because of the variety of intervening objects which furnish ideas. The apparent diameters being nearly the same in both cases, we are apt to judge that object largest, the distance of which we conceive greatest. This explanation is a very old one, being given by Alhazen in the ninth century. Roger Bacon, Kepler, Des Cartes, and others also, were of the same opinion. colat. |