])ecember 2, 1889.1 



KNOWLEDGE 



31 



velocity with which the rays are earned athwart the 

 refracting masses is large compared with the velocity of 

 the wind, or rather is large compared with the velocity of 

 the wind across the line of sight. At a distance of 50 

 miles from the observer the rays from a star sweep through 

 still air with a thwart velocity of about 12 miles an hour, 

 and at a distance of 100 miles from the observer with a 

 thwart velocity of 24 miles an hour. 



Let us now consider the separation of the different 

 coloured rays coming from a star at different distances 

 from the observer. Ketteler gives, in the Forturkntti- iL-r 

 Phi/sif, 22nd JKhnianij, p. 179, the refractive index for the 

 B ray on passing from vacuum into air at a barometrical 

 IJressure of 0-76 met. as 1-00029350, and the refrac- 

 tive index for the G rav, under similar circumstances, as 

 1-00029873. Dr. J. H. Gladstone, who has made the 

 subject of refractive indexes a special study, tells me that 

 Ketteler's measures, though dating back to 1865, are still 

 perhaps the best in regard to the dispersion of gases. 

 According to these measures, it may be shown that for 

 small de%'iations the dispersion of the G and B rays 

 amounts to about e'fjth of the atmospheric refi-action. 



We know that at a height of 45° above the horizon the 

 atmospheric refraction amounts to nearly 1', at a height of 

 27° it is nearly 2', and at a height of 10° it is about 5', 

 and the horizontal refraction ranges from about 34' to 89'. 

 Consei]uently the deviation between the G and B rays, at 

 sea-level, for these altitudes is about 1", 2", and 5" (34" 

 to 89") respectively. The greater part of the deviation is 

 caused in the lower atmosphere ; we may therefore be 

 sure that the actual path of the rays lies closer togetlier 

 than two lines inclined at the angle of dispersion with 

 which the rays enter the observer's eye. Consequently, 

 for a star at an altitude of 45° (at which altitude scintilla- 

 tion is very e\'ident) the violet ray G of the spectrum will, 

 at a distance of 25 miles from the observer, be within 

 1\ inches of the red ray B, which, on reaching the 

 observer's eye, will merge with the G ray in making up 

 the image of the star. At a distance of 50 miles fi-om the 

 observer, the distance between the two rays will be less 

 than 1 foot 3 inches. We know that the two rays suff'er 

 very different refraction — for one part of the spectrum is 

 dinmied while the other is bright ; we may therefore be 

 sure either that the diameter of the refi'actLng masses is 

 small, or that the refraction is caused at a very great 

 height m the atmosphere. 



A\'e have at our disposal another means of estimating, m 

 a rough and general way, the (hameter of the refracting 

 masses which deflect the rays, much in the same manner 

 as the distance between the waves on the surface of water 

 might be estimated by a fish whose eyes would only per- 

 mit him to look at the bottom. He might form an esti- 

 mate of the average size of the waves, by obser\ing the 

 average distance between the bright and dark mottlings 

 of sunlight on the bottom — so we may get some notion of 

 the size of the refracting masses by looldng at the disc of 

 light which corresponds to the image of a bright star when 

 out of focus in a large telescope. This disc of light is 

 never perfectly uniform and traiKjuil ; mider certain condi- 

 tions it seems almost to boil, the agitation is so great. 

 Ivich part of the disc receives light from a different part of 

 the object glass (or of the specuhim, if the instrum -nt be a 

 reflector), and it is evident, from the dark patches continu- 

 ally passing across the disc, that less light from the star 

 is falling on some areas of the object-glass or speculum 

 than on others. With an 18-iuch reflector, with which 1 

 have observed, one sees in the centre of the disc a black 

 circular patch corr(>sponding to the flat wliii-li reflects the 



light to the eye-piece. Dark and bright patches are con- 

 tinually passing across the luminous disc. As a general 

 rule, they move parallel to one another. If they took a 

 second to pass across the whole 18 inches, the actual velocity 

 at right angles to the direction of the star of the refracting 

 masses producing the patches would be a foot and a half 

 per second, or a mile an hour. They usually pass more 

 rapidly than this, but not so rapidly that the eye cannot 

 follow them. 



It has frequently been suggested that the refracting 

 masses may be due to aggregations of aqueous vapour in 

 the air ; and it has been pointed out that the masses of 

 aqueous vapour which become \'isible as cloud in the lower 

 au- are large, and that as you ascend the cloud masses 

 become smaller and smaller ; but the small refracting 

 masses which produce the black bands which flit across 

 the spectrum, and the black patches which move across the 

 illuminated image of an object glass or speculum, cannot 

 owe their dift'erence of refracting power to excess or defect 

 of aqueous vapour. If such aggregations of aqueous vapour 

 were possible in the air, they would not produce the ob- 

 served irregularities of refraction. For, according to 

 .Jamin {Ann. Cli. Phi/x. [8] xlix. 382), the difference between 

 the refi-active index of dry air and air saturated with 

 moisture at 20° C. is only 0-000000726, a (juantity which, 

 as Dr. (jladstone (to whom 1 am indebted for the reference) 

 says, " may safely be neglected for astronomical pur- 

 poses. " 



But the diff'erence in the refractive index of air is 

 materially altered by a change of temperature — an in- 

 crease of one degree Centigrade in the temperatiu-e of a 

 mass of air increases its volume (the pressure remaining 

 the same) in the proportion of 1 to 1-003665. Its density 

 is therefore decreased in similar but inverse proportion, or 

 as 1-003666 to 1, and we mav calculate the change in the 



M-1 

 refi-active index from the law — 7-= a constant. 



In orduiary language this law may be stated thus. The 

 excess of the index of refraction over unity, or the " index 

 of deviation " (as Sir G. B. Airy happily christened the 

 quantity /x-1) varies as the density, or varies inversely as 

 the volume of a mass of gas when the pressure does not 

 change. 



A decrease of temperature of one-himdredth of a degree 

 Fahrenheit will cause a mass of air to decrease in volume 

 in the ratio 1-00002036 to tmity, and the focal length for 

 parallel rays of a spherical lens of radius r and refractive 



index u. is ^ ' Therefore a spherical mass of 



2(^-1) 

 cooler air of one foot radius and one-hundredth of a 

 degree Fahrenheit below the surroimding air, woidd bring 



, 1-0000203(5 

 parallel rays to a tocus at a distance of », /o-0000">OSrr 



that is, at a distance of a little less than five miles. 



At a distance much less than five miles, or at a distance 

 much greater than five miles, the concentration of light 

 by such a spherical mass of cooler air would not make 

 itself apparent ; but the deviation caused in the direction 

 of transmitted rays will be the same whether the mass of 

 denser air is near or far from the observer. 



We know, from the fact that the red and the blue rays 

 coming from a star are very differently aflecttd by the 

 refracting masses, that they cannot be largo in diameter 

 compared with the distance between the path of the red 

 and blue ray ; and the small areas dimmed by them on the 

 object-glass of a telescope also point to the conclusion 

 that the masses are generally not many inches in diameter. 

 We also know that the refracting masses which produce 



