January 27, 1898] 



NATURE 



299 



a considerable amount of patience, Mr. J. M. Pemter 

 has calculated the tints and the angular deviations of the 

 rainbow colours for various sizes of rain-drops, and has 

 devised experiments in support of his deductions. A 

 parallel beam of sunlight after reflection and refraction 

 in a spherical rain-drop does not emerge as a parallel 

 beam, or as a bunch of parallel beams of various 

 colours, but as a series of caustics of a somewhat com- 

 plicated nature, in which the divergence of the colours, 

 and hence their distinctness, separation, or coincidence 

 depend upon the ratio of the radius of the drop to the 

 wave-length of the light. The influence of size is very 

 formidable in the smaller drops, say of ooi mm. radius. 

 This would be a very fine spray. The actual size of 

 rain-drops is supposed to vary between o"i mm. and 2'6 

 mm., but the heavy drops of tropical rains are said to 

 attain diameters of 3'4 mm. Their size may be estimated 

 by catching up and weighing a definite number, or by 

 the more difficult method of diffraction. The tables 

 drawn up by Pemter consider drops of twelve different 

 sizes between 0*005 ^^^d i mm. radius. In order to deter- 

 mine the resulting colours, Pernter selects eight of Max- 

 well's twenty-two colour equations, which number he finds 

 sufficiently accurate. The first set of his tables state, for 

 a point source of light, the sequence of colours, their 

 composition in terms of red, green, and violet, the 

 relative intensity (admixture of white, after Abney) and 

 position on the colour triangle of each shade for various 

 deviations between 42° 20' and 36''. These tables are then 

 verified by experiments with cylindrical streams of drops, 

 according to Babinet's method. With i mm. drops, 

 Pernter observed red, orange-yellow, green, violet, blue' 

 second violet, and then twenty-four secondaries or 

 spurious colours, chiefly pinkish-violet and green or 

 blue ; after the twelfth violet came a whitish band, 

 and then a reversal in the sequence of the colours. 

 The o"5 mm. drops gave 1 1 bows with 40 shades. The 

 outer bow and its secondaries were also observed. Veri- 

 fications in nature are hardly possible, as we cannot 

 measure simultaneously the angles and the size of the 

 drops producing the bow ; it is striking, however, that so 

 very few angular measures are extant. 



The white or pale rainbows (fog or mist bows) around 

 moon and sun may appear pale owing to (i) the feeble 

 intensity of the light, (2) the uneven size of the drops, 

 and (3) the mixture of colours. The first cause is 

 probably a real one ; the second Pernter is inclined to 

 reject, since the accompanying, often well-defined features 

 such as " glories," Brocken spectra, &c., and also his own 

 tests require homogeneous conditions. As regards the 

 third, Abney has proved that all colours of any shade 

 disappear on being diluted with 75 parts of white, and 

 Pernter's tables show that such cases may well occur. 

 Further, Airy's theory renders white bands possible for all 

 sizes of drops, and necessary for radii below 25 /i. As a 

 stream of water of such fineness cannot be maintained, 

 Pernter produced a mist spray by fixing a 0*5 mm. glass 

 tube in a lead pipe connected with the Innsbruck water 

 mains (pressure 5 atmospheres), and directing the jet 

 against a metallic plate ; the size of drops was derived 

 from measurements of diffraction rings. Drops of 

 radius 5 /i gave a yellow margin at 41° 59', white 

 between 41^8' and 38^ 27', and then blue to 37° 41'; 

 larger drops were more difficult to manage. From 

 measurements of fog-bows on Ben Nevis, J. McConnell 

 had in 1890 already calculated the sizes of the respective 

 drops. But some of these observations speak of a red 

 outer margin, for which Pernter looked in vain, and 

 which his calculations do not indicate ; Crailheim- 

 Gyllenskiold (Swedish North Pole expedition, 1882) also 

 describes the margin as of ochre colour. The classical 

 white bows of Bouguer (1744) and of Scoresby (1821), 

 however, do not fit into the theory at all, and were 

 probably due, as the observers remarked, to ice-needles. 



NO. 1474, VOL. 57] 



The general conclusions are interesting to meteoro- 

 logists. The greater the drops, the more secondaries 

 (spurious bows). A chief bow of intense pink and green 

 (hardly any blue) indicates drops of diameters ranging 

 from I to 2 mm. ; intense red always speaks for big 

 drops. Secondaries of green and violet (the blue is 

 masked by contrast) without yellow, immediately joining 

 the chief bow, correspond to drops of 05 mm., while 

 five and more secondaries without white and without 

 breaks mark drops of o'l mm. A partly white bow is 

 produced by drops of o"o6 mm., and when the drops are 

 still smaller, a real white bow with orange-yellow and 

 blue margins is the result. The net result of these 

 elaborate investigations will be to add a new interest to a 

 natural phenomenon already endowed with many as- 

 sociations of magic and beauty. 



EDUARD LINDEMANN AND OSCAR 

 STUMPE. 



'X'HE last days of the old year witnessed the lemoval 

 -*■ by death of two astronomers who have rendered 

 valuable services in the respective positions in which 

 they were situated, though not occupying prominent 

 places in the history of the science. Both are mentioned 

 by the authorities under whom they served with the 

 utmost respect, and their loss is acknowledged with 

 profound regret. 



Dr. Eduatd Lindemann, who died suddenly on 

 December 21, was born in Nishni-Novgorod in 1842, and 

 pursued his scientific studies in the Universities of 

 Kasan and Dorpat. The latter University he left in 

 1868 to enter the observatory of Pulkova, wherein he 

 filled the office of scientific secretary. In this capacity 

 he had the management of the library, and the prepara- 

 tion of the second part of the " Librorum in Bibliotheca 

 Speculee Pulkovensis contentorum Catalogus system- 

 aticus" was entrusted to him, and very admirably did 

 he fulfil the trust. The duties of his office did not 

 permit him to take a great part in the astronomical 

 •observations there carried on ; but his tastes led him to 

 take great interest in the Zollner photometer, and the 

 series of careful measures which he made with that in- 

 strument have led to his being regarded as an authority 

 in its use. His paper on the " BriUiancy of Bessel's 

 Stars in the Pleiades," published in tome xxxii. of the 

 Mem. de PAcad. Imp. des Set. de S. Petersbourg, is well 

 known, and he has further used his measures to de- 

 termine the scale of magnitude employed in the Bonn 

 D urch m usterung. 



The second astronomer whose death (at the early age 

 of thirty-five) we have regretfully to mention is Dr. 

 Oscar Stumpe, well known for his contribution on the 

 motion of the solar system. Dr. Stumpe's early life 

 appears to have been one of great hardship and a 

 severe struggle against adverse circumstances. When 

 ten years old he lost his father, but, in face of all diffi- 

 culties, he determined to win his way to the Berlin 

 University as a student of science. This he accom- 

 plished in 1883, though he had had occasionally in 

 previous years to interchange the parts of student and 

 teacher in order to obtain a livelihood and be enabled, 

 to continue his career. Even at Berlin, his studies of 

 mathematics and astronomy were interrupted by his 

 duties as a shorthand writer in the Government and 

 Law Courts. From Berlin he went to Bonn, and became 

 a teacher in a private institution. Here he appears to 

 have prepared the heavy calculations which he after- 

 wards incorporated in his inaugural dissertation on 

 the Solar Motion. In this work. Dr. Stumpe based his 

 computations on 1054 stars, whose annual proper motion 

 exceeded o""i6 in the arc of a great circle. The peculiar 

 feature in the treatment was the introduction of a term. 



