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SCIENCE. 



[N. S. Vol. XV. No. 373. 



this year and again close in. Observations 

 show that this has happened. In July, 

 1901, the distance was approximately 0".15. 

 It has now decreased to less than 0".05, or 

 approximately the same as in the autumn 

 of 1900. The data at present available ap- 

 pear to show that the period of 5.7 years 

 is substantially correct. 



The Duration of Twilight tvithin the 



Tropics: S. I. Bailey. 



The atmosphere renders many services to 

 man. Not the least of these, perhaps, is 

 the twilight. If there were no atmosphere, 

 there would be no twilight, and the bright- 

 ness of midday would be succeeded, the 

 moment after sunset, by the darkness of 

 midnight. Such a condition of affairs 

 would cause considerable inconvenience. 

 Twilight may be said to last until the last 

 bit of illuminated sky disappears from the 

 western horizon. In general it has been 

 found that this occurs when the sun has 

 sunk about 18° below the horizon. The 

 duration of time which the sun takes in 

 reaching this position is very different at 

 different latitudes. At the North Pole one 

 would have about six months of daylight, 

 followed by nearly two months of decreas- 

 ing twilight, followed in turn by more than 

 two months of night. In summer, at lati- 

 tudes greater than 50°, twilight lasts from 

 sunset to sunrise. There is no night there, 

 during this season. In the temperate zones 

 the duration of twilight ranges from an 

 hour and a half to more than two hours. 

 "Within the tropics the sun descends nearly 

 or quite vertically; but even here the time 

 required for the sun to reach a point 18° 

 below the horizon is more than an hour. 

 There seems to be no reason, therefore, in 

 the general theory, for the widespread be- 

 lief that the duration of the tropical twi- 

 light is extremely brief. This idea is found 

 not only in current popular literature, but 

 also in some of the best text-books on gen- 



eral astronomy. Young 's ' General Astron- 

 omy,' p. 69, says: "At Quito and Lima it 

 (the twilight) is said to last not more than 

 twenty minutes." ^Tiy Quito should be 

 classed with Lima I do not know, except 

 that both are within the tropics. ' The 

 Heavens Above,' by Gilbert and Rolfe, re- 

 marks : ' ' Within the tropics, where the air 

 is pure and dry, twilight sometimes lasts 

 only fifteen minutes." Since Arequipa, 

 Peru, lies within the tropics and has an 

 elevation of 8,000 feet, and the air is espe- 

 cially pure and dry, the conditions appear 

 to be exceptionally favorable for an ex- 

 tremely short tmlight. On Sunday, June 

 25, 1899, the following observations were 

 made at the Harvard Astronomical Station, 

 which is situated there: The sun disap- 

 peared at 5 :30 P.M., local mean time. At 

 6 :00 P.M., 30 m. after sunset, I could read 

 ordinary print with perfect ease. At 6 :30 

 P.M. I could see the time readily by an 

 ordinary watch. At 6 :40 p.m., 70 m. after 

 sunset, the illuminated western slry was 

 still bright enough to cast a faint shadow 

 of an opaque body on a white surface. At 

 6 :50 P.M. the illumination was faint, and 

 at 6 :55 P.M., 1 h. and 25 m. after sunset, 

 it had disappeared. On August 27, 1899, 

 the following observations were made at 

 Vincocaya. The latitude of this place is 

 about 16° south, and the altitude 14,360 

 feet. Here it was possible to read coarse 

 print 47 m. after sunset, and twilight could 

 be seen for an hour and twelve minutes 

 after the sun's disappearance. It appears, 

 therefore, that while the tropical twilight 

 is somewhat shorter than occurs elsewhere, 

 and is still further lessened by favorable 

 conditions, such as great altitude, and a 

 specially pure air, it is never less, and gen- 

 erally much longer, than an hour. 



The Determination of Double Star Orhits: 

 George C. Comstock. 

 The usual data for the determination of 



