Dr. Wilhelm von Bezold on Twilight. 423 



a pin at one end and a notched piece of metal plate at the other, 

 the whole being attached to a graduated arc. Telescopes, or strictly- 

 dioptric apparatus, are of no use, inasmuch as they limit the 

 view too much, and introduce disturbing effects of contrast. 

 For the results of the measurements I must refer to my before- 

 mentioned paper. 



II. All the theoretical investigations which have hitherto been 

 made upon twilight are fundamentally nothing more than further 

 developments of the theory promulgated by the Arabic astrono- 

 mer Alhazen. According to this view, the part of the sky from 

 which light can reach us after a single reflexion, is separated 

 from the part which cannot give us light except by at least two 

 reflexions by a bow, which was called the first twilight-bow, 

 and whose height above the horizon depended only, according to 

 this view, upon the position of the sun, and upon the height of 

 the atmosphere. Hence the phenomena of twilight were re- 

 garded as affording a proper basis for determining the height of 

 the atmosphere; but it is well known that no serviceable results 

 were thus arrived at. A definition, similar to that of the first, 

 was given of a supposed second twilight-bow ; and places were 

 said to be in the first twilight when the first twilight-bow was 

 above their horizon, and in the second twilight when the second 

 bow was above their horizon. 



A glance is enough to show the insufficiency of this theory. 

 The dark segment, of which, according to this supposition, the 

 first twilight-bow marks the limit, and which ought therefore 

 to advance over the whole sky according to a perfectly definite 

 law, disappears at a very moderate elevation, and follows in 

 other respects quite a different course. If, for instance, the 

 height of the atmosphere is calculated on the basis of this 

 theory from the measurements of this phenomenon, each ob- 

 servation gives a greater value than the preceding one. The 

 results, indeed, vary from 0-05 to 2 geographical miles. The 

 bright segment and that very remarkable phenomenon the 

 purple light, are left entirely out of consideration in the old 

 theory. 



Moreover the observed division into the first and second 

 twilight does not by any means answer to what the theory re- 

 quires. For, according to this, the end of the first twilight 

 ought to coincide with the beginning of the second, whereas in 

 reality the two encroach upon each other. The course of the 

 second is, indeed, completely analogous to that of the first, if 

 only we assume that the first purple light plays exactly the 

 same part in relation to the production of the second twilight 

 that the sun does in the case of the first. That is to say, the 



