6 ABBE — THE ALTITUDE OF THE AUEOEA. [Jan. 7, 



cult than to recognize the fact that all our ideas are wrong, and that 

 we are wholly in the dark with regard to the nature of that which 

 our eyes behold so plainly. How many thousands of years elapsed 

 before modern science gave us any clue to the true nature of the 

 rainbow, and how difficult it has been to eradicate from our text- 

 books the crude ideas of Descartes, Huyghens and Sir Isaac Newton 

 which made the rainbow to be a phenomenon of dispersion and 

 substitute the correct view of Thomas Young, who showed it to be 

 a phenomenon of interference. 



Possibly we must go through a similar series of changes in our 

 views with regard to the auroral light until we recognize that each 

 observer sees his own aurora as a so-called optical illusion. 



There are several forms of optical illusion that are evidently con- 

 nected with the aurora. Some of these were recognized long 

 since, while others are still deceiving our senses and perplexing our 

 calculations. 



As we pursue our reading chronologically, among the different 

 authorities, we shall perceive how one after another is led to suspect 

 and fully recognize some one or other of these optical or perspec- 

 tive illusions, while others, inattentive thereto, plunge deeper into 

 misleading calculations. If, at the end of our consideration of the 

 subject, we sum up all that has been shown to be probable or 

 demonstrated to be true, we shall almost necessarily conclude that the 

 determination of the altitude of the aurora is a much more delicate 

 problem and perhaps also a more indefinite problem than we have 

 hitherto believed. 



After reviewing the literature of the subject since the time of 

 Halley, we find that the methods of determining the altitude of 

 specific features of the aurora may be enumerated as follows: (i) 

 Parallax method ; (2) Galle's first method ; (3) Galle's second 

 method ; (4) Bravais' method of amplitudes and its modifications 

 by Fearnley, Newton, Nordenskiold and Bergmann ; (5) Bravais' 

 method by the apparent breadth of the arch ; (6) Bravais' velocity 

 method ; (7) my method, by the simultaneous motion of waves at the 

 zenith and beam.s above an arch; (8) Gyllenskiold's method, by 

 the apparent length of the auroral beam. 



All these agree in one fundamental assumption, that the observed 

 beams and arches have an individual existence and a definite locus. 

 But this assumption is negatived by the equal frequency of negative 

 and positive parallaxes whenever the parallax method is applied. 



