138 Lord Rayleigh on the 



the star observed at A, as appears from (4) and (5). In 

 general, y is greater than h, so that 8a, is somewhat less than 

 the value given by (18). 



The interest of (18) lies in the application of it to find the 

 time occupied by a band in traversing the spectrum in virtue of 

 the diurnal motion, according to Eespighi's observation (II.). 

 The time required is that necessary for the star to rise or fall 

 through the angle of its dispersion-spectrum at the altitude 

 in question. At an altitude of 10°, this angle will be 8", 

 being always about ^ of the whole refraction. The rate at 

 which a star rises or falls depends of course upon the declina- 

 tion of the star and upon the latitude of the observer, and 

 may vary from zero to 15° per hour. At the latter maximum 

 rate the star would describe 8" in about one half of a second, 

 which would therefore be the time occupied by a band in 

 crossing the spectrum under the circumstances supposed. In 

 the case of a star quite close to the horizon, the progress of 

 the band would be a good deal slower. 



The fact that the larger planets scintillate but little, even 

 under favourable conditions, is readily explained by their sen- 

 sible apparent magnitude. The separation of rays of one 

 colour thus arising during their passage through the atmo- 

 sphere is usually far greater than the already calculated 

 separation, due to chromatic dispersion ; so that if a fixed star 

 of no apparent magnitude scintillates in colours, the different 

 parts of the area of a planet must a fortiori scintillate indepen- 

 dently. But under these circumstances the eye perceives only 

 an average effect, and there is no scintillation visible. 



The non-scintillation of small stars situated near the 

 horizon may be referred to the failure of the eye to appre- 

 ciate colour when the light is faint. 



In the case of stars higher up the whole spectrum is 

 affected simultaneously. A momentary accession of illumina- 

 tion, due to the passage of an atmospheric irregularity, may 

 thus render visible a star which on account of its faintness 

 could not be steadily seen through an undisturbed atmosphere*. 



In the preceding discussion the refracting obstacles have 

 for the sake of brevity been spoken of as throwing sharp 

 shadows. This of course cannot happen, if only in conse- 

 quence of diffraction ; and it is of some interest to inquire 

 into the magnitude of the necessary diffusion. The theory 

 of diffraction shows that even in the case of an opaque screen 

 with a definite straight boundary, the transition of illumina- 

 tion at the edge of the shadow occupies a space such 



* The theory of Arago leads him to a directly opposite conclusion (loc. 

 cit. p. 381). 



