Theory of Stellar Scintillation. 139 



as V(b\), where X is the wave-length of the light, and b is 

 the distance across which the shadow is thrown. We may- 

 take \ at 6 x 10 -5 centirn., and if b he reckoned in kilometres, 

 we have as the space of transition, s/ (66) . Thus if b were 



4 kilometres, the space of transition would amount to about 



5 centim. The inference is that the various parts of the 

 aperture of a small telescope cannot be very differently 

 affected unless the obstacles to which the scintillation is due 

 are at a less distance than 4 kilometres. 



One of the principal outstanding difficulties in the theory 

 of scintillation is to see how the transition from one index to 

 another in an atmospheric irregularity can be sufficiently 

 sudden, The fact that the various parts of a not too small 

 object-glass are diversely affected seems to prove that the 

 transitions in question do not occupy many centimetres. 

 Now, whether the irregularity be due to temperature or to 

 moisture, we should expect that a transition, however abrupt 

 at first, would after a few minutes or hours be eased off to a 

 greater degree than would accord with the above estimate. 

 Perhaps the abruptness of transition is, as it were, continually 

 renewed by the coming into contact of fresh portions of light 

 and dense air as the ascending and descending streams pro- 

 ceed in their courses. The speculations and experiments of 

 Jevons on the Cirrus form of Cloud"* may find some applica- 

 tion here. A preliminary question requiring attention is as 

 to the origin of the irregularities which cause scintillation. 

 Is it always at the ground, and mainly under the influence of 

 sunshine ? Or may irregular absorption of solar heat in the 

 atmosphere, due to varying proportions of moisture, give rise 

 to transitions of the necessary abruptness ? Again, we may 

 ask how many obstacles are to be supposed operative upon the 

 same ray ? Is the ultimate effect only a small residue from 

 many causes in the main neutralizing one another ? It does 

 not appear that in the present state of meteorological science 

 satisfactory answers can be given to these questions. 



A complete investigation of atmospheric refraction can only 

 be made upon the basis of some hypothesis as to the distribu- 

 tion of temperature ; but, as has already been hinted, a 

 second approximation to the value of the refraction can be 

 obtained independently of such knowledge and without 

 difficulty. In Laplace's elaborate investigation it is very 

 insufficiently recognized, if indeed it be recognized at all, 



* Phil. Mag. xiv. p. 22, 1857. For a mathematical investigation, by 

 the author, see Math. Soc. Proc. xiv. April 1883. 



