132 Lord Kayleigh on the 



The observations recorded in (III.) are of special interest 

 as establishing a connexion between the rates with which 

 various parts of the object-glass and of the spectrum are 

 affected. Since the spectrum is horizontal, various parts of 

 its width correspond to various horizontal sections of the 

 objective, and the existence of bands at a definite inclination 

 shows that at the moment when the shadow of the obstacle 

 thrown by blue rays reaches the bottom of the glass the 

 shadow at the top is that thrown by green, yellow, or red 

 rays of less refrangibility. When the altitude of the star 

 reaches 30° or 40°, the difference of path due to atmospheric 

 dispersion is insufficient to differentiate the various parts of 

 the spectrum. The bands then appear longitudinal. 



The definite obliquity of the bands at moderate altitudes, 

 reported by Bespighi, leads to a conclusion of some interest, 

 which does not appear to have been noticed. In the case of 

 a given star, observed at a given altitude, the linear separa- 

 tion at the telescope of the shadows of the same obstacle 

 thrown by rays of various colours will of necessity depend 

 upon the distance of the obstacle. But the definiteness of 

 the obliquity of the bands requires that this separation shall 

 not vary, and therefore that the obstacles to which the effects 

 are due are sensibly at one distance only. It would seem to 

 follow from this that, under " normal atmospheric conditions," 

 scintillation depends upon irregularities limited to a compa- 

 ratively narrow horizontal stratum situated overhead. A 

 further consequence will be that the distance of the obstacles 

 increases as the altitude of the star diminishes, and this 

 according to a definite law. 



The principal object of the present communication is to 

 exhibit some of the consequences of the theory of scintillation 

 in a definite mathematical form. The investigation may be 

 conducted by simple methods, if, as suffices for most purposes, 

 we regard the whole refraction as small, and neglect the 

 influence of the earth's curvature. When the object is to 

 calculate with accuracy the refraction itself, further approxi- 

 mations are necessary, but even in this case the required 

 result can be obtained with more ease than is generally 

 supposed. 



The foundation upon which it is most convenient to build 

 is the idea of James Thomson *, which establishes instanta- 

 neously the connexion between the curvature of a ray 

 travelling in a medium of varying optical constitution and 

 the rate at which the index changes at the point in question. 

 The following is from Everett's memoir : — 



* Brit. Assoc. Rep. 1872. Everett, Phil. Mag. March 1873. 



