136 Lord Rayleigh on the 



a being the radius of the earth ! The substitution of a for I 

 increases the calculated result some 800 times. But this is 

 in a large measure compensated by the factor sec 2 # in (13) , 

 for at low altitudes sec is large. According to Montigny 

 the separation at moderately low altitudes would be nearly 

 independent of the altitude, a conclusion entirely wide of the 

 truth. 



The value of (f6 — 1) for air at 0° and 760 millim. at 

 Paris is -0002927, so that Bfi (for the lines B and H) is 

 •000007025. The height of the homogeneous atmosphere is 

 7*990 x 10 s centim., and thus Brj reckoned in centim. is 



£77 = 5-612 



h sin 6 



COS' 



6 



(15) 



The following are a few corresponding values of 6 and 

 sin 6 /cos 2 6 : — 



e. 



sin 9 /cos 2 9. 



9. 



sin 0/cos 2 9. 



0° 



o-ooo 



i 60° 



3-46 



20 



0-387 



70 



8-03 



40 



1095 



, 80 



32-66 



„ 1 



Thus at the limit of the atmosphere the separation of rays 

 which reach the observer at an apparent altitude of 10° is 

 185 centim. Nearer the horizon the separation would be 

 still greater, but its value cannot well be found from (15). 

 Although these estimates are considerably less than those of 

 Montigny, the separation near the horizon seems to be suffi- 

 cient to explain the vertical position of the bands in the 

 spectrum, recorded by Respighi (I.). The fact that the 

 margin is not very great suggests that the obstacles to which 

 scintillation is due may often be situated at a considerable 

 elevation. 



We have now to consider the effect of an obstacle situated 

 at a given point B at level y on the course of the ray. And 

 the first desideratum will be the estimation of the separation 

 at A, the object-glass of the telescope, of rays of various 

 colours coming from the same star, which all pass through 

 the given point B. It will appear at once that no fresh 

 question is raised. For, since the rays come from the same 

 star at the same time, 8cc=0, and thus by (9) 87) A =8/3. The 



