676 Profs. Morley and Miller : Experiments to 



The equality is exact for the central ray. For rays inclined 

 as much as five minutes of arc on either side of the central 



cos h' cos 8 == A v d 



~\> ^<°' 2 T 3 - 



At azimuths other than those specified, the quantity 



cos O COS O V 



-—, — is not greater than 0*3 m for central rays? 



A A, o V 



and not greater than 0*5 ^ for extreme rays. We may set 



side by side the magnitudes of this disturbing effect for 

 central rays at several azimuths according to rigorous com- 

 putation and according to Dr. Hicks's approximate formula. 



Disturbing Effects Compared. 



Azimuths. Dr. Hicks's I Rigorous 



formula. formula. 



It will be seen that the effect detected by Dr. Hicks 

 proves, by rigorous computation, to be entirely negligible 

 for the central rays. Its extreme value for marginal rays 



is not greater than 0*5 ™, which is entirely too small to 



influence the observations. This result is very satisfactory. 

 It is proved for the specified adjustment of the angles, but it 

 is easy to see that the rotation of mirror I about a perpen- 

 dicular line in its surface, by a quantity like ten seconds of 

 arc, will not change all relations of residual aberrations by 

 important amounts. It is therefore established, at least for 

 the adjustment specified, that the wave-fronts a and a' of 

 fig. 4 intersect in the line B II, if the wave-fronts h and h" 

 do, rigorously for eight principal positions, very approxi- 

 mately for all other positions. If, then, we can measure the 

 linear distance between a and a' at some convenient position 

 T, we may determine the angle between the wave-fronts a 

 and a' 3 which is the same as the angle between h and h", the 



