672 Profs. Morley and Miller : Experiments to 



return to the point in the mirror D at which it first passed 



through this semitransparent mirror ; or the ray which, after 



reflexion from I, returns to D with the same exactness. 



The simplest treatment is possible when we select that 



system of wave-fronts which make with the mirror II an 



v 

 angle sin -1 ^ cos a, where a is the azimuth of the apparatus 



measured from the position in which its motion through the 

 sethier is parallel to the axis of the observing telescope. The 

 azimuth of the motion assumed in figs. 2 and 3 is 67° 30'. 



We will now examine the condition of the wave-fronts in 

 the apparatus, fig. 3, at two specified instants, using two 

 diagrams to avoid confusing the numerous lines. In fig. 3 

 are shown nine wave-fronts making the specified angle 

 with II. The wave-fronts of the transmitted fraction are 

 denoted by accented letters. Seven have not yet reached 

 the mirror II ; b 1 intersects II in the common point B ; 

 a 1 has been reflected from II, and its upper part begins to be 

 reflected from D. At the same instant are shown the wave- 

 fronts of the other system by unaccented letters. All have 

 been in part reflected from D ; c begins to be reflected from 

 I ; b intersects I in the common point ; a is quite cleared 

 from the mirror I. In fig. 4 we follow the same nine wave- 

 fronts. Of the transmitted waves, a 1 has quite cleared the 

 system of mirrors ; V is just clearing D ; five are but partly 

 reflected from D ; JJ passes through the common point B, 

 and is beginning to be reflected by D ; %' has not yet reached 

 II. Of the other system of waves, a and b have cleared the 

 system of mirrors ; five are passing through the semitrans- 

 parent mirror D ; li passes through the common point B, 

 having just finished its reflexion from I ; i is just beginning 

 this reflexion. For all azimuths except four the general 

 conditions are those of the diagram, but the amount and 

 direction of the various inclinations alter with the azimuth. 



The wave-front li is established in its whole length when 

 it passes through the common point. The wave-front corre- 

 sponding to it in the other system is, this instant, infinitely 

 short, and a' is the first to be established in its entirety. 

 But the position of a fictitious wave of this system, hf\ is 

 determined by two conditions — first, that it be parallel 

 to a', and, secondly, that it coincide with the infinitely short 

 wave-front h' at the common point B. Except at four 

 certain azimuths, these two wave-fronts, in the same phase, 

 and intersecting in a common point B, will be inclined to 

 each other at a small angle. To measure or to detect this 

 inclination is to measure or to detect the secondary aberration 



