detect Aberrations of the Second Degree. 671 



moves to the new position Do. The angle of reflexion from 

 D is no longer equal to the angle of incidence. The ray 

 moving from D towards II rinds the latter in the position 

 IIj, returns to IK and is reflected from D 2 nearly in the 

 same direction with the ray from I. In four azimuth..; of 

 the apparatus the coincidence is exact ; for all others, the 

 ray I and the ray II are inclined at a small angle which, at 

 its maximum, is numerically equal to v 2 /V 2 , v and V being 

 the velocities of the apparatus and of light. Since the 

 angle 8. the total aberration, cannot be observed, being 

 annulled by the motion of the observing telescope at T, 

 we can hope to detect merely this aberration of the second 

 degree, namely, the small angle between the emergent rays 



I and II. 



With the adjustments just supposed, there are four methods 

 of measuring interference phenomena which in turn measure 

 tin 1 ano-le sought. We may use a micrometer in the telescope, 

 or a scale engraved on I or on II ; we may use mechanical 

 compensation to return a displaced fringe to its marked 

 position, or we may use optical compensation. 



In another adjustment the fringes are made infinitely 

 broad. We are then limited to the last pair of methods. 

 This pair, especially the last method, is capable of very great 

 precision. When Michelson and Morley set up the first 

 apparatus in which they utilized this method, the mean error 

 of a setting, in which the observer did not himself see the 

 reading, was less than the two-hundredth part of a wave- 

 length. Since the theory of the apparatus in this special 

 case is simpler, the discussion will assume this adjustment. 



Accordingly, let the angles I B D, II B D, fig. 3 (PL IX.), 

 be equal to each other and to -15°. Let the three planes inter- 

 sect in a common point B. For brevity, imagine that the 

 mirror- themselves are produced so as to intersect in this 

 point. Assume that the system is moving through the aether 

 in a direction making an angle of 67£° with the direction of 

 the light entering the telescope, as indicated in fig. 2. The 

 velocities of the apparatus and of light being denoted by 

 /•. V. -i— nine that 0/V=l/5. 



A certain wave-front enters the apparatus, making with 



II an angle which is to be specified. If some given ray 

 enters the apparatus so a- to pass axially through the 



jope, rays making an angle of 5 minutes on either 

 side of it will pass through our actual apparatus. Almost 

 any ray, wisely -elected, may be used to determine what we 



• to know about the whole pencil. For instance, we 

 might 'lie ray which, after reflexion from II, shall 



2 Y 1 



