detect Aberrations of the Second Degree. 675 



angles of reflexion are given by the equation 



6' 6 Y-u 



tan 2 = tan 2-V+^' 



where u is the velocity of the surface perpendicular to it» own 

 plane : negative, if moving away from the approaching light. 

 With tJie assumed adjustments, we therefore have for the 

 reflexion of the unaccented system at D: 



sin 45° -f sing sin 45° + sin 0° 2 + VCK) 

 cos 45°+cos 8 ~ cos 45° + cos 0° ' 2 — VO 7 ^ 



cos 



8 = 0-8. 



V0-5 + O8' 

 For the reflexion of the accented system we have : 



sin 45° — sin 8' 



sin 45° - sin 0° 



2— V0*5 



cos 45 c -f cos 8' 



~ cos 45° + cos U° 



" 2 + V0 r 5 





~~ =r 12 ' ' 



VO-o +T 3 



» 12 



By equation (3) of Dr. Hicks's* paper, putting L^ for the 

 perpendicular distance between wave-fronts of the light 

 incident on D from the moving source, 



X 4-n-.~> V 4-1 4-0-5 _ 21 



Li-4 + 0-5-2 ; and I^-^ + l^^ + O'SH^-lS* 



Therefore X r n , „ 1 _ K T 



? =L, 1*4 -^- 0'8 = l-7o L n 



cos 6 



and X' T 21 12 t _- T 



c^sT =Li 13^13 =1 ' <0L; 



accordingly. X' X — /' — / 



COS 8' ~~ COS 6 



Therefore, if the intersection of fc ls and i' V) is on the line 

 xy parallel to <jT Vr the intersection of i V) and /i' 15 is a l so on 

 the same line ; that is. the phase-difference of the two sets 

 of waves i- constant along any line parallel to the axis of the 

 rving telescope. The same thing may easily be proved 

 for any one of eight equidistant points of the circumference 

 commencing from the point where the motion of the apparatus 

 i- parallel to the axis of the telescope. 



* PhiL Mag. [6] iii. p. 17 (1902). 



