detect Aberrations of the Second Degree. 079 



wide. We simply remark that, if we understand rightly his 

 statement, this aberration is annulled by the motion of the 

 telescope. Also, his discussion contains a term expressing 

 the fact that the waves of one system gain upon those of the 

 other while passing towards the observer. We have shown 

 that, in the conditions assumed (and realized), this effect is nil 

 for central rays in the eight principal azimuths, and is small 

 in all others. At its maximum, for central rays, it is 



v 



O'o— . With our present large apparatus, whose length is 



54 x 10*X, the gain of one wave-front over the other in the 

 whole length is much less than 10 -(5 X. 



In the theory of 1887. powers of the velocity-ratio higher 

 than the second were expressly regarded as negligible. Dr. 

 Hicks virtually supplies one such term. He writes, displace- 



p c . -^f 2 L cos 2a i j- • i 



ment or fringes = — — ~ . % ,-*^ t~ 3 where t is the 



sm (B — A)— fg 8 cos 'lec 



velocity-ratio, L is the length of path in the apparatus, from 



D to I. tig. 5. and B — A is the difference between the angles 



DB I and DB II. Without the small term in the denom- 



nutor. this gives precisely the same value as the expression in 



the paper of 1887, as a simple numerical computation shows. 



The effect of the small term is the following : — the value of 



the denominator is decreased or increased by J^., at alter- 

 nate quadrants, and the value of the fraction is therefore in- 

 creased or decreased at alternate quadrants. But, according 

 to the present solution, the expression should have a mean value 

 at 90° and 270 c . and have, further, a maximum at 180° and 

 a minimum at 0°. At three quadrants we agree, but at the 

 fourth we differ by twice the term in question. The dif- 

 ference is easily explained and is negligible, especially in view 

 of the null result of experiment. 



It should be noted that, when there is aberration of the 

 wave- front, there are four closely related magnitudes. One 

 is the distance travelled by the wave-front in the period ; a 

 second is the perpendicular distance between consecutive 

 wave-fronts, called \ in Dr. Hicks's paper ; a third is the 

 distance between wave-fronts, resolved parallel to some line 

 dictated by the geometric conditions of the case ; and the 

 fourth is the distance between wave-fronts in the line of 

 sight, which is the true wave-length. The perpendicular 

 di>tance between wave-front- is u^ed rightly, as we conceive, 

 Lablishing the conditions of the network of intersecting 

 wave-ironts in Dr. Hieks's admirable paper. But in one 



