748 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
Definition ofi Ray. 
23. In § 13 we defined a ray as the path of a labelled disturbance,for it is that 
which enables an eye to fix direction, it is that which determines the line of coUunation 
of a telescope. Now in order that a disturbance from A may reach B, it is necessary 
that adjacent elements of a wave front at A shall arrive at B in the same phase ; hence 
the path by which a disturbance travels must satisfy this condition from point to 
point, viz., that disturbances arriving at any point from a preceding point of a ray 
agree in phase. This condition will be satisfied if the time of journey down a ray 
and down all infinitesimally differing paths is the same. 
The equation to a ray is therefore contained in the statement that the time taken 
by light to traverse it is a minimum ; or 
ds . . 
— = minimum. 
J A V 
If the medium, instead of being stationary, is drifting with the velocity v, at angle 6 
to the ray, we must substitute for V the modified velocity V cos e v cos 6, and so 
the function that has to be a minimum in order to give the path of a ray in a moving 
medium is 
1“ 
ds 
A V (cos e + « cos 6) J A V- (1 — a“ 
= f 
V cos e — V cos 6 
ds = minimum. 
Path of Ray, and. Time of Journey, through an Irrotationally Moving Medium. 
o 
4. Writing a velocity-potential ^ in the above equation to a ray, that is putting 
d<f) 
V cos 6 = 
e.s ’ 
and ignoring possible variations in the minute correction factor 1 — a^, between the 
points A and B, it becomes 
m- p • P cos e ds 
lime of journey = --- • — 
J A i- a V 
4^u 4 ’a 
(1 - 
= minimum. 
Now the second term depends only on end points, and therefore has no effect on 
path. The first term contains only the second power of aberration magnitude; and 
hence it has much the same value as if everything were stationary. A ray that was 
* [It lias been objected that a bit of wave-front cannot be labelled, because of diffi'action effects. This 
seems to me only a practical difficulty, and a more practical definition based upon preserved phase-con¬ 
nexion follows a few lines later in the text; but the meaning conveyed by the convenient phrase 
“ labelled disturbance” can equally well and I think unobjectionably be expressed by calling a ray the 
path of a definite, or identical, portion of energy—the direction of energy-flux.-—July, 1893.] 
