800 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
A 
its value being’ easily obtainable if ever wanted. The displacement of Fraunhofer 
lines due to the Sun’s rotation is a small thing to detect with a prism spectroscope, 
but this effect of motion on terrestrial sources, if it is ever to be seen, is 660 times 
smaller. 
70. It may, ])erhaps, be well to check over our results by the less geometrical 
method employed by Sir George Stokes, viz., by expressing the fact that the inter¬ 
section of the three waves (incident, reflected, and refracted) with the mirror is a joint 
intersection, and runs along the mirror at a pace wdricli can easily be written down 
(viz., AC/^); for the wave advances through the medium at a speed V, and the 
medium helps it along with a component of its drift velocity v cos (^ -|- e) ; so the 
total speed of the joint rvave intersection as it runs along the mirror is 
V -f V cos (^+6) 
sin (^ + e) ’ 
which it is easy to see is precisely the same as what wm should have obtained by 
attending to rays and to the figure, viz., 
AC V cos e -t- cos ^ 
t sin (r + e)/cos e 
So tlie equations for reflection a,nd refraction can be written down at once, thus : 
V -f V cos (i — (/) + e) V — V cos (V + <p — e') \l/x — vj/jr cos (./ — 0 — e") 
sin (?■ -I- e) sin {i' — e') sin {j — e") 
together with the values of the aberration angles, obtained, say, by resolving the 
wave and drift velocities perpendicular to the ray, or resultairt direction of advance, 
and expressing tlie fact that they must neuti’alize each other ; 
V _ sin 6 sin e' _ /x sin e" 
V sin(7 — (f)) sin (f + 0) sin (j — (j>) 
These two sets of equations contain the entire solution, and of course fi may be 
written jU-oZ/x^ if it is a question of passage from one medium to another instead of 
from vacuum to a medium ; the V and v then expressing speeds in first medium. 
71. In Sir George Airy’s'" beautifully performed and described experiment of the 
value of the coefficient of aberration measured by a zenitb sector full of water, there 
should, we see, on Fresnel’s theory, have been a sliglR disci’epancy, but one wholly 
too small to observe with the various inaccuracies inseparable from star-light. If it 
is to be detected it must be with light from a terrestrially fixed source. The obser- 
‘ Pliil. Ma£>'.,’ iv., voL 43, p. 310. 
