74G 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
Fig. 6. 
A telescope receiving light from S and moving from OE to O^Ej while light traver.ses OEj, 
A stationary telescope receiving the same ray at the same instant would have had 
to occupy the position OE^, and would have looked straight at the object (with a 
sliglitly greater focal length). Hence the angle O^E^O or OSOq is the angle of aberra¬ 
tion, the amount by which the object appears to be displaced in the direction of 
motion. A telescope which had been revolving round the source, instead of being 
translated, would have gone from AB to OE^ in tire time, and have rotated through 
this same angle. Call it e; it is such that 
sin e ^ EEj 
sin <p OEj 
- = say. 
the medium, remember, being stationary. 
The focal length of the moving telescope differs from that necessary for a fixed one; 
being OE instead of OE^ or 
f'—f (cos e — ^ cos (j)) ; 
but this is best regarded as part of the Doppler effect, since its principal term repre¬ 
sents radial motion. With a non-achromatic lens the change of refrangibility due to 
motion tends to compensate* this effect. But whereas the chairge of refrangibility 
is produced equally by motion of source’ or motion of receiver, this change of focal 
length seems to be caused only by motion of receiver. It is a shortening of focus as 
a telescope recedes from the light. T suppose it is too small to observe, else it would 
seem able to discriminate motion of earth from motion of star, and give absolute 
motion of telescope through the ether. 
A terrestrial source {e.g., a sodium flame) might be used, and a perfectly achromatic 
lens; but surely no focussing could be delicate enough to discriminate such sort of 
difference as exists between the two sodium emissions ? 
The way in which motion of receiver to or from source causes an apparent change 
of frequency, i.e., a real change in the frequency with which waves are received, is too 
well known and simple to be more than mentioned. Its amount in any direction is 
01 / 
log — = log (cos e /3 cos ^) cos (j), 
where /S = ^^/V, sin e = /8 sin and u is the velocity of the telescope at angle (f> 
with tht^ ray. 
* Tin's was originally written “ exaggerate.” 
