i:)R. OLIVER LODGE ON ABERRATION PROBLEMS. 
737 
self-propelled, at its own definite velocity. No aberrational effect can be produced 
bv any cause which does not act on a wave-front for a finite time. 
Fio-. 2. 
Diagram of disturbances or waves emitted without momentum from a moving source; leaving target or 
telescope, at Y if stationary, at Z if moving. The line ABCD is the locus of successive disturb¬ 
ances, but is not the raj or real path. The diagram may also be taken to represent the effect of a 
cross stream of medium, with source stationary. 
Hence waves emitted by a revolving source advance just as they would if it were 
stationary ; any peculiarity on the surface, say a Sun spot, is depicted in a precisely 
radial direction, and there will be no displacement of the Sun’s centre. So also with 
light from a flying star : the star will be seen in its position at time of emission, just 
as it is seen in the physical state corresponding to that instiint, not to the instant 
of vision. 
Fig. 3. 
B 
Diagram of parallel beams emilted from a revolving lighthouse. ABCD is the apparent beam, but 
AS, BS, &c., are the lines of vision or true rays. 
As to a beam from a revolving lighthouse, it is not the path of a labelled distur¬ 
bance, or true ray, which displays itself by illuminating dust particles, but it is the locus 
: of successive disturbances sent out from a given moving point; so if the source has 
I revolved through an angle 6 while the light travels a distance r, 6 = (w/V) r, 
and their shape is a spiral of Archimedes as suspected above ; though the direction 
of vision is not tangential to them, but is truly radial as already stated. 
I The analogy between rays of light and lines of force is fairly close, and just as it is convenient to say 
; that a rotating source revolves its rays, so it is convenient to say that a rotating magnet revolves its 
lines of force. The induction phenomena obtained from a magnet spinning on its own axis are a 
sufficient justification of this statement.* 
j In an old note-book of date 1876, I find a suggestion for measuring the speed of magnetic ^Dropaga- 
I tion, by rotating a long bar magnet on its axis and observing its actmn on a distant magnetic needle; 
j * See also Mr. Tot.vki; Preston, ‘Phil. Mag.,’ February and March, 188o. 
MDCCCXCIIT.—A. 5 R 
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