568 Professor Oliver Lodge [April 1, 



case of emitted waves. The tube is a source emitting a succession of 

 disturbances without momentum. A B C D may be thought of as 

 horizontally flying birds, or as crests of waves ; or they may even be 

 thought of as bullets, if the gun stands still every time it fires, and 

 only moves between whiles. 



The line A B C D is now neither the line of fire nor the line of 

 aim : it is simply the locus of disturbances emitted from the successive 

 positions 12 3 4. 



A stationary target will be penetrated in the direction A Y, and 

 this line will point out the correct position of the source when the 

 received disturbance started. If the target moves, a disturbance 

 entering at A may leave it at Z, or at any other point according to its 

 rate of motion ; the line Z A does not point to the source, and so there 

 will be aberration when the target moves. Otherwise there would be 

 none. 



Now Fig. 2 also represents a parallel beam of light travelling from 

 a moving source, and entering a telescope or the eye of an observer. 

 The beam lies along A B C D, but this is not the direction of vision. 

 The direction of vision to a stationary observer is determined not by 

 the locus of successive waves, but by the path of each wave. A ray 

 may be defined as the path of a labelled disturbance. The line of vision 

 is Y A 1, and coincides with the line of aim ; which in the projectile 

 case (Fig. 1) it did not. 



The case of a revolving lighthouse, emitting long parallel beams 

 of light and brandishing them rapidly round, is rather interesting. 

 Fig. 3 may assist the thinking out of this case. Successive dis- 



FiG. 3. 



Beam from a Revolving Lighthouse. 



turbances A,B, C,D, lie along a spiral curve, the spiral of Archi- 

 medes ; and this is the shape of the beams as seen illuminating the 

 dust particles, though the pitch of the spiral is too gigantic to be dis- 

 tinguished from a straight line. At first sight it might seem as if an 

 eye looking along those curved beams would see the lighthouse 

 slightly out of its true position ; but it is not so. The true rays or 

 actual paths of each disturbance are truly radial ; they do not coincide 

 with the apparent beam. An eye looking at the source will not look 

 tangentially along the beam, but will look along AS, and will see the 



