498 



NATURE 



[September 22, 1892 



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 disturbances a,b,c,d, lie along a spiral curve, the 

 spiral of Archimedes ; 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 distinguished 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 dis- 

 turbance 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 source 

 in its true position. It would be otherwise for the case of pro- 

 jectiles from a revolving turret. 



Thus, neither translation of star nor rotation of sim can affect 

 direction. There is no aberration so long as the receiver is sta- 

 tionary. 



Fig. 3. 



But what about a wind, or streaming of the medium past 

 source and receiver, both stationary ? Look at Fig. i again. 

 Suppose a row of stationary cannon firing shots, which get blown 

 by a cross wind along the slant Iay (neglecting the curvature 

 of path which would really exist) : still the hole in the target 

 fixes the gun's true position, the marker looking along YA sees 

 the gun which fired the shot. There is no true deviation from 

 the point of view of the receiver, although the shots are blown 

 aside and the target is not hit by the particular gun aimed at it. 

 "With amoving cannon, combined with an opposing wind, Fig. i 

 would become very like Fig. 2. 



(N.B. — The actual case, even without complication of spin- 

 ning, &c., but merely with the curved path caused by steady 

 wind-pressure, is not so simple, and there would really be an 

 aberration or apparent displacement of the source towards the 

 wind's eye : an apparent exaggeration of the effect of wind as 

 shown in the diagram. ) 



In Fig. 2 the result of a wind is much the same, though the 

 details are rather different. The medium is supposed to be drift- 



FlG. 4. 



ing down across the field opposite to the arrows. The source is 

 stationary at s. The arrows show the direction of waves in the 

 tnedium ; the dotted slant line shows their resultant direction. A 

 wave centre drifts from D to 1 in the same time as the disturbance 

 reaches a, travelling down the slant line DA. The angle be- 

 tween dotted and full lines is the angle between ray and wave 

 movement. Now, if the motioti of the viedium inside the 

 receiver is the same as it is outside, the wave will pass straight on 

 aloncf the slant to z, and the true direction of the source is fixed. 

 But if the medium inside the target or telescope is stationary, 

 the wave will cease to drift as soon as it gets inside, under cover 

 as it were ; it will proceed along the path it has been really 

 pursuing in the medium all the time, and make its exit at Y. In 

 this latter case, of different motion of the medium inside and out- 

 side the telescope, the apparent direction, such as ya, is not 

 the true direction of the source. The ray is in fact bent 

 ■where it enters the differently-moving meditun (as shown in 

 Fig- 4). 



NO. II 95, VOL. 46] 



A slower moving stratum bends an oblique ray (slanting with 

 the motion) in the same direction as a denser medium does, 

 A quicker stratum bends it oppositely. If a medium is both 

 denser and quicker moving, it is possible for the two bendings 

 to be equal and opposite, and thus for a ray to go on straight. 

 Parenthetically I may say that this is precisely what happens, 

 on Fresnel's theory, down the axis of a water-filled telescope 

 exposed to the general terrestrial ether drift. 



In a moving medium waves do not advance in their normal 

 direction, they advance slantways. The direction of their 

 advance is properly called a ray. The ray does not coincide 

 with the wave-normal in a moving medium. 



All this i? well shown in fig. 5. 



Fig. 



s is a stationary source emitting successive waves, which drift 

 as spheres to the right. The wave which has reached m has its 

 centre at c, and CM is its normal ; but the disturbance, M, has 

 really travelled along SM, which is therefore the ray. It has 

 advanced as a wave from s to P, and has drifted from p to M. 

 Disturbances subsequently emitted are found along the ray, pre- 

 cisely as in Fig. 2. A stationary telescope receiving the light 

 will point straight at s. A mirror, M, intended to reflect the 

 light straight back must be set normal to the ray, not tangential 

 to the wave front. 



The diagram also equally represents the case of a moving 

 source in a stationary medium. The source, starting at c, has 



moved to s, emitting waves as it went, which waves as emitted 

 spread out as simple spheres from the then position of source as 

 centre. Wave-normal and ray now coincide : SM is not a ray, 

 but only the locus of successive disturbances. A stationary 

 telescope will look not at s, but along MC to the point where 

 the source was when it emitted the wave M ; a moving telescope, 

 if moving at same rate as source, will look at S. Hence SM is 

 sometimes called the apparent ray. The angle SMC is the 

 aberration angle. 



Fig, 6 shows normal reflection for the case of a moving source. 



