September 22, 1892] 



NATURE 4:^ 



497 



ABERRATION PROBLEMS} 

 "PVERYBODY knows that to shoot a bird on the wing you 

 ■^ must aim in front of it. Every one will readily admit that 

 to hit a squatting rabbit from a moving train you must aim 

 behind it. 



These are examples of what may be called " aberration " from 

 the sender's point of view, from the point of view of the source. 

 And the aberration, or needful divergence between the point aimed 

 at and the thing hit, has opposite sign in the two cases— the case 

 when receiver is moving, and the case when source is moving. 

 Hence, if both be moving, it is possible for the two aberrations to 

 neutralize each other. So to hit a rabbit running alongside the 

 train, you must aim straight at it. 



If there were no air that is all simple enough. But every 

 rifleman knows to his cost that though he fixes both himself and 

 his target tightly to the ground, so as to destroy all aberration 

 proper, yet a current of air is very competent to introduce 

 a kind of spurious aberration of its own, which may be called 

 windage ; and that he must not aim at the target if he wants to 

 hit it, but must aim a little in the eye of the wind. 



So much from the shooter's point of view. Now attend to 

 the point of view of the target. 



Consider it made of soft enough material to be completely 

 penetrated by the bullet, leaving a longish hole wherever struck. 

 A person behind the target, whom we may call a marker, by 

 applying his eye to the hole immediately after a hit, may be 

 able to look through it at the shooter, and thereby to spot the 

 successful man. I know that this is not precisely the function 

 of an ordinary marker, but it is more complete than his ordinary 

 function. All he does usually is to signal an impersonal hit ; 

 someone else has to record the identity of the shooter. I am 

 rather assuming a volley of shots, and that the marker has to 

 allocate the hits to their respective sources by means of the holes 

 made in the target. 



Well, will he do it correctly ? assuming, of course, that he 

 can do so if everything is stationary, and ignoring all curvature 

 of path, whether vertical or horizontal curvature. If you think 

 it over you will perceive that a wind will not prevent his doing 

 it correctly ; the line of hole will point to the shooter along the 

 path of his bullet, though it will not point along his line of aim. 

 Also, if the shots are fired fiom a moving ship, the line of hole 

 in a stationary target will point to the position the gun occupied 

 at the instant the shot was fired, t hough it may have moved 

 since then. In neither of these cases (moving medium and 

 moving source) will there be any aberration error. 



But if the target is in motion, on an armoured train for in- 

 stance, then the marker will be at fault. The hole will not 

 point to the man who fired the shot, but to an individual ahead 

 of him. The source will appear to be displaced in the direction 

 of the observer's motion. This is common aberration. It is the 

 simplest thing in the world. The easiest illustration of it is that 

 when you run through a vertical shower, you tilt your umbrella 

 forward ; or, if you have not got one, the drops hit you in the 

 face ; more accurately, your face as you run forward hits the 

 drops. So the shower appears to come from a cloud ahead of 

 you, instead of from one overhead. 



We have thus three motions to consider, that of the source, 

 of the receiver, and of the medium ; and of these only motion of 

 receiver is able to cause an aberrational error in fixing the positioti 

 of the source. 



So far we have attended to the case of projectiles, with the 

 object of leading up to light. But light does not consist of pro- 

 jectiles, it consists of waves ; and with waves matters area little 

 different. Waves crawl through a medium at their own definite 

 pace ; they cannot ho. flung forwards or sideways by a moving 

 source ; they do not move by reason of an initial momentum 

 which they are gradually expending, as shots do ; their motion is 

 more analogous to that of a bird or other self-propelling animal 

 than it is to that of a shot. The motion of a wave in a moving 

 medium may be likened to that of a rowing boat on a river. It 

 <:rawls forward with the water, and it drifts with the water ; its 

 resultant motion is compounded of the two, but it has nothing to 

 do with the motion of its source. A shot from a passing steamer 

 retains the motion of the steamer as well as that given it by the 

 powder. It is projected therefore in a slant direction. A boat 

 lowered from the side of a passing steamer, and rowing off, re- 

 gains none of the motion of its source ; it is not projected, it is 

 self-propelled. That is like the case of a wave. 



» A lecture on " The Motion of the Ether near the Earth," by Dr. Oliver 

 l.odge, at the Royal Institution, Friday evening, April i, 1S92. 



The diagram illustrates the difference. Fig. i shows a moving 

 cannon or machine-gun, moving with the arrow, and firing a 

 succession of shots which share the motion of the cannon as well 

 as their own, and so travel slant. The shot fired from position 

 I has reached A, that fired from the position 2 has reached B, 

 and that fired from position 3 has reached c by the time the 

 fourth shot is fired at D. The line abcd is a prolongation of the 

 axis of the gun ; it is the line of aim, but it is not the line of 

 fire ; all the shots are travelling aslant this line, as shown by the 

 arrows. There are thus two directions to be distinguished. 

 There is the row of successive shots, and there is the path of any 

 one shot. These two directions enclose an angle. It may be 

 called an aberration angle, because it is due to the motion of the 

 source, but it need not give rise to any aberration. True 

 direction may still be perceived from the point of view of the 

 receiver. Attend to the target. The first shot is supposed to be 

 entering at A, and if the target is stationary will leave it at Y. 

 A marker looking along ya will see the position whence the shot 

 was fired. This may be likened to a stationary observer looking 

 at a moving star. He sees it where and as it was when the light 



started on its long journey. He does not see its present position, 

 but there is no reason why he should. He does not see its 

 physical state or anything as it is now. There is no aberration 

 caused by motion of source. 



But now let the receiver be moving at same pace as the gun, as 

 when two grappled ships are firing into each other. The motion 

 of the target carries the point Y forward, and the shot A leaves 

 it at z, because z is carried to where Y was. So in that case the 

 marker looking along ZA will see the gun, not as it was when 

 firing, but as it is at the present moment ; and he will see like- 

 wise the row of shots making straight for him. This is like an 

 observer looking at a terrestrial object. Motion of the earth 

 does not disturb ordinary vision. 



Fig. 2 shows as nearly the same sort of thing as possible for the 

 case of emitted waves. The tube is a source emitting a suc- 

 cession of disturbances without momentum, abcd may be 

 thought of as horizontally flying birds, or as crests of waves ; or 



A' 



Fig. 2. 



they may even be thought of as bullets, if the gun stands still 

 every time it fires, and only moves between whiles. 



The line aucd is now neither the line of fire nor the line 

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

 successive positions 1234. 



A stationary target will be penetrated in the direction AY, 

 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 ZA 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 abcd, 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 YAl, and coincides with 

 the line of aim ; which in the projectile case (Fig. i) it did not. 



NO. II 95, VOL. 46] 



