CONTEMPORARY ADVANCES IN PHYSICS 289 



those which do not, then no matter how small it is it shields the point 

 P completely against corpuscles. Not, however, against waves. 

 Suppose that the point P is in water, where the actual waves may be 

 seen; suppose that before the obstacle is dipped in, each of the wave- 

 crests extends straight east and west, and they move straight north- 

 ward. When the obstacle is inserted southward from P, the water at 

 P does not become perfectly quiet. Apparently the waves curl around 

 the edge of the obstacle, invading the zone behind it which it could 

 have protected perfectly against corpuscles. One cannot stop a wave- 

 motion from reaching a point merely by interrupting with some small 

 obstruction the line along which the waves seem to be approaching it. 



Now what this means is simply that, whether the obstacle be present 

 or absent, and even though the undisturbed wave-crests move steadily 

 due northward, the motion at P is not controlled exclusively by the 

 motions at earlier moments at the points due south of P. To put it a 

 little more loosely : the wave-motion at a point arrives not solely from 

 the direction from which the wave-fronts appear to be coming, but 

 from all directions. To put it much more strictly: imagine a sphere 

 drawn, with any radius r, around P as centre. When we were dealing 

 with corpuscles, we found that the state of affairs at the centre of this 

 sphere at the moment t was entirely controlled by the state of affairs 

 at the moment {t — rjc) at one single point on the sphere (the point due 

 south from P) . Now that we are dealing with waves, we shall find that 

 the state of affairs at the centre of the sphere at / depends upon the 

 state of affairs all over the sphere at (/ — r/c). Every point upon the 

 sphere influences the centre. Every point in the medium which the 

 waves traverse sends forth an influence to every other point; the in- 

 fluence is not instantaneous, but travels from one point to another with 

 the wave-speed c. This "influence" is often called the wavelet. 



Too much emphasis has been laid, in the foregoing passage, upon 

 the spheres which are centred at P; and this must now be rectified. 

 Any closed surface whatever may be drawn around P, and the state of 

 affairs in P at / will be determined by the state of affairs prevailing all 

 over this surface, S, at certain prior moments t'; only, since the area- 

 elements of 5 are not in general equidistant from P, the corresponding 

 values of /' are not in general the same for all of them. The distance 

 r, measured from P along any direction to the surface S, is in general 

 a function of direction; consequently the time-interval, r/c, required 

 for a wavelet to arrive at P from 5 along any direction is itself a func- 

 tion of direction; and so also is /', which is {t — r/c). To every point 

 P' on 5 corresponds its own value of t' ; and if we know the wave- 

 motion in every P' at its proper t', we can determine the wave-motion 



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