and the Evolutions of Reflected Wave-Fronts. 151 



which is in this case a very tapering funnel, as is shown well 

 by the geometrical construction (fig. 5). 



Efc. 5. 



In the stage where the curved sides of the saucer have 

 come to a focus, we must have a ring of condensed air, sur- 

 rounding a somewhat less condensed circular sheet ; and it 

 seems not unlikely that this ring could be photographed, in 

 an oblique direction, appearing on the plate as an ellipse. 

 Its optical analogy can be very nicely shown by cutting a 

 large round-bottomed flask in two, and silvering it, forming 

 in this way a fairly good hemispherical mirror. A small 

 source of light is mounted in the principal focus, and on 

 holding a sheet of ground glass a little outside of the centre 

 of curvature, a brilliant ring of light appears on it. Small 

 electric sparks from a coil and leyden-jar, or a pea incan- 

 descent lamp, make a suitable light source. 



If, now, we substitute for the hemisphere a complete 

 sphere, we obtain very complex forms which cannot be 

 followed except by geometrical constructions, for the wave 

 is shut up in the mirror and reflected back and forth, be- 

 coming more complicated at each reflexion (fig. 6). That 

 all of these very intricate forms can be constructed by geo- 

 metry I shall show presently ; and by means of the animato- 

 graph, which Mr. Paul has most kindly placed at our disposal, 

 w T e can actually see the wave going through its gymnastics. 



The principle of Huygens, that any small portion of a 

 wave-front can be considered as the centre of a secondary 

 disturbance, and that a small portion of this new disturbance 

 can in turn be regarded as a new centre, can be shown by 

 the sound-waves, as well as the obliteration of the shadow 



