and the Evolutions of Reflected Wave-Fronts. 155 



About a hundred pictures are prepared for each series, and 

 the pictures then photographed separately on the film, which, 

 when run through Mr. Paul's animatograph, will give us a 

 very vivid representation of the motion of the wave-front. 



The series illustrating reflexion inside of a complete sphere 

 was the most difficult to prepare, as several reflexions have 

 to be considered. It has been completed for three reflexions, 

 and Mr. Max Mason, of Madison, to whom I am greatly 

 indebted for his patient work in assisting me, is going on 

 with the series. As will be seen, the wave has already 

 become quite complicated, and it will be interesting to see 

 what further changes result after three or four more re- 

 flexions. I am also under obligations to Prof. A. B. Porter, 

 of Chicago, who prepared the set of drawings illustrating the 

 passage of a wave out from the principal focus of a hemi- 

 spherical mirror. 



A number of points taken at intervals along the film are 

 here reproduced, and give a fair idea of the transformations. 

 Fig. 9 shows the plane wave entering the hemispherical 



Fisr. 9. 



\ < ^j v^y v^y Vi^y 



oOOO 



mirror, while in fig. 10 we have a spherical wave starting on 

 the principal focus of a similar reflecting surface (compare 

 fig. 9 with fig. ; 2, and fig. 10 with fig. 4). Fig. 11 shows the 

 evolutions of the wave shut upon the complete spherical 



