1061 SUMMARY OF CURRENT RESEARCHES RELATING TO 



cylinder behaves, therefore, like a convex lens, and can be treated 

 in a similar way as rogards the calculation of the sizes and positions 

 of images, &c. Precisely similar considerations will show that a 

 cylinder in which the index increases from the axis towards tho 

 circumference will behave as a concave lens (fig. 237). 



It might be supposed that if at any point a ray is travelling 



Fig. 237. 



parallel to the axis it will continue to do so, since it is travelling 

 along strata of constant index ; but if wo consider the elementary 

 waves which constitute the ray, it will be seen that those which are 

 nearer the axis are propagated with diminished velocity, so that the 

 ray as a whole will have a curved path. 



Two points of interest proved in tho mathematical investigation 

 are : (1) Whatever be the law according to which the index varies, in 

 the immediate neighbourhood of the axis it will be a parabolic law ; 

 in other words, if from all points of the base lines be drawn parallel 

 to the axis and proportional to the index of refraction at those points, 

 their extremities will form a surface of revolution which is in all 

 cases a paraboloid near the axis. (2) If all the rays diverging from 

 a point in the axis are to converge to a point after refraction through 

 the cylinder, the law of the index must be a parabolic law. 



To put the theory to the test of experiment, Professor Exner, fol- 

 lowing the example of Matthiessen, prepared cylinders of varying 

 optical density from celloidin and gelatin. The celloidin was for 

 this purpose cut from a plate with a cork-borer into cylinders 5-10 

 mm. in length and breadth, placed between glass plates to protect the 

 ends, and then immersed for some hours or days in a mixture of 

 alcohol and ether. Gelatin cylinders were prepared by filling a glass 

 tube with a gelatin solution, treated with salicylic or carbolic acid ; 

 this is allowed to harden, and then extracted by warming the tube for 

 a few seconds. A cylinder cut from such a column is then fixed 

 between glass plates, and immersed for a day in water. Cylinders of 

 celloidin and gelatin treated in this way are found to act as lenses in 

 accordance with the theory. Thus Exner was able to manufacture 

 some of two inches focal length, which gave fairly good images, and 

 could be used as rough magnifying lenses, enabling him to verify 



approximately the formula - + " = /" Cylinders which act as con- 

 cave lenses may be made by exposing the rod of gelatin to the air for 



