314 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



an angle of 82° round tlie direct beam (Fig. 58), so that there is 

 room for additional beams. 



On this form of the angular aperture view again, therefore, the 

 number of rays in equal (plane) angles of air, water, and oil, are 

 seen to be as the refractive indices, that is, as 1*0, 1'33, and 1*5, 

 and different angles are compared by the values of n sin u. 



Fig. 57. 



Fig. 58. 



We may also point out here that even in the case of the pencils 

 being in the same medium (as air), the angular aperturist, in insist- 

 ing that the angles are a true measure, falls into what was formerly 

 a very general mistake among microscopists, viz. the supposition 

 that from a luminous surface-element there is equal intensity of 

 emission in all directions. If this were so, then of course a given 

 portion of the pencil taken close to the perpendicular would be iden- 

 tical with another portion taken at a distance from the perpendicular, 

 provided only that the angular extension of each portion was equal. 

 A pencil of 60° round the perpendicular (that is, of 120° angular 

 extension) would contain 3 • 8 times the amount of light of one of 30° 

 round the axis (that is, of 60° angialar extension), the contents of the 

 solid cones being as 1 : 3* 8. A pencil would thus be represented by 

 Fig. 59. 



It has, however, been established for more than 100 years that 

 this view is not correct, but that, on the contrary, the emission of 



Fig. 60. 



light is greater according as it takes place closer to the perpendicular, 

 decreasing towards the horizon with the cosine of the obliquity of 

 emission, so that the pencil is not correctly represented by Fig. 59 

 but by Fig. 60. 



When, therefore, the same medium is alone considered, the pencils 

 must be compared by the squares of the sines of the semi-angles — 

 that is, by (sin uy. A pencil of 120° (60° round the perpendicular) 

 does not therefore contain nearly four times the amount of light 

 of one of 60° (30° round the perpendicular), but three times only.* 



* On this subject see further, infra, III., No. 1, "Difference of Radiation in 

 the same Medium," 



