212 



THEORY OF MICROSCOPIC OBSERVATION. 



are, however, as calculation shows, so small that they may in 

 general be neglected. We have tabulated below a few values of n 

 and F. The assumed ratio of the radii is r = "8 R. 



If the refractive index remains constant, while the ratio of the 

 radii is altered, the difference between r and F will increase until 

 r becomes about \ R, and afterwards becomes less again when 

 r < J R. But here also the changes are so slight that they may, 

 in most cases, be disregarded. For r = *8 to r = '5 they scarcely 

 reach *007 . R. For comparison is also appended a table, in which 

 the quantity r F (the distance of the bright line from the wall) 

 is given for different values of r. We have taken the refractive 

 index n = 1/649. 



If the cylinder is filled with air and surrounded by water, the 

 inner bright line takes almost the same position as in an air-bubble ; 

 it is brought only very slightly nearer the centre by the influence 

 of the cylinder- wall. If, for instance, the absolute refractive index 

 of the cylinder- wall = 1/4, and that of water = 1*3356; then we 

 obtain for the distances F, of the line from the centre, the values 

 in the first series below, to which have been added, as a second 

 series, the somewhat higher ones, obtained with equal value of r 

 in the air-cylinder. The numerical relations are expressed in 

 fractions of R, as before. 



