440 Dr. Gr. J. Stoney on Microscopic Vision. 



lohich is produced by a single pair of beams that are alike and 

 polarized, either both in the plane of incidence or both perpendicu- 

 larly to it. 



A similar treatment applies to standard image No. 2, the 

 only difference being that to analyse it we are to employ a 

 sector of the hemisphere in the figure on p. 438 instead of the 

 whole hemisphere. 



Hence Theorem 2 is fully proved. 



31. The resolution not unique. — In order to follow the most 

 simple process when combining the secondary beams in pairs, 

 we have taken both the members of each pair from the same 

 meridian. We might of course have combined them laterally 

 or obliquely, and we shall find it necessary to bear this in 

 mind when dealing with some kinds of illumination that are 

 found useful, e. g. annular illumination. It is obvious that 

 it is legitimate to combine the secondary beams in any way 

 which ivhen completed has used up all the light : and our object 

 should be to combine them in each case in whatever order is 

 most convenient for the problem in hand. In the practical 

 use of the microscope it is usually quite easy to see into 

 what groups it is most advantageous to throw them. In 

 whatever order they are taken the final result is the same; 

 but one order differs from another in the degree in which it 

 gives us information that is of use to us. 



It is sometimes convenient to think of an optical image as 

 a kind of picture, and that the rulings are, as it were, suc- 

 cessively painted in upon the field of view to form it. But 

 if we conceive matters in this way we must remember that 

 this luminous paint behaves after a very peculiar fashion. 

 Where one ruling crosses another or overlies it, they may 

 obliterate one another in some parts as well as strengthen 

 one another in others, effects which will depend on the 

 lengths and positions of the transversals in the two rulings and 

 upon the relation in which their phases stand to one another. 



In this connexion it is very necessary to bear in mind 

 that two rulings may be seemingly identical — i. e., identical 

 in position, spacing, intensity, &c, in such matters as the eye 

 can perceive — and yet these rulings may behave quite 

 differently towards the other rulings with which they are 

 associated, owing to differences affecting the transversals and 

 phases which our eyes are not fitted to take note of. Thus, 

 what are apparently identical rulings might result from the 

 interference of two beams little inclined to the optic axis, 

 and from two others much inclined ; or from two beams in 

 the same meridian and two others in other positions : but 

 these seemingly identical rulings would all behave differently 

 towards the rest of the light with which they have to act. 



