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



speak of the grasp of a beam, and of the grasp of the objective. 

 This designation is justified, since, as we shall presently see, 

 the quantity designated by it, when it is applied to an ob- 

 jective, is the proper measure of its resolving power, i. e. of 

 the minuteness of detail which that objective can reach ; and 

 when applied to an individual beam or to its axial ray, it 

 indicates the farthest that two rays of that obliquity can go 

 in the representation of detail, in other words their utmost 

 grasp. When applied to the most inclined beam in any 

 meridian plane whose axial ray can be caught by the ob- 

 jective, it measures the grasp of the objective, and may 

 conveniently be represented by G, and it may be symbolized 

 by g when applied to any less inclined beam. 



When the beams are in the same meridian but differently 



inclined, we may proceed as follows : — Let kg be the front of 

 the objective, o the middle of image C, and ob and oh' the 

 axial rays of two beams lying in the same meridian plane. 

 These beams, if reversed, will under ordinary circumstances 

 (i. e. if the transversals are not in altogether discordant 

 positions) produce a ruling* in image C. The spacing of this 

 ruling is given by the formula 



V = a (sin a + sin a) , 



where a is the spacing of the ruling, V the wave-length in 

 medium c, and where a and a are counted as positive when 

 on opposite sides of the vertical. Multiply both sides by n, 

 the index of refraction of medium c. Then 



n\' = a(n sina-fn sin a'), 



* To prevent misapprehension it may be well to call attention to the 

 circumstance that this ruling may have a very "brief existence— lasting for 

 something like one foot of time in cosmic measure, see footnote, p. 425 — 

 and may be succeeded on the image-plane by other rulings parallel to and 

 equally spaced with the first, but perhaps shifted in the direction perpen- 

 dicular to the ruling. Such rulings would be unseen by us. They only 

 become visible when the two beams have some common origin so that 

 their phases maintain the same relation to one another in successive 

 small intervals of time. This prevents the shifting spoken of above. 



