Dr. Gr. J. Stoney on Microscopic Vision, 503 



which is the same as 



°=^» (2) 



where A ( = n\ f ) is the wave-length in air, and g and g f the 

 " grasps " of the two beams. Hence cr and g + g' are in- 

 versely as one another : in other words, the minuteness of <r 

 is proportional to g+g' '. Of course at least two beams have 

 to be associated with one another to produce a ruling. If, 

 however, the two beams are equally inclined and on opposite 

 sides of the vertical, g' becomes equal to g, so that in this 

 case 



•-£ ® 



whence the appropriateness of calling g the grasp of beams 

 that have this obliquity. 



If oh and ob f are the most inclined axial rays on opposite 

 sides of the vertical that can be taken in by the objective, 

 formula (3) becomes 



2 =^> w 



where 2 is the spacing of the finest ruling which can be seen 

 by that objective transmitting light of wave-length X. 

 Whence the appropriateness of calling G the grasp of the 

 objective. 



The case of two beams which are not in the same meridian 

 plane is dealt with in the next section. 



34. Of the Information supplied by Image x. In any of the 

 cases we have to deal with, the angle of the figure on 

 page 501 is so small that its tangent may be written for its 

 sine. In fact the two do not differ, in the cases we need 

 consider, by one part in a thousand, a difference which may 

 legitimately be disregarded. Now look down the tube of the 

 microscope. The beams of parallel light emitted from the 

 objective field are concentrated into the points of the luminous 

 image x which is then seen. Let us direct our attention to 

 that one of these beams which is represented in the diagram 

 on p. 501. Its light is concentrated in the point p of image x. 

 It is convenient to have a name for this concentration of a 

 beam in image x, and we shall call it the punctum of the 

 beam. Let r be the radius from the axis of the microscope 

 out to this punctum, and let / be the distance from image x 

 to the focal image of the microscope at D. Then tan j3 = r//\ 

 whence finally equation (1), Lagrange's theorem, may be 



2N2 



