ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
75 
In fig. 4 let o b and o V be the axial rays of two beams lying in the 
same meridian plane, Jcq the front of the objective, and o the middle 
Fig. 4. 
of image C. These beams, if reversed, will produce a ruling in image 
C, the spacing of which is given by the formula 
V = o- (sin a -j- sin a), 
where X' is the wave-length in c, 
. * . n X' = X (the wave-length in air) = cr (9 +’</)• 
For two beams equally inclined on opposite sides of the vertical 
cr 
and for the most inclined rays 
2 
where S is the spacing of the finest ruling which can be seen by the 
objective for light of wave-length X. 
The information which is supplied by the image x (seen by looking 
down the Microscope after removal of the eye-piece) is next considered. 
Taking the case of the beam represented in fig. 3, let r be the 
radius from the axis of the Microscope to the point p where the beam 
is focused in the image x , and let / be the distance from image x to the 
focal image D. 
Then r/f= tan /3 — sin /3 for small values of /3. 
. • . by Lagrange’s theorem 
™ „ M 
g = M sin ft = — r, 
and 
where R is the radius to the border of the disc of light seen on looking 
down the tube. 
9 = 
G 
R 
