250 Mr. Atry on Achromatic Eye-pieces of Telescopes, 
microscope: at C is the diaphragm which admits a cone of rays 
smaller than the object-glass. Since the position of this diaphragm 
determines the part of the object-glass, through which the rays 
coming from any point 4 of the object must pass, it is evident 
that the refraction, and consequently the dispersion of the dif- 
ferently coloured rays will depend upon its position. 
(25). We shall begin the investigation by finding the effect 
produced by variation of refrangibility upon the directions of the 
axes of the pencils from 4, passing through C. Let v be the 
distance of the object from the object-glass: suppose Bd pro- 
duced, Fig. 6, to meet the axis of the microscope at a point 
whose distance from the object-glass = y. Let m be the tangent 
of the angle made by the pencil, after refraction at the object- 
glass, with the axis of the microscope. Then it is easily seen 
that (if w be the distance of the point of the object from that axis,) 
: - — =1: and since a similar expression is true for rays of all 
colours, 
v(5 +3. Pena =i 
Eliminating w, 
3 r) 3 
» (5 +82) Sg Aoi =<. or v.8o=(1-2) 2. 
y ™m 
Now i St Silene EE 
Y P Y Pp pxr-i 
_v én 0 v\ 8m 
ogy gat ge) ™m 
And v is always very nearly = p; 
_ vo dn _v dm dma mz én 
Set aah, ait) Ot Sate 
(26). Now the axes of the pencils after refraction at q will 
