and the Achromatism of Microscopes. 249 
To find the intersection after refraction at the third lens, we 
have, by (16), 
b 
s=m Se ee ee ee ee tt): 
PY 9 PP par qr pr pg | 
gab bats 
22 it tas | P 
hence x 3ab_ ab a(a+8) aa, 1 11 
POT wy UE PE Pq Big 2? 
r(bp+a+6.q—2ab) 
-—3ab+2bp+2.a+b.q+2ar—pq—pr—qr_ 
(22). Robison has proposed as a general rule in constructing 
eye-pieces of four glasses, to unite all the differently coloured 
pencils on the third lens or field-glass. For this purpose, it is 
merely necessary to make b= arert 
(25.) These investigations, it is evident, can be extended to 
five or a greater number of lenses, ‘and the formule, though 
troublesome, will be as simple as the nature of the subject will 
allow. And any other problems, relating to the intersection of 
the rays &c., can be solved on the same principles. On this 
subject therefore we shall not stop any longer. 
(24.) On the Achromatism of Microscopes. In the con- 
struction of the common microscope there is no part similar to 
the achromatic object-glass of the telescope, for the purpose of 
making the rays of any one colour from a point of the object enter 
the eye parallel to each other. The aperture of the object-glass 
is so small, that the colour arising from this chromatic aberration 
is not perceptible. The only endeavour is to make the axes of 
the differently coloured pencils enter the eye parallel to each 
other: which is effected by properly placing the diaphragm that 
determines the quantity of light received from the object. Fig. 5. 
represents the path of the axis of a pencil of rays in the common 
