- 4 \\\ 
(A). 
With this one condition of achromatism among the seven quantities, 
we are at liberty to conjoin other conditions, subject of course to 
their possibility. The most obvious collateral condition is that the 
combination DE be achromatic in itself, so that it may be used 
separately as an inverting eye-piece, This achromatism is expressed 
by the equation 
achromatic at the same time with the pair D, E, because this would 
imply the condition fi+f 2 ~ 2& x = 0, and would necessitate an 
infinite value for b 2 . The equation (C) may be written in the form 
in which the second member is altogether independent of f 3 and / 4 . 
Now, in arranging a Huygenian eye-piece, we may assume any 
ratio between / 3 and / 4 . If we wish to use a field-bar, as in sur- 
veying instruments, we make / 4 the greater, otherwise we prefer to 
make / 4 the lesser, because then, the image of the object-glass is out- 
side of and close to the lens E, and so a large field of view is had. 
In this case it is important that the Eheita’s lens D be well out of 
the focus of E, in order that any minute imperfections or dust- 
particles on its surface may be out of view. One maker may prefer 
the ratio two to one; another maker may adopt that of three to one. 
If then we have fixed upon some ratio n , and resolved to make in 
all our Huygenian eye-pieces 
fs=nf 4 
P), 
