The President's Address. By E. M. Nelson. 
169 
First the bi-conyex lens may be cut in two, fig. 21, and the exterior 
plano-convex may be placed with its plane side in apposition to the 
plane side of the plano-concave ; this forms the triple front of old 
achromatic objectives (fig. 22). 
Fig. 21 . Fig. 22 . Fig. 23 . 
Secondly, the exterior plano-convex that was cut off in the previ- 
ous example is equivalent to two equal plano-convex lenses of double 
the radius ; one of these may be left in its original position, and the 
other placed against the plano-concave as in the previous example. 
This will form an equi-convex triple (fig. 23). 
The advantage gained by these forms is that the conditions which 
affect the spherical aberration and the curvature of the field, are 
altered, while those which control the achromatism are undisturbed. 
Setting aside the smaller error of spherico-chromatic aberration it 
matters not in what order the component lenses are placed, so far as 
the achromatism is concerned, but it makes a very great difference 
with respect to spherical aberration and curvature of the image. 
Therefore, by suitable alterations in the form of the achromatic doublet, 
considerable control in these respects can be secured, without appre- 
ciably disturbing the achromatism. 
I must now bring this unfinished subject to a close, with many 
apologies for the imperfect manner in which it has been dealt with, 
and with many thanks for the patient attention you have given me. 
