602 DE. GL W. EOYSTON-PIGOTT ON A SEAECHEE FOE APLANATIC IMAGES. 
achromatic combination slightly overcorrected for spherical aberration of 2 inches focal 
length, or less according to the power required*. 
An additional cap containing a supplementary achromatic lens is sometimes advan- 
tageously fixed upon the lenses of the searcher, when (for instance) a power of 700 
diameters is desired to be developed by a half-inch objective (for test Podura beading). 
In conclusion, the experiments detailed in this paper, selected from a great number 
made within the last few years, it is hoped will induce more able observers to repeat 
them in a more general form ; but, so far as they are detailed, they appear satisfactorily 
to demonstrate the detection of residuary aberration of considerable amount in the very 
finest microscopes, and enable one to measure it and to suggest means of diminishing the 
errors of the glasses whilst greatly increasing the power. Whether a similar method 
can be applied also to telescopes has been some time under the author’s consideration, 
with results which he hopes on a future occasion to have the honour of communicating 
to the Society. 
Appendix. 
The law of displacement followed by the final focal image corresponding to a minute 
displacement of the internal lenses of a complex objective, the front lenses or facet 
remaining fixed, possesses some interest and may thus be expressed: — 
Let F be the distance of the final focal image when the objective lenses are closed 
together. 
F + &F its distance when the front sets of the objective are displaced by a quantity bx. 
Then it will be found if f\ be the distance of the virtual image conjugate with the 
object as formed by the front set of lenses, 
&F:&f:: — F 2 :/ 2 ; 
and consequently every slight change of the screw-collar of an adjusting objective pro- 
duces comparatively a very large displacement in the final focal image, and therefore of 
the traversing image-searcher ; so that the searcher-traverse represents a movement 
conjugate with the objective index. Again, since this traverse towards the objective 
encounters rays of increasing divergence, an increasing breadth of pencil is encountered 
by the lenses of the searcher, and its own peculiar aberration receives an instantaneous 
increase, which introduces an important new element in definition, it having been ob- 
served that the glasses must he very gradually overcorrected as the image is formed 
nearer the objective, within the tube of the microscope. 
* I may be permitted to add a note here (Nov. 7, 1870), that a Wray one-fifth, made expressly, admitted of 
as great amplification as an ordinary one-twelfth. In fact these researches appear to point decisively to greater 
advantages to be expected from raising the quality of the lower objectives rather than deepening focal length. 
Observers are more numerous every year who prefer the ooe-eighth to the one-twenty-fifth and one-fiftieth. 
