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In this paper are described— 
I. Some experiments which suggested an inquiry into a 
method of raising microscopic power consistent with a corre- 
sponding improvement in the precision of definition, so 
generally destroyed by excessive amplification. 
II. The inquiries by which the construction of an aplana- 
tic-image searcher was gradually arrived at; the object of 
which was to search for aplanatic foci, to compensate residuary 
errors by new spherical and chromatic corrections whilst 
amplifying power, and to increase the small interval existing 
between a deep objective and its object, whilst the focal 
perspective or depth was also increased. 
The research was originally suggested by the accidental 
resolution of the Podura scale. ‘This exquisite object, so 
justly prized by the optician for the trial of microscopes, 
affords peculiar markings resembling notes of admiration, of 
sufficient delicacy to put even the defining-power of objectives 
of one fiftieth of an inch to a severe ordeal. Dr. Pigott had 
observed these markings to disappear and be resolved into 
black beads. ‘The objective employed had nearly one seventh 
of an inch focal length, and an aperture of 50°. The object 
was illuminated by solar rays reflected obliquely by a plane 
mirror. Having related this effect to eminent opticians, he 
was informed that no objectives (at that time, 1862) could 
resolve this test. Messrs. Powell and Lealand were, however, 
prevailed upon to construct a “ very fine” one eighth ex- 
pressly for this resolution ; as this totally failed, a one six- 
teenth was carefully constructed with no better success, and 
finally a one fourth of very large aperture ; all these failed 
to exhibit the Podura beading. Some unsuspected cause of 
this failure evidently remained to be investigated. ‘he evi- 
dently delusive character of the standard test, so much relied 
upon for the construction of microscopic object-glasses, sug- 
gested the necessity of a search for other less uncertain 
methods of testing. The principle of proceeding from the 
known to the unknown appeared to offer the only sound 
basis of inquiry. 
Simple objects were now examined. ‘The finest glass 
threads presented linear images of any conceivable degree of 
proximity, whilst their fused extremities, when selected as 
forming refracting spherules one thousandth of an inch in 
diameter, presented miniature landscapes and points of light 
of remarkable precision, the spherical aberration of which 
could be easily calculated to be of insignificant amount for 
limited apertures. Even a plano-conyex lens of one thirtieth 
of an inch focal length and three hundredths aperture dis- 
