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Transactions of the Royal Microscoincal Society. 
enable ns to study certain classes of objects in a far more satis- 
factory manner than heretofore. The very striking facts on which 
this method is based were first shown publicly at our scientific 
evening meeting on the 18th of April last year, when their true 
explanation was still unknown ; and were again shown at a sub- 
sequent meeting on the 31st of October, after the general principles 
of the subject had been sufficiently well established. The various 
facts seemed to attract so much attention, that I have often felt 
desirous to bring the subject before this Society, and now take the 
opportunity, since I fear another may not occur for some time to come. 
In the first instance my attention was exclusively directed to 
the application of the method to the study of comparatively large 
portions of minerals, having a thickness of \ of an inch or more, in 
order that the various measurements might be made with sufficient 
accuracy to establish general principles, and to verify or correct 
certain theoretical deductions of Professor Stokes, who undertook 
that part of the subject. The results fully convinced me that the 
method would enable us to determine, with very considerable 
accuracy, some of the most important optical constants of crystal- 
line minerals, provided that the section be cut in the plane of any 
two of the axes. This alone was a great gain for mineralogy, 
since, in order to determine them by the methods previously adopted, 
more numerous and complex measurements were necessary, and it 
was requisite to cut the section in one very special direction. The 
new method enables us to approximately determine several im- 
portant particulars, no matter what may be the direction in which 
the section is cut. This is of course a very great advantage when 
we come to apply it to the study of thin sections of rocks, in which 
the minerals lie in every possible position. Even when compara- 
tively large specimens and a low magnifying power are used, the 
special characters observed by this method depend entirely upon 
the collection by an object-glass of more or less divergent rays. It 
is not, as so often happens, a case where the microscope merely 
magnifies an appearance which might be seen with the naked eye 
or a simple lens, but a new class of properties is, so to speak, created 
by the peculiar optical conditions of a compound microscope. 
Though the deductions have a direct bearing mainly on mineralogy 
and tlieoretical optics, it would not therefore be out of place to 
enlarge even on this department of my subject, but still I will not 
say more than is absolutely necessary, since I am anxious to 
describe more fully the applications of the new method to the 
study of minute objects somewhat highly magnified. 
Before proceeding any farther it will, I think, be well to give 
a short history of this subject. 
At the meeting of the Koyal Microscopical Society, November, 
1876, Dr. Koyston-Pigott exhibited and described an instrument 
