Tue Microscope. 3 
the same magnifying power. The difference is due alone to the 
fact that the six-inch glass increases the angular aperture of the 
eve three times more than the two-inch. The principal endeavor 
of the optician in constructing optical instruments is not the 
highest possible magnifying power—indeed there is no special 
difficulty in this direction—but to combine with a given magni- 
fying power such high angular aperture with a minimum of op- 
tical errors so as to increase the resolving power to the highest 
possible degree, so that the closest lines or dots can be distinctly 
separated from each other. But any optical instrument, how- 
ever perfect it may be in its construction, will fail to perform 
to the satisfaction of even the most experienced operator if his 
eye is optically defective in such a way as to interfere directly 
* with the normal performance of the instrument, and astigma- 
tism must be regarded as such a defect. Near and long sight is 
corrected by simply focusing the instrument. But on our pres- . 
ent instruments there is no means provided to correct astigma- 
tism. The astigmatic microscopist may fail to separate some 
close and fine lines, which the day before under more favorable 
conditions to his astigmatism he saw quite distinctly ; and, on 
another occasion, he perhaps experienced a similar change 
within a few minutes without any change in conditions except 
that he accidently changed his own position to his microscope 
by a turn of ninety degrees around the table, thus placing his 
astigmatic axis in a more favorable or unfavorable direction, as 
the case may be, to the direction of the fine lines. 
The telescope as well as the microscope shows the errors 
produced by astigmatism. Close double stars appear different 
in the angle of separation at different times, or, at times become 
too indistinct to be separated at all, owing to the change of 
their line of position to the astigmatic axis of the observer’s eye. 
Circular objects, such as faint clusters, nebula and comets, ap- 
pear elongated, winged, or in other way of irregular shape. In 
fact there is not a case possible where astigmatism could not be 
to some degree injurious to the perfect definition of the fine de- 
tails of an object, and this is increased the higher the perfection 
of the instrument. 
Having thus explained the general injurious effects of as- 
tigmatism on telescopic and microscopic observations, it remains 
