difficult that the user of the telescope cannot ordinarily effect
it. But the perpendicularity of the whole objective to the tube of
the telescope is liable to be deranged in use, and every one who
uses such an instrument should be able to rectify an error of this
kind.

The question may be asked, How much of a telescope can an amateur
observer, under any circumstances, make for himself? As a general
rule, his work in this direction must be confined to the tube and
the mounting. We should not, it is true, dare to assert that any
ingenious young man, with a clear appreciation of optical
principles, could not soon learn to grind and polish an object-
glass for himself by the method we have described, and thus obtain
a much better instrument than Galileo ever had at his command. But
it would be a wonderful success if his home-made telescope was
equal to the most indifferent one which can be bought at an
optician's. The objective, complete in itself, can be purchased at
prices depending upon the size.

[Footnote: The following is a rough rule for getting an idea of
the price of an achromatic objective, made to order, of the finest
quality. Take the cube of the diameter in inches, or, which is the
same thing, calculate the contents of a cubical box which would
hold a sphere of the same diameter as the clear aperture of the
glass. The price of the glass will then range from $1 to $1.75 for
each cubic inch in this box. For example, the price of a four-inch
objective will probably range from $64 to $112. Very small object-
glasses of one or two inches may be a little higher than would be
given by this rule. Instruments which are not first-class, but
will answer most of the purposes of the amateur, are much