for the Mirrors of Reflecting Telescopes. 117 
(19). The coefficients of the equation of (16), may then be 
found, and by assuming values of g and gq, the corresponding 
values of k may be found. 
(20). The place of the second image may now be found ; and if 
Ses fe 3 
the value assumed for Dp Was not sufficiently accurate, the process 
may be repeated, and a more correct value found for p, &c. The 
equation of the eye-piece will probably not require alteration. 
(21). It is scarcely necessary to observe that the small mirror 
must not be changed as in telescopes with metal reflectors; the 
power must be altered only by changing the eye-piece. 
(22). The investigations have all been made on the sup- 
position that the telescope was Gregorian. For one of Cassegrain’s 
construction it is merely necessary to take a and f negative. 
The advantages which telescopes on this construction might 
be expected to possess over those in use may be estimated from 
the following statement. The principal difficulty in the construc- 
tion of the achromatic lens arises from the irregularities in flint- 
glass, which render it almost impossible to make an object-glass 
of large diameter. As only one kind of glass is necessary for the 
construction here proposed, the artist evidently has the power of 
selecting that which will be most easily found free from irregu- 
larities. From the different laws of dispersion in different kinds 
of glass the exact correction of colour by the achromatic lens is 
impossible; but as in the proposed construction the same kind 
of glass is used in every part of the telescope, it is not liable to 
the same objection. Considerable difficulty is found in adapting 
to each other two lenses of crown and flint; for this telescope 
the radii, &c. might be calculated with the certainty of removing 
all aberration. For the object-metal in reflecting telescopes of 
