This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
In the manufacture of specula, plate glass is used, provided the size of the mirror is not such that the disc has to be specially cast. The thickness is in proportion to the diameter, the general ratio being as 8 to 1 - that is to say, the diameter of the speculum should be eight times its thickness. A safer ratio is 6 to 1 - at any rate for large mirrors, where the question of flexure is an important consideration. Supposing the diameter of the speculum to be l()in.,its thickness would be 1 2/3 in. certainly not less than 1 1/2 in. Before deciding the curve, the focal length of the speculum must be determined, as this, of course, in turn determines the length of the telescope. If the latter must be short, the former must be short also, and the curve of the mirror must be correspondingly deep. This will render the figuring much more difficult to work than when the speculum has a long focus. The general practice is to make the focal length twelve times the diameter of the mirror, which, in the case of a 10-in., will be 10ft. The curve of a speculum, though first ground spherical, is not left so, but is deepened to a parabolic form, as it is found that a spherical surface is unfitted for astronomical work.
Parallel rays, when received on such a surface, result in an indistinct image at the eyepiece. Practical experience shows that the curve should be such that parallel rays received on it will come to a focus midway between the mirror and its centre of curvature. Therefore, in a 10-in. speculum the curve must be part of the circumference of a circle having a radius of 20 ft.
 
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