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X. On Polishing the Specula of Reflecting Telescopes. 
By W. Lassell, F.R.S., V.P.R.A.S . , LL.D. 
Received November 11, — Read December 17, 1874. 
During my sojourn in Malta (1861 to 1864) I made many experiments in repolishing 
my four-foot mirrors, with a view to the obtaining, if possible, further excellence in 
figure and polish. To obtain perfection in both these qualities, or so near an approach 
to it that no fault is discoverable in a four-foot surface, is not easy, at least I have not 
found it so. 
Errors of figure may be of various kinds. A surface may be so near to the true para- 
bolic curve that the central and circumferential rays may come to the same focus ; but 
the intermediate rays, those halfway between the centre and circumference, may have a 
different focus. If this error be considerable, and the telescope be turned to an object 
requiring fine definition, the effect is most annoying. A first glimpse may lead you to 
expect you are coming to a very sharp image ; but just as the image ought to be formed 
in perfection, the outstanding intermediate rays introduce confusion, and after several 
vain attempts to improve the focus you retire in disgust. This irregularity of curve I 
consider to be the most vexatious fault a mirror can have. A deviation from the para- 
bola at the circumference of the mirror, whether the deviation be within or beyond the 
parabola, is far more tolerable, if it be in a regular progress from the centre to the 
circumference. Indeed a figure which deviates sensibly, but moderately, towards the 
edge, whether within or beyond the parabola, may give very tolerable vision, if the 
curve deviate from the parabola only in regular proportion from the centre outwards. 
There is another error which is of less consequence, but still desirable to be got rid of, 
as it practically reduces the available aperture of the mirror, and consequently the size 
of the telescope. The figure may be sensibly parabolic up to near the margin of the 
mirror, where it rapidly falls off and becomes grossly hyperbolic. Probably this may 
arise from some different action of the polisher upon those parts of the speculum which 
in the process of working are alternately covered and exposed, or from the injudicious 
application of the rouge and water only near the edge. With a view to obviate this 
defect of figure, I have found it advantageous to increase the sweep or stroke of the 
polisher, or, in other words (referring to the description of my polishing-machine in the 
eighteenth volume of ‘Memoirs of the Eoyal Astronomical Society’), to increase the throw 
of the quick-moving crank. While attempting to do this at Malta, using the same 
machine which had been originally constructed for the two-foot speculum, and had given 
repeated indications of its being too weak for the work, it broke down hopelessly, and 
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