LORD OXMANTOWN ON THE REFLECTING TELESCOPE. 
523 
and it is vain to look for a guide in searching for the proper one in calculations 
founded on the principles of exact science, as the effect of friction in polishing is not 
conformable to any known law ; still from a number of experiments it might be pos- 
sible to deduce an empirical formula practically valuable : this I have endeavoured 
to accomplish. 
The weight of the polisher was constant, being the least possible consistent with 
its working properly, viz. ten pounds for a speculum three feet diameter. The di- 
stance of the counterpoising lever would obviously influence the curve ; that I have 
regarded as constant also, viz. twelve feet, as also, in all my most recent experiments, 
the length of the stroke of the first eccentric B, which was one-third of the diameter 
of the speculum ; the only variable quantity was, therefore, the stroke of the second 
eccentric G. Under these circumstances, the most accurate determination at which 
I have as yet been enabled to arrive is, that when the stroke of the second eccentric 
G is such as to communicate a lateral motion to the polisher equai to about "27 of 
the diameter of the speculum, the curve will be nearly parabolic. The curvature I 
measure as Mudge did, by means of diaphragms; and when the surface is true, the 
separate portions of it, though the general figure may be indifferent, will define 
sharply, and their focus can be ascertained with great precision. If the surface is 
not true, the curvature cannot be ascertained with any degree of accuracy ; the watch- 
dial, the test object, is but ninety feet from the speculum, and could not be placed 
higher without inconvenience; it is therefore necessary in measuring the curvature of 
the speculum to allow for its distance. This I do simply by calculating the spherical 
aberration, the radiant being ninety feet distant, at two points, one tjth of the radius, 
and the other -grd of the radius from the centre of the face, deducting that from the 
aberration for parallel rays at these points, and endeavouring so to figure the specu- 
lum that it should be over corrected that much. Any further refinement would be 
but waste of time in the present state of these experiments ; and although we cannot 
hope to obtain anything but an approximation, still the limits of error will be so 
small that even a large fraction of that quantity may not in practice be very import- 
ant. The adjustment, however, can be made with such accuracy, that the three-feet 
metal at present in the telescope, with its whole aperture, is thrown perceptibly out 
of focus by a motion of the eye-piece, amounting to less than the thirtieth of an inch ; 
and even with a single lens of one-eighth of an inch focus, giving a power of 2592, 
the dots on a watch-dial are still in some degree defined. 
A watch-dial is, upon the whole, as good a test for very large specula as can be 
desired, as there is so much light that the magnifying power can always be increased 
till indistinctness is perceptible ; and although eventually the performance of the 
instrument on the heavenly bodies, the development of new details, or the discovery 
of new objects, which other instruments have not reached, are the proofs that an ac- 
cession of instrumental power has been obtained, still as a test to have recourse to 
during the progress of experiments, a watch-dial, which is always at hand, and so 
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