522 
LORD OXMANTOWN ON THE REFLECTING TELESCOPE. 
portions of such dimensions, that, presuming the original figure to have been accurately 
spherical, each should by calculation have one-half of the whole aberration : by draw- 
ing, therefore, the central portion back the proper calculated distance by a delicate 
screw adjustment, and bringing the images into exact coincidence, the aberration 
should have been reduced to one-half. The experiment was so far successful, that an 
instrument of eighteen inches aperture was commenced, and the castings of the spe- 
culum in three adjustible portions were completed. In the mean time, however, with 
additional experience, I found it necessary to adopt new views, and was soon con- 
vinced that it was not impossible to work figures which, though not rigidly accurate, 
were, however, better for specula than the spherical. The undertaking was, there- 
fore, abandoned, but the original instrument still remains, and is so far curious as 
showing that an adjustment of such delicacy can be practically accomplished. The 
experiments to which I have alluded, were made with the elliptic polisher of Mr. 
Edwards, a contrivance in my opinion possessing more merit than has usually been 
ascribed to it: I found that a speculum of four inches aperture, and eighteen inches 
focus, after having been polished by hand as truly spherical as I could make it, was 
invariably improved by working it on the elliptic polisher ; however, on applying the 
same principle to larger specula, the result was less successful ; and after a great many 
trials with a speculum of eighteen inches aperture, I found it would not answer. On 
measuring the focal length of the surface at different distances from the centre of the 
face, it was certain that the radius of curvature always increased much too rapidly 
towards the edge ; and when the principle upon which the elliptical polisher acts is 
considered, it is evident that such a result might have been anticipated, and that the 
defect, though scarcely perceptible in very small specula, would have been very im- 
portant where the dimensions were considerable. 
Having observed that when the extent of the motions of the polishing machine 
were in certain proportions to the diameter of the speculum, its focal length gradu- 
ally and regularly increased, that fact suggested another mode of working an ap- 
proximate parabolic figure. If we suppose a spherical surface, under the operation of 
grinding and polishing, gradually to change into one of longer radius, it is very evi- 
dent that, during that change, at no one instant of time will it be actually spherical, and 
the abrasion of the metal will be more rapid at each point as it is more distant from the 
centre of the face. When, however, the focal length neither increases nor diminishes, 
the abrasion will become uniform over the whole surface, producing a spherical figure. 
According, however, as the focal length (the actual average amount of abrasion 
during a given time being given) increases more or less rapidly, the nature of the 
curve will vary, and we might conceive it possible, having it in our power completely 
to control the rate at which the focal length increases, so to proportion the rate of 
that increase as to produce a surface approximating to that of the paraboloid. Of 
course the chances against obtaining an exact paraboloid are infinitely great, as an 
infinite number of curves may pass between the parabola and its circle of curvature, 
