[3] Scheiner also devised a crude parallactic mount which he used in his solar observations, probably the first European to grasp the principle of the equatorial. It was only near the end of the century that Roemer followed his example, and both had been anticipated by Chinese instruments with sights.
[4] He attempted to polish them on cloth, which in itself was sufficient to guarantee failure.
[5] In Fig 13, A is the support of the tube and focussing screw, B the main mirror, an inch in diameter, CD the oblique mirror, E the principal focus, F the eye lens, and G the member from which the oblique mirror is carried.
[6] In fact a “four foot telescope of Mr. Newton’s invention” brought before the Royal Society two weeks after his original paper, proved only fair in quality, was returned somewhat improved at the next meeting, and then was referred to Mr. Hooke to be perfected as far as might be, after which nothing more was heard of it.
[7] Commonly, but it appears erroneously, ascribed to Lord Mansfield.
[8] This was probably due not only to unfavorable climate, but to the fact that Herschel, with all his ingenuity, does not appear to have mastered the casting difficulty, and was constrained to make his big speculum of Cu 75 per cent, Sn 25 per cent, a composition working rather easily and taking beautiful, but far from permanent, polish. He never seems to have used practically the SnCu4 formula, devised empirically by Mudge (Phil. Trans. 67, 298), and in quite general use thereafter up to the present time.
[9] An F/3 mirror of 1m aperture by Zeiss was installed in the observatory at Bergedorf in 1911, and a similar one by Schaer is mounted at Carre, near Geneva.
[10] More recently his condition proves to be quite the exact equivalent of Abbé’s sine condition which states that the sine of the angle made with the optical axis by a ray entering the objective from a given axial point shall bear a uniform ratio to the sine of the corresponding angle of emergence, whatever the point of incidence. For parallel rays along the axis this reduces to the requirement that the sines of the angles of emergence shall be proportional to the respective distances of the incident rays from the axis.
[11] It is interesting to note that in computing Fig. 54a for the sine condition, the other root of the quadratic gave roughly the Gaussian form of Fig. 53.
[12] The curvature of the image is the thing which sets a limit to shortening the relative focus, as already noted, for the astigmatic image surfaces as we have seen, fall rapidly apart away from the axis, and both curvatures are considerable. The tangential is the greater, corresponding roughly to a radius notably less than ⅓ the focal length, while the radial fits a radius of less than ⅔ this length with all ordinary glasses, given forms correcting the ordinary aberrations. The curves are concave towards the objective except in “anastigmats” and some objectives having bad aberrations otherwise. Their approximate curvatures assuming a semiangular aperture for an achromatic objective not over say 5°, have been shown to be, to focus unity