d = (f + f′)/2 where d is the distance between the lenses and f, f′, their respective focal lengths. If this condition of achromatism be combined with that of equal refraction at _A_ and _C_, favorable to minimizing the spherical aberration, we find f = 3f′ and d = 2f′. This is the conventional Huygenian ocular with an eye lens ⅓ the focus of the field lens, spaced at double the focus of the eye lens, with the diaphragm midway. In practice the ratio of foci varies from 1:3 to 1:2 or even 1:1.5, the exact figure varying with the amount of overcorrection in the objective and under-correction in the eye that has to be dealt with, while the value of d should be adjusted by actual trial on the telescope to obtain the best color correction practicable. One cannot use any chance ocular and expect the finest results. [Illustration: FIG. 101_a_.—Airy and Mittenzuey Oculars.] The Huygenian eyepieces are often referred to as “negative” inasmuch as they cannot be used directly as magnifiers, although dealing effectively with an image rather than an object. The statement is also often made that they cannot be used with cross wires. This is incorrect, for while there is noticeable distortion toward the edge of the wide field, to say nothing of astigmatism, in and near the center of the field the situation is a good deal better. Central cross wires in the plane of the diaphragm are entirely suitable for alignment of the instrument, and over a moderate extent of field the distortion is so small that a micrometer scale in the plane of the diaphragm gives very good approximate measurements, and indeed is widely used in microscopy. It should be noted that the achromatism of this type of eyepiece is compensatory rather than real. One cannot at the same time bring the images of various colors to the same size, and also to the same plane. As failure in the latter respect is comparatively unimportant, the Huygenian eyepiece is adjusted so far to compensate the paths of the various rays as to bring the colored images to the same size, and in point of fact the result is very good. The field of the conventional form of Huygenian ocular is fully 40°, and the definition, particularly centrally, is very excellent. There are no perceptible ghosts produced, and while some 10% of light is lost by reflection in the extra lens it is diffused in the general field and is damaging only as it injures the contrast of faint objects. The theory of the Huygenian eyepiece was elaborately given by Littrow, (Memoirs R. A. S. Vol. 4, p. 599), wherein the somewhat intricate geometry of the situation is fully discussed.