Thus constituted, the Ramsden ocular, known as “positive” from its capability for use as a magnifier of actual objects, gives a good flat field free from distortion over a field of nearly 35° and at some loss of definition a little more. It is the form most commonly used for micrometer work. In all optical instruments the aberrations increase as one departs from the axis, so that angular field is rather a loose term depending on the maximum aberrations that can be tolerated.[18] [18] The angular field a is defined by tan ½a = γ/F where γ is, numerically, the radius of the field sharp enough for the purpose in hand, and F the effective focal length of the ocular. Of the Ramsden ocular there are many modifications. Sometimes f and f′ are made unequal or there is departure from the simple plano-convex form. More often the lenses are made achromatic, thus getting rid of the very perceptible color in the simpler form and materially helping the definition. Figure 104_a_ shows such an achromatic ocular as made by Steinheil. The general arrangement is as in the ordinary Ramsden, but the sharp field is slightly enlarged, a good 36°, and the definition is improved quite noticeably. A somewhat analogous form, but considerably modified in detail, is the Kellner ocular, Fig. 104_b_. It was devised by an optician of that name, of Wetzlar, who exploited it some three quarters of a century since in a little brochure entitled “Das orthoskopische Okular,” as notable a blast of “hot air” as ever came from a modern publicity agent. As made today the Kellner ocular consists of a field lens which is commonly plano-convex, plano side out, but sometimes crossed or even equiconvex, combined with a considerably smaller eye lens which is an over-corrected achromatic. The focal length of the field lens is approximately 7/4 F, that of the eye lens 4/3 F, separated by about ¾ F. This ocular has its front focal plane very near the field lens, sometimes even within its substance, and a rather short eye distance, but it gives admirable definition and a usable field of very great extent, colorless and orthoscopic to the edge. The writer has one of 2⅝″ focus, with an achromatic triplet as eye lens, which gives an admirable field of quite 50°. [Illustration: FIG. 104.—Achromatic and Kellner Oculars.] The Kellner is decidedly valuable as a wide field positive ocular, but it has in common with the two just previously described a sometimes unpleasant ghost of bright objects. This arises from light reflected from the inner surface of the field lens, and back again by the front surface to a focus. This focus commonly lies not far back of the field lens and quite too near to the focus of the eye lens for comfort. It should be watched for in going after faint objects with oculars of the types noted.