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templated by the single negative. By this he also reached a speed of approximately f :2.0 with a satisfactory quality of definition for short focus lenses. This expedient has also been developed by other designers adding to the complication and with some increase of speed. Bielicke's is sold under the trade name of Astro Tachar in speeds of f:1.8 and f:2.3.
The second general method of attack may therefore be said to consist in splitting either the front or the back element of a Cooke
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Fig. 10 — Rudolph's Double Gauss Lens of 189 7.
triplet into two parts and then elaborating much or little, according to the degree of refinement it is regarded as desirable to reach in correcting aberrations.
There is a third general type of lens which permits the attainment of high speed and which has a long and interesting history. It goes back to a form of telescope objective proposed by Gauss which consisted of two meniscus lenses and which was characterized by the fact that chromatic aberration was corrected for two zones (say the marginal and the axial zone) instead of one as in the ordinary lens. In 1889 Alvan G. Clark, of Cambridgeport, Massachusetts, described a photographic lens whose front and back component were each of the form of a Gauss telescope objective. This lens had many excellent features, but it was not corrected for astigmatism. In 1897 the United States Patent Office granted a patent No. 583336 to Dr. Rudolph on a photographic objective consisting of two Gauss telescope objectives of which the concave member in the one case and the convex number in another case were made compound, and in which he made use of the new kind of glass available to the end that he finally succeeded in correcting astigmatism and curvature of field. With this construction he reached a speed of f:4.0. The form which appears to have been most successful is shown in Fig. 10.