1909.] NATURAL SCIENCES OF PHILADELPHIA. 181 



and placing of the lines, measurements being of course made between 

 the interior edges of the lines, and the diameter of the latter allowed 

 for in comparing with stage micrometer. In the fifth measurement, a 

 slight error might occur from comparison with a different-sized division 

 of stage micrometer, as owing to the variation in magnification over 

 the field of ocular, even if errors of screw are immaterial, no filar micro- 

 meter is likely to give exactly double the reading on two equal divisions 

 that it will on one of them. This difference, if only centre of field is 

 employed, is too small to be serious, but in very accurate measurements 

 it is always well to compare with divisions of stage micrometer as nearly 

 as practicable corresponding to size of object measured. 



From these data it will be evident that the unquestionable presence 

 of "antipoint" phenomena need not be taken into consideration in con- 

 nection with micrometry with white light, as a trained eye can select 

 the same margins to measure under any ordinary conditions of illu- 

 mination. This is not in the least contradictory to the theory, but 

 demonstrates the possibility of overcoming a theoretical difficulty 

 in actual practice. As anyone skilled at micrometry is likely to use a 

 large cone whenever practicable, the only occasions when this question 

 will be of importance will be when successive measurements must be 

 made through covers of widely differing thickness. Owing to the 

 impossibility of making any adjustment for this variation, it may be 

 necessary to cut down the cone of illumination and depend on experi- 

 ence to select the margins to be measured. 



In considering diffraction phenomena originating in the object, it 

 will be well to first assume conditions under which the objective will 

 be of greater aperture than the illuminating cone, and will therefore, 

 when examined with ocular removed, exhibit a disk of light, the diop- 

 tric beam, surrounded by an unilluminated space. The insertion of an 

 object in the focus of the objective will result in this dark space show- 

 ing more or less light which may be both refracted and diffracted by 

 the object. If the latter has a fine structure, periodically arranged, 

 this light reaching the outer zone of the objective's aperture will be 

 mostly of diffraction origin and will take the form of separated spectra. 

 As is well known, the examination of such spectra will enable us to 

 predicate in advance what will be the arrangement and distance of 

 The structural elements visible, or if the objective is not of sufficient 

 aperture to include at least the first order spectra, no image of the struc- 

 ture will be seen. Thus in arranging the illumination for the resolu- 

 tion of a difficult object — for instance, Amphipleura pellucida in dots, 

 with a suitable objective— the easiesl way is to pay little attention to 



