1892.] MICROSCOPICAI. JOURNAL. 77 



had been given as to how to see at all. One of the most novel and at 

 the same time important portions of the work is the discussion on the 

 modern theory of microscopical vision, to the elucidation of which Dr. 

 Abbe has done so much. Sixty pages are devoted to this topic, and 

 the subject is very ably treated. In some respects it is not as clear as 

 the excellent article by Frank Crisp published in 1881 in the Royal 

 Microscopical Journa/, while in many other ways it is much superior, 

 Dr. Dallinger having had the advantage of all of Dr. Abbe's latest 

 investigations in the same line. The illustrations, many of them partly 

 colored, add greatly to the value of the article, which, having been 

 revised by Dr. Abbe himself, must be regarded as the most authorita- 

 tive as well as the latest exposition of this very important and difficult 

 subject. There can be little successful work done with high-power 

 and wide-angled objectives without a clear and thorough knowledge 

 of the laws of microscopical vision, for, as Dr. Dallinger well 

 shows, not only is it possible to produce totally different appearances 

 in an object bv varying the illumination and collar adjustment, 

 but the observer will be totally unable to decide which is the 

 true and which is the spurious image without a knowledge of optics. 

 The author says : " We learn that dissimilar structures will give identical 

 microscopicaf images when the difference of their diflractive effect is 

 removed, and conversely similar structures may give dissimilar images 

 when their diffVactive Tmages are made dissimilar. A purely dioptric 

 image answers point for point to the object on the stage, and therefore 

 enables a safe inference to be drawn as to the true nature of that ob- 

 ject ; but the diffraction or interference images of minute structure stand 

 "in no direct relation to the nature of the object, and are not of necessity 

 conformable to it. * * * Minute structural details are not imaged 

 bv the microscope geometrically or dioptrically, and cannot be inter- 

 preted as images of material forms, but only as signs of material differ- 

 ences of composition of the particles composing the object, so that 

 nothing more can safely be inferred from the image as presented to the 

 eve than the presence in the object of such structural peculiarities as 

 will produce the specific diffraction phenomena on which the images 

 depend." This is not consoling, especially as the author adds, "our 

 finest homogeneous objectives of greatest aperture inevitably fail to re- 

 veal to us the real structure of the finer kinds of diatom valves." It 

 would be interesting and profitable could Dr. Abbe find time to tell us 

 by theory how much our widest angled objectives vary from the truth ; 

 that is, for instance, what would be the shape given to a series of mi- 

 nute circular or hemispherical dots by an objective of 1.30, 1.35, and 

 140 N. A. Also, to show if there is any ratio or connection between 

 the spectra shown and the real shape, so that we can deduce the one 

 from the other. Inasmuch as a true picture can only be had by the 

 utilization of all the diffracted rays, and as no objective can ever be 

 made which will contain them all, can theory tell us how near the truth 

 we get with our present lenses? It is known that with a dry ^ objec- 

 tive, for instance, the rays beyond about 130° or 140° air angle are of little 

 value in the representation of form — does the same rule apply with dif- 

 fraction images. If the diffraction fan is homogeneous, that is, if 

 the rays are equally spread, then the loss of, say, 30° of angle out of 

 180^ would cause an error of i6| per cent., while in a medium power dry 



