NATURE 



409 



THURSDAY, MARCH 2, 1893. 



MODERN OPTICS AND THE MICROSCOPE? 



The Microscope : its Construction and Management. In- 

 cluding Technique, Photomicrography, and the past 

 and future of the Microscope. By Dr. Henri van 

 Heurck, &c. English edition re-edited and augmented 

 by the author from the fourth French edition, and trans- 

 lated by Wynne E. Baxter, F. R.M.S., F.G.S. (London : 

 Crosby Lockwood and Son, 1893.) 



THIS is a handsome, even a luxurious, book. It is 

 beautifully printed on highly-finished paper, and 

 with a margin ample enough to satisfy the most exacting 

 connoisseur. The illustrations are clearly produced, the 

 binding is admirable, and after a careful comparison with 

 the last French edition, we do not hesitate to say that 

 the translation is as felicitous as it is accurate. 



Its author has aimed apparently at an elementary 

 treatise on the microscope, which is nevertheless intended 

 to cover almost the entire field involved in its history, 

 production, and use. The difficulties of such a task are 

 not a few. To be elementary and thoroughly popular up 

 to a limit, very sharply defined, and then to lead on those 

 who choose to follow into the deeper aspects of this many- 

 sided subject, is at once practical and natural. The optics 

 of the modern microscope are the possession of the 

 specialist. Abbe himself has failed to make them ac- 

 cessible to and understanded by any but those education- 

 ally equipped. Hence the constant misunderstanding of 

 the fundamental principles of the Diffraction Theory and 

 its related applications so frequently manifest even where 

 the subject is supposed to be more or less familiar. 



As might have been readily supposed, the author of 

 this treatise has given evidence of skill in the presentation 

 of the main points of elementary optics ; it is, however, 

 clearness and conciseness, not originality, that is to be 

 noticed. The illustrations are those familiar to English 

 text-books for the last quarter of a century, and the 

 diffraction theory has in no way been simplified to the 

 reader of an elementary treatise by that most efficient of 

 all elementary modes of imparting ideas on more or less 

 abstruse subjects, viz. carefully devised and well- explained 

 diagrams. 



Considering the object of this treatise, viz. theimparta- 

 tion of knowledge to those not mathematically prepared to 

 follow it in that direction, by giving a concise, clear, and 

 comprehensive view of the meaning and application of the 

 diffraction theory of microscopic vision, the transitioft 

 from the first to the second chapter will be so abrupt and 

 unlinked as to leave the elementary reader practically in 

 the dark. The chapter on " The Theory of Microscopic 

 Vision" is unexceptional so far as it goes. It cannot be 

 other, it is Prof. Abbe's ; but in a treatise claiming to 

 maintain its elementary character more completely than 

 any other similar work which covers so wide a range this 

 is surely not enough. 



The diffraction theory of vision is introduced to the 



tyro with no explanation of what diffraction is, and with 



no illustration of its action until he is plunged in medias res 



in Abbe's application of it to the profoundly important 



NO. 1218, VOL. 47] 



and inestimably valuable theory itself. The " elementary " 

 character of this is at least questionable. Beyond this 

 that most important factor in the diffraction theory in its 

 practical application, Numerical Aperture, is wholly with- 

 out explanation, save such as arises from its technical 

 introduction and employment ; but there are few points 

 on which it is more important that an elementary student 

 should be more clearly instructed, and there are few that 

 lend themselves more to efficient diagrammatic presenta- 

 tion. In the same relation it may be noted that the very 

 essential formula n sin «— expressing the general relation 

 discovered by Abbe between the pencil of light admitted 

 into the front of the objective, and that emerging from the 

 back lens of the same, which is such that the ratio of the 

 semi-diameter of the emergent pencil to the focal length 

 of the objective could be expressed by the sine of half the 

 angle of aperture («) multiplied by the refractive index of 

 the medium (;/) in front of the objective or n sin. «— but 

 this is a German mathematical formula ; and its English 

 equivalent is /x sin. 0, and although the German form of 

 symbol is employed in England, and thoroughly under- 

 stood by mathematicians, those who are entering for the 

 first time upon a study of this difficult subject, and there- 

 fore unaccustomed to the mathematical formulae em- 

 ployed, might readily fall into confusion, seeing that the 

 " elementary " source of their information leaves them 

 without a hint on the subject. 



Another serious defect, as we believe, in this " ele- 

 mentary " presentation of the diffraction theory of 

 microscopic vision is the absence of an easy explanation 

 of the photometrical equivalent of different apertures. 

 Certainly it is not of the essence of the problem, but it is 

 just one of those points which in a very marked and in- 

 structive manner illustrate the meaning and value of 

 numerical aperture as such ; and for elementary 

 exposition this must be of importance. Thus, if two 

 circles be taken to represent the backs of two objectives 

 of the same power but of different apertures, and the 

 radius of one be twice that of the other, then each radius 

 will represent the angle « sin. u. But because the areas 

 of these circles are to each other in the proportion of the 

 squares of their radii, it follows that if each radius be 

 designated by n sin. u, the area of the lesser circle will be 

 to the area of the greater circle as the square of the radius 

 of the former is to the square of the radius of the latter. 

 Hence the area of the greater circle will be four times as 

 great as that of the lesser, which teaches that since the 

 numerical aperture of one objective is twice as great as 

 that of another its illuminating power will be four times 

 as great — a most important incidental and explanatory 

 raison d'etre for great N. A. 



In this connection we notice what is certainly not 

 easily explicable as an exposition of the details of Abbe's 

 great theory. On page 56 of " The Microscope " Dr. 

 Van Heurck almost incidentally states the very important 

 fact that " Prof. Abbe has satisfactorily established the 

 fact that a certain relation must exist between magni- 

 fication and angular (?) aperture." This is undoubtedly 

 one of the most important demonstrations of the theory. 

 Great numerical apertures have proved of untold value 

 to the competent student of minute details, by opening 

 up structures that mere amplification must have left for 

 ever impenetrable. But that does not annul the import- 



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