August 3, 191 1] 



NATURE 



141 



should be replaced by "ammonium sulphide"; on 

 p. 333 "afferent" by "efferent"; and on p. 415 

 '"inspiratory" by "expiratory." 



The present edition is a distinct advance on the 

 earlier issues, the more recent additions to physiology 

 being: fully given. Such are some of the chief char- 

 acteristics of this book. So brief a review as the 

 foregoing necessarily leaves unmentioned many other 

 important features. The book is a remarkable 

 achievement, especially in view of the fact that it is 

 the work of a single author, and appears to the 

 reviewi-r In possess special qualities and merits, which 

 entitle it to a high place amongst the existing English 

 text-books of physiology. The issue of the remaining 

 three volumes will be eagerly awaited by all who 

 have studied the present volume. 



ABBE'S THEORY OF IMAGE FORMATION IN 

 THE MICROSCOPE. 



Die Lehre von der Bildentstehung im Mikroskop von 

 Ernst Abbe. Edited by Otto Lummer and Fritz 

 Reiche. Pp. xii+108. (Braunschweig: F. Vieweg 

 und Sohn, 1910.) Price 5 marks. 



AN account of Abbe's theory of the microscope 

 image given by so distinguished an optician as 

 Prof. Lummer cannot fail to arouse a large amount 

 of interest among all students of optical theory, as 

 well as among workers with the microscope. It de- 

 mands the more attention in that it is professedly a 

 reproduction of Abbe's theories as propounded by him- 

 self. Lummer tells us that in the winter of 1887, in 

 company, among others, with Winkelmann, Czapski, 

 Rudolph, and Straubel, he attended a series of lec- 

 tures given bv Abbe in Jena, and it is clear that he 

 enjoyed exceptional opportunities of becoming 

 acquainted with Abbe's views and his manner of 

 regarding microscope theory. 



The work, we are told, is founded solely on the 

 carefully preserved notes of these lectures. One ques- 

 tion only, it was thought, needed to be reviewed from 

 the modern point of view : Is the Fresnel-Huyghens 

 secondary-wave interference theory a satisfactory 

 basis for the discussion of the phenomena, or will the 

 mi ire modern theory of Kirchhoff and Maxwell lead 

 to some modification of the conclusions arrived at? 

 It may be answered at once that Lummer attacks 

 the problem of image formation by limited beams 

 from the latter point of view, and shows that it leads 

 to identical results with the former. 



The intrinsic interest of the book is very great, and 

 the methods employed are most instructive, both in 

 the establishment of general principles and in 

 their application to the special cases which arise 

 in microscope imagery when periodic structures are 

 viewed by transmitted light. Thus, in the latter 

 case, the determination of the distribution of light 

 intensity in the image plane requires an integration 

 over the plane of the structure viewed, and over that 

 of the actual or virtual aperture. By variation of 

 the order of integration the authors are able to bring 

 out 'clearly the part played by the different "diffrac- 

 tion spectra " in the formation of the image. The 

 NO. 2179, VOL. 87] 



same thing is shown in a different manner more 

 fully, and still more clearly, in Lord Rayleigh's well- 

 known paper of 1896, " On the Theory of Optical 

 Images, with special reference to the Microscope." 



The special cases here dealt with are those of a 

 single luminous slit, two parallel slits, self-luminous 

 or viewed by transmitted light, and a single slit of 

 finite breadth, with or without phase difference; 

 finally, in a separate chapter the case of a grating is 

 considered, and the effect discussed of limiting the 

 image-forming rays to certain of the grating maxima. 

 In dealing with images formed by transmitted light, 

 the case of oblique illumination is also treated. The 

 source of light is supposed either at a finite or in- 

 finite distance, but, as might be anticipated, there is 

 no special discussion of the case of "critical" illu- 

 mination. Throughout, the treatment is not for a 

 circular aperture, but an aperture of special form is 

 assumed to simplify the integration. 



The main interest of the volume, however, lies in 

 the light it throws on the manner in which Abbe 

 derived his well-known theory. From this point of 

 view we must confess that we find the book a little 

 disappointing. It is not easy to agree with Prof. 

 Lummer as to the necessity, or even the desirability, 

 in this book, of devoting space to showing how far 

 the older theory is in agreement with more modern 

 views, and this is not the only feature which tends to 

 produce a sense of uncertainty as to how far the 

 account given can be regarded as a direct reproduc- 

 tion of Abbe's presentation of the subject. What 

 admirer's of Abbe's work would wish to have is a 

 close and faithful transcript of Abbe's own develop- 

 ment of the theory, with the minimum of variation 

 from the line of argument he may have followed. 

 The volume is, however, inspired by a true enthusiasm 

 for Abbe's teaching, and a just appreciation of the 

 value of his work, and the future historian of science 

 will be indebted to Prof. Lummer for the trouble he 

 has taken to present in a manner worthy of its origin 

 the material at his disposal. 



THE NUTRITION OF THE ALGM. 

 Die Erndhrung der Algen. By O. Richter. Pp. viii + 

 192. (Leipzig: Dr. W. Klinkhardt, 1911.) Price 

 1 j marks. 



SINCE the appearance in 1905 of the second part 

 of Oltmann's work on the morphology and 

 biology of the alga, so large a number of memoirs on 

 the nutrition of the algae have appeared, that Dr. 

 Richter has thought it worth while to collect them 

 into a volume for the Internationa] Review of Hydro- 

 biology and Hydrography. The references are 

 grouped under three headings— (1) the significance of 

 chemical elements and certain chemical compounds 

 in the physiology of nutrition; (2) the influence of 

 various chemical and physical factors of the nutrient 

 substratum on the form and development of the 

 algae; and (3) an appendix on the influence of tem- 

 perature and light on the algae with reference to 

 their culture. 



