I/O 



NA TURE 



[June 25, 1896 



naturalist at one end of his master's kitchen table, " whilst 

 the housekeeper was occupied at the other end with the 

 several processes of providing the day's dinner." At the 

 age of seventeen, Williamson wrote an important memoir 

 on a tumulus near Gristhorpe Bay, which called forth a 

 letter from Prof. Buckland praising the article, and 

 prophesying that the author's name would " figure in the 

 annals of British science." Passing from these early days 

 of youthful enthusiasm and the pursuit of natural his- 

 tory in all its branches, and over many years of activity 

 in zoological and ^medical work, we come to the latter 

 part of Williamson's career. The memoirs on the Coal- 

 measure plants, published in the Philosopliica! Trans- 

 actions, between the years 1S70 and 1893, furnish a 

 splendid record of original work, which will always rank 

 among the most important additions to botanical know- 

 ledge during the later decades of the present century. It 

 would be difficult to find a more striking illustration of 

 the continuance of vigorous industry, and the power of 

 adaptability to modern methods, than is aflforded by the 

 pateobotanical writings of a man whose early days were 

 spent before modern science began. 



Did space permit, one might quote numerous passages 

 in which recollections are given of the "sober-minded 

 quaker John Ualton," and of the first meeting with Joule, 

 "a young and extremely unassuming man." The auto- 

 biography gives us an epitome of the advance of scien- 

 tific thought during the present century, with the added 

 charm and freshness of a persona! history of the almost 

 ideal scientific career of a genuine naturalist. " Writing 

 these reminiscences of his life's work, was one of the 

 pleasures of Dr. Williamson's later years " ; and we are 

 grateful to Mrs. Williamson forgiving us the opportunity 

 of sharing the enjoyment of so fascinating a retrospect. 



It is a matter of regret that Dr. Williamson's name 

 does not appear in the title of the book ; it would have 

 afibrded a better index to the interesting contents. 



A. C. S. 



OUR BOOK SHELF. 

 Die Protrophie, eine neus lebensgeineinschaft in ihren 



auffcilligsten erscheinungen. Von Arthur Minks. 



(Berlin: Friedlander and Sohn, 1896.) 

 Dr. Minks is already well known as the author of several 

 treatises on the biology and morphology of Lichens, in 

 each of which the ideas set forth are quite original, and 

 at the same time directly opposed to modern views 

 regarding the structure presented by this group of plants. 

 The present contribution must be considered as part iii. 

 of "Contributions to a knowledge of the structure and 

 life of Lichens," of which the previous parts appeared in 

 an Austrian scientific publication (A'. A', zool.-bot. Gesell. 

 zu IVieu). The present, preceded by a digest of the 

 leading ideas embodied {Oestcr. Hot. Zeitschr., 1896, 

 p. 50) appears as an independent publication. The 

 previo'us parts contain, amongst other new views, the 

 ptatement that many species considered as valid by 

 slichenologists, are the outcome of parasitism between 

 two or more originally distinct species, the product being 

 a pseudo-species, diflering in structure and general 

 appearance from the species concerned in its production. 

 In the book under consideration, the contents of which 

 could not be understood without a knowledge of the 

 author's previous views and theories, we are introduced 

 to a second method which, as before, results in the 



NO. I 39 1, VOL. 54] 



wholesale production of what may be termed pseudo- 

 species, due to the intermingling and gradual changing 

 of the layers of the thallus. This change is said to be due 

 to " Protrophie" ; a statement which must be accepted 

 in good faith. The definition given would be next to 

 meaningless in English, hence it is offered in the original 

 language. 



" Ich erachte es fiir statthaft, die Unselbststiindigkeit, 

 die nur den Anfang des Lebens betrifft, daher auch nur 

 fiir diese Zeit der schiitzenden und unterstutzenden 

 Flechte zur Einleitung und .Sicherung von dessen 

 hauptsiichlicher Dauer in aller Selbststandigkeit bedarf, 

 unter Protrophie zu begreifen und die dazu bestimmten 

 Flechten als Lichenes protrophici zu bezeichnen." 



The most remarkable circumstance in connection with 

 these supposed discoveries is the fact that the author 

 was enabled to utilise herbarium specimens for his re- 

 searches, and had not to resort to the more laborious and 

 exact method of pure cultures. G. M.assee. 



Matliematical Pcxpers read at tlie International Matlte- 



matical Congress held in connection ivitli the World's 



Columbian Exposition, Chicago, 1893. (New York : 



Macmillan and Co.) 

 This book, which is an excellent specimen of mathe- 

 matical printing^, constitutes vol. i. of " Papers published 

 by the American Mathematical Society." The 400 pages 

 contain thirty-nine papers. German and American 

 mathematicians are the largest contributors ; there are a 

 few pages from France, Italy, Austria and Russia also, 

 but the mathematicians of England are not represented. 

 Papers of great interest are given by Dr. Schdnflies, 

 " Gruppentheorie und Krystallographie" ; by Dr. Heinrich 

 Burkhardt, " Ueber einige mathematische Resultate 

 neuerer astronomischer Unsuchungen, insbesondere iiber 

 irregulare Integrate linearer DitYerentialgleichungen " : 

 by M. Maurice d'Ocagne, " Nomographic : sur les 

 Equations representables par trois syst^mes rectiligues de 

 points isoplcthes" ; by E. H. Moore, "A doubly infinite 

 system of simple groups." Prof. Felix Klein, of Gottingen, 

 whose work at the Congress has been already published 

 in a separate volume, is only represented here by two 

 short communications, one on " The Present State of 

 Mathematics," the other on "The Development of the 

 Theory of Groups during the last Twenty Years." They 

 are of the nature of lightning sketches by a master 

 hand. 



The book is an evidence of the formation, gradual but 

 sure, of an American school of mathematicians which, at 

 first mainly inspired by Cayley and Syhester, appears 

 now to be coming under the influence, principally, of 

 modern German methods. 



Modern Optical Instruments and their Construction. 



By Henry Orford. Pp. 100. (London : Whittaker 



and Co., 1896.) 

 When a book bearing the title " Modern Optical 

 Instruments" is found to contain nothing about the 

 telescope, merely a reference to the microscope, and but 

 two pages on the spectroscope, it is the duty of a 

 reviewer to declare that the volume is not what it pre- 

 tends to be. The contents belong almost entirely to 

 ophthalmoscopy ; that is to say, to the determination of 

 optical defects by means of the opthal.moscope, and the 

 amelioration of them by means of spectacles. There 

 are, in addition, brief chapters on stereoscopic projection 

 and the optical lantern. As a short work on these 

 matters, the book is not altogether bad (though the 

 illustrations are very coarsej, and opticians may find 

 interest in parts of it. But to say the book is "a descrip- 

 tion of a itw of what may safely be termed the more 

 popular optical instruments in use," and to give it the 

 title it has, is to court adverse criticism. 



The book as published contains two-thirds text and 

 one-third advertisement. 



