412 



NATURE 



[March 3, 1892 



In reviewing the work there are two parts to be noticed, 

 and two points of view from which to criticize them : the 

 first fifty pages or so are concerned with a general 

 popular account of the morphology of Fungi in the wider 

 sense, while the remainder is devoted to the setting forth 

 of the British genera and species (so far as they have 

 been worked up) of the two groups specially dealt with. 



The general account must strike a careful reader as not 

 only exhibiting a good deal of knowledge on the part of 

 a writer who is wishful to put it at the disposal of all who 

 care for it, and in a pleasant style ; but also as showing 

 what enormous advances have been made in the popular 

 exposition of these matters within the last few years. 

 When we look back to the systematic books on Fungi of 

 ten to fifteen years ago, they appear hopelessly dry and 

 uninteresting ; whereas here we have a compact, neat 

 little volume, with a store of interesting information 

 thrown in as an introduction to the more serious detailed 

 work which follows. 



We do not mean to say that this part of the book is 

 without mistakes or slips, either of fact {e.g. the state- 

 ment on p. 49 regarding mutualism between Fungi and 

 Phanerogams) or judgment {e.g. the reference to 

 "phanerogamic Fungi" on p. ii). Moreover, there are 

 evidences of careless proof-reading, as at the foot of 

 pp. 41 and 42. But it is far more easy to pick small 

 holes in a book like this than to do proper justice to 

 what is good and useful in it ; and we prefer to dwell on 

 the more important positive points, than to emphasize 

 the fewer and more trivial drawbacks. 



The more purely systematic part of the work shows 

 evidence of careful and conscientious industry, suggesting 

 constant reference on the part of the author to type- 

 specimens and authorities. Of course, it is not so inter- 

 esting to the general reader, but the diagnoses are so 

 clear, and so simply written, that we think any amateur 

 ought to be able to follow them with the object in hand ; 

 as for professional mycologists, they will probably wonder 

 that it could all be put so plainly — at the same time, they 

 will suspect something is wrong with the German refer- 

 ence on p. 162, ajid will probably remark on the chapter 

 on " Fossil Fungi." They may also inquire why Ustila- 

 ginecB are taken with Phycoviycetes. The author answers 

 this question on p. i6o : he follows Brefeld in regarding 

 Protomycetes as linking the two groups. The somewhat 

 antiquated method of obtaining sections, on p. 62, had 

 better have been omitted. 



The most interesting points to the systematists will be 

 Mr. Massee's almost consistent alterations of Plowright's 

 authorities for the species of the Ustilaginece, and his 

 addition of one or two new ones — e.g. L stilago salveii 

 (p. 177), Doassansia comari (p. 198), and Protomyces 

 purpureo-tingetis (p. 164) ; they will also notice the fusion 

 of some species kept a(jart by Plowright — e.g. on pp. 178 

 and 186 — and the separation of the two species of Tuber- 

 ciftia, on pp. 203 and 204. 



We note, also, that Massee has altered the name of 

 Trail's Entyloina matricaria; to E. Trailii, possibly on 

 good grounds ; but we think it a mistake to use such 

 specific names, here and elsewhere, seeing how much 

 Fungi are in need of useful distinctive appellations. 



The figures on the six plates are fairly well drawn 

 and selected, and the references to them are useful and 

 NO. T 166, VOL. 45] 



to the point. We have not tested the indices in detail^ 

 but they are very well planned, and appear to be accurate. 

 On the whole, and without being blind to its faults, we 

 think this little book should be welcomed as a useful 

 manual on the subject, and should certainly be in the 

 hands of students of botany who wish to know something 

 of British mycology. 



OUR BOOK SHELF. 

 A Treatise on the Geometry of the Circle., and some 

 Extensions to Conic Sections by the Method of Re- 

 ciprocation. With numerous Examples. By W. J. 

 M'Clelland, M.A. (London: Macmillan, 1891.) 

 This is a full book, written on the lines which previous 

 works by Irish mathematicians have made familiar to 

 us. The author acknowledges his indebtedness to the 

 writings of Mulcahy, Salmon, and Townsend. He has 

 also freely consulted the similar works by Cremona and 

 Catalan, and in his treatment of the recent geometry has 

 in many cases gone to the fountain-head in the memoirs 

 of Brocard, Neuberg, and Tarry. Though in parts pro- 

 ceeding on parallel Imes with Casey's " Sequel," there is 

 a good deal of other matter not to be found in that work. 

 The writer's object is to give a concise statement of those 

 propositions which he considers to be of fundamental 

 importance, and to supply numerous illustrative examples. 

 Many of the exercises are worked out in an elegant 

 manner, and to the major part of the others useful hints 

 are given. Chapter i. is introductory ; chapter ii., in four 

 sections, is devoted to " Maximum and Minimum " ; 

 chapter iii., also in four sections, rapidly touches upon 

 " Recent Geometry" ; chapter iv. discusses the general 

 theory of the mean centre of a system of points ; and 

 chapter v. treats of collinear points and concurrent lines. 

 Chapters vi., vii., and viii. are concerned with inverse 

 points with respect to a circle, poles and polars (with 

 respect to a circle), and coaxal circles. In these chapters 

 will be found ample food for the student. Chapter ix. 

 gives an account of the theory of similar figures, and 

 here we specially notice the sketch of Neuberg's and 

 Tarry's researches on three similar figures. Circles of 

 similitude and of antisimilitude form the subject of 

 chapter x. Here some interesting problems are solved. 

 Inversion (chapter xi.), general theory of anharmonic 

 section (chapter xii.), involution (chapter xiii.), and double 

 points (chapter xiv.) close what must unhesitatingly be 

 called a varied and ample menu. The work, being con- 

 fessedly to a great extent elementary, of course brings 

 before the reader much that is old ; there is, however, 

 novelty in the treatment and also in the matter. There 

 is one feature we have omitted to mention, to which Mr. 

 M'Clelland draws attention, and that is the application of 

 reciprocation to many of the best known theorems by 

 means of which the corresponding properties of the conic 

 are ascertained. To go through all the examples would 

 occupy more time than we can spare, but we have 

 dipped into all parts and brought up good results. In 

 the text we have noted one slip: p. 60, I. 12 up should 

 be TT— B. No doubt we have omitted to mark other 

 errata. The figures, which are white lines on a black 

 block, carry our thoughts back to old Cambridge days, 

 when we turned over the pages of our Miller's " Hydro- 

 statics." The geometer will find much to interest him in 

 Mr. M'Clelland's work. 



Kalm\i Account of his Visit to England on his Way 

 to America in 1748. Translated by Joseph Lucas. 

 (London: Macmillan and Co., 1892.) 

 Kalm was a well-known Swedish botanist and economist 

 of the eighteenth century. In 1747 he became Professor 

 of Economy at Abo, and in the same year the Swedish 



