September lo, 1896] 



NATURE 



435 



We have not, of course, made use of this new volume 

 practically ; but from what we see of it, we should, with- 

 ojt hesitation, recommend it to any person beginning the 

 delightful study of mosses as the most likely of all those 

 within our knowledge to suit his needs. E. F. 



OUR BOOK SHELF. 

 Catalogue of the Described Diptcra from South Asia. 

 By F. M. Van der Wulp. 8vo. Pp. 220. Published 

 by the Dutch Entomological Society. (The Hague : 

 M. Nijhoff, i8g6.) 

 Comparatively few entomologists interest then)selves in 

 Diptern, and therefore the number of species of the order 

 enumerated in the present catalogue is only 2889, and 

 doubtless represents only a small percentage of those 

 actually existing in the rich fauna which it samples ; 

 for the Diptcra. are probably the third most numerous 

 order of insects, surpassed only, according to the 

 indications of our present knowledge, by the Hymcn- 

 optcra and Colcoptera in the total number of species 

 which they may be expected to include. Prof Van der 

 Wulp is recognised as one of our first living authorities 

 on Diptcra, and his work will prove of great use to 

 specialists, especially as M. Bigot's " Catalogue of the 

 Diptcra of the Oriental Region," published in ihejoitriial 

 of the Asiatic Society of Bengal for 1S91 and 1892, is 

 both imperfect and inaccurate. The introductory part 

 of the work is written in English, and includes a " Review 

 of the Literature of Oriental DipterologA'" and a biblio- 

 graphical list of books and papers consulted. There is 

 also a table of contents at the beginning, and an index 

 of families and genera at the end. We cannot have too 

 many books of this description ; for although the number 

 of undescribed species of insects is enormous, it is per- 

 haps even more important to attempt to keep pace with 

 the rapidly-accumulating mass of descriptive matter by 

 means of carefully compiled monographs and synonymic 

 reference catalogues, than to confine our energies to piling 

 up additional descriptions by the hundred or the thousand. 



W. F. K. 



History of Modern Mathematics. By David E. Smith. 



(London : Chapman and Hall, Ltd., 1896.) 

 " HiGHKR Mathematics," edited by Mansfield Merriman 

 and Robert S. Woodward, is a text-book for classical and 

 engineering colleges, and is a work containing 600 pages. 

 Each chapter is written by a different author, and is de- 

 voted to some special branch of mathematics ; chapters i., 

 ii., iii., iS:c., dealing with solutions of equations, determin- 

 ants, and projective geometry respectively. The eleventh 

 and last chapter, a reprint of which we have before us, 

 is written by Mr. David E. Smith, of the Michigan State 

 Normal School, and deals with the " history of modern 

 mathematics." Of course it has not been intended here 

 to give a complete history of modern work, but just a 

 sufficient survey of the whole domain to give a student 

 an intelligent idea of the way in which the more recent 

 advances have been made, and the ends gained thereby. 

 Each mathematician has, as a rule, his own speciality ; 

 but each of these is one link in the chain which, when 

 put together, forms the whole. Such a history as Mr. 

 Smith gives here fulfils this point, and its shortness and 

 conciseness will be favourable to students of mathematics. 

 The text is increased in value by the numerous foot- 

 notes, and a short bibliography is given at the end ; this 

 latter is, however, by no means complete, as the author 

 remarks, but he gives references for those who wish to 

 go further afield. For a biographical table of mathe- 

 maticians he refers to Fink's " Geschichte der IVIathe- 

 niatik," p. 240, and for the names and positions of living 

 mathematicians to the " Jahrbuch der Gelehrten Welt," 

 published at Strassburg. 



NO. 1402, VOL. 54] 



Graphical Calculus. By Arthur H. Barker. (London : 



Longmans, Green, and Co., 1896.) 

 A VERY timely book ; and useful to instructors in the 

 elements of the subject in providing a number of apt and 

 eloquent illustrations of fundamental ideas. It represents 

 a series of lectures addressed to engineering students, 

 liable to be repelled by pure abstractions, and preferring 

 concrete representations in which their ideas can take 

 root ; a complete contrast to the ordinary mathematical 

 te.xt-book of the school of Todhunter. The author should 

 point out that the gradient of i in 100 (p. 13) means an 

 angle whose tangent is o'oi only in the indoor mode of 

 reckoning on a plane ; but that in construction of the rail- 

 way, the angle is made with a sine of o'oi ; the two> 

 modes of measurement are indistinguishable practically. 



Integration is introduced simultaneously with differen- 

 tiation, as in many respects a simpler idea to grasp ; we 

 can realise the growth of a tree at the end of a year, 

 although the rate of growth is imperceptible. Our 

 ordinary mathematical text-books make the mistake of 

 keeping integration in the background too long. G. 



LETTERS TO THE EDITOR. 



{The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he iindertalte 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonymous communications.'^ 



The Utility of Specific Characters. 



I MUST confess to still feeling some difficulty in understanding 

 my friend Prof. Lankester's position, notwithstanding his ex- 

 planations. 



The correlation principle was arrived at by Mr. Darwin after 

 a careful examination of a large body of facts. I quote the 

 carefully considered words in which he sums up his conclusions ; — 



"Correlation is an important subject ; for with species, and 

 in a lesser degree with domestic races, we continually find that 

 certain parts have been greatly modified to serve some useful 

 purpose ; but we almost invariably find that other parts have 

 likewise been more or less modified, without our being able to 

 discover any advantage in the change. No doubt great caution 

 is necessary in coming to this conclusion, for it is difficult to 

 overrate our ignorance on the use of various parts of the organ- 

 isation ; but, from what we have now seen, we may believe that 

 many modifications are of no direct service, having arisen in 

 correlation with other and useful changes." ("Animals and 

 Plants under Domestication," vol. ii. pp. 354-5-) 



It does not appear to me that there is anything in this which 

 conflicts with the doctrine of the " utility of specific characters." 

 The non-useful parts of the correlated chain (if any) are sus- 

 tained by the useful, and the w/wle seems to me part of the 

 "specific character." If Prof Lankester had no other object 

 but to call attention to Mr. Darwin's correlation principle, I 

 think this was a little superfluous, for it is part of the mere 

 grammar of Darwinism. 



But the point of his speech at the Linnean Society, and of 

 the subsequent account he gave of it in Nature, appeared to 

 me to go a good deal beyond this, and to be of considerable 

 interest and importance. 



In the cases cited by Mr. Darwin, the correlated structures 

 are almost all, to use Prof. Lankester's words, "obvious and 

 measurable." This we would expect in the correlated varia- 

 tion of homologous parts on which Mr. Darwin lays such stress, 

 and which form the bulk of the instances which he gives. 



Prof Lankester's "suggestion" was that "obvious species 

 marks may be only superficial and non-significant phenomena 

 correlated . . . with other less obvious but really important 

 life-saving peculiarities, which might well escape the observation 

 of the describer of specific characters." He then adduces 

 Wells's theory as " a case which seemed to [him] most striking 

 and suggestive in connection with the utility of specific 

 characters." And so I think it is. I ventured to express an 

 opinion that if established it would prove very damaging to, at 

 any rate, the universatility of that doctrine. I certainly sup- 

 posed that that was Prof. Lankester's object in bringing it 

 forward. 



