February 2, 191 1] 



NATURE 



435 



him, makes all his papers stimulating in a way 

 which encourages research. His scattered hints and 

 surmises, his digressions and scholia, his occasional 

 fantastic notes, all add to the fascination of his work. 

 Thus, to take an example quite at random, he con- 

 cludes a paper on irreducible concomitants by re- 

 marking : — 



" I have always thought and felt that beyond all 

 others the algebraist, in his resarches, needs to be 

 guided by the principle of faith, so well and philo- 

 sophically defined as ' the substance of things hoped 

 for, the evidence of things unseen.'" 



This might as certainly be ascribed to Sylvester as 

 a characteristic passage of " Sartor Resartus " to 

 Carlyle. 



One of the memoirs on quantics deserves particular 

 notice; it is that which represents concomitants by 

 graphic symbols, such as those used in organic 

 chemistry. It is curious that this method, which at 

 one time engrossed Clifford as well as Sylvester, 

 should have been so barren in results. Perhaps the 

 most interesting things in the paper are Sylvester's 

 remarks on the possibilit}- of algebraic theorems 

 having corresponding propositions in chemistr\-; for 

 instance, he says, 



"Hermite's law of reciprocity . . . amounts to 

 affirming in chemical language that in any com- 

 pound an arbitrarily selected group of «i tz-adic atoms 

 may be replaced by a group of n w-adic atoms ; but 

 how far this law of replacement has objective validity 

 in the chemical sphere, I am not able to say." 



Among the arithmetical papers, of which there 

 are several, the longest, and one of the most interest- 

 ing, is that on the diophantine equation x^ + y^^Az'. 

 Although Sylvester did not reach so definite a result 

 as that stated by Lucas, he considerably extended 

 he theorems of Pepin, and the way in which he does 

 this is of a strictly elementary kind. Besides this, he 

 gives a beautiful proof of a fundamental theorem 

 connected with " residuation " of points on a cubic 

 curve; by the application of elliptic functions this 

 can be done in a line or two, but Sylvester's demon- 

 stration is far more instructive. 



Another paper of interest is that on the distribution 

 of primes, in which he extends the method of 

 Tchebicheff, while several scattered notes on partis 

 tions, Farey series, and the theory of vulgar frac- 

 tions, contain hints which may very likely admit of 

 development. 



One definite suggestion may be mentioned here 

 ic\. pp. 414-25). It is well known that Sylvester 

 proved, and generalised, Newton's rule for discriminat- 

 ing the roots of an equation j(x) = o. This rule 

 employs the coefficients of / and also those of a 

 derived function the coefficients of which are quadratic 

 in those of /. Now the question is whether there 

 may not be other derived functions, with coefficients 

 formed by some simple rule, which may settle those 

 cases in which Newton's rule is insufficient. 



The care with which Dr. Baker performs his duty 



as editor again deserves cordial recognition ; on .pp. 



357-8 the sign + in several places seems to be a 



misprint for - , and it is possible that a few other 



NO. 2153, VOL. 85] 



such mistakes may have been overlooked, but con- 

 sidering Sylvester's great inaccuracy in proof reading, 

 the correctness of the text, so far as the present 

 reviewer has been able to test it, is remarkable. 



G. B. M. 



SXTVRE-STVDY AND ROSE PESTS. 

 (i) Battersea Park as a Centre for Nature Study. By 

 W. Johnson. Pp. 128 + map. (Published under 

 the direction of the Battersea and Wandsworth 

 Educational Council.) (London : T. Fisher Unwin, 

 1910.) Price IS. net. 



(2) How to Know the Trees. By H. Irving. Pp. 

 vi+179. (London: Cassell and Co., Ltd., 1910.) 

 Price 35. 6d. net. 



(3) Rosenkrankheiten und Rosenfeinde. By Dr. 

 K. Laubert and Dr. M. Schwartz. Pp. vi + 59. 

 (Jena : Gustav Fischer, 1910.) Price i mark. 



THE pursuit of natural history observations on the 

 part of children in towns can be in man}* ways 

 more profitably directed in parks than in the open 

 countn.-, at any rate until such time as the children learn 

 how and what to note. Proximity to the schools, the 

 aggregation of many features within a small area, and 

 opportunities for repeated visits all favour the sys- 

 tematic use of advantages offered by the London public 

 parks. The chief opportunities for study in Battersea 

 Park (i) are provided by the birds, both wild and cage- 

 bound, insects, wild flowers, and trees. These themes 

 are well elaborated by Mr. Johnson with a knowledge 

 arising out of intimate acquaintance. In addition, 

 there are chapters on history, geography, and set sub- 

 jects for rambles, while other facts are collated in 

 the outline calendar, and a map serves for general 

 purposes, as well as for indicating the positions of 

 the large trees. The volume represents an effective 

 triple cooperation of an observant author, a well-, 

 guided educational council, and an interested pub- 

 lisher. 



Although numerous books on trees are extant, 

 it is doubtful whether any one of modest dimen- 

 sions describes more precisely the ever-changing 

 appearances and distinctive features of the trees 

 than the volume provided by Mr. Ining (2). 

 •About sixty different kinds are described, some 

 very brieflj', when they are closely allied plants, 

 as the various pines, others, as the ash, at 

 great length, but in all cases full indications are 

 furnished of distinguishing characters. The illustra- 

 tions have appeared before, but they are so excellent 

 that they bear repetition. The author introduces but 

 few technical words, even to the extent of leaving out 

 the scientific names of the trees ; in the case of the 

 Himalayan pine the scientific name is required for 

 purposes of identification, and, generally speaking, 

 they are desirable. The book can be thoroughly 

 recommended. 



In the volume on rose pests (3) Dr. Laubert deals 

 with fungi, and distinguishes seven definite diseases. 

 Rust, mildew, canker, and leaf blotch are the com- 

 monest, to which are added rot mould (Perotiospora 

 sparsae), a root disease {Roesleria sp.), and a Botry- 

 tis rot (Sclerotinia Fuckeliana). Two other diseases 



