58o 



NATURE [July 7, 192 1 



psycho-physics. Weber's law was the first 

 definite discovery of the fact on which the quan- 

 tum theory rests. He discovered that in sensible 

 experience changes are not continuous — that is, do 

 not correspond to the continuity of the changes of 

 the physical stimulus, but occur in discrete 

 quanta. He was a parallelist, and thought that 

 changes in the physical environment were con- 

 comitant with changes in sensation. He never 

 Suspected, probably would have found it difficult 

 to conceive, that changes in the physical world 

 are discrete. Planck's quantum theory is the 

 discovery that the same fact which Weber found 

 to characterise the psychical world characterises 

 the physical world; that energy is emitted, not 

 continuously, but in discrete quanta; that, as 

 Lord Haldane says, we may even have to regard 

 space as a discrete manifold. This comparison 

 is not a fanciful notion, nor purely imaginary. 

 The whole problem was discussed by Henri 

 Poincar^ in " Science et Hypothfese " before 

 Planck's discovery. Poincar^ cites Weber's law 

 ^s actual proof that the concept of mathematical 

 continuity is only a postulate, declares that it is 

 unverifiable, and suggests that it may be dis- 

 proved or superseded. This is peculiarly signifi- 

 cant in regard to Lord Haldane 's concept of the 

 fconcrete universal, the concept that reality is rela- 

 tive to the character of knowledge. 



The practical gain in such a concept when we 

 are dealing with biology and with the mental 

 sciences is the topic of chap. vi. of the book. The 

 most striking thing about the new scientific 

 revolution is the havoc it is making of the once 

 unchallengeable and universally accepted notions 

 at the basis of the purely mathematical sciences. 

 It is not, for example, Newton's law of inertia, 

 primarily and mainly based on empirical observa- 

 tion, which is suspect. It is the much more 

 fundamental law, the law of the equivalence of 

 action and reaction, a purely rational principle, 

 which seems now to be on its trial. The whole 

 direction of scientific speculation in the nineteenth 

 century was towards the conscious goal of me- 

 chanical interpretation. Scientific advance was 

 practically identified with the confident anticipa- 

 tion that all the biological and mental sciences, 

 even including such purely human interests as 

 art and religion, would be mechanistically ex- 

 plained. The new spirit ahd the new direction in 

 scientific speculation at least recognise that the 

 abstract can never comprehend the concrete; and 

 this recognition more than anything else is bring- 

 ing about the rapprochement between science and 

 philosophy, so long and so unreasonably 

 estranged. H. Wildon Carr. 



NO. 2697, VOL. 107] 



A New Book on Cactaceae. 



The Cactaceae. By N. L. Britton and J. N. 

 Rose. Vol. ii. (Publication No. 248.) Pp. vii + 

 239 + 40 plates. (Washington: The Carnegie 

 Institution of Washington, 1920.) 



ALL cultivators of cacti and all botanists who 

 are interested in this remarkable family of 

 plants will feel satisfaction in knowing that at 

 last we have in the English language a standard 

 up-to-date monograph of the natural order Cac- 

 taceae, which is universally recognised as being 

 the most difficult of all flowering plants to study. 

 With the exception of a few scattered but excel- 

 lent papers upon them by Drs. Britton and Rose, 

 Dr. Engelman, and Berger, this is the first 

 work in the English language that gives a com- 

 plete account of the order as we know it to-day. 

 This fine book is so excellently planned and so 

 fully illustrated as to be a long way in advance 

 of the very unsatisfactory German works that 

 have hitherto held the field, and will be found to 

 be a real boon to all who study these plants. 



From the introduction to the first volume (a 

 notice of which was published in Nature for Sep- 

 tember II, 1919) we learn that Drs. Britton and 

 Rose at first intended to monograph only the 

 Cactaceae of North America, but, happily, upon 

 a proposal made by Dr. D. T. MacDugal, the 

 plan was extended to include the whole of the 

 family. Extensive preparations were made and a 

 large army of workers was enlisted to collect and 

 photograph the species in their native habitats, 

 the result being that the authors have had at their 

 disposal a larger amount of living and other 

 material, accompanied by field-notes, drawings, 

 etc., than any other students of this group have 

 ever been able to obtain. As the types (when 

 existing) of the older as well as of modern 

 species have also been consulted, the authors have 

 been able to detect and correct many errors of 

 determination that are found in existing mono- 

 graphs. 



Vol. ii. is of quarto size, well printed and pro- 

 fusely illustrated with photographs, drawings, and 

 coloured plates, which, it is a pleasure to note, 

 are nearly all originals. There are good keys to 

 the tribes, subtribes, genera, and species, so that, 

 taking into ' account the aid afforded by the 

 figures, there should be no great difficulty in 

 naming cultivated specimens when in flower. 



Each tribe, subtribe, and genus is separately 

 characterised, and the type of each genus indi- 

 cated. Under each species the synonyms, with 

 the date of their publication, a description, men- 



