December io, 1891J 



NATURE 



125 



in conjunction with his wife, both in western and eastern 

 tropical Africa, and his modest volumes on Angola and 

 the River Congo, dedicated to his partner in the pleasures 

 and dangers of life in a tropical climate, and his zealous 

 aid in the collecting of objects of natural history. He was 

 one of the three almost contemporaneous discoverers of 

 that very remarkable plant the Welwitschia inirabilis — 

 the others being Welwitsch and Baines ; and he sent 

 some of the finest specimens of it in existence to this 

 country. 



After the loss of her husband. Mrs. Monteiro returned 

 to Delagoa Bay, and spent five years in solitude, in the 

 cottage built for her under happier circumstances, 

 devoting her time to collecting insects, birds, and other 

 natural objects, and studying the life history of insects 

 and their relations to plants. The present book is an 

 unpretentious narrative of her life and labours during that 

 period, and a record of her observations and her experi- 

 ments in breeding insects, illustrated with some of her 

 own discoveries in the animal and vegetable kingdoms. 



A Hand-book of Industrial Orgaiiic Chemistry. By Samuel 

 P. Sadtler, Ph.D. (Philadelphia: J. B. Lippincott 

 Company, 1891.) 



In this book Prof. Sadtler has attempted to compress into 

 about 500 octavo pages an account of those manufactures 

 which depend upon the applications of organic chemistry. 

 For what particular class of readers such a book is in- 

 tended is rather difficult to determine. The scientific man 

 is hardly likely to consult it in preference to the numerous 

 special manuals to which he has access ; and to the manu- 

 facturer the book is practically useless, owing to the com- 

 parative absence of all working detail. Considering the 

 volume of literature which is required to give an approxi- 

 mately adequate representation of one industry alone^ 

 viz. the tar-colour manufacture — it would seem hopeless 

 to expect anything of value from a chapter on the arti- 

 ficial colouring-matters, which, in well-leaded "roman 

 spaced," attempts to give in 45 pages an account of 

 the production and chemical nature of the numerous 

 artificial and natural organic colouring-matters used in 

 the arts, including their identification, chemical analysis, 

 and detection on dyed fabrics. Certain of the other sub- 

 jects are, it must be stated in fairness, treated. with greater 

 detail ; and, as we should expect from Dr. Sadtler's con- 

 nectionas an expert with the mineral oil industry, his de- 

 scription of the manufacture of petroleumand its associated 

 products is reasonably complete. So also is the account of 

 the cane-sugar industry. But, with the exception of the 

 bibliographical and statistical information which occupies 

 a relatively large share of the space devoted to each article, 

 we see little else to commend. The book, hdwever, is 

 well got up ; the paper and printing are all that can be 

 desired, and the illustrations are, as a rule, much better 

 executed than is usual in works of this class. 



Progressive Mathematical Exercises. First Series. By 

 A. T. Richardson. (London : Macmillan and Co., 

 1891.) 



The examples contained in this book are of the most 

 elementary nature, and are intended for the use of 

 those who have got no further than quadratic equations. 

 In this series the exercises only deal with arithmetic 

 and algebra, and are arranged in sets of papers which 

 gradually become more difficult. The examples in arith- 

 metic commence by dealing with the first four rules, 

 simple and compound, and fractions ; while those in 

 algebra consist mostly of numerical values, addition and 

 subtraction. Cube root and compound interest in arith- 

 metic, and quadratic equations in algebra, form the highest 

 limit to which these subjects are carried in this series. 

 Throughout the work the author seems to have paid 

 great care to insure accuracy in the answers ; and 



NO. I I 54. VOL. 45] 



though we have worked out many problems, picked out 

 at random, we failed to find any errors. 



We may mention that, in working through the papers, 

 the beginner will occasionally come across examples 

 which appear to be far above the average standard ; but 

 these, on trial, will always be found very simple, and are 

 placed there with the intention of encouraging boys to 

 look up methods they have not reached, and so to find 

 that " a little research enables them to do a new sort of 

 question." 



Teachers and taught alike should find this book a 

 useful adjunct to the text-book thev have in use. W. 



LETTERS TO THE EDITOR. 



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

 pressed by his correspondents. Neither can he undertake 

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

 manuscripts intended for this or any other pari of ^\t:vr.il. 

 No notice is taken of anonymous communications. 1 



The Implications of Science. 



It would be a great misfortune if such views as were expressed 

 by Dr. St. George Mivart in a lecture delivered under the segis 

 of the Royal Institution, and reported at length in your columns 

 (pp. 60 and 82), were allowed to pass unchallenged. In case no 

 abler challenger appears, will you allow me to say a few words 

 about "the implications of science"? 



The great objection I take to Dr. Mivart's view is, that he 

 does not appear to recognize any distinction between a real and 

 a verbal truth. He apparently puts our knowledge of "the 

 law of contradiction " into precisely the same category as our 

 knowledge of "our own continuous existence," and draws but 

 a slight distinction between these items of knowledge and such 

 an item as the law of gravitation. Whereas, in fact, the so- 

 called "law of contradiction" is not a necessary truth at all, it 

 only expresses a verbal convention. It is not a law, but is of 

 the nature of a definition. On the other hand, our knowledge 

 of our own existence, in the present, comes to us by direct ap- 

 prehension, and really is a "necessary truth" to each of us 

 individually ; though, since our knowledge of our existence in 

 the past depends on the accuracy of our memories, this latter 

 may easily be erroneous. That the memory exists is of course 

 indisputable, buf it may well be that the fact it professes to 

 recall either took place differently, or even did not take place 

 at all. Our confidence in our memories depends upon induction 

 — ultimately on inductio per enumerationem simplicem — in just 

 the same way as our belief in the law of gravitation does, and 

 neither of these items of knowledge can therefore be necessary 

 truths, though we may well hold them with so strong a convic- 

 tion that the distinction may for practical purposes be ignored. 



The "implications of science " which Dr. Mivart insists on 

 are nearly all truisms (that is, purely verbal assertions) — all 

 those to which he ascribes universal validity in any regions of 

 time or space are such. I may repeat here what I have said 

 elsewhere : " The supposed peculiar certainty of mathematical 

 conclusions is solely due io the fact that they are truisms.'" 



For example, the assertion " Two straight hnes cannot inclose 

 a space " is certainly not a " necessary truth." Either its terms 

 are defined by connotation, so that its truth depends .solely on 

 those definitions, or else its terms are defined by denotation, as 

 representing real things in space, and the truth of the assertion 

 can only be proved by induction from actual experience with 

 those things. In the first case the truth is arbitrary, not neces 

 sary ; and in the second case it might conceivably be false, 

 as was shown by Helmholtz. It is of course true that the 

 imaginary dwellers on a sphere might still conceive what we call 

 "straight lines," but if they chose to reserve that term for 

 geodesies of their space they would be within their rights in 

 doing so. This is practically what Euclid does, and this is why 

 he requires "axioms" which are not necessary truths; even 

 though, in fact, they are true as far as we can test them. 



So also there is no useful sense in saying that twice two must 

 be ecjual to four under any conditions of time or space. Doubt- 

 less, i/the inhabitants of the Dog Star defined "twice," "two," 

 and "four "as we do, then "twice two" would to them be 

 "four": but to say that it was so could only give verbal in- 



