i8o 



NATURE 



[yan. 8, 1874 



place, they are not algebraic functions ; and, besides this, 

 the student is unlikely to form an adequate comprehen- 

 sion of their purpose, or to appreciate the importance of 

 acquiring skill in the use of his tables if he takes them 

 up in the course of a study to which they have no appli- 

 cation. If logarithms must needs be combined with any 

 other branch of mathematics, their true alliance, on 

 grounds both theoretical and practical, is not with algebra 

 but with trigonometry." In point of fact, logarithms are 

 usually included in works on trigonometry ; and we can 

 see no reason why their principle should not also be ex- 

 plained, as at present, in treatises on algebra, to which 

 the theory does really belong. Ordinary students of 

 mathematics never learn to use logarithms properly, not 

 so much owing to deficiency of explanation in the exist- 

 ing works as to the fact that they never meet in the course 

 of their reading with anything requiring such a know- 

 ledo'e. Prof. Peirce's work contains 82 small octavo 

 pages, and is intended for readers possessed of only a 

 very trifling knowledge of algebra. It is simply what a 

 chapter on logarithms in an ordinary algebra would become 

 if printed separately, with the addition of copious ex- 

 amples and an appendix on their use in trigonometry. 

 To show how limited is the range of the book, it is only 

 necessary to state that all the rules have reference merely 

 to three and four figure tables, and that the natural base e 

 is not even alluded to, though it is stated that a chapter 

 on the Napierian system will be added in another edition. 

 There is little either to commend or blame in the book. 

 It is partly intended for the entrance examination at Har- 

 vard, but it seems to us it would be most useful to com- 

 puters who wished to obtain some notion of the reason 

 for the rules they were in the habit of employing. In 

 one respect the book is in advance of the time, viz., some 

 paragraphs are devoted to the history of the subject. 

 We believe the day will come when no scientific treatise 

 will be considered complete that does not contain short 

 historical notices relative to the discovery of the principal 

 results. 



Prof. Peirce defines the arithmetical complement as 

 the complement from 10 ; we should much prefer to see 

 it defined as the complement from zero, so that the arith- 

 metical complement of a logarithm of a number should 

 be the logarithm of the reciprocal of the number, viz. its 

 cologarithm. We also hope the day will come when the 

 addition of 10 to the mantissa; in our logarithmic trigono- 

 metrical canons will be abandoned, and the true negative 

 characteristics printed and used. A complete seven-figure 

 table with negative mantissa; was published at Paris by 

 M. J. Dupuis in 186S, which was a step in this direction. 



PEDIGREE AND RELATIONSHIP OF MAN 

 The Story of the Earth and Man. By J. W. Dawson, 



LL.D., F.R.S. (Hodder and Stoughton.) 

 Man and Apes. By St. George Mivart. (Hardwicke.) 



THESE two works possess some points in common. 

 Neither of their authors accept Darwinism in its 

 entirety, the former absolutely rejecting it. They both 

 treat of the relations of man to the lower animals, and 

 both find the chasm of the human mental and moral 

 phenomena the great drawback against bringing man 

 into the same category with the apes. The manner in 



which the subject is treated, and the facts employed, are 

 however not the same, while the results arrived at are 

 very different, as will be seen from the following remarks. 



Dr. Dawson is very much irritated by the manner in 

 which many of the biologists of the present day, without 

 feeling any necessity for giving the reasons for their 

 belief, are in the habit of writing and talking as if the 

 evolution hypothesis were fully proved, and established 

 as a fundamental principle of nature. " That in our day 

 a system destitute of any shadow of proof, and supported 

 merely by vague analogies and figures of speech, and by 

 the arbitrary and artificial coherence of its own parts, 

 should be accepted as a philosophy, and should find able 

 adherents to string upon its thread of hypotheses our vast 

 and weighty stores of knowledge, is surpassingly strange,' 

 remarks our author in a spirit which we are surprised 

 to meet in one who thinks that " in the present state 

 of natural science in Britain this evil (of regarding geo- 

 logic facts from an evolutionary point of view) is to be 

 remedied only by providing a wider and deeper culture 

 for our young men." In the same dogmatic and un- 

 scientific spirit all the theoretical questions which are 

 discussed, are written for the perusal of the readers of a 

 popular journal, and such being the case, it is hardly sur- 

 prising that false notions are so common as to the direct 

 bearing and tendency of the greatest theory of modern 

 times. 



" We need not stop to mention the usual inaccuracies 

 as to facts" is the way in which a criticism of a paragraph 

 in one of Mr. Herbert Spencer's works is commenced, 

 and as might be almost predicted from so self-satisfied an 

 author, it is in the criticism only in which the inaccuracy is to 

 be found. On the following leaf we are astonished to learn 

 with reference to the Ascidian, that its " resemblance to a 

 vertebrate animal is merely analogical, altogether tem- 

 porary and belonging to the young state of the creature, 

 without affecting its adult state or its real affinities with 

 the mollusks." The author can hardly have studied 

 Kowalevsky's memoir on the subject, in detail. 



In his anatomiL:al structure, man, according to Mr. 

 Dawson's distorted view, presents differences from all the 

 apes which are at least of ordinal importance, distinctions 

 '• mainly dependent on grade or rank, and not to be 

 broken down by obscure resemblances of internal ana- 

 tomy having no relation to this point, but to physiological 

 features of very secondary importance." When, in asso- 

 ciation with this, we are told that it is merely begging the 

 question to say that " the fact that the human skeleton is 

 constructed on the same principles as that of an ape or a 

 dog, must have some connection with a common ancestry 

 of these animals," we think it hardly necessary to make 

 further comment on the work in question, except to hope 

 that it will not fall into the hands of commencing bio- 

 logical students, who would find it difficult to shake off the 

 false associations that, in it, surround the facts which are 

 discussed. 



Mr. Mivart treats his subject in a very different man- 

 ner. His object is " to investigate by the unimpassioned 

 process of enumeration and weighing facts of structure, 

 what is the teaching of Nature as to the affinities of 

 various apes to man." In doing this, after a rapid review 

 of the clasification of Mammalia generally, and the geo- 

 graphical distribution of the apes and lemurs, or half 



