May 7, 1897.] 



SCIENCE. 



737 



The book is written in a cliarming style, 

 picturesque witliout loss of dignity and viva- 

 cious without flippancy. The discussion is at 

 once so orderly and so complete as to give a 

 high impression of unity and elegance. To one 

 interested in the subject the book will prove 

 easy and delightful reading. While we have 

 in English many books upon parts of the field 

 and many special investigations concerning 

 molecular action we have yet no general work 

 like this upon the foundations of atomism. 

 Stallo's Modern Physics comes nearest to it and, 

 although elementary in character and limited 

 in scope, deserves to be better known than it is. 



It is easy to see that the main interest of the 

 author is philosophy and yet he shows every- 

 where wide and thorough reading in the history 

 of atomistics and also in modern physics and 

 mathematics. But with competent knowledge 

 his perspective is often false. Leibnitz, though 

 not better known, seems distinctly nearer to 

 him than Maxwell, and he does not scruple to 

 put down Cantor with a quotation from Des- 

 cartes. Indeed the book is not only scholarly, 

 but distinctly scholastic. This is perhaps the 

 reason why the author takes everywhere a hard 

 and fast view of science as a fixed body of 

 knowledge instead of the growing, elastic, ten- 

 tative thing that it really is. Having proved 

 that the universe cannot be explained by the 

 atom of Greek philosophy, a hard, round, indi- 

 visible solid, without parts or qualities, he fails 

 to do justice to, although he shows a full con- 

 sciousness of, modern atomistic speculation. 

 M. Hannequin's statement on page 225, and 

 everywhere implied throughout the book, that 

 "the rigorous unity and the perfect simplicity 

 of an explanation are the highest guarantees of 

 its truth," should be limited to pure science. 

 For experimental science this is an early and 

 naive view. The universe, and every part of 

 it, is infinitely complex and diverse, and any 

 view that makes it small and plain is the view 

 of innocence, or of one who cares more for 

 method than for matter. 



The argument of the book runs in part as 

 follows : 



As the mind knows completely only what it 

 creates — knows of things only what it projects 

 into them — so science is rigorous and exact in 



such measure as it is a creation of the mind. 

 Science takes its rise in the human need of ren- 

 dering intelligible that which falls beneath the 

 intuition of the senses. Number the mind has 

 created and so knows completely, but extension 

 and direction the mind cannot know directly. 

 It can know these categories only by breaking 

 them up into equal parts and counting them, 

 that is, by measuring. 



The first step in progress is the reduction of 

 the physics of fact and phenomenon to the 

 physics of law, which in its more generalized 

 form becomes the physics of succession and 

 change. The fundamental change — change of 

 place or motion — turns one side toward fact and 

 the other toward a rigorous mathematic, in 

 terms of which the laws of succession and 

 change are expressed. Thus science becomes 

 universal in motion only as it breaks up its con- 

 tinuity by number. So we triumph over con- 

 tinuity by dividing it into units of time and 

 mass, units small enough to measure any time 

 and any space. These units, the differentials of 

 mathematics, are the atoms of pure science — of 

 geometry, of algebra, of kinematics, etc. Thus 

 atomism is a necessary hypothesis growing out 

 of the nature of knowledge. 



So far we follow our author mainly with 

 satisfaction, even in his long argument to prove 

 that number and measurement are fundamental 

 in geometry. A straight line is the shortest 

 distance between two points ; found shortest by 

 measuring. Other definitions of a straight line 

 he endeavors to reduce to the same notion. But 

 all lines are made up of straight lines, and all 

 figures are bounded by lines, so that all figures 

 bear about with them quantitative relations. 

 To arrive at this conclusion he ignores projec- 

 tive geometry, and discredits transcendental 

 geometry by arguments which are familiar. 



But the atom in pure science is a concept, the 

 object of a definition. We must not project it 

 into the real world. So how about atomism in 

 nature ? This is, of course, the main theme of 

 the book, and is pursued through the various 

 fields of chemistry, mineralogy, optics, elec- 

 tricity, etc., with intelligence and thorough- 

 ness. Mainly he will carry the great body of 

 physicists with him. Sometimes he will part 

 company with them ; as when he insists that 



