26 



NATURE 



[November 9, 1899 



summarised in lists of fossils, occupying about fifty pages 

 at the end of the work ; these, and the detailed lists of 

 fossils appearing throughout the book, will be of the 

 utmost value to the strati graphical palceontologist. 



The form in which the book is presented to the reader 

 is excellent, and the work is well illustrated. In addition 

 to the numerous diagrams and sections illustrative of the 

 geology of the area, which are scattered through the 

 memoir, there are seventeen plates reproduced from 

 photographs illustrating the appearance of some of the 

 sediments, including the radiolarian cherts, and especially 

 of the volcanic rocks, both lavas and fragmental ac- 

 cumulations ; in connection with the lavas, we may 

 particularly note the illustrations of the remarkable 

 rocks with " pillow-form " structure which are associated 

 with the radiolarian cherts. Of the remaining plates, 

 eight represent microscopic sections of various rocks, 

 while two are devoted to illustrations of characteristic 

 graptolites. In addition to these plates, there is a well- 

 coloured geological map of the area, on the scale of ten 

 miles to the inch. 



The third chapter of the book, in which the authors 

 give a general description of the Silurian rocks of the 

 Southern Uplands, will be read by all geologists ; the 

 detailed descriptions in the other chapters will be largely 

 utilised by those who visit the region ; and, if we mistake 

 not, these visitors will in future become very numerous, 

 attracted to the district owing to the publication of a 

 memoir upon a region of exceptional complexity but also 

 of exceptional interest — a memoir which will at once take 

 its place as a classic in geological literature. J. E. M. 



THE PHILOSOPHY OF ATOMIC THEORIES. 



Essai critique sur F Hypothec des Atomes dans la 

 Science contemfioraine. Par Arthur Hannequin, Pro- 

 fesseur k la Faculte des Lettres de I'Universitd de Lyon. 

 Second edition. Pp. 457. (Paris : Alcan, 1899.) 

 pROF. HANNEQUIN attempts, in the first of the 

 -*- two books into which his work is divided, by a dis- 

 cussion of the first principles of mathematical knowledge 

 and a study of the progress of physical and chemical 

 science, to establish at once the necessity and the 

 contradictions of atomism ; in the second book it is 

 sought to reconcile the contradictions by an appeal to 

 metaphysics. 



According to M. Hannequin it is by a necessity of its 

 nature that human science reduces all to the atom as it 

 has already reduced all to motion— the need to render 

 intelligible all that falls under the intuition of the senses 

 or all phenomena. Our mind can only take hold of or 

 comprehend what comes from itself, it only knows fully 

 what it creates. Thus science in the measure of its 

 rigour and certainty is a creation of our mind. The 

 science par excellence, the science derived entirely from 

 the mind is the science of number. Physical atomism is 

 not imposed on science by reality, but by our method and 

 by the nature of our knowledge. It does not necessarily 

 imply the real discontinuity of matter ; it implies only 

 that we make it discontinuous in order to comprehend it. 

 It has its origin in the universal use of number. 

 NO. 1567, VOL. 61] 



" The atom is found at the end of all analysis as the 

 product of the struggle of quantity against magnitude, of 

 unity and number against the multiplicity and continuity 

 of space and time." 



In Chapter i. of the first book M. Hannequin discusses 

 the question whether pure geometry itself involves the 

 notion of quantity, and therefore of number, and con- 

 cludes that it does. Amalytical geometry more obviously 

 does so, and the author discusses at some length what is 

 involved in the process of differentiation. Infinitesimal 

 analysis appears to him to lead the mind necessarily to 

 postulate in every geometrical object indivisible elements. 

 On the other hand he concludes that all attempts, such as 

 that of Cantor, which is criticised at some length, to 

 express continuity by means of number must fail. 



The analysis which gives us the concept of the 

 geometrical element would not of itself, according to M. 

 Hannequin, have given us that of the atom, had not our 

 mind demanded the mathematical explanation of nature. 



With mechanics our mathematics approaches as 

 closely as it can phenomena and reality. In Chapter ii., 

 on " Atomism and Mechanics," the author sets out to 

 show that our ideas of motion lead us straight to the 

 discontinuity of matter. His treatment of the funda- 

 mental notions of mechanics, of motion, force, mass, is 

 interesting but not always convincing. For instance, it 

 scarcely seems legitimate to make the first law self- 

 evident by saying that when a body is in a state of 

 uniform rectilinear motion or is at rest, one has the right 

 to afifirm by definition that it persists in an identical 

 state, and that to no change corresponds no cause ; on 

 the other hand, to every definite variation of velocity or 

 to every acceleration must correspond a definite cause 

 which we call a force. 



The hypotheses of centres of force, such as that of 

 Boscowich, are condemned by Hannequin on what appear 

 to be inadequate grounds. Vortex rings meet with no 

 better fate. 



When we come to " kinetic atomism " the necessity of 

 postulating atoms becomes more apparent than the 

 author has thus far succeeded in making it, and at the 

 same time contradictions also appear. The difficulties 

 of kinetic atomism as brought out by M. Hannequin 

 are twofold. In the first place, we have the contradiction 

 between the indivisibility of the atom and its perfect 

 elasticity. In the second place, the number of atoms can 

 neither be infinite nor finite. It is apparently atomism 

 of the most thorough-going kind that is here considered, 

 action at a distance being excluded and gravitational 

 energy being taken as kinetic ; otherwise there is no 

 difficulty in holding the number of atoms to be finite. 



In Chapter iii., on atomism and nature, the author 

 attempts to show that the particular sciences of nature 

 arrive at atoms of different and decreasing orders. 



The chemical atom is first considered ; the laws of 

 definite and multiple proportions, and the methods of 

 determining the relative masses of the atoms with the 

 aid of Avogadro's and Dulong and Petit's laws being 

 discussed. The possibility of the existence within the 

 chemical atoms of smaller primordial atoms is next 

 treated with reference to Prout's hypothesis and the facts 

 of thermal chemistry and chemical affinity. 



