266 



NA TURE 



[January 23, 1902 



" thing " is an experience (erlebniss), generally ex- 

 ternal to ourselves, which we regard as separable or 

 distinguishable from other experiences. But "things" 

 are related to each other, and a collection of things 

 forms a "manifold" or multiplicity (Mannigfaltigkeit). 

 Ostwald illustrates the meaning of a "manifold" 

 by the analogy of the contents of a boy's pocket ; 

 the articles have no other relation to each other than 

 that they happen to be there. The laws of the manifolds 

 of our experiences are represented by time and space. 

 Time is characterised by continuity and by its being a 

 "simple manifold," that is, from one point of time to 

 another, there is only one path ; and this implies that in 

 time there are no points of intersection, there is only an 

 earlier and a latei, and these cannot be interchanged. 

 Space, on the contrary, is a complex manifold, inasmuch 

 as there is an infinite number of ways from any one 

 point to any other, and it is " isotropic," or free from 

 direction. 



Manifolds (or collections of things in some way re- 

 lated) can be divided in an affinity of ways ; their parts 

 can be placed in order, and, in fact, all real manifolds 

 must be ordered. A consideration of such order brings 

 into operation our faculty of comparison. An instance is 

 to be found in "ordinal" numbers, which form a mani- 

 fold limited on one side, but unlimited on the other, 

 uniform and ordered. The cardinal numbers, on the 

 other hand, define merely the extent of a manifold, with- 

 out reference to distinguishing between individuals. 

 But ordinal numbers may be made unlimited in both 

 directions by use of a negative sign. 



The conception of magnitude next claims attention. 

 The conceptions of identity and equality, and the im- 

 possibility of reaching certainty as regards the latter, 

 the conditions of equality in time, the notion of con- 

 tinuity, and the law of interpolation lead up to the con- 

 sideration of two kinds of magnitude — those which may 

 be termed intensities or " strengths " (Stiirken), and 

 those for which the English word "capacity" or "quan- 

 tity" appears the best translation (Grossen). While 

 capacities may be subdivided into similar portions, these 

 portions may be recombined in any proportion to repro- 

 duce a capacity of equal kind. On the other hand, 

 intensities cannot be divided into similar portions, for 

 each portion retains the characteristic property due to 

 its position in the original intensity, even after subdivision. 

 Capacities can be measured by use of cardinal num- 

 bers ; thus, five litres of water remain five litres, whether 

 they be contained in one or in a hundred vessels, 

 whereas intensities require ordinal numbers to denote 

 them, the first second of time is not the same as the 

 tenth second, although it is equal to it ; it is impossible 

 to substitute the one for the other. 



The restrictions of human thought by the conditions 

 of time and space depend on the fact that while it is 

 impossible to predict certainly what will be the con- 

 sequence of any events, it is nevertheless possible to 

 predicate what consequences are necessarily excluded. 

 And no events in the external world are possible unless 

 they happen in time and space. Given these conditions, 

 however, there is an infinite possibility of events occur- 

 ring. Kant's contention that space and time are "forms 

 of thought" is considered by Ostwald to be due to our 

 NO. 1682, VOL. 65] 



having inherited countless experiences in which these 

 conditions of thought regarding external phenomena are 

 essential. 



And now, after 146 pages of preliminaries, we come to 

 the features of this work which give it its definite 

 character. Relying on the fact that in all our impres- 

 sions from without the repetition of a certain individual 

 impression at different times and seasons conveys 

 to our minds a conviction of permanence, inas- 

 much as the mountains and the sea, our neighbours 

 and ourselves, preserve identity, while exhibiting con- 

 tinual change, Aristotle summed up the conclusions 

 formed by innumerable generations of his predecessors 

 in attributing to each thing an unchangeable su/is/ance, 

 its changes being ascribed to aciidcntiil variations. 

 Ostwald now proceeds to inquire, What is the universal 

 substance f And in what way are diverse things differ- 

 entiated from each other ? What is the most general 

 accidence or condition of modifying substance ? To this 

 question the answer is, energy ; it is the most general 

 substance (the word being used in the signification of 

 that which underlies all external things), for it is present 

 in time and space, and it is also the most general 

 accidence, for it can be differentiated in time and space. 

 The substance of physicists and chemists is termed 

 matter ; but a definition of matter is avoided in most 

 treatises on chemistry and physics. It is customary, how- 

 ever, to use the word " mass " in the sense of " quantity 

 of matter.'' The seventy or eighty different kinds of 

 matter are called elements. Extension, form and 

 impenetrability are ascribed to matter, and it is regarded 

 as indestructible, .\mong other properties imputed to 

 it are inertia, weight, divisibility and porosity, but, as 

 a rule, little emphasis is laid on the ([uestion as to which 

 of these properties is essential and which adventitious. 

 To the old conception of matter has been added in recent 

 years that of ether ; not, according to Ostwald, because 

 its assumption leads to a satisfactory presentation of 

 facts, but because people have been unable to devise any 

 better assumption. Indestructibility, or permanence, too, 

 has been ascribed to matter, but ponderable substances 

 are not the only ones which possess permanence ; that 

 quality, for example, may likewise be predicated of 

 momentum. Again, a quantity of electricity is permanent, 

 regard being paid to positive and negative signs. Energy 

 also possesses the quality of permanence, and it has the 

 supreme advantage that all natural phenomena can be 

 grouped in an orderly fashion by means of the conception 

 of energy as an entity, and it embraces, not only the 

 conception of substance, but also that of causality. The 

 definition chosen for energy is "work, and all that 

 arises from, or can be converted into, work." If the 

 amounts of energy which result when one kind is com- 

 pletely converted into any other kind be termed equal, 

 then Julius Robert Mayer's law that "during any change 

 the total amount of the energies present remain un- 

 changed" holds. The object of the book under review 

 is to construct a scheme of the world by the exclusive 

 use of the concept of energy, instead of the concept 

 of matter. 



The next chapter treats of the various forms of energy 

 in a manner which will be familiar to those who have 

 read Ostwald's " Allgemeine Chemie." There are here 



