SCIENCE. 



[X. S. Vol. XXI. No. 5.36. 



This is the meaning of natural law, and the 

 extent of its validity and the validity of all 

 our reasoning must be judged in the light of 

 this meaning. Our elementary laws of mo- 

 tion can not be assumed to hold of bodies too 

 small for observation, or too remote in space. 

 Science is not absolute in any sense (p. 8). 

 But not only do we react on our environment 

 in accord with many acquired beliefs ; we seek 

 economy in our reactions and our beliefs. We 

 find it easier to indicate what will happen in 

 the various sensorial cantons by using the 

 terms of one sense, namely, sight. Because 

 sight gives greater precision and covers a 

 wider field of phenomena than any other sense, 

 we find it most convenient to frame our hy- 

 potheses in regard to the constitution of the 

 other cantons in terms of what sight reveals — 

 namely, the motion of bodies. Thus we de- 

 scribe sound, heat, light as wave-motion. It 

 is the hope of covering all the phenomena of 

 the other cantons by the terminology of sight 

 that leads to monism. Yet what is vouch- 

 safed by the various senses remains really dis- 

 parate, sui generis in each canton. 



In Book II. we consider the sciences of the 

 ' optical canton ' — more familiarly known as 

 the exact sciences. The language of mathe- 

 matics is the language of vision. It is based 

 directly on sense-impressions. There is no 

 ' free creation by the mind ' of the fundamen- 

 tal mathematical conceptions. The straight 

 line is given in the thread suspending a 

 weight, the plane in the surface of a liquid, 

 the continuum in any body in which we see 

 no gaps. These sense-impressions may turn 

 out later to be illusions, but are none the less 

 really given. Arithmetic, algebra and geom- 

 etry detail the properties of such data omit- 

 ting the element of time; kinematics and me- 

 chanics include the latter. The infinite and 

 infinitesimal are not picturable, therefore they 

 arc figures of speech. Nor could we tell what 

 laws they would obey, since logic is based on 

 what we have exj^erienced, and can not be 

 assumed to hold of regions beyond our senses. 

 Just so, atoms may not obey the laws which 

 larger bodies obey, and the ether may not be 

 impenetrable;. 



IIf)w do we come to use other conceptions 



here besides those of space and motion ? Be- 

 cause these are found insufficient for the pre- 

 diction of the behavior of bodies. Thus we 

 find it convenient to speak of mass, which the 

 author defines as ' that coefficient found in 

 one and the same body, in all the systems of 

 which it forms a part' (p. 87). Velocity is 

 that which corresponds to the intensity of our 

 sensation of motion (p. 94). Force is not a 

 cause of motion ; for such a conception im- 

 ports the muscular sense into the visual field, 

 which is not allowed. Quantity does not ap- 

 ply beyond the visual field. Incidentally, 

 Fechner's law is declared impossible, since it 

 attributes quantity to other cantons besides 

 the visual. What we really measure is not 

 force as an existing quantity of something, 

 but only my^a, a numerical product. That 

 force is a fiction is shown also when we re- 

 member that in statics any one force may be 

 replaced by an infinity of others equivalent to 

 it. Since all these can not be really present, 

 there is no reason for saying any one is more 

 real than the rest. The law of action and re- 

 action is the experimental fact that in an 

 isolated system the algebraic sum of the par- 

 tial energies is nil. The conservation of mass 

 has become so well known as to be almost an 

 a priori law. 



In Book III., ' The Other Cantons,' the dis- 

 cussion is confined to sound and heat, prin- 

 cipally to heat. Temperature can be studied 

 scientifically because it alters the shape of 

 bodies. The conservation of heat is simply a 

 definition of a complete system: a complete 

 system is one in which the algebraic sum of 

 the quantities of heat gained by the parts is 

 nil (p. 148). 'Source of heat' and 'absolute 

 zero,' like force, are fictions. Equivalence of 

 heat and mechanical energy does not mean 

 preservation of a permanent something; it is 

 only a useful device for correlating heat with 

 visual phenomena. The conservation of en- 

 ergy is only such a correlation made general; 

 it is an empirical truth at most, and even if 

 radium creates energy de novo it need not dis- 

 turb us (pp. 207-9). 



Book IV., ' Explanations,' resumes the gen- 

 eral position of the author in regard to the 

 meaning of scientific law. Atomic models do 



