January 7, 



3-] 



SCIENCE. 



ision of molecular action we must admit 

 that, when the position and motion of every 

 atom of a given substance are defined, the 

 chemical properties of that substance are 

 ■completely determined. If we take two 

 •collections of atoms of the same substance, 

 put them together in the same way, and 

 endow them with the same kinds of vibra- 

 tory motion, we ought, on any mechanical 

 theory of matter, to obtain substances of 

 identical properties. N"ow, there seem to 

 be reasons which I cannot stop at present 

 to develop that might make us believe in 

 changes of properties and attributes of sub- 

 stances not completely explained by molecu- 

 lar changes. That such is the.case with vital 

 phenomena can be demonstrated beyond 

 •doubt ; that it is the case with chemical 

 phenomena when they approach the vital 

 character seems very probable. Certainly 

 there is some essential difference between 

 that form of molecular motion in which 

 heat is commonly supposed to consist and 

 the motion of masses. Perhaps the most 

 remarkable of these differences consists in 

 the relation of this motion to the ether. 

 The motion of a mass suffers no resistance 

 by passing through the ether with the high- 

 est astronomical velocities. Matter so rare 

 as that of the diffuse comets may move 

 around the sun with a speed of many miles 

 per second without suffering the smallest 

 resistance from the ether — in a word, with- 

 out any friction between the matter and 

 the ether. But when the molecules have 

 the motion of heat, that motion, if motion 

 it be, is always communicated to the ether, 

 and is radiated away from the body, which 

 thus becomes cool. Whatever form we at- 

 tribute to the energy of heat, it is certainly 

 a form which is constantly communicated 

 from matter to the ether by a fundamental 

 law of matter. Consequently, if heat be 

 really a mode of motion, as is now generally 

 supposed by physicists, it follows that there 

 is some essential difference between the 



character of this motion and the motion 

 of the smallest masses into which mat- 

 ter can practically be divided. The hy- 

 pothesis of vibration in the fourth dimen- 

 sion merely suggests the possibility that 

 this kind of motion may mark what is 

 essentially different from the motion of 

 masses. Of course, such an hypothesis as 

 this is not to be put forward as a theory. 

 It must be worked out with mathematical 

 rigor, and shown to actually explain phe- 

 nomena before we assign it to any such 

 rank. 



I cannot but fear that some confusion on 

 this subject is caused by the tendency among 

 both geometers and psychologists to talk of 

 space as an entity in itself. As I have al- 

 ready said, a fourth dimension in space is 

 nothing more than the addition of a fourth 

 possibility of motion to material bodies. 

 The laws of space are only laws of relative 

 position. Certain fundamental axioms are 

 derived from experience, not alone indi- 

 vidual experience, perhaps, but the experi- 

 ence of the race, giving rise to hereditary 

 conceptions born in the mind and corre- 

 sponding to the facts of individual experi- 

 ence. A tree confined to one spot, even if 

 it had eyes to see and a brain to think, could 

 never have a conception of space. For us 

 the limits of space are simply the limits to 

 which we can suppose a body to move. 

 Hence when space itself is spoken of as hav- 

 ing possible curvatures, hills and hollows it 

 seems to me that this should be regarded 

 only as a curvature, if I may use the term, 

 of the laws of position of material bodies in 

 space. Clifford has set forth, with great 

 acuteness and plausibility, that the minute 

 spaces occupied by the ultimate atoms of 

 matter may, in this respect, have properties 

 different from the larger space which alone 

 makes itself known to our conceptions. If 

 so, we should only regard this as expressive 

 of some different law of motion, or, since 

 motion is only change of position, of some 



