April 20, 1900.] 



SCIENCE. 



611 



evident signB of being ultimately as futile 

 as mechanical explanations in general have 

 proved for all classes of phenomena the ques- 

 tion immediately arises, why not abandon 

 it ? Especially when we are already in pos- 

 session of so elegant and flexible a method 

 for the statement of phenomena as is fur- 

 nished by the language of mathematics. — 

 An instrument so highly developed, so fer- 

 tile in suggesting interrelations, by its fa- 

 cility in bridging long mental processes as 

 often to create an uncanny feeling to which 

 the great Euler gave expression, that " his 

 science in the person of his pencil surpassed 

 himself in intelligence." 



Should we not rather agree with Mach 

 who has defined physics (including of 

 course all physical science) as " experience 

 ari'anged in economical order," that the 

 " aim of research is the discovery of the 

 equations which subsist between the ele- 

 ments of phenomena." 



This I take it may be regarded as a 

 fair presentation of the ' phenomenology ' 

 or, ' mathematico-physico-phenomenology ' 

 point of view in contradistinction to that of 

 ' atomistics.' Of the many contributions to 

 the discussion, direct or indirect which con- 

 temporaneous literature furnishes, perhaps 

 the most notable is from Boltzmann. He 

 insists that both methods of presenting 

 phenomena are but methods ; that each pos- 

 sesses inherent advantages, that neither can 

 with fairness be dogmatically declared su- 

 perior, and until it shall have come about 

 that the one has absorbed the other, both 

 methods should be developed together. By 

 both methods it is possible to present com- 

 prehensive conceptions of fields of phenomena 

 not possible to direct description. But we 

 should guard against introducing any un- 

 necessary arbitrariness, rather than follow 

 Ostwald in attempting no concept at all. 

 That as a matter of fact, the concepts of the 

 calculus rest fundamentally on the notion 

 of a finite number of elements ; otherwise 



the theory of limits has no meaning and the 

 differential equation does not represent a 

 possibility. This is of course an essentially 

 atomistic conception. 



In avoiding arbitrariness as far as possi- 

 ble, by assigning as few properties as may 

 be necessary to the atoms in any particular 

 field of phenomena, we obtain special hy- 

 potheses. 



Phenomenology attempts to co-ordinate 

 these special hypotheses in one concept. 

 There are at least two difficulties ; the cor- 

 respondingdifferentialequations differ, mak- 

 ing their comparisons a very complicated 

 matter ; they relate to stationary or nearly 

 stationary conditions and cannot fairly 

 represent turbulent reactions. The ' ener- 

 getic phenomenology ' attempts to consider 

 what is common to these various fields, 

 such as the energy laws, but fails because 

 its results are too general, and the analogies 

 are not applicable in all details. 



Atomistics would attempt to co-ordinate 

 these fields, by modifying the assigned prop- 

 erties of the atoms, and thus obtain a 

 simultaneous, comprehensive view of the 

 whole, to an extent not approached by 

 phenomenology. Further, by this method 

 some notion is to be had of turbulent ac- 

 tions. But the assigned properties of the 

 atoms must be in accord with the special 

 concept of the phenomenology, and there- 

 fore this latter should be developed also. 

 So that atomistics, though they have 

 hindered progress at times, still have a use. 

 And the danger is in confusing the pheno- 

 menology of results alraedj' established 

 with the atomistic hypotheses which sever 

 to hold them together. 



Volkmann suggests a further qualification 

 to these views to which Boltzmann assents, 

 dividing physical phenomena into three 

 classes : Coarser phenomena as elasticity 

 or capillarity, where atomistic hypotheses 

 are unnecessary ; finer phenomena as elec- 

 trolyses, dispersion of light, etc., when 



