RECENT ADVANCES IN SCIENCE 



209 



tion to the kind of " thing " considered in thermodynamics, 

 which is the degree to which a system has approached a state 

 of quiescence or equilibrium, i.e. its " degree of run-downness," 

 as Dr. Tolman calls it. 



In addition to these fundamental quantities, we have also 

 certain indefinable operations which enter into the definition 

 of derived quantities ; they are five in number, multiplication, 

 division, differentiation and the two types of vector multipli- 

 cation leading to the scalar and vector products of two vectors. 



Dr. Tolman then proceeds to build up a table of derived 

 quantities, using the well-known dimensional symbolism. 

 Many of these are already commonplaces, but a few which 

 bring out his particular choice of fundamentals may be given. 

 Using e and S as shorthand symbols for electrical charge and 

 entropy we have, for example : 



Potential [m/ 2 T 2 e" 1 ] 



Current 



Resistance 



Electric Field Strength 



Magnetic Field Strength 



Magnetic Pole Strength 



Permeability 



Magnetic Induction 



Temperature 



Specific heat 



[It 1 e] 

 [mlt- 1 e~ 2 ] 

 [mlt- 2 e- 1 ] 



[l- 1 r 1 e] 



[mPt^e- 1 ] 

 [mle~ 2 ~\ 

 [mt' 1 e" 1 ] 

 [mPf'S- 1 ] 

 [m- 1 S] 



Future developments of science — not merely physical 

 science, but other branches which may come into the field of 

 mathematical analysis — may require us to increase the number 

 of fundamental kinds of quantity ; thus we may shortly have 

 to separate gravitational mass from ordinary mass as a quite 

 different kind of thing, whose accidental proportionality 

 to it in materials hitherto experimented upon has disguised 

 an essential dissimilarity. Also the desirability of looking 

 at phenomena from a new point of view may cause us to add 

 to the number of fundamentals, just as already the desirability 

 of viewing thermal phenomena from the statistical and micro- 

 scopic standpoint rather than from the molecular, kinetic 

 and microscopic point of view has led to the introduction of 

 entropy. There appears to be little hope, however, of a decrease 

 in the number of fundamental kinds of quantity. 



