June 20, 1902.] 



SCIENCE. 



96E 



sumed fundamental quantities. It is by 

 no means certain, however, that these units 

 will best satisfy the requirements of 

 science in the future. On the contrary, it 

 seems rather probable that advancing 

 knowledge will fmd some other system of 

 units preferable, if it does not find sev- 

 eral different though interconvertible, 

 systems essential. We have, in fact, 

 already attained two such diverse systems 

 in the units of electro-magnetic science. 



The study of such systems by the aid of 

 the theory of dimensions, which shows 

 algebraically how the assumed units enter 

 into more complex quantities, is very in- 

 structive, not only to the mathematical 

 physicist, but to the general student of 

 physical science.* To illustrate this idea 



* Designating the units of energy, length, mass 

 and time by E, L, M, T respectively, the dimen- 

 sions of some of the most frequently used quan- 

 tities in ijiechanics are shown in the following 

 tables. In the first of these length, mass and 

 time appear explicitly; in the second, length does 

 not appear explicitly; and in the last, time does 

 not appear explicitly. A glance at the exponents 

 (dimensions) of the symbols shows clearly how 

 definite the meanings of the terms force, energy, 

 power, etc., may be in comparison with the utter 

 ambiguity attaching to them in common par- 

 lance. 



Table I. 



Table II. 



bj-- some simple examples, it is well Imown 

 that all quantities used in rational me- 

 chanics are commonly expressed in terms 

 of length, mass and time. But these quan- 

 tities might be expressed equally well, sc 

 far as algebraical statement is concerned, 

 in many other ways. Thus, we might take 

 energy as one of the fundamental quanti- 

 ties instead of either length, mass or time ; 

 in which case our mechaxiical quantities, 

 would be expressed in terms of energy, 

 length and mass; or of energy, length and 

 time; or of energy, mass and time. A 

 consideration of these simple systems 

 shows us, among other things, that rational 

 mechanics might have been developed along 

 lines of thought very different from the 

 lines followed by our predecessors; and 

 the fact that we do not visualize equally 

 clearly all these systems shows that the 

 experience of humanity with physical phe- 

 nomena has been extremely limited. Most 

 curious and instructive are the system in 

 which length does not appear explicitly 

 and the system in which time does not 

 appear explicitly. May we not see in 

 these systems opportunities respectively 

 for the development of those individuals 

 of our race who seem to possess no reali- 

 zation of distance or no conception of 

 time 1 



Confining attention to the simpler and 

 more familiar units of length, mass and 

 time, and to a few of the more complex 

 quantities expressed thereby, let us first 

 consider briefly the present status of these 

 fundamental units and the possibility of 

 maintaining their invariability. The stand- 

 Table III. 



