56 POPULAR SCIENCE MONTHLY. 



THE FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE.* 



By Professor EDWARD L. NICHOLS, 



CORNELL UNIVERSITY. 



ALL algebra, as was pointed out by von Helmholtz nearly fifty 

 years ago, is based upon the three following very simple proposi- 

 tions : 



Thmgs equal to the same thing are equal to each other. 



If equals be added to equals the wholes are equal. 



If unequals be added to equals the wholes are unequal. 



Geometry, he adds, is founded upon a few equally obvious and 

 simple axioms. 



The science of physics, similarly, has for its foundation three 

 fundamental conceptions: those of mass, distance and time, in terms 

 of which all physical quantities may be expressed. 



Physics, in so far as it is an exact science, deals with the relations 

 of these so-called physical quantities; and this is true not merely of 

 those portions of the science which are usually included under the head 

 of physics, but also of that broader realm which consists of the entire 

 group of the physical sciences, viz., astronomy, the physics of the 

 heavens; chemistry, the physics of the atom; geology, the physics of 

 the earth's crust; biology, the physics of the matter imbued with life; 

 physics proper (mechanics, heat, electricity, sound and light). 



The manner in which the three fundamental quantities L, M and 

 T (length, mass and time) enter, in the case of a physical quantity, 

 is given by its dimensional formula. 



Thus the dimensional formula for an acceleration is LT~~ 2 which 

 expresses the fact that an acceleration is a velocity (a length divided 

 by a time) divided by a time. Energy has for its dimensional formula 

 L 2 MT~ 2 ; it is a force, LT~ 2 M (an acceleration multiplied by a mass), 

 multiplied by a distance. 



Not all physical quantities, in the present state of our knowledge, 

 can be assigned a definite dimensional formula, and this indicates that 

 not all of physics has as yet been reduced to a clearly established 

 mechanical basis. The dimensional formula thus affords a valuable 

 criterion of the extent and boundaries of our strictly definite knowl- 

 edge of physics. Within these boundaries we are on safe and easy 

 ground and are dealing, independent of all speculation, with the 

 relations between precisely defined quantities. These relations are 



* An address at the International Congress of Arts and Science, St. Louis, 

 September, 1004. 



fVon Helmholtz, Populiire Wissenschaftliche Vortrage, p. 136. 



