THE FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 



BY EDWARD LEAMINGTON NICHOLS 



[Edward Leamington Nichols, Professor of Physics, Cornell University, and 

 Editor-in-chief of the Physical Review, b. September 14, 1854, Leamington, 

 England. B.S. Cornell University, 1875; Ph.D. Gottingen, 1879; Fellowship in 

 Physics, Johns Hopkins University, 1879-80; Professor of Physics and Chem- 

 istry, Central University, 1881-83; Professor of Physics and Astronomy, Uni- 

 versity of Kansas, 1883-87. Member of National Academy of Science, American 

 Academy of Arts and Sciences, American Institute of Electrical Engineers, 

 American Philosophical Society, American Physical Society. Author of A Lab- 

 oratory Manual of Physics andApplied Electricity; The Outlines of Physics, etc.] 



ALL algebra, as was pointed out by von Helmholtz 1 nearly fifty 

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

 tions : 



Things 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 funda- 

 mental 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 matter im- 

 bued 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 di- 

 vided 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 

 1 Von Helmholtz, Populare Wissenschaftliche Vortrage, p. 136. 



