FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 19 



mechanical basis. The dimensional formula thus affords a valuable 

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

 ledge 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 

 mathematical, and the entire superstructure is erected upon the three 

 fundamental quantities, L, M, and T, and certain definitions; just as 

 geometry arises from its axioms and definitions. 



Of many of those physical quantities, for which we are not as yet 

 able to give the dimensional formula, our knowledge is precise and 

 definite, but it is incomplete. In the case, for example, of one import- 

 ant group of quantities, those used in electric and magnetic measure- 

 ments, we have to introduce, in addition to L, M, and T, a constant 

 factor to make the dimensional formula complete. This, the sup- 

 pressed factor of Riicker, 1 is p., the magnetic permeability, when the 

 quantity is expressed in the electromagnetic system, and becomes k, 

 the specific inductive capacity, when the quantity is expressed in 

 terms of the electrostatic system. 



Here the existence of the suppressed factor is indicative of our 

 ignorance of the mechanics involved. If we knew in what way a 

 medium like iron increased the magnetic field, or a medium like glass 

 the electric field, we should probably be able to express /JL and k in 

 terms of the three selected fundamental dimensions and complete the 

 dimensional formula of a large number of quantities. 



Where direct mechanical knowledge ceases, the great realm of 

 physical speculation begins. It is the object of such speculation 

 to place all phenomena upon a mechanical basis; excluding as unsci- 

 entific all occult, obscure, and mystical considerations. 



Whenever the mechanism by means of which phenomena are pro- 

 duced is incapable of direct observation either because of its remote- 

 ness in space, as in the case of physical processes occurring in the 

 stars, or in time, as in the case of the phenomena with which the 

 geologist has to do, or because of the minuteness of the moving parts, 

 as in molecular physics, physical chemistry, etc., the speculative ele- 

 ment is unavoidable. Here we are compelled to make use of analogy. 

 We infer the unknown from the known. Though our logic be without 

 flaw, and we violate no mathematical principle, yet are our con- 

 clusions not absolute. They rest of necessity upon assumptions, 

 and these are subject to modification indefinitely as our knowledge 

 becomes more complete. 



A striking instance of the uncertainties of extrapolation and of the 

 precarious nature of scientific assumptions is afforded by the various 

 estimates of the temperature of the sun. Pouillet placed this tempera- 

 ture between 1461C. and 1761C.; Secchi at 5,000,000; Ericsson 

 1 Riicker, Philos. Mag., 27, p. 104. 1889. 



