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 important group of quantities, those used in electric and magnetic measurements, we have to introduce, in addition to L, M and T, a constant factor to make the dimensional formula complete. This, the suppressed factor of Rücker,[1] is μ, the magnetic permeability, when the quantity is expressed in the electromagnetic system, and becomes Tc, the specific inductive capacity, when the quantity is expressed in terms of the electro-static 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 μ and k in terms of the three selected fundamental dimensions and complete the dimensional formulæ 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 unscientific all occult, obscure and mystical considerations.
Whenever the mechanism, by means of which phenomena are produced, is incapable of direct observation either because of its remoteness 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 element 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 conclusions 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 temperature between 1461° C. and 1761° C; Secchi at 5,000,000°; Ericsson at 2,500,000°. The newer determinations,[2] of the temperature of the surface are, to be sure, in better agreement. Le Chatelier finds it to be 7600°; Paschen 5400°; Warburg 6000°. Wilson and Gray publish as their corrected result, 8000°. The estimate of the internal temperature is of a more speculative character. Schuster's computation gives
