Note 149 — Chapter XXXVIII · THE METHODOLOGY OF SCIENCE (continued 3)

The development and gradual acceptance of the kinetic theory of gases is particularly instructive in this connection. Some two centuries ago Daniel Bernoulli had suggested that the tendency of a gas to expand might be attributed to a rushing hither and thither of its molecules. But inasmuch as the idea was not worked out quantitatively, no great attention was paid it. Not till a century or so later was it investigated in a mathematical way by Maxwell and by Boltzmann. For this reason these scientists receive the credit for the kinetic theory; and Bernoulli’s name (in connection with this theory) has lost all but a historical interest. Maxwell’s and Boltzmann’s theoretical anticipations were borne out quantitatively by the experiments performed in their day, and a large number of scientists accepted the theory as sound. Even so, the doctrine still had its detractors, for subsequent experiment proved that in the matter of specific heats at low temperatures, theory and observation were in utter conflict. Further difficulties related to the problem of the equipartition of energy. The net result was that other physicists (Kelvin and Ostwald in particular) were hostile to the kinetic theory.

At this stage we must mention that as far back as 1827 an English doctor named Brown had noticed that fine particles suspended in a liquid appeared to be quivering when viewed under the microscope. Brown attributed these curious motions to the presence of living organisms; others suggested that they were due to inequalities of temperature brought about by the illumination of the microscope. On the other hand, the adherents of the kinetic theory maintained that these Brownian movements were due to the impacts of the molecules of the fluid on the suspended particles. Now the important point to understand is that this latter hypothesis could serve only as a suggestion. Before any reliance could be placed in it, it would be necessary to prove that the precise Brownian movements actually observed were in complete quantitative agreement with the theoretical demands of the kinetic theory; and a quantitative theory of this sort had never been formulated. Such was the state of affairs when Einstein, in one of his first papers, gave an exhaustive quantitative solution of the problem of Brownian movements (in the case both of translations and of rotations), stating what the precise movements would have to be if the kinetic theory of fluids corresponded to reality.

Perrin then submitted the Brownian movements to precise quantitative measurements with a view to checking up on Einstein’s anticipations. The result was a disappointment; for Perrin found a considerable discrepancy between those anticipations and experiment. And so the kinetic theory of Brownian movements appeared to be untenable, and, more generally, the whole kinetic theory of gases and fluids to be in peril. When informed of Perrin’s results, Einstein went over his calculations afresh and discovered a numerical mistake in his computations. On rectifying this error he found that the theoretical anticipations were in perfect agreement with Perrin’s measurements. About the same time, by means of mathematical calculations based on the quantum theory, Einstein succeeded in accounting for the specific-heat difficulty mentioned previously. As for the arguments directed against the kinetic theory by reason of the “equipartition-of-energy theorem,” they in turn were answered, thanks to the quantum theory, itself a product of quantitative investigation. The net result was that the kinetic theory was finally established, the principle of entropy ceased to be regarded as an absolute principle, and Ostwald surrendered.

Our purpose in giving this brief historical sketch of the problem of Brownian movements has been to show that loose guesses, unless supported by arguments of a precise quantitative nature, are of little interest to physical science. For this reason no great importance is attributed to the vague atomistic speculations of Democritus or to the relativistic speculations of Mach, even though, in the light of subsequent developments, the latter may prove to be correct. In all cases of this sort, the credit goes (and rightly so) to the theoretical investigator who has succeeded in overcoming the major difficulty, that of working out the theory along rigid mathematical lines. To be sure, in many instances the thinker who makes the guess or advances the hypothesis also follows it up mathematically. Such was the case with Einstein when he formulated the postulate of equivalence for the purpose of interpreting the significance of the equality of the two masses. When a dual contribution of this type occurs, the credit is of course twofold.