TABLE XIV

1.68 125

1.67 136

1.645 321

1.695 202

1.73 171

1.65 200

1.66 84

1.785 411

1.65 85

When weights are assigned proportional to the number of observations taken, as shown in the last column of Table XIV, there results for the weighted mean value which represents an average of 1,735 displacements, or , as against , the value found in electrolysis. The agreement between theory and experiment is then in this case about as good as one-half of 1 per cent, which is well within the limits of observational error.

This work seemed to demonstrate, with considerably greater precision than had been attained in earlier Brownian-movement work and with a minimum of assumptions, the correctness of the Einstein equation, which is in essence merely the assumption that a particle in a gas, no matter how big or how little it is or out of what it is made, is moving about with a mean translatory kinetic energy which is a universal constant dependent only on temperature. To show how well this conclusion has been established I shall refer briefly to a few later researches.

In 1914 Dr. Fletcher, assuming the value of which I had published[90] for oil drops moving through air, made new and improved Brownian-movement measurements in this medium and solved for the original Einstein equation, which, when modified precisely as above by replacing by and becomes He took, all told, as many as 18,837 ’s, not less than 5,900 on a single drop, and obtained . This cannot be regarded as an altogether independent determination of , since it involves my value. Agreeing, however, of as well as it does with my value of , it does show with much conclusiveness that both Einstein’s equation and my corrected form of Stokes’s equation apply accurately to the motion of oil drops of the size here used, namely, those of radius from cm. to cm. .

In 1915 Mr. Carl Eyring tested by equation (29) the value of on oil drops, of about the same size, in hydrogen and came out within .6 per cent of the value found in electrolysis, the probable error being, however, some 2 per cent.

Precisely similar tests on substances other than oils were made by Dr. E. Weiss[91] and Dr. Karl Przibram.[92] The former worked with silver particles only half as large as the oil particles mentioned above, namely, of radii between 1 and . and obtained instead of 9,650, as in electrolysis. This is indeed 11 per cent too high, but the limits of error in Weiss’s experiments were in his judgment quite as large as this. K. Przibram worked on suspensions in air of five or six different substances, the radii varying from 200 to 600 , and though his results varied among themselves by as much as 100 per cent, his mean value came within 6 per cent of 9,650. Both of the last two observers took too few displacements on a given drop to obtain a reliable mean displacement, but they used so many drops that their mean still has some significance.

It would seem, therefore, that the validity of Einstein’s Brownian-movement equation had been pretty thoroughly established in gases. In liquids too it has recently been subjected to much more precise test than had formerly been attained. Nordlund,[93] in 1914, using minute mercury particles in water and assuming Stokes’s Law of fall and Einstein’s equations, obtained . While in 1915 Westgren at Stockholm[94] by a very large number of measurements on colloidal gold, silver, and selenium particles, of diameter from 65 to 130 (), obtained a result which he thinks is correct to one-half of 1 per cent, this value is , which agrees perfectly with the value which I obtained from the measurements on the isolation and measurement of the electron.

It has been because of such agreements as the foregoing that the last trace of opposition to the kinetic and atomic hypotheses of matter has disappeared from the scientific world, and that even Ostwald has been willing to make such a statement as that quoted on p. 10.