PERRIN'S EXPERIMENTAL ARGUMENT
A discovery was made in 1827 by the English botanist Robert Brown that small microscopic particles suspended in a liquid do not sink but exhibit rapid, haphazard motion—so-called Brownian motion.
In 1908, Perrin conducted a series of experiments involving microscopic particles of gamboge (a gum resin extracted from certain Asiatic trees) in a dilute emulsion. These particles exhibited Brownian motion which was visible using a microscope. The emulsion was contained in a cylinder of known height h. Perrin determined the density D of the material making up the particles, the density d of the liquid, the mass m of the particles (all of them prepared by him to be the same weight), the temperature T of the liquid, and (with microscopes) the number of suspended particles per unit volume at various heights. He performed experiments with different emulsions, particles of different sizes and mass, different liquids, and different temperatures.Using an argument that I shall note presently, he derived the following equation, which relates the quantities just cited:[112]
n _ 1 Nmg(1 - d/D)h
(1)
~ RT
Employing different experimental values obtained for all the quantities in equation (1) except for N, Perrin used this equation to determine whether Avogadro's number N is really a constant, and if so, what its value is.
He arrived at equation (1) by assuming that the motions of the visible Brownian particles are caused by collisions with the molecules making up the dilute liquid in which these visible particles are suspended. Accordingly, he also assumed that the visible particles will mirror the behavior of the invisible molecules. Finally, he assumed that molecules in a dilute solution of the sort in question will behave like molecules in a gas with respect to their vertical distribution. He then derived the following formula (the law of atmospheres) that governs a volume of gas contained in a thin cylinder of unit cross-sectional area and very small elevation h:[113]
g_ = Mgh p RT
(2)
The pressure of a gas is proportional to its density, and hence, Perrin assumed, to the number of molecules per unit volume. So he replaced the ratio of pressures p'/p by the ratio n'/n, where n' and n are the number of molecules per unit volume at the upper and lower levels.
He also replaced M by Nm, where m is a mass of a molecule of gas and N is Avogadro's number. With these substitutions, Perrin obtainedHe now transformed equation (3) into equation (1) by letting n' and n represent the number of Brownian particles per unit volume at the upper and lower levels, and in (3) substituting the expresion mg(1-d/D)—the “effective weight” of a Brownian particle—for mg, the weight of a molecule.[114] Strictly speaking, in equation (1), N represents a number for Brownian particles: any quantity of these particles equal to their molecular weight will contain the same number N of particles. Perrin assumed that this number will be the same as Avogadro's number for molecules.
On the basis of various experiments involving different values for the observable quantities n', n, m, h, and T, Perrin used equation (1) to determine a value for Avogadro's number N and discovered that N is indeed a constant, whose approximate value is 6 1023. He concluded that molecules exist:
Even if no other information were available as to the molecular magnitudes, such constant results would justify the very suggestive hypotheses that have guided us [including that molecules exist], and we should certainly accept as extremely probable the values obtained with such concordance for the masses of the molecules and atoms.... The objective reality of the molecules therefore becomes hard to deny.[115]
Now for antirealist responses. There are two general kinds I shall consider: first, that Perrin's argument for molecules is invalid; second, that even if valid, it does not suffice to establish scientific realism.
2.