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Here one can click on and read slightly modified sections of the paper. These sections are reasonably self-contained, they generally contain more figures than the essentially equivalent downloadable sections, and the web site references are clickable.

I. Introductory - This describes the contents of the paper and consists largely of the Home page and this page.

II. History - The discovery of Clarkia pulchella and the men involved are treated here. It was found by Meriwether Lewis in 1806 in Idaho on the return trip of the Lewis and Clark expedition. It was named and published in 1814 in England by Fredrick Traugott Pursh. Its seeds were first collected and sent to England in 1826 from the Northwest Pacific coast by David Douglas. They arrived in London in 1827 and were grown there, providing flowers for Brown's investigations. This section contains subsections devoted to each man.

III. Jiggly - Here is an in-depth review of Brown's paper, with many quotes, as well as some remarks on Brown's microscopes and on Brownian motion.

IV. Botany - Some history of early pollen research and a summary of some present understanding of pollen physiology is presented here.

V. Microscopy - This contains a discussion of quantitative observations with modern apparatus which shed light on Brown's qualitative observations. It begins with a description of how one may go about growing Clarkia pulchella, how to prepare its pollen for observation, and what one sees. Studies are made of particle sizes. A discussion is given of how diffraction affects what is seen, and comparison is made of the spherosome sizes Brown reported, the sizes seen through a modern day compound microscope and the actual sizes. The amyloplst Brownian motion and rotation is observed and compared with theory. It is shown how to construct a one-lens microscope using a readily available product, a ball lens, and observations of amyloplast sizes are made with it and compared with what Brown saw.

VI. Theory - This is meant for advanced physics undergraduate students or graduate students, and their teachers. Most of this material has been known for over a century. Some of it has found its way into textbooks. Apart from the benefit of finding all the relevant material in one place, in self-contained form, each appendix contains some novel treatment, as compared with the treatment given in the textbooks referenced below.

The appendices contain seven mathematical tutorials on aspects of classical physics.

Appendix A contains a derivation due to Langevin, of the well known expression, given first by Einstein(1), for the mean-square displacement of an object undergoing Brownian motion.(2) The method is easily applied to give the mean-square angular displacement of an object undergoing Brownian rotation.

These expressions depend upon the viscous force or viscous torque on the object. Such fluid flow analysis is not treated in places which treat the material of Appendix A.

Appendix B derives the viscous force and viscous torque on a sphere.(3) For an ellipsoid, results are just cited.(4)

Appendix C presents a derivation of geometrical optics starting from the wave equation. The discussion here, utilizing the WKB approximation in 3 dimensions, does not seem to be given elsewhere, although the result (the eikonal approximation of geometrical optics) is well known.

Appendix D, a digression, applies this result to mirrors and lenses. It is emphasized, because of the approximate solution's abrupt discontinuities at the boundaries of mirrors and lenses, that it must be modified in order to better satisfy the wave equation.

Appendix E contains the modification, obtaining from Green's theorem, in a standard way, the Huyghens-Fresnel-Kirchhoff expression for a diffracted wave emanating a lens.(5)

Then, in Appendix F, this theory is used to discuss lens imaging of a point source. Usually, books on optics discuss the diffraction of a lens (due to its limited aperture) and the spherical aberration of a lens (due to the image made by rays at the rim of the lens having a different focal plane than the image made by near-axial rays) separately. Then, no expression is given for their combined intensity. Here, diffraction and spherical aberration receive a unified treatment. As a concrete example, the theory is applied to what is seen through a 1mm diameter ball lens used as a microscope. The optimum choice for the exit pupil for such a lens, to minimize spherical aberration, is discussed.

Appendix G
applies these results for a point source to an extended light source, an illuminated hole of radius a. The apparent radius of the image is discussed, for small and large a. As discussed in section 3H, results are obtained which illuminate (sic) Brown's observations of ``molecular" size.


1) A. Einstein, Ann. d. Phys.17, 549 (1905).

2) P. M. Morse, Thermal Physics (Benjamin, New York 1969), p. 228; C. Kittel, Elementary Statistical Physics (Wiley, New York 1958), p. 153; D. Jia et. al., Am. J. Phys 75, 111 (2007) (see also textbook references therein).

3) K. Huang, Statistical Mechanics (Wiley, New York 1965), p. 119 and and L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford 1978), p.63: the latter also contains a problem that discusses the viscous torque on a sphere, p. 68.

4) The viscous force on an ellipsoid moving parallel to an axis is discussed in Lamb's classic volume, H. Lamb, Hydrodynamics (Dover, New York 1945), section 339. The viscous torque on an ellipse rotating about an axis is calculated in a 1922 paper, G. B. Jeffery, Proc. Roy. Soc. London, series A 102, 161(1922), Eq. (36).

5) See chapter IX of M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford 1983), sixth (corrected) edition, p. 459.