Leipzig: Johann Ambrosius Barth, 1855. 1st Edition. FIRST EDITION OF A “SEMINAL” WORK, FICK’S CLASSICAL EQUATION OF DIFFUSION (Philibert, Fick, Einstein, Before and Beyond, 2005, 3). The laws Fick presents in this paper remain “the empirical foundations of many phenomena in the macroscopic world” and were of significant import to Einstein (Lepri, Thermal Transport, 305). Also included are two papers by Helmholtz on optics (see end of write-up). “Today, Fick's Laws form the core of our understanding of diffusion in solids, liquids, and gases (in the absence of bulk fluid motion in the latter two cases)” (Philbert, 5).
While this paper also appeared in translation in the Phil Mag (and we offer that work separately, "On Liquid Diffusion") this German original includes ideas that “do not appear in the translation (Philbert, 4). Specifically, “Fick [here makes] allusion to the atomic theory, as accepted by most of the physicists as an aide to get “an insight, a description and a discovery”, allowing a mechanical account of the observed phenomena. [While] these ideas about atoms and molecules are very far from our modern concepts, they nevertheless… were important to understand that dissolution and diffusion processes in water result from the movement of separate entities of salt and water. But Fick was unable on this basis to deduce a quantitative law. It took another fifty years for this ambitious purpose to be realized by A. Einstein” (ibid, 3).
Inspired by earlier work by Thomas Graham and sensing a deep analogy between diffusion and the conduction of electricity or heat, Fick’s experiments “dealt with measuring the concentrations and fluxes of salt, diffusing between two reservoirs through tubes of water” (Philbert, 5).
“Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). Fick's second law predicts how diffusion causes the concentration field to change with time” (ibid).
Einstein’s first paper on Brownian motion (to date his most cited) – “the irregular movement of macroscopic particles suspended in a liquid” – was published in 1905. By inverting a formula by Boltzmann, “Einstein described its mathematics, deriving the probability of a macroscopic state for the distribution of gas molecules” (Calaprice, 15).
Einstein realized that Brownian motion was associated with diffusion, with laws already written by Fick in 1855 relating to the flux of particles arising from a gradient in concentration” (Jones, Diffusion MRI, 46). In the case of Brownian motion, no macroscopic concentration gradient is needed as the molecules undergo a process of ‘self-diffusion’ arising from local concentration fluctuations” (ibid).
“Fick’s laws were developed to describe the behavior of solute molecules as a consequence of a non-uniform concentration, the drifting from higher to lower concentration so as to equalize concentration gradients. This process, also known as “mutual diffusion”, requires a countercurrent of solute and solvent particles to maintain the overall mas density. [What Einstein elucidated was] “that the language of Fick’s laws still applied in the case of self-diffusion where no macroscopic gradient existed, provided one takes n(r, t) to be the local probability of finding the molecule (ibid).
In no small part due to the work of Fick, as regards diffusion, “the bridge between the microscopic and macroscopic world was built by A. Einstein: his fundamental result expresses a macroscopic quantity – the coefficient of diffusion – in terms of microscopic data (elementary jumps of atoms or molecules)” (ibid).
HELMHOLTZ PAPERS: “In 1851, Helmholtz revolutionized the field of opthalmology with the invention of the opthalmoscope; an instrument used to examine the inside of the human eye” (Wikipedia). These two papers are part of a continued study by Helmholtz of vision and color. The translations of their titles are “On the sensitivity of the human retina to the most refractile rays of sunlight” and “On the Composition of Spectral Colors”. Item #891
CONDITION & DETAILS: Leipzig: Barth. 8vo. (206 x 138mm). Full volume. 644 pp. 7 plates. Ex-libris with the usual markings (only stamps and a gilt number at the spine). Minor tattering at edges some of the pages. Bound in brown buckram over marbled paper – slight rubbing and scuffing at the edges; gilt-lettered at the spine; gilt top edge. Tightly bound. Bright and clean throughout.