L2.3 - Essays on formulae

Summary

for⋅mu⋅lary\′fȯr-myǝ-′ler-ē\n, pl -lar⋅ies (1541) 1: A book or other collection of stated and fixed forms, such as prayers 2: A statement expressed in formulas 3: A fixed form or pattern; a formula 4: A book containing a list of pharmaceutical substances along with their formulas, uses, and methods of preparation—formularyadj

The American Heritage Dictionary of the English Language, Fourth Edition Copyright © 2000 by Houghton Mifflin Company.

Between the ecclesiastic (definition 1) and the operative (definition 4), between origin (Level 3) and result (Level 2 tables), is exegesis. Different minds will find different ways to work from Level 3 Foundations to Level 2 tabulations. Each of the following sections describes not simply one particular set of steps but, more important, the kinds of steps to take:

• Examining the full expression for the interaction between half-spaces to see which features are revealed in its specialized limiting forms (Section L2.3.A.);

• Generalizing the original half-space geometry to layered and inhomogeneous planar bodies (Section L2.3.B);

• Converting to cases of curved structures (Section L2.3.C);

• Reducing to Hamaker theory (Section L2.3.D) for gases and dilute suspensions, but now

• Incorporating fluctuations and screening in ionic solutions (Section L2.3.E), and then

• Extending to include interactions between small particles and substrates (Section L2.3.F) as well as between one-dimensional linear bodies (Section L2.3.G).

In what follows, the numbers in parentheses next to or below the equations are the actual equation numbers.