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  • Print publication year: 2005
  • Online publication date: January 2010

L2.3 - Essays on formulae



for⋅mu⋅lary\′fȯr-myǝ-′ler-ē\n, pl -laries (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.