Without Loss of Generality in Mechanics

  1. (Reductions) When a typical case [Matv, p.122, (16.2)] can represent the general case [Hec, p.111, (4.12), (4.13), and (4.14)] we must explain why the discussion of the typical will not lose the generality. First, note that er and et are independent of r on the interface. Then by comparing [Hec, p.112, Fig. 4.38] with [Matv, p.123, Fig. 58], we see that if we had chosen the origin to be in the interface, er and et would have been zero [Hec, p.113, l.c., l.2]. [Matv, Sec. 16] lacks this important justification.

  2. (Assumptions must be clarified and justifiable) [Wangs, p.411, l.-12] just assumes the directions of Ei^, Er^, and Et^ by brute force in one case and vaguely describes their directions in the other case. In contrast, [Hec, p.113, l.c., l.-11-l.-9] gives a more subtle reason why we may do so. In addition, [Hec, p.117, r.c., l.7-l.10] clarifies the meaning of phase shift by defining carefully what in-phase and out-of-phase mean.
    Remark. If we trace the definition given in [Hec, p.117, r.c., l.7-l.10] to its root, we see that it  is the consequence of the convention given in [Born, p.37, l.-12-l.-11].

  3. (Derivations) [Matv, p.131, (16.43a)] is valid if  ni < nt or if (ni > nt and qin < qlim) even though the proof is based on the former case [Matv, p.129, Fig. 65]. The same proof is also valid for the latter case. The formula for the the later case has an application in [Hec, p.663, lc, l.-5]. Another example is given by [Matv, p.129, (16.33c)]. The formula for the case (ni > nt and qin < qlim) has an application in [Hec, p.117, l.c., l.-5].