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To solve the L-L law and E-O theorem, we note that (6.1.46a) and (6.1.46b) form a system of simultaneous homogeneous equations for the unknown amplitudes X~M) and X~N). For a nontrivial solution, the determinant of the coefficients must vanish, yielding an equation for the effective wavenumber K in terms of k, the scattering coefficients T~M) and T~N), and the fractional volume of the scatterers. This is the dispersion relation for the composite medium. Hence, the procedure is to first find the solution K of the generalized Lorentz-Lorenz law, leaving an arbitrary constant to be next determined by the single scalar equation (6.1.49) of the generalized Ewald-Oseen extinction theorem.

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A closed-form solution can be obtained for the effective propagation constant K in the low-frequency Rayleigh limit. In such a case, only the electric dipole term TiN) contributes in (6.1.46a) and (6.1.46b). Thus including n = 1 term only in (6.1.46b) gives an equation involving the unknown amplitude Setting the coefficient equal to zero gives the dispersion relation

xi N).

L a(l, 11- 1, 1Ip)A(1, 1,p) (Lp(k, Klb) + Mp(k, Klb)) = 0

(6.1.50)

As discussed in 2, Section 8 of Volume I, in the low-frequency limit,

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The rst is on the left side of the left shoulder; the second is at the right side of the left shoulder (which is also the left side of the head); the third is at the right side of the head; the fourth is at the right side of the right shoulder, at which point the price breaks beneath the neckline; and the fth point (which is optional, in a sense) is when the price retraces back up to the neckline before falling hard once again Once the price has broken beneath the neckline, the H&S pattern has validity only if the price remains below the neckline (When the price retraces, you may want to allow for a few pennies of violation before dismissing the pattern altogether).

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+ iTi[y) and Ti:') = -Ti[y)2. In calculating the effective propagation constant K, it is to be noted that K i = Im(K) is a combination of absorption and scattering effects. We note that K r = Re(K) is of order 0(1) and K i is of order O(J) for absorption and is of order 0(Jk 3 a 3 ) for I ITi~\ However, canscattering. Since ITi~) I 1, we have I not be neglected because it contributes to the attenuation rate K i Thus, in

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FIGURE 16-8 The governors of both New Hampshire and Vermont attended the dedication ceremony. (See 16 for discussion of the Cornish-Windsor Bridge.)

Ti:')

performing the low-frequency approximation of terms in (6.1.50), we shall (i) keep only the leading term of the real part and the leading term of the imaginary part, (ii) ignore the real part of a term if it is less than O( k 3 a 3 ) of the corresponding imaginary part, and (iii) ignore the imaginary part of a term if it is less than O(k 3 a 3 ) of the corresponding real part. Using these rules, the low-frequency approximations for TiN) is (6.1.51) where

(6.1.52)

The low-frequency approximation of L p is (6.1.53) Only the p = 0 term in L p has a nonzero second term in (6.1.53) because for p ~ 1, the real part is of an order smaller than O(k 3 a 3 ) of the imaginary part. Similarly, Mp(k, Klb) = ()poMo with

[g(r) -1]

Just because the price goes above the neckline doesn t absolutely mean the stock will not fall, but it does indicate strength that is normally not part of a good, strong H&S breakdown Figure 127 shows an instance where the price broke below the neckline, went well above it again, then once more fell beneath it A pattern with noise such as this should be viewed with more skepticism than a pattern absent such noise What you instead want to see is more along the lines of the chart shown in Figure 128, which is actually the same stock as the one in Figure 127 but at a different point in time.

(6.1.54)

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