Full Tables 2 and 3a-3w are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/489/1271 The FTS spectra used in this study are also available from the same location, by courtesy of K. H. Hinkle and S. T. Ridgway (Kitt Peak National Observatory).

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Sample of Tables 2, 3 and Figs. 5, 7, 9, 11, 14 are only available in electronic form at http://www.aanda.org

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... Table 4

Abundances are expressed throughout on the scale of log $A_{\element[][]{H}}~=~12.0$ .

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... Table 5

We refer to a model by its case/mass (in $M_{\odot }$ )/radius (in $R_{\odot}$ )/ $T_{\rm eff}$ (in K). For example, the first model photosphere in Table 5 is referred to as a/1.0/50/4000.

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...1997)

This research has made use of the VizieR catalogue access tool, CDS, Strasburg, France, via ADC/NAOJ.

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...b

Some differences with the result for $\alpha$ Her in Table 4 of Paper I ( $\xi_{\rm micro} = 3.30 \pm 0.38$ km s^-1 and log $A_{\rm C} = 7.93 \pm 0.28$ ), may be due to the use of SS instead of PP models in the present analysis. Thus, the effect of sphericity is certainly not negligible but rather small.

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... study

With the critical value that discriminates the lines well interpreted by the classical line formation theory from those that cannot be, we distinguish three groups of lines to be referred to as; 1) the weak lines (log ${W/\nu} \la -4.75$ , although these lines are not necessarily very weak lines free from saturation effect). 2) the intermediate-strength lines ( $-4.75 < {\rm log}~{W/\nu} \la -4.4$ ), and 3) the strong lines (log ${W/\nu} > -4.4$ , these lines are mostly low excitation lines of CO discussed in Paper II).

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... $-5.3 < {\rm log}~W/\nu < -4.4$

Note that our previous analysis of the CO first overtone lines with $-5.1 < {\rm log} W/\nu < -4.5$ appeared to provide a solution (Fig. 1c of Paper I), but it now appears to be a wrong solution because of the two reasons. First, as we have just found, it included the intermediate-strength lines to which the line-by-line analysis based on the classical micro-turbulent model cannot be applied. Second, it included only few weak lines. With such lines of the CO first overtone bands, the line-by-line analysis converged to an incorrect solution, and this is an example of a systematic error due to an improper selection of lines, as noted in Sect. 3. Such a convergence to a wrong solution could be prevented and the correct critical value could be found, if a sufficient number of weak lines could have been included in our analysis of Paper I.

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... R Lyr

While the intermediate-strength lines of CO in R Lyr (Fig. 9b) and SW Vir (Fig. 9c) show negative abundance corrections, the intermediate-strength lines of OH fundamentals in R Lyr (Fig. 11b) and SW Vir (Fig. 11c) do not. However, OH fundamental bands were not observed simultaneously with CO bands (see Table 2) and it is possible that line formations took place at different conditions in these variable stars.

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... Paper III)

The macro-turbulent velocity is derived by subtracting the effect of the micro-turbulent velocity from the line width on the assumption of Gaussian micro- and macro-turbulence. The resulting values are; $\xi_{\rm macro} = 2.7$ , 2.1, 3.9, and 2.8 km s^-1 for 10 Dra, RZ Ari, $\lambda$ Aqr, and RR UMi, respectively.

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... abundance

Strong lines noted by the open triangle in Fig. 16d are mostly originating from ¹²C¹⁶O (3, 1) and they are too strong to be used as indicator of the carbon abundance.

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... stars

We noticed that the lines of log $W/\nu > -4.5$ show excess absorption in some early M giants in Paper II (see its Fig. 2), but we regret that we did not pursue this case in more detail. With the critical value of log $W/\nu \approx -4.5$ , the lines showing excess absorption were limited to only few lines in the early M giant stars.

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... method

From a detailed measurement of the shifts and shapes of CO lines, we showed that the line asymmetries and differential line shifts of CO lines are as high as 0.5 km s^-1(Paper III). This can also be interpreted as evidence for the presence of extra molecular layers that may have different velocities than the photosphere.

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... undisturbed

We assume that the MOLsphere is almost transparent to the continuum radiation at least in the near infrared and that the infrared flux method with the L band flux can still be applied. However, it is possible that the MOLsphere is opaque to continuum radiation at longer wavelengths, as has been shown for the radio domain of Mira variable stars (Reid & Menten 1997).

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