GdNi$_{2}$B$_{2}$C (Fig.1) reveals the onset of the magnetic order at $T_{N}=$19.5 K and the spin reorientation process at $T_{R}=$13.5 K, in agreement with earlier studies. [@Canfield-GdNi2B2C; @Detlefs-GdNi2B2C-XRES; @Tomala-GdNi2B2C-MES; @Godart-GdNi2B2C-composition; @Massalami-GdNi2B2C-GdNiBC] The thermal evolution of $C_{M}(T)$ within the amplitude-modulated state is distinctly different from that within the equal-amplitude, low-temperature state (see below). As mentioned above, within the modulated region the linearized spin-wave analysis is not applicable and one should resort to the findings of Schmitt and co-workers [@Bouvier-Gd-AM-state-Cm-1]. In particular, these authors demonstrated that $C_{M}(T_{N})$ of such a state suffers a strong reduction (almost 1/3) in comparison with the value (20.15 J/moleK) expected for an equal-amplitude AF state (our results are in excellent agreement with this statement).

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On the other hand, Fig.1 shows that for temperatures below 3.5 K, $C_{M}(T)$ follows faithfully Eq.\[Cm-bessel\] with $\theta$=12.5$\pm$0.2K and $\Delta
$=1.9$\pm$0.3 K.  The numerical value of $\theta$ (for $\Delta$ see Sec.V) is physically acceptable as can be seen from the following arguments. First, the substitution of this $\theta$ into Eq.\[Theta\] yields $J_{eff}$= 0.58$\pm
$0.2 K, which is in close agreement with the value reported for HoNi$_{2}$B$_{2}$C (Ref.[@Amici-thesis],[@Cho-Crystal-field-2]) and TmNi$_{2}$B$_{2}$C (Ref.[@Movshovich-TmNi2B2C]). Secondly, the substitution of $\theta$ into Eq.\[Cm-AF-highT\] predicts correctly the high temperature 