is reminded that this analysis is not adequate for the description of the contribution of the modulated state since the involved ordered components do not have equal magnitudes. Finally, the above zero-field treatment is obviously not appropriate for the description of the field-induced metamagnetic phases.

Experimental
============

Single crystals of $R$Ni$_{2}$B$_{2}$C ($R$=Er-Gd) were grown by floating zone method.[@Takeya-FZ-method] Physical characterization were carried out utilizing a dc magnetometer \[$H$$<$50 kOe, 2 K $<$$T$$<$20 K\], a mutual-induction ac-susceptometer \[$\nu$=250-500 Hz, $H_{pp}\approx$1 Oe, 30 mK $<$$T$$<$20 K\], and a dc resistivity set-up \[$H$$<$50 kOe, 2 K $<$$T$$<$20 K\]. Structural, magnetic and transport characterizations are in agreement with published results. 

The temperature-dependent specific heat was measured on a semi-adiabatic calorimeter \[80 mK $<$$T$$<$25 K, precision better than 4%\]. The total specific heat  curves measured above 2 K are in agreement with the reported data.[@Canfield-HoNi2B2C-M-Cp; @Cho-ErNi2B2C-ansitropy; @Tommy-Dy-superconductivity; @Tommy-Tb-reorientation] However, we observed some discrepancy between the absolute values of $C_{M}(T)$ of single crystal and polycrystalline samples: though both specific heats were found to be given by approximately the same functional form, the absolute values of the fit parameters ($\theta$ and $\Delta$) differ by as much as 40%.

For each compound, the total specific heat, $C_{tot}$, was 