of $R_c$. Condition (\[P\_Rc\]), using Eq. (\[Mech-Eq\]), evidently gives us $$\label{R_c-def}
R_c = \frac{2 \sigma}{P_0 - \Pi}\; ,$$ and condition (\[n\_Rc\]) allows us to connect value $P_0$ with the supersaturation $\zeta$.

Substituting Eqs. (\[P\_Rc\]) and (\[n\_Rc\]) in Eq. (\[Chem-Eq-Henry\]) (Henry’s law) and Eq. (\[Chem-Eq\]) (Sievert’s law) we have correspondingly $$\label{n_0/n_inf-Henry}
\frac{n_0}{n_\infty} = \frac{P_0}{\Pi}$$ and $$\label{n_0/n_inf}
\frac{n_0}{n_\infty} = \sqrt{\frac{P_0}{\Pi}}\; .$$ For Henry’s law we have evidently from Eq. (\[n\_0/n\_inf-Henry\]) using Eq. (\[zeta\]) $$\label{P_0-zeta-Henry}
P_0 = \Pi \left( \zeta + 1 \right).$$ And, substituting Eq. (\[P\_0-zeta-Henry\]) in Eq. (\[R\_c-def\]), we have $$\label{R_c-Henry}
R_c = \frac{2 \sigma}{\Pi \zeta}\; ,$$ the well-known expression for the radius of a critical bubble (e. g. \[\[Slezov-2004\], \[Skripov-1972\]\]).

For Sievert’s law, when Eq. (\[n\_0/n\_inf-Henry\]) is replaced by Eq. (\[n\_0/n\_inf\]), we have $$\label{P_0}
P_0 = \Pi \left( \frac{n_0}{n_\infty} \right)^2,$$ or, using Eq. (\[zeta\]), $$\label{P_0-zeta}
P_0 = \Pi \left( \zeta + 1 \right)^2.$$ Finally, substituting Eq. (\[P\_0-zeta\]) in Eq. (\[R\_c-def\]) for the critical bubble radius, we have $$\label{R_c}
R_c = \frac{2 \sigma}{\Pi \left[ (\zeta + 1)^2 - 1 \right]}\; .$$

Using Eq. (\[R\_s\]) and Eq. (\[R\_c-Henry\]) or Eq. (\[R\_c\]) correspondingly we can write the relations between $R_\sigma$ and $R_c$ for both Henry’s and Sievert’s laws $$\label{R_s-R_c-Henry}
R_\sigma = \frac{2}{3}\zeta R_c\; 