p(z) = p_0 + \rho_0 \cdot g \cdot (z-z_0)

p(z) = p_0 \cdot \exp \left[ - \frac{\rho_0 \, g}{p_0} \cdot (z-z_0) \right]

\frac{1+ c_0 \, p(z)}{1 + c_0 \, p_0} = \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z-z_0)}{1+c_0 \, p_0} \right]

p_2 - p_1 = \rho_0 \cdot g \cdot (z_2-z_1)

p_2 - p_1  = p_1  \cdot \left( \exp \left[ \frac{  \rho_0 \cdot g \cdot (z_2-z_1)} {p_0}  \right] - 1 \right) 

p_2 - p_1  = \frac{ (1+c_0 \, p_1)}{c_0}  \cdot \left( \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z_2-z_1)}{1+c_0 \, p_0} \right] - 1 \right)