Akhmeteli and Gavrilin note, however, that the compressive strength calculation disregards buckling, and using R. Zoelli's formula for the critical buckling pressure of a sphere where formula_13 is the modulus of elasticity and formula_14 is the Poisson ratio of the shell. Substituting the earlier expression gives a necessary condition for a feasible vacuum balloon shell: The requirement is about formula_16. Akhmeteli and Gavrilin assert that this cannot even be achieved using diamond (formula_17), and  propose that dropping the assumption that the shell is a homogeneous material may allow lighter and stiffer structures (e.g. a honeycomb structure). A vacuum airship should at least float (Archimedes law) and resist external pressure (strength law, depending on design, like the above R. Zoelli's formula for sphere). These two conditions may be rewritten as an inequality where a complex of several physical constants related to the material of the airship is to be lesser than a complex of atmospheric parameters. Thus, for a sphere (hollow sphere and, to a lesser extent, cylinder are practically the only designs for which a strength law is known) it is formula_18, where formula_19 is pressure within the sphere, while formula_20 («Lana coefficient») and formula_21 («Lana atmospheric ratio») are:  where formula_28 formula_29 and formula_30 formula_31 are pressure and density of standard Earth atmosphere at sea level, formula_32 and formula_33 are molar mass (kg/kmol) and temperature (K) of atmosphere at floating area. Of all known planets and moons of the Sun system only the Venusian atmosphere has formula_21 big enough to surpass formula_20 for such materials as some composites (below altitude of ca. 15 km) and graphene (below altitude of ca. 40 km). Both materials may survive in the Venusian atmosphere. The equation for formula_21 shows that exoplanets with dense, cold and high-molecular (formula_37, formula_38, formula_39 type) atmospheres may be suitable for vacuum airships, but it is a rare type of atmosphere. In the Edgar Rice Burroughs novel "Tarzan at the Earth's Core" Tarzan travels to Pellucidar in a vacuum airship constructed of the fictional material Harbenite. In "Passarola Rising", novelist Azhar Abidi imagines what might have happened had Bartolomeu de Gusmão built and flown a vacuum airship.