The lightest possible filling for a balloon is not hydrogen, but vacuum. But how to make it strong enough to withstand the pressure of the atmosphere, while still being light enough to rise? Daedalus's answer is a graded-cell polymeric foam.

Inspired by that foaming urethane monomer, he is devising a new liquid monomer that polymerizes with release, not of carbon dioxide, but hydrogen. It will be placed in a hollow, evacuated, spherical mould which will be spun rapidly about three axes simultaneously. The resulting uniform, radial, centrifugal force field will spread the monomer over its interior surface as an even coating. When it begins to foam, the bubbles will swell towards the centre. Their strong expansion into the central vacuum will be opposed by the centrifugal field. But this field, of course, declines towards the centre of the spinning sphere. So the more the foam advances towards the centre, the more its cells will expand, and the lower the gas pressure within them. When the reaction is over, the mould will contain a spherical foamed balloon. Its smooth outer skin will be supported by a foam whose cells grow ever larger, and contain an ever lower pressure of hydrogen, as they extend towards the centre. The largest cell, the remains of the original interior space, will occupy the central region, and will contain vacuum. At each radius, the cellular foam will just be strong enough to support the difference of pressure across it. Thus the balloon as a whole will safely withstand atmospheric pressure.

Released into the atmosphere, the new rigid vacuum balloon will rise until it reaches that height at which it has the same density as the ambient air. There it will float indefinitely, drifting randomly around the globe with the winds. The obvious use is in cellular telephony. In this application, each balloon will carry a solar-powered radio repeater, and will be designed to float perhaps 20 km up, safely above the commercial air lanes. For this height, about a thousand balloons wandering at random should ensure that anywhere on Earth, at least one will be above the horizon. They will maintain effortless global coverage far more cheaply than any satellite system. Like satellites, they will have a limited life, but will be much easier to replace. As fast as air diffuses into them, or their electronics fails, they will be punctured by laser beams fired from aircraft, and new ones lofted up to replace them.