“Agreeably to the advice of my council, I order the pain of death against the transgressor. And in order to encourage the suppliant to apply himself with zeal toward improving the machine which is capable of producing the effects mentioned by him, I also grant him the first Professorship of Mathematics in my University of Coimbra, and the first vacancy in my College of Barcelona, with the annual pension of 600,000 reis during his life.” The “patent” seemed liberal enough, and yet Gusmao never resumed his aërial experiments. He was accused of magic, and may have feared persecution on that account; accordingly he engaged in naval construction till 1724, when he left Portugal. The first vacuum balloon was proposed by the Jesuit father, Francis Lana, and described in his book _Podromo dell’Arte Maestra Brecia_, which appeared in 1670. Though not a practical project like Gusmao’s, it was very ingenious, and marks an interesting phase in the evolution of the fundamental idea of the air ship, or “balloon” as it was called by the inventor, who then coined the word now in common use. Lana proposed to use four copper spheres each 25 feet in diameter and 1/225 inches in wall thickness, quite well exhausted of air, to give ascensional force which he computed at 1,200 pounds aggregate for the four spheres. From these he would suspend the passengers in a boat having a mast and sail to propel the ship in time of favorable wind. Having computed the buoyancy according to well-known physical laws, he could see no possible objection to his project “unless,” he writes, “it be that God would never permit this invention to be practically applied, in order to prevent the consequences that would ensue therefrom in the civil and political government of men.” [Illustration: FIG. 4.—LANA’S PROPOSED VACUUM BALLOON.] Of recent years inventors having less delicate scruples about embarrassing Providence, have revived Lana’s project with improvements. It has been proposed to replace the sail by a motor-driven propeller, and to ensure the hull against collapse from the prodigious external air pressure—a ton per square foot—by ample internal bracing. Even within the past twelve months this scheme has been soberly advocated by several technical journals and by the author of an elaborate book on aërial warfare. To a mathematician this is amusing, when not too pathetic; for it can be rigorously proved that no vacuum balloon of present day material, whatever its design, can possibly resist crushing if made light enough to float.