“Nothing is easier,” answered Barbicane; “I can give you some examples.  At the siege of Constantinople by Mahomet II., in 1453, they hurled stone bullets that weighed 1,900 lbs.; at Malta, in the time of its knights, a certain cannon of Fort Saint Elme hurled projectiles weighing 2,500 lbs.  According to a French historian, under Louis XI. a mortar hurled a bomb of 500 lbs. only; but that bomb, fired at the Bastille, a place where mad men imprisoned wise ones, fell at Charenton, where wise men imprison mad ones.”

“Very well,” said J.T.  Maston.

“Since, what have we seen, after all?  The Armstrong cannons hurl projectiles of 500 lbs., and the Rodman Columbiads projectiles of half a ton!  It seems, then, that if projectiles have increased in range they have lost in weight.  Now, if we turn our efforts in that direction, we must succeed with the progress of the science in doubling the weight of the projectiles of Mahomet II. and the Knights of Malta.”

“That is evident,” answered the major; “but what metal do you intend to employ for your own projectile?”

“Simply cast-iron,” said General Morgan.

“Cast-iron!” exclaimed J.T.  Maston disdainfully, “that’s very common for a bullet destined to go to the moon.”

“Do not let us exaggerate, my honourable friend,” answered Morgan; “cast-iron will be sufficient.”

“Then,” replied Major Elphinstone, “as the weight of the projectile is in proportion to its volume, a cast-iron bullet, measuring nine feet in diameter, will still be frightfully heavy.”

“Yes, if it be solid, but not if it be hollow,” said Barbicane.

“Hollow!—­then it will be an obus?”

“In which we can put despatches,” replied J.T.  Maston, “and specimens of our terrestrial productions.”

“Yes, an obus,” answered Barbicane; “that is what it must be; a solid bullet of 108 inches would weigh more than 200,000 lbs., a weight evidently too great; however, as it is necessary to give the projectile a certain stability, I propose to give it a weight of 20,000 lbs.”

“What will be the thickness of the metal?” asked the major.

“If we follow the usual proportions,” replied Morgan, “a diameter of 800 inches demands sides two feet thick at least.”

“That would be much too thick,” answered Barbicane; “we do not want a projectile to pierce armour-plate; it only needs sides strong enough to resist the pressure of the powder-gas.  This, therefore, is the problem:—­What thickness ought an iron obus to have in order to weigh only 20,000 lbs.?  Our clever calculator, Mr. Maston, will tell us at once.”

“Nothing is easier,” replied the honourable secretary.

So saying, he traced some algebraical signs on the paper, amongst which n^2 and x^2 frequently appeared.  He even seemed to extract from them a certain cubic root, and said—­

“The sides must be hardly two inches thick.”