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"Then I am obliged to tell you, Cantor," Lieutenant Trent went on, "that at the courtmartial I shall be obliged to appear as one of Darrin's witnesses. Further, I shall be obliged to testify that you said to him, 'you lie. Then Darrin knocked you down, as any other self-respecting man must have done." "But I didn't tell him he lied," protested Cantor, with much seeming warmth.
Here Cantor proceeded in the only proper way. He took pairs of contradictory propositions, in which both sides of the contradiction would be usually regarded as demonstrable, and he strictly examined the supposed proofs. He found that all proofs adverse to infinity involved a certain principle, at first sight obviously true, but destructive, in its consequences, of almost all mathematics.
But nowadays the limit is defined quite differently, and the series which it limits may not approximate to it at all. This improvement also is due to Cantor, and it is one which has revolutionised mathematics. Only order is now relevant to limits.
Professor Silvanus Thompson, in his recent Cantor Lectures, had shown an ingenious graphical method of proving these important fundamental laws.
"It was, sir," Darrin admitted. "And yet, by the report which Lieutenant Cantor has turned in, you opened fire on Cosetta and his band and have returned to ship with two men killed and four men wounded. Is that report correct?" "It is, sir," admitted the young ensign, "with one exception." "State the exception, Ensign Darrin," ordered the captain, coldly.
Suddenly, over the blended passion of cantor and congregation, an ominous sound broke from without the complex clatter of cavalry, the curt ring of military orders. The swaying figures turned suddenly as under another wind, the women's eyes grew astare and ablaze with terror.
"You are authorized to be ashore, of course?" continued Trent, surveying his brother officer, keenly, for, at such a time, it was strange to see a naval officer ashore in anything but uniform. "I have proper authority for being ashore," Cantor nodded. "That is all, then," said Lieutenant Trent. "You may proceed, of course, but you are going to be halted and held up by every sentry who sees you.
He had been glazier, synagogue beadle, picture-frame manufacturer, cantor, peddler, shoemaker in all branches, coat-seller, official executioner of fowls and cattle, Hebrew teacher, fruiterer, circumciser, professional corpse-watcher, and now he was a tailor out of work.
"Be seated, Lieutenant. I will go through these papers at once." For some minutes there was silence in the room, save for the rustling of paper as Captain Gales turned a page. At last he glanced up from the reading. "I note, Lieutenant Cantor, that you are still of the opinion that the fight could have been avoided." "That is my unalterable opinion, sir," replied the lieutenant.
Lieutenant Cantor, after one or two upward looks, bowed his head and kept his eyes to the ground, but I am positive, sir, of my identification of both men." "And Cosetta's bandits?" inquired Trent. "Did you see any signs of them?" "No, sir, but the adobe house is large enough to hide them all." "Any trenches near the house?" "No, sir."
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