Read Ebook: Encyclopaedia Britannica 11th Edition Equation to Ethics Volume 9 Slice 7 by Various

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"You are under the dead-fall, aye," said Mason. "The cunning of my enemy is sublime."

"Your enemy?" gasped Walcott. "When did you come into it? How in God's name did you know it? How your enemy?"

Mason looked down at the wide bulging eyes of the man.

"Who should know better than I?" he said. "Haven't I broken through all the traps and plots that she could set?"

"She? She trap you?" The man's voice was full of horror.

"The old schemer," muttered Mason. "The cowardly old schemer, to strike in the back; but we can beat her. She did not count on my helping you--I, who know her so well."

Mason's face was red, and his eyes burned. In the midst of it all he dropped his hands and went over to the fire. Samuel Walcott arose, panting, and stood looking at Mason, with his hands behind him on the table. The naturally strong nature and the rigid school in which the man had been trained presently began to tell. His composure in part returned and he thought rapidly. What did this strange man know? Was he simply making shrewd guesses, or had he some mysterious knowledge of this matter? Walcott could not know that Mason meant only Fate, that he believed her to be his great enemy. Walcott had never before doubted his own ability to meet any emergency. This mighty jerk had carried him off his feet. He was unstrung and panic-stricken. At any rate this man had promised help. He would take it. He put the paper and envelope carefully into his pocket, smoothed out his rumpled coat, and going over to Mason touched him on the shoulder.

"Come," he said, "if you are to help me we must go."

The man turned and followed him without a word. In the hall Mason put on his hat and overcoat, and the two went out into the street. Walcott hailed a cab, and the two were driven to his house on the avenue. Walcott took out his latch-key, opened the door, and led the way into the library. He turned on the light and motioned Mason to seat himself at the table. Then he went into another room and presently returned with a bundle of papers and a decanter of brandy. He poured out a glass of the liquor and offered it to Mason. The man shook his head. Walcott poured the contents of the glass down his own throat. Then he set the decanter down and drew up a chair on the side of the table opposite Mason.

"Sir," said Walcott, in a voice deliberate, indeed, but as hollow as a sepulchre, "I am done for. God has finally gathered up the ends of the net, and it is knotted tight."

"Am I not here to help you?" said Mason, turning savagely. "I can beat Fate. Give me the details of her trap."

He bent forward and rested his arms on the table. His streaked gray hair was rumpled and on end, and his face was ugly. For a moment Walcott did not answer. He moved a little into the shadow; then he spread the bundle of old yellow papers out before him.

"To begin with," he said, "I am a living lie, a gilded crime-made sham, every bit of me. There is not an honest piece anywhere. It is all lie. I am a liar and a thief before men. The property which I possess is not mine, but stolen from a dead man. The very name which I bear is not my own, but is the bastard child of a crime. I am more than all that--I am a murderer; a murderer before the law; a murderer before God; and worse than a murderer before the pure woman whom I love more than anything that God could make."

He paused for a moment and wiped the perspiration from his face.

"Sir," said Mason, "this is all drivel, infantile drivel. What you are is of no importance. How to get out is the problem, how to get out."

Samuel Walcott leaned forward, poured out a glass of brandy and swallowed it.

"Well," he said, speaking slowly, "my right name is Richard Warren. In the spring of 1879 I came to New York and fell in with the real Samuel Walcott, a young man with a little money and some property which his grandfather had left him. We became friends, and concluded to go to the far west together. Accordingly we scraped together what money we could lay our hands on, and landed in the gold-mining regions of California. We were young and inexperienced, and our money went rapidly. One April morning we drifted into a little shack camp, away up in the Sierra Nevadas, called Hell's Elbow. Here we struggled and starved for perhaps a year. Finally, in utter desperation, Walcott married the daughter of a Mexican gambler, who ran an eating-house and a poker joint. With them we lived from hand to mouth in a wild God-forsaken way for several years. After a time the woman began to take a strange fancy to me. Walcott finally noticed it, and grew jealous.

"One night, in a drunken brawl, we quarrelled, and I killed him. It was late at night, and, beside the woman, there were four of us in the poker room,--the Mexican gambler, a half-breed devil called Cherubim Pete, Walcott, and myself. When Walcott fell, the half-breed whipped out his weapon, and fired at me across the table; but the woman, Nina San Croix, struck his arm, and, instead of killing me, as he intended, the bullet mortally wounded her father, the Mexican gambler. I shot the half-breed through the forehead, and turned round, expecting the woman to attack me. On the contrary, she pointed to the window, and bade me wait for her on the cross-trail below.

"It was fully three hours later before the woman joined me at the place indicated. She had a bag of gold dust, a few jewels that belonged to her father, and a package of papers. I asked her why she had stayed behind so long, and she replied that the men were not killed outright, and that she had brought a priest to them and waited until they had died. This was the truth, but not all the truth. Moved by superstition or foresight, the woman had induced the priest to take down the sworn statements of the two dying men, seal it, and give it to her. This paper she brought with her. All this I learned afterwards. At the time I knew nothing of this damning evidence.

"We struck out together for the Pacific coast. The country was lawless. The privations we endured were almost past belief. At times the woman exhibited cunning and ability that were almost genius; and through it all, often in the very fingers of death, her devotion to me never wavered. It was dog-like, and seemed to be her only object on earth. When we reached San Francisco, the woman put these papers into my hands." Walcott took up the yellow package, and pushed it across the table to Mason.

"She proposed that I assume Walcott's name, and that we come boldly to New York and claim the property. I examined the papers, found a copy of the will by which Walcott inherited the property, a bundle of correspondence, and sufficient documentary evidence to establish his identity beyond the shadow of a doubt. Desperate gambler as I now was, I quailed before the daring plan of Nina San Croix. I urged that I, Richard Warren, would be known, that the attempted fraud would be detected and would result in investigation, and perhaps unearth the whole horrible matter.

"The woman pointed out how much I resembled Walcott, what vast changes ten years of such life as we had led would naturally be expected to make in men, how utterly impossible it would be to trace back the fraud to Walcott's murder at Hell's Elbow, in the wild passes of the Sierra Nevadas. She bade me remember that we were both outcasts, both crime-branded, both enemies of man's law and God's; that we had nothing to lose; we were both sunk to the bottom. Then she laughed, and said that she had not found me a coward until now, but that if I had turned chicken-hearted, that was the end of it, of course. The result was, we sold the gold dust and jewels in San Francisco, took on C denote known quantities, either positive or negative.

and

Thus we have obtained a value of the unknown quantity y, in terms of the known quantities q and r; therefore the equation is resolved.

and put

Then, from what has been shown , it is evident that v and z have each these three values,

which are therefore the three values of y.

The first of these formulae is commonly known by the name of Cardan's rule .

where A, B, C, D denote known quantities.

so that x may have these four values,

+b, -b, +b-1, -b-1,

two of which are real, and the others imaginary.

We have already explained how an equation which is complete in its terms may be transformed into another of the same degree, but which wants the second term; therefore any biquadratic equation may be reduced to this form,

where the second term is wanting, and where p, q, r denote any known quantities whatever.

then, from the theory of equations we have

We square the assumed formula

and obtain

or, substituting -P for a + b + c, and transposing,

Let this equation be also squared, and we have

and since

and

the same equation may be expressed thus:

Thus we have the biquadratic equation

and it immediately appears that

and from these equations we find

Hence it follows that the roots of the proposed equation are generally expressed by the formula

where a, b, c denote the roots of this cubic equation,

But to find each particular root, we must consider, that as the square root of a number may be either positive or negative, so each of the quantities a, b, c may have either the sign + or - prefixed to it; and hence our formula will give eight different expressions for the root. It is, however, to be observed, that as the product of the three quantities a, b, c must be equal to R or to -q; when q is positive, their product must be a negative quantity, and this can only be effected by making either one or three of them negative; again, when q is negative, their product must be a positive quantity; so that in this case they must either be all positive, or two of them must be negative. These considerations enable us to determine that four of the eight expressions for the root belong to the case in which q is positive, and the other four to that in which it is negative.

becomes, after reduction,

it also follows, that if the roots of the latter equation are a, b, c, the roots of the former are 1/4 a, 1/4 b, 1/4 c, so that our rule may now be expressed thus:

and find its roots, which let us denote by a, b, c.

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