jury! This is the most heartless case of overwork within school doors that it has ever been my fate to hear of or be interested in. There is no money on earth or no punishment that can heal my client's bruised heart or atone for his loss in the person of little C for whom he always had a gentle, brotherly feeling. We seek some balm for this shattered heart-the arithmetical sum of a series of 500 terms beginning with 3 when the difference is 7-a mere bagatelle. That will not return one-half of my client's lost manhood and assertiveness. Yet we will take it-take it as a lesson to future mathematicians (Gestures to audience.) tempted to overwork those in their power. I ask you to shed tears for my client if you have any to shed. If you have none, think of the deceased. He (Indicates B.) has told you the solemn truth in all its harrowing details. To further substantiate the truth spoken by him, I call to the witness stand D, at one time affiliated in this partnership. (D comes to stand.) He will corroborate all the details so reluctantly given by B, my client.

(Court clerk takes big book to D at the witness stand.)

Clerk-Do you swear to tell the truth, the whole truth, and nothing but the truth?

D-Yes, sir.

Clerk-Put your hand on the book and say, "I do so swear." D-(Very awed, places hand on book.) I do so swear.

(Clerk returns to take notes.)

Judge--What is your occupation?

D-I just scratch about in the garden, sir, and grow a bit of logarithm or raise a common denominator or two. But Mr. Euclid he use me still for them propositions, he do.

Judge Do you realize the nature of an oath?

D-I've heard my father use them.

Second Lawyer-(Arises.) Your Honor, and gentlemen and ladies of the jury. I represent the much-maligned person A, alias John of "John, William, and Henry," alias x of "x, y, and z," my client. First I will cross-examine the witness. Do you know the defendant?

D-Do I know 'em, sir? Why, I knowed 'em all ever since they was little fellows in brackets. Master A, he were a fine lad, sir. Though I always said, "Give me Master B for kindheartedness like." Many's the job as we've been on together, sir. Though I never did no racing or aught of that, but just the plain labor, as you might say.

Second Lawyer-(quickly, with an aim at bewildering D.)

Do you know any of the details leading up to this most infamous attempt at blackmail, coercion, and vilification?

D-(Not comprehending.) N-n-no, sir.

Second Lawyer-Has the plaintiff ever told you of the prospects he would have in case he sued said defendant in this court of appellate jurisprudence and legal acumen?

D-(Still not understanding.) N-n-no, sir.

Second Lawyer-Did you behold said manslaughter coming under the head of fatigé corpus, Sec. 2, pg. 45, state laws of jurisprudence, Littleton or Coke?

D-N-n-no, sir.

Second Lawyer-Nor would the actual occurrence, having taken place homicidal or technical, with malice or forethought, create a desire for his perpetual incarceration?

D-No, sir.

Second Lawyer-Your Honor, their star witness is on the stand. (Mimic.) Yes, sir; no, sir; no, sir. Gentlemen and ladies of the jury, is this evidence in a court of law? A child could have fathomed my legal phrases and meaning. (To D.) Did you comprehend the significance of my interpellations

D-(With the same bewildered look.) N-n-no, sir.
Second Lawyer-Do you speak French?

D-No, sir.

Second Lawyer-Do you speak German?
D-No, sir.

Second Lawyer-Do you speak Spanish?
D-No sir.

Second Lawyer-Do you speak Italian?
D-No, sir.

Second Lawyer-Do you speak Hindoo?
D-No, sir.

Second Lawyer-(To jury.) You will observe that I have addressed him in seven different languages and he can't understand one. (To D.) That is all. You may come down.

First Lawyer (Interrupts.) Your Honor, I would like to question this witness.

Judge-Let this proof be brief and to the point.

First Lawyer-Were you not present at the melancholy end of your former acquaintance, C?

D-(Face clearing up as he understands.) Yes sir.

First Lawyer-Tell what you know.

D-Well, sir, A and B had been rowing on the river for a wager

and C had been running on the bank and then sat in a draught. Of course the bank refused the draught and C was taken ill. A and B came home.

First Lawyer-(Interrupts.) And found C lying helpless in bed?

D-Yes, sir.

First Lawyer-(Questioning.) A shook him roughly and said, "Get up, C, we are going to pile wood." C looked so worn and pitiful that B said, "Look here, A, I won't stand this. He isn't fit to pile wood tonight." Is this so?

D-Yes, sir, and C smiled weak like and said, "Perhaps I could pile a little if I sat up in bed."

First Lawyer-(As a question.) Then B, thoroughly alarmed, said, "See here, A, I'm going to fetch a doctor; he's dying"? D-(Humbly.) Yes, sir, and A got mad, sir, and said they had no money to fetch a doctor.

First Lawyer-What did B do then? D-He said, "I'll get a doctor. terms. That will fetch him."

First Lawyer-Yes, and then?

I'll reduce him to his lowest

D-Well, sir, C's life might have been saved even then if it hadn't been for a mistake about the medicine. It stood at the head of the bed on a bracket, and the nurse accidentally removed it from the bracket without changing the sign.

After that blunder C sank rapidly. On the evening of the next day (Melancholy.) as the shadows deepened in the little room, it was clear to all that the end was near. I think even A was affected at the last as he stood with bowed head aimlessly offering to bet with the doctor on C's labored breathing. “A," whispered C, "I think I'm going fast." "How fast do you think you'll go, old man?" murmured A. "I don't know," said C, "but I'm going at any rate."

The end came soon after that. As his soul sped heavenward, A watched its flight with melancholy admiration, and B (Sniffling.) burst into a flood of tears. (Sobs.) We put away his little cistern and the rowing togs he used to wear and we, B and I, sir, we feel as if we could hardly ever dig again. (Cryingdeep sob.)

(Judge raps for order.)

First Lawyer-That will do.

come down.

Calm yourself. You may

Second Lawyer (Jumping up.) Oh, your Honor, and-I

came near forgetting-ladies and gentlemen of the jury, I want you to look in the face of my client. His life has been arduous and full of peril. A mistake in the working of a sum might keep him digging a fortnight without sleep. A repeating decimal in the answer might kill him, yet he was not deterred. He went right on betting and supplying arithmetics and algebras with page after page of problems. Now you will have a chance of showing your gratitude. Is he to be held accountable if C's strength was in inverse proportion to his own? Because he is a full-blooded, energetic fellow with much initiative, do you think he is without a heart, without emotions? Ah, you forget his panting sides as he pumped water four times as fast as C. You forget his eager counting of the last exhalations of the dying C. Did he not admit himself baffled by the rate and direction of the flight of C's soul? I have here a vector diagram of that same occurrence which he constantly carries with him to have for reference when his own soul flees. He is still confident that his soul will overtake C's before the former comes to rest. Did he not attend that little funeral so plain and unostentatious? Is this acting as a murderer? No! (Ringing tone.) but as a true sporting man and mathematician he engaged two hearses, one for himself and one for B. Both vehicles started at the same time, B driving the one which bore the sable parallelepiped containing the last remains of his ill-fated friend. A, on the box of the empty hearse, generously consented to a handicap of 100 yards, but arrived first at the cemetery by driving four times as fast as B.

As the sarcophagus was lowered, the grave was surrounded by the broken figures of the first book of Euclid.

It may be noticed that A has become a changed man, has lost interest in racing, and digs but languidly. He has given up work and settled down to live on the interest of his bets. Oh, your Honor, and ladies and gentlemen of the jury, look at my client. The learned legal brother is trying to get the sum of an arithmetical series from him as balm. Oh, again I say to you, this is a base conspiracy, and I rely on your sound judgment, and I feel sure that conspirators and blackmailers will fail in their attempt to extort money from my client. I am attending to that myself. (Sits down and fans himself.)

Judge Gentlemen and ladies of the jury. You have heard the evidence on both sides. If you have a verdict for the plaintiff, let it be balm enough to revive his interest in mathematics.

If you find a verdict of acquittal on the charge of murder and extortion for the defendant, so let it be known.

(Silence in the court while the jury confers.)

(Jury files out of the room-in a very short time files back again, Chairman first. B weeps and A begins to bet with his lawyer on the length of time it will take the jury, etc. When jury is seated judge raps for order.)

Chairman of the jury-(Arises.) We have agreed upon a verdict that is, I have, and the rest have come down to the same terms.

Judge What is your verdict?

=

Chairman of the jury-Guilty, your Honor, in the nth degree. Judge-In the eyes of the court, the problem through the proper reduction of radicals involves the personal equation such that A B+C. C approaches infinity, through no fault of his own, leaving A and B to settle. B, in his charge of murder and extortion, has proved his claim, and A by his own demonstration has proved his intellectual quantities imaginary. Treat them both simultaneously. If A finishes before B, who will drink only half as fast, he will devote the rest of his term to determining the value of, especially Omega and Nu . The result is to be sent to Mr. Hoover and the Housewives' League. (Exit judge, then jury, then the rest.)

A GRAPHICAL REPRESENTATION OF APPROXIMATIONS FOR SQUARE ROOT.

BY OTTO DUNKEL,

Washington University, St. Louis, Mo.

In the January, 1918, number of SCHOOL SCIENCE AND MATHEMATICS a simple rule was given for approximations to any root of a number, and it was pointed out how any degree of accuracy could be obtained by successive applications of the rule. In this article it will be shown how the process can be represented graphically in the case of square root in a manner which exhibits the rapidity of convergence of the successive approximations and which also yields a test of the accuracy of each step. In the article referred to there is an inaccurate statement of the rough estimate of the number of decimals which could be depended upon, and this inaccuracy will be corrected below. It will also be shown algebraically how the method can be supplemented by certain corrections which yield additional correct figures.