Ralph read the letter, which was written in printed characters, through slowly a second time. Then he looked up at the superintendent with a troubled expression on his face.

“You needn’t say anything about the letter, Mr. Osborn,” the superintendent remarked in a kindly tone. “It contains nothing but lies and the writer is a contemptible coward. But have you any idea as to who the writer may be?”

“Not the slightest, sir,” replied Ralph, much relieved at the superintendent’s words. “Had you heard about Mr. Bollup’s watch being stolen and of how it was found on my watch-chain, sir?”

“Oh, yes, I have the letters you four young gentlemen wrote before me now. Do you think this letter was written by a midshipman or somebody else?”

“I have no idea, sir; I can’t imagine any midshipman would wish to hurt me. I have never had any trouble that amounted to anything with anybody here, except Mr. Short; you know about that, sir.”

“Yes, and Mr. Short is a long ways off. I’ll keep this letter carefully and perhaps something may turn up——”

“Sir, may I offer a suggestion?”

“Certainly, Mr. Osborn; what is it?”

“I would request that that letter be published to the battalion with your order that the writer of it, if a midshipman, should report to you.”

The superintendent thought a moment and then said: “I won’t publish the letter, that could do no good, but I will have an order read requiring the writer of a letter to me signed ‘Indignant Fourth Classman’ to report to me. Now, Mr. Osborn, whenever a charge of any kind is made against any person in the Navy it is always investigated. So I have directed Professor Scott to go over your papers himself, and then to come here with them. I expect him here in a few moments—here he is now. Good-morning, professor.”

“Good-morning, admiral. I have been over Mr. Osborn’s papers, and——”

“One minute, professor; just read this letter and you will know why I had you go over Mr. Osborn’s semi-annual examination papers in mathematics.”

The professor read the letter, and then indignantly threw it down on the desk. “That’s contemptible, sir; in his work Mr. Osborn has shown thorough comprehension. In his algebra questions Mr. Osborn stumbled somewhat on a few of the problems but in every case displayed a good knowledge of the principles involved. A number of answers he obtained by original methods; this has pleased me very much. In spite of his low marks last month—I looked into that—he has shown a real knowledge, and has not made his good marks by means merely of a good memory. But his geometry paper is magnificent, admiral,” continued Professor Scott, enthusiastically. “Had I been the one to have first marked his paper I would have called attention to a beautiful piece of original work. In the December examination he stumbled over the problem in geometry of proving the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. He clean forgot how to do it; the same problem was given in the semi-annual, and Mr. Osborn proved it in his own way by a method I have never before seen or heard of. I have examined every book we have in the department and can find no mention of this method. I talked with every one of my assistants and all were delighted with Mr. Osborn’s method. I suppose the method must be known; it’s not possible that Mr. Osborn could be the original discoverer of it, but I’ve never seen the method before nor can I find any one who has; admiral, here it is——” and Professor Scott took one of the sheets of Ralph’s paper on which was written the following:

Question:

Prove the square of the hypotenuse of a right-angled triangle, is equal to the sum of the squares of the other two sides.

Demonstration:

Let ABC be a right-angled triangle.

To prove (AB)² = (AC)² + (BC)².

On AB erect the square ABED. Draw BM parallel and equal to AC. From A erect a perpendicular through M.

By inspection triangle AMB = triangle ABC.

From point E drop a perpendicular to the line BM. The triangle thus formed, ENB, having a side and angles equal to a side and angles of triangle AMB, is seen by inspection to be equal to triangle AMB, and therefore to triangle ABC. Hence BN is equal to BC.

In a similar way construct the triangles ADH and DKE. By inspection each of these is seen to be equal to triangle ABC.

The square erected on AB is thus equal to four times the triangle ABC plus the rectangle HMNK.

Rectangle HMNK = MN × MH.

MN = BM - BN = AC - BC.

MH = AH - AM = AC - BC.

Four times area of triangle ABC = 4 × (1/2) AC × BC.

Hence (AB)² = 4 × (1/2) AC × BC + (AC - BC) (AC - BC) = 2 AC × BC + (AC)² - 2 AC × BC + (BC)². Or, (AB)² = (AC)² + (BC)². Q. E. D.

“Now, admiral,” continued the delighted professor, “I’m going to send Mr. Osborn’s demonstration to some of the colleges and mathematical societies. Although it is original with Mr. Osborn, at least I imagine that it is, I really cannot believe that it is possible that he is the first discoverer of this method. If it should prove that Mr. Osborn is the original person who has ever used this method it will go down in the books as ‘The Osborn Demonstration.’”

“How did you happen to fall on that method, Mr. Osborn?” asked the admiral.

“Why, sir, I failed miserably on this question in the December examination and afterward I was determined to get it without referring to the book. One time when I was working at it, wondering why I couldn’t do it, I happened to erect the square on the hypotenuse and somehow drew in the triangles. Then when I looked at the figure I started to add up the areas of the different triangles and the square in the center and it all worked out naturally.”

“It’s an algebraic rather than a geometrical proof, or rather a combination of both,” remarked Professor Scott, “and Mr. Osborn deserves much credit. And as for the statement that Mr. Osborn cheated by carrying books in the examination with him, why that is as ridiculous as it is false and contemptible.”

“That is just my notion,” assented the superintendent. “Now, Mr. Osborn, don’t worry about this letter and don’t talk with anybody about it. There is undoubtedly somebody determined to do you terrible injury, but I think we can take care of you. Keep your eyes wide open, say nothing, not even to your closest friend, and if you learn anything whatever come to me immediately.”

Ralph left the superintendent’s office in a very happy and comfortable state of mind. He was indeed perplexed at the persistent hidden enmity that had been displayed against him, and for which he could imagine no cause, but he felt that he had a powerful friend who would protect him.

The next month, February, Ralph was in the fourth section in mathematics. The regular instructor assigned to this section was sick so that the head of the department, Professor Scott, took the section. He displayed much interest in Ralph’s work; this was apparent to all, and inspired by this Ralph devoted himself to preparing his recitations with a zest he had never felt before. He worked enough on his rhetoric and French to get satisfactory marks in these subjects, but in most of his study hours and much of his leisure after drill and on Saturdays and Sundays he devoted himself to his algebra. Before going to recitations he had always studied the principles carefully and worked out most, if not all of the problems.

At the end of February the monthly examinations were held.

“How did you do, Os?” asked Creelton, after they had returned to their rooms.

“I feel I hammered it hard. How did you do, Creel?”

“Oh, I biffed it. I’ve good recitation marks and hope to stand number one this month. I’d like to cook Himski and Bollup this month.”

“I hope you did well,” said Ralph heartily. “I suppose you fellows in the first section will all stay there, but I hope I may pull up into the second.”

“That would be a good rise for you, Os; I hope you will. You’ve been working hard at math this month and will probably land in the third section if you don’t make the second.”

While Ralph, Creelton, Bollup and Streeter were returning together from drill a few days later, Bollup said: “Hello, there’s a crowd at our bulletin-board; I guess our math marks are posted.”

They all ran up to the board, Bollup leading. As soon as he had looked at the bulletin-board he gave a yell and cried:

“Jumping Jehoshaphat! Ralph Osborn! Just look at those marks. By the tall American green-eyed prophet, you made a 4.0 on every daily recitation in the month, and to make matters worse, knocked a cold 4.0 on the exam!”

Ralph looked with staring eyes. He had the sensation of the man who has won the capital prize in a lottery. Many were the exclamations of surprise from his classmates when they saw what Ralph had done. Most of the fourth section had risen in class rank, and much credit was given to Professor Scott’s illuminating instruction by the young men who had been in his section; and now all of these declared they had known that Osborn had been doing excellent work and they were not at all surprised he had landed first in the class. But Ralph in his secret heart felt that Professor Scott had been very generous to him in his daily marks.

“And only a month ago I was in danger of being bilged,” remarked Ralph to Creelton when they entered their room.

Creelton did not answer, but slammed things around in a very angry way.

“What’s the matter with you?” asked Ralph in surprise.

“Do you think I like being cooked by everybody?” snapped Creelton. “You and Bollup and Himski all came out ahead of me; I stood number seven; I ought to have stood one.”

“If you can only make a 3.32 on such an easy exam you’ve no right to stand even number seven,” returned Ralph with spirit. “As you didn’t deliver the goods and other people did, I fail to agree that you should have stood number one or any number higher than the one given you.”

“You talk mighty big for a man whom I saved from bilging in French last term,” retorted Creelton.

“You offered to help me; I didn’t ask it. And you did help me a great deal and I thanked you then and I thank you now. But that has nothing whatever to do with the matter we’re talking about.”

“Great heavens! Will you shut up? I wish I had never seen you. Oh, I can’t stand it!” And Creelton burst into tears, and dropping heavily into a chair by the study table, he flung his head down on his arms and sobbed convulsively.

“Why, Creel, don’t feel badly, old fellow; I’m awfully sorry,” and Ralph, much touched as well as astonished, went to Creelton and tried to comfort him, but to no avail. Then, much perplexed, he left the room and went off to see Bollup. Later when he returned, Creelton, now entirely over his sad feelings, said: “Os, please excuse and forgive my words. I cannot tell you how disappointed I was; I had counted so much on standing number one; and getting class rank of seven was a bitter blow to me; I just gave way to my feelings.”

“Don’t speak of it—it’s all right; let’s talk of something else,” returned Ralph. “It seems glorious to stand number one, but I’ll never keep it. You may get it next month; cheer up, Creel.”