Prob. 17.—If the base d c in the square a b c d, Fig. 21, is 8.75 in., what is the area of the square? From Prop. XX: A square has four equal sides, and has four right angles; therefore, the perpendicular sides are equal to the altitude, and the altitude is the same in length as the base. 8.75 in. X 8.75 in. 76.5625 sq. in. Prob. 18.-If the rhomboid g hij, Fig. 21, has the altitude k j and the base ji 10 in., what is the area of the rhomboid? = From Prop. XX: 5 in. x 10 in. 50 sq. in. Ans. 50 sq. in. Prob 19. In the rectangle I m no, Fig. 21, suppose the altitude m n is 16 ft., and the base o n is 24 ft., what is the area of the rectangle? From Prop. XX: 16 ft. X 24 ft. = 384 sq. ft. Ans. 384 sq. ft. Prob. 20. A piece of land similar in form to the trapezoid a b c d, Fig. 22, has the following dimensions: The base d c = 1,875 ft., the parallel side a b = 3,930 ft., and the altitude e d= 1,600 ft. in square feet? What is the area of the land Ans. 4,644,000 sq. ft. From Prop. XXI. The sum of the two parallel sides = 5,805 ft., half of which is 2,902.5 ft. Then, 1.600 ft. X 2,902.5 ft. = 4,644,000 sq. ft. Prob. 21. If one side of the hexagon 1 m n p q r, Fig. 23, is 8 in., and the apothem o s is 7 in., what is the area of the hexagon? 7 in. 2 Ans. 168 sq. in. The apothem o s= From Prop. XXII: The base q p of the triangle o p q 8 in. 7 in. and is the altitude of the triangle o p q. Prob. 22. If the sides of the scalene triangle e f g, Fig. 20, are as follows: ef 19 in., g f=10 in., and e g 13 in., what is the area of the triangle? Ans. 60.79474 sq. in. The product of the three remainders 11X8X2 X21 3,696. The area of From Note 1: One-half the sum of all the sides is 21 in. The differences are as follows: 22-10-11, 21-13-8, 21-19-2. and half the sum of all the sides is as follows: the triangle is 3,696, or 60.79474 sq. in. Prob. 23. Let us suppose that we are required to find the area of a sheet of steel similar in form to the trapezium f g h i, Fig. 22. The trapezium is divided into two triangles by drawing the diagonal f h. The perpendicular f j is let fall from the vertex f to the base i h in the triangle f h i. The perpendicular gk is let fall from the vertex g to the base f h in the triangle g h f. We find, by aid of a scale, the following dimensions: ih 28 in., fj 10 in., fh= 26 in., k g = 8 in. What is the area of the sheet of steel? From Note II: First find the area of the triangle f h i, as follows: 28 in. (the base) X5 in. (1⁄2 the altitude) = 140 sq. in. Next find the area of the triangle g h f, as follows: 26 in. (the base) X 4 in. (11⁄2 the altitude) = 104 sq. in. The area of the sheet of steel is the sum of the areas of the two triangles, or 140 sq. in. + 104 sq. in. 244 sq. in. F RED LOWMAN, at the time the incidents narrated in this sketch befell him, had been for some years running an engine on the D. & W., in the State of Illinois. Fred had a regular freight run, and, in railroad parlance, was a "good man" with an engine, in every way up to date in his calling, well liked by his associates and by the company's officials, yet he had one habit that was dragging him surely down to ruin. Twice he had been summoned before Mr. Cole, the master mechanic, and after a severe reprimand for his drinking, and a warning to avoid the use of liquor in the future, had been sent back to his run. Each time he had done better for awhile, but his good resolves were not strong enough to sustain him, and each time he had gone back into his old way of doing, Now he was summoned for a third interview with Mr. Cole, and he felt that the loss of his position, under the circumstances, was almost certain. He had been on a drunken spree for a week, and when he had reported to the night foreman to go out on his run in the morning, hoping by so doing to avoid coming in contact with the "Old Man," he was informed that Mr. Cole wished to see him in his office when he reported for work, and that that gentleman was now in his den. Fred's heart sank. He felt his guilt and knew that he deserved punishment, but he had always put the thought of his wrong-doing coming home to him as far as possible from his mind, but now he could not conceal from himself the fact that he had reached the end of his rope. He thought of his wife and children, and the thought of them being compelled to share in his disgrace and deprivation cut him to the heart. However, he might as well have it over, and mustering all the courage he could summon, he walked into Mr. Cole's office. Mr. Cole was busy with some papers, which he laid aside on Fred's entrance. "Good evening, Mr. Lowman; have a chair, please," said Mr. Cole. The reception was not auspicious; ordinarily Mr. Cole would have addressed him as Fred, and been much less formal in his manner. "Good evening, Mr. Cole," replied Fred. as he took a chair. "I believe you wished to see me about something." "I am sorry to say that I do," said Mr. Cole. The fact of the matter is that more of your doings have come to my ears, in reality some of them under my personal observation. Two days ago 1 saw you reeling arm in arm down the main street with Zeb Pike, a man that any self-respecting man would shun as he would a viper. Your conduct is not only ruining yourself, but it has a tendency to demoralize other of our employes if you are allowed to go on your career unchecked. For that reason I have called you here, Is there any possible excuse you can offer for conduct such as yours of late?" and Mr. Cole paused to give Fred an opportunity to exonerate himself if possible. "How can I excuse myself? It is my own weakness. Twice you have warned, nay, talked to me as a father might to a son. My wife has pleaded with me, and I have formed resolves that I would never touch or taste liquor again, but you see how miserably I have failed to keep them. I have meant to do what was right. I have fought it off until a mad impulse that seemed to dim everything else in my mental vision came on me, and then I drank, and soon I no longer cared for anything. An utter disregard for my deeds and their consequences comes over me and I drink until stupefied, and then when once more I am myself I am too ashamed to even gaze at my own reflection in a glass, much less look respectable people in the face," replied Frad. "I have been lenient with you, not so much on your own account, although I am glad to help a man build up, but on your wife's account, whom I personally know and esteem as a lady of worth and merit, and, I must add, since you force me to say it, who is married, unfortunately, to a man who admits that he hasn't the will power to control the mad impulses of his appetite for drink, but allows those impulses to push him down in disgrace and drag his family along," and Mr. Cole looked at him severely over his glasses. For any other offense Fred would have resented the words of the "Old Man," but he felt there was a certain amount of truth in them, and to be discharged for drunkenness meant simply the loss of his occupation, for no other road would care to employ him. "For a man who has never been the slave of a habit I suppose it is impossible for him to realize how utterly one forgets everything else when this desire comes on him. I know I was foolish to acquire a fondness for liquor, but it was done in my youth, when, with a lot of foolish boys, we thought we had to drink to convince the world we were men," replied Lowman. "There is no question that men often form habits in youth during thoughtless moments that are a curse all through their lives, because they have not the will power to back away from the associates and associations which keep them under the spell of such habits. I, too, drank in my youth, but I saw where it was leading me, and I broke loose from the associates that were helping me on the down ward path, and to do it I left my native Fred was silent. He felt the full force "I have overlooked your shortcomings as long as I feel that I can," continued Mr. Cole. "Others are commenting on the fact that you still hold your position after conducting yourself as notoriously as you have done. These comments reach my ears, and what have I to offer? Our rules are made to apply to all equally. I should be above discriminating, which I have not been in your case, but I can forbear no longer. You may report to the timekeeper tomorrow and receive what is due Should you secure a place someyou. where else I will do all I honestly can for you, and under new conditions if you profit by the lesson you have received here, you can make a sober man of yourGood evening, Mr. Lowman," and self. Fred went out with the sentence of dismissal for drunkenness ringing in his ears, his face bent toward the ground, and his attitude one of dejection. He avoided the roundhouse; he had no desire to meet any of his acquaintances and he walked down the track that lead east out of the village. He Fred did not wish to go home now. felt that he had not the courage for that. His wife had warned him, had pleaded with him to let drink alone, and he had not respected her wishes, and now what she feared and dreaded had come to pass and he was out of a situation. He knew that now the worst had happened she would not upbraid him, but would accept the conditions brought on by his misdoings without complaint, and that thought made him the more miserable. He wanted to be alone. The companions, who yesterday he thought he could not do without, were now hated memories to him. How he loathed them and despised his own weakness. His spirits, made low by a week's debauch, were sunk to the lowest ebb by the loss of his position. The whole world looked miserable and uninviting to him as he walked along in the darkness. He crossed a bridge over a small river and paused for a moment, half tempted to cast himself in the water below, but no! He resolved that whatever else he might be he was no coward, and he would fight it out, and he would show the world yet that he was a man. The cool air and the walk were having their effect. His brain was growing clearer and his mind more composed, and he was about to turn back, when he dimly saw a large dark object on the track close ahead of him with several figures grouped about it in absolute silence. The whole thing looked queer to him, and, forgetting his own troubles momentarily in a desire to know more of the object ahead of him, he pushed up close to it, when a voice that he recognized instantly hailed him: "Who are you, and what do you want here at this time of night?' it asked. "Hello! Zeb Pike. I might ask the same of you, but I won't," said Fred. Fred did not need to. The dark object on the track had outlined itself plainly to his vision now as a pile of ties, and the men about it as a band of train robbers. He was in a tight place, but he made up his mind to save himself and the threatened train if possible. "I don't know as it would do you any good if you did ask, but it is necessary for us to know how you happen to be here at this hour of the night," replied Zeb, suspiciously. Fred could see enough in the half darkness to know that they were all watching him closely, but he did not flinch. Не remembered that the Chicago express would soon be due along there and he meant to save it. "Easy enough," explained Fred. "I went down to the roundhouse to report for work tonight and the 'Old Man' fired 'me bodily for being drunk, and when I left his office I didn't care what became of me. I couldn't go home. There was no one I cared to meet up town. I started on an aimless walk down the track. Back here I came near throwing myself in the river; why I did not do so I do not know, but I came on and here I am. Now, what are you up to, although I think I can guess?" "And what do you guess," asked Zeb, and he looked at Fred keenly through the darkness. "Train robbing," said Fred. "You've guessed it, and so you just stumbled on to us?" said Zeb, inquiringly. "That's all. I don't think I owe the railroad company anything, and don't you think if I had known you were here I should have went elsewhere?" asked Fred. If "No doubt. Now that you are here we have got to have an understanding. any other man but you had happened along here a bullet would have settled it, but I believe under the circumstances you will play square, at least we will give you a chance to save your life by becoming one of us," replied Zeb. 'A desperate man is ready for anything that promises gain," vowed Fred. "Gain is what we are after. The railroad has plenty of money and we are going to help them care for a part of it by ditching the express and robbing it," said Zeb. "Don't you think that to stop the train and rob it would be better? Things might pile up so that you couldn't get at the express car," argued Fred. "That's what Jack said, but I was afraid they wouldn't stop, and we want to be sure," said Zeb. "No fear of an engineer running by a stop sign, especially after night, if he can possibly stop. Have you got a lantern," asked Fred. "Yes, Jack's got a red one." "Let me have it and I will go just a little farther down the track and signal him so he will stop right in the cut there. You can have the boys on each side of the cut and go after them as soon as they stop," said Fred. "All right, but don't try any horse play. We have men here that can shoot after dark," warned Zeb, "No fear of me. I'll do the right thing," replied Fred, and while the words sounded all right to the robbers they had a double meaning. "They can't get by the ties, anyway," ventured Jack, "and. I have argued all along that the lantern was the proper thing to use." The lantern was produced; it was a typical hay-burner affair, but it gave a good light and that was the main thing desired by Fred. He lighted the lantern and gave it several violent swings across the track to see if it would go out, but it did not, and Fred was fully satisfied it would work all right. He knew that John Broughton would never pass a flagman if in his power to stop, and he relied upon this fact to assist him in outwitting the robbers. Zeb asked him if he had a gun, and, finding he had not, gave him one. Fred dropped it in his pocket and moved down the track, followed by the robbers, who lined themselves on either side of the little cut, beyond which Fred advanced as far as he thought he could without exciting the suspicion of the gang behind him. He knew that he had half a mile of straight track ahead of him, ample enough room for the stopping of a passenger train, but he wanted to get it stopped far enough from the robbers to warn the engineer and give him time to back the train out of the way before the outlaws could come up. There was some argument among the cutlaws as to whether they could trust Fred or not, but Zeb favored him and so did the one called Jack, because he had adopted his idea as the proper one to stop the train, and then there was the pile of ties; the train could not pass that, and all they thought about was stopping it. Fred glanced at his watch by the lantern's light. In six minutes the train would be due at the station. He laid his eur close to the rail and could hear the . far-off hum of the wheels, carried to him by the steel conductor. The time for action was close at hand and he nerved himself for it. The headlight shot into view and Fred waved his lamp back and forth as far as he could swing it from the momert he saw the light, yet it seemed an age to him before the answering notes of the whistle told him that his signal was observed. He still swung the lantern with the engine close to him, and its brightly burning headlight blinding his eyeballs. Then all at once he realized that the train was stopping, and he swung his lantern violently in a circle for Burroughs to back up, and, running toward the engine steps, he shouted a warning to the engineer that the cut was full of robbers. Burroughs did not need to wait for any further explanation, for the robbers heard Fred's warning cry and half a dozen pis tols were fired at him as he ran, but the distance and darkness favored him and he escaped being hit, and in another moment he was safe behind the boiler head, and the big machine was slowly forcing the heavy train in motion back the way it had come. The outlaws were running toward the train, firing as they came, and the crash of the glass in his front windown warned Burrounghs that there were safer places than his seat box, and he joined the fireman down behind the boiler head. The efforts of Pike and his gang were fruitless. Hampered in their running by the darkness and the uneven ground, the engine gathered speed enough to carry the train out of their reach, and the only thing left for the outlaws to do was to make themselves scarce in that part of the country, and they proceeded to do it with many a vow of vengeance on Fred's head. A couple of miles back the train was stopped and the train crew and passengers, who had formed a good idea of what was going on from the shooting, were fully informed of what had transpired, and it was decided to form a guard from the armed men on the train and got back, and if the robbers were there they would fight them. Preparations were made accordingly and the train returned, but the outlaws had vanished. The ties were thrown one side and the train pulled on into the station, where the news of the attempted hold-up was sent over the land. The robbers were never caught, despite the fact that some of them were known, and great effort was made to apprehend them. The next day Fred Lowman was again summoned to Mr. Cole's office and he went there with a lighter heart than he had carried on the previous day. Mr. Cole informed him that he was fully reinstated, and advised him to profit by his latest experience. It is needless to say that Fred did so, and no more sober or steady man could be found on the D. & W. from that day forward than Fred Lowman. |