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Page 1 ANS W ERS TO THE PRACTICAL QUESTIONS AND PROBLEMS CONTAINED IN THE FOURTEEN WEEKS COURSES Physiology, Philosophy, Astronomy, and Chemistry (old and New Edition). BY J. DORMAN STEELE, PH.D., F.G.S., AUTHOR OF THE FOURTEEN WEEKS SERIES IN PHYSIOLOGY, PHILOSOPHY, CHEMISTRY, ASTRONOMY, AND GEOLOGY. A. S. BARNES & COMPANY, NEW YORK AND CHICAGO.
Page 2 THE FOURTEEN WEEKS' COURSES IN NATURAL SCIENCE, BY J. DORMAN STEELE, A.M., PHI.D. Fourteen Weeks iq Natural Philosophy, Fourteen Weeks iq Ctlenqistry, Fourteen Weeks iq Descriptive Astroqonqy, Fourteel Weeks iq Popular Geology, Fourteeq Weeks iQ2 Human P1ysiology, Fourteen Weeks iq Zoology, Fourteeq Weeks iq Botany, A Key, containing Answers to the Questions and Problems in Steele's I4 Weeks' Courses, 4 1ISTORIC4L SERIES, ON THE PLAN OF STEELE'S 14 WEEKS IN THE SCIENCES. A Brief History of the Urlited States, A Brief History of France, The same publishers also offer the following standard scientific vworks, being more extended or difficult treatises than those of Prof. Steele, though still of Academic grade. Peck's Ganot's Natural Philosophy, Porter's Principles of Chemistry, Jarvis' Physiology and Laws of Healtl, Wood's Botanist and Florist, Clanlbers' Elenments of Zoology, lcIqtyre's Astroqomy and tle Globes, Page's. Elen.
ents of Geology, Entered according to Act of Congress, in the year 1869, by A. S. BARNES & CO., In the Clerk's Office of the District Court of the United States for the Southern District of New York. sTERLE'S KEY.
Page 3 PREFACE. THIS little work is designed to aid teachers who are using the Fourteen Weeks Course. The problems contained in all the books are fully, and, it is thought, accurately solved. Great pains have been taken to revise and compare them carefully. The practical questions are answered, often not in full, yet enough so to give the key to the more perfect reply. The use of the text-books is presupposed, and the statements merely supplement, or apply the fuller theories therein contained and explained. On many points there may be a difference of opinion. The author often finds in his own classes a wide diversity. On mooted questions he has merely advanced one view, leaving the subject open for the discussion of other theories. Minute directions are given, pages 71-82 inclusive, for performing a course of experiments in Chemistry. It is hoped that these may be of service to teachers who, with incomplete appadatus, are trying to illustrate to their pupils some of the principles of that science. In all cases of doubt or misunderstanding with regard to the answers or solutions, the author will be pleased to correspond with any teacher using the Series ELMIRA, Mdrch 19, 1870.
Page 5 ANS WERS TO THE PRACTICAL QUESTIONS IN THE FOURTEEN WEEKS COURSE NATURAL PHILOSOPHY. LThe bold-faced figures refer to the pages of the Philosophy; the others to the number of the Practical Questions.] INERTIA. 26. I. If one is riding rapbidly, in which direction will he be thrown when the horse is suddenly stopped f. In the same direction in which he is going. He has the inotion of the carriage, and his inertia carries him forward. 2. Wkhen standing in a boat, why, as it starts, are we thrown backward? Because the inertia of our bodies keeps them stationary, while the boat carries our feet forward. 3. WIhen carrying a cup of tea, if we move or stop quickly, why is the liquid liable to spill? The inertia of the tea tends to keep it still or in motion, as the case may be. If we move the cup quickly, the motion is not imparted to the liquid soon enough to overcome the inertia. When, therefore, we start, the tea spills out backward; or, when we stop, it spills out forward. We understand this if we can tell why a cup of tea is more liable to spill than one of sugar.
Page 6 6 ANSWERS TO BRACTICAL QUESTIO.NY 4. Why, whzen closely Jbursued, can we escape by dodging? We turn sharply. Our pursuer, ignorant of our design, cannot overcome his inertia so as to turn as quickly, and hence is carried past. 5. tWhy is a carriage or sleigh, when sharply turnino, a corner, liable to tiz over? Because its inertia tends to carry it directly forward. A puzzling question in this connection is-Why is a sleigh more liable to tip over than a wagon? 6. Why, if you Pklace a card on your fnger, and on to q/ zit a cent, can you snap the card fi-om under the cent without knockinfg the latter offyourfingcr? Because the friction between the card and the cent is so slight that, by a quick snap, you can overcome the inertia of the former without imparting any fbrce to the latter. 7. Why, after the sails of a vessel are furled, does it s;ll continue to move; and why, after the sails are all spread, does it require some time to -et under full headway? Its inertia must be overcome in the one case by the resistance of the air and water, and in the other by the force of the wind. COHESION. 40. I. Why can we not weld a piece of copper lo one oj iron? Cohesion acts only between molecules of the same kind. 2. 4Why is a bar of iron stronger than one of wood? Because its force of cohesion is stronger. 3. WVhy is a piece of iron, when perfectly welded, stronger than before it was brokcn? By the hammering, more particles are brought within the range of cohesion. 4. Why do drops of dz/]'ie-eunt liquids vary in size? Because they vary in cohesive force. 5. Why, when you drop medicine, will the last few dr'fp. contained in the bottle be of a larger size fhan the others?
Page 7 IN AA NTURAL PHIILOSOPHY. 7 The pressure of the liquid in the bottle is less, and therefore they form more slowly. 6. Why are drops larger if you drop them slowly f There is more time for the adhesive force of the bottle to act on the liquid, and so a larger drop can be gathered. 7. Why is a tube stronger than a rod of the same weight? I.et a rod supported at both ends be broken in the middle. \Ve shall see that it yields first on the circumference. So true is this, that long beams heavily loaded have been broken by a mere scratch of a pin on the lower side. The particles along the centre break last. They rather aid in the fracture, since they afford a fulcrum for the rest of the rod, acting as the long arms of a lever, to act upon. In a tube the particles at the centre are removed and all concentrated at the outside, where the first strain is felt. (See Physiology, p. 20). 8. Why, if you melt scraps of zinc, will they form a solid mass when cooled? The heat overcomes, in part, the attraction of cohesion, so that the particles flow freely on each other. They now all come within the range of cohesion, so that when the metal cools they are held by that force in a solid mass. 9. In what liquids is the force of cohesion greatest? Mercury, molasses, etc. io. Name some solids that will volatilize without melting? Arsenic, camphor. ADHESION. 47. I. Why does cloth shrink when wet? By capillary attraction the water is drawn into the pores ot the cloth. The fibres are thus expanded sidewise and shortened lengthwise. The cloth "fulls uIf" or thickens while it shortens and narrows (shrinks) in the process. 2. IWhy do sailors at a boat-race wet the sails? The pores being full and expanded make the sails more compact. They will therefore hold the wind better.
Page 8 8 ANSWERS U'0 PRACTICAL QUESTIONS 3. Why does not writing-ipaer blot? Because the pores are filled with size. (See Chemistry, p. I6I.) 4. Why does iainztprevent woodfrom shrinking? Because it fills the pores of the wood. 5. ihat is the s/hate of the surface of a glass qf water and one of mercury? Ordinarily the former is concave and the latter convex. 6. Why can we not dry a toweltierfectly by wringing? Because of the strength of the capillary force by which the water is held in the pores of the cloth. 7. Why will not water run through a fine sieve when the w7ires have been greased? Because the grease repels the water and so prevents capi!. lary action. 8. Why will camnihor dissolve in alcohol and not in water? Because there is a strong adhesion between the alcohol and camphor, and little, if any, between the water and camphor. 9. Why will mercury rise in zinc turbes as water does zn glass tubes? Because of the strong adhesion between zinc and mercury. io. Why is it so diffcult to lift a board out of water? Because of the adhesion between the board and the water. i I. Why will ink spilled on the edge of a book extendfurther inside than f stsilled on the side of the leaves? Because the capillary pores of the paper are short, being only the thickness of a leaf, while the capillary spaces between the leaves are longer and continuous. 12. If you should hali ten to spill some ink on the edge of,your book, ought you lo press the leaves togfether?.No. Because you would make the capillary spaces between tlie leasves smaller, and so the ink would rise in them further. 13. WZhy can you not mix oil and water? Because there is no adhesion between them.
Page 9 IN NATURAL PHILOSOPHiI. 9 15. Why will water we/tyour hand while mercury will noat! Because in the former case there is an adhesion, in the latter none. I 6 Why is a tub or fail liable to fall to pieces if noalflled with water or kefpt in the cellar? Because the moisture dries out of the pores, and the wood shrinks so as to let the hoops fall off. 17. NAame instances where the attraction of adhesion is stronger than that of cohesion. WXTood fastened by glue will often split before the glue will yield. Paper stuck with paste, and bricks with mortar, are also examples. GRAVITATION. 63. I. When an afttle fills to thegroulrd, how izmuch doesthe earth rise to meet it? The earth falls as much less distance than the apple, as its mass is greater. 2. Uthat causes the sawdust in a mill-ofind to collect in large masses? The attraction of gravity which exists between all bodies, whereby they attract each other. All bodies on the earth would tend to approach each other, and the big ones would gather all the little ones around them were they as free to move as the sawdust floating on water. 3. Will a body weigh more in a valley than on a mountain P It will, because the attraction of the earth is greater. 4. Will a pfound weight fall mIore slowly than a tzwo-fiound Veight? They will both fall in the same time, except the slight difference which is caused by the resistance of the air. Galileo propounded this view and proved it, in the presence of a xast crowd, by letting unequal weights fall from the leaning towez of Pisa.
Page 10 [0 ANSSWERS TO PRACTIUAL QUESTIONS 5, How deey5 is a well, if it takes three seconds for a stone to fall to the bottom of it? (2) equation of falling bodies, d = 16t2; hence d = 16 x 32 = 144 feet. 6. Is the centre qf gravity always within a body-as, fao examiple, a ring.? It is not. In the case given it is at the centre of the circle. 7. If two bodies, weighing respectively 2 and 4 pounds, be coznneced b't a rod 24 inches long, where is the centre of ravity? To be in equilibrium the weight of one multiplied by its distance from the centre of gravity iust equal the weight of the other mtltiplied by its distance. 24. 6 = 4; hence 4 in. is the unit for each pound. Therefore the centre of gravity is 8 in. from the larger weight and 16 in. from the smaller. 8. In a balli of equai density throughout, where is the centre of gravity? At the cefitre of the ball. 9. Why does a ball roll down hill? Because the line of direction falls without the small base of the ball. Io. Why is it easier /o roll a round body than a square one? Because the base of the ball is so much smaller, and therefore the centre of gravity need not be raised to bring the line of direction without. I I. Why is it easier to tifz over a load of hay than one of stone? Because the centre of gravity in a load of hay is very high, and in a load of stone very low. Therefore the centre of gravity in the former need not be raised much to bring the line of direction without the base, while in the latter it must be. I2. Why is a fyranmid the stablest of structures? Because the base is so broad and the centre of gravity so low. The centre of gravity must therefore be lifted very ligh before the line of direction will fall without the base. 13. When a hamner is thrown, on which end does it always strike? On the heavy end or head, because that part is attracted by the earth more strongly.
Page 11 IN NATURAL PHILOSOPHY. I 14. WIhy does a rope-walker carry a heavy balancing-oleI Because in this way he can easily shift his centre of gravity. I5. What would become of a ball if droApied Zilto a hoie bored through the centre qf the earth? In falling, it would gain a momentum which would carry it past the centre of the earth. But as it is constantly coming to a part having a slower axial revolution than itself, it would scrape on the east side of the hole until it reached the centre; beyond that point it would scrape on the west side. This friction would prevent its reaching the opposite side of the earth. It would therefore vibrate to and fro, each time through a shorter distance, until, at last, it would come to rest at the centre of the earth. i6. Would a clock lose or gain time if carried to the top of a mountain? It would lose time, because the force of gravity would be lessened. At the North Pole it would gain time, because there the force of gravity would be increased. I7. In the winter, would you raise or lower the pendulzumbob of your clock? I would lower it, since the cold of winter shortens the pendulum, and this movement of the bob would counteract that change. i8. Why is the iendulum-bob always madeflat? To decrease the friction of the air. i9. What beats off the time in a watch? The vibration of the balance-wheel. 20. Is solved in the book. 21. WIhatshould be the leI^t/h of a fiendulum at New YorA to vibrate half-seconds? (1 sec.)2: (/, sec.)2:: 39.1 in.: x = 9.7 + inches. To vibrate quarter-seconds? (1 sec.)2: (1/4 sec.)2:: 39.1 in.: = 2.4 + inches. To vibrate hours? (1 sec.)2: (3600 see.)2:: 39.1 in.: x -: 7!97.7 miles.*
lNearly the ditineter of the earth.
Page 12 I2 ASVSWERS TO PRACTICAL QUESTIONS,' 22. What is the profiortionate time of vibration of two pen. duzirns, I6 and 64 inches long, respectively? According to the 2nd. law of pendulums, Time of vib. of 1st: Time ofvib. of 2d. /16: 4/6:: 4: 8:: 1: 2 23. Why, when you are standing erect against a wall, and a piece of money is placed between your feet, can you not stoyV forward and ftick it upf? By leaning forward you bring the centre of gravity in front of your feet, and, as on account of the wall, you cannot throw any part of your body back to preserve the balance, you fall forward. 24. If a tower were i 98 feet high, with what velocity would a stonle droPifiedfromn the summnit, strike the ground? According to equation (3), v2 = 61 d. v2 = 64 x 198. v=112.5 feet. 25. A bodyfalls in 5 seconds: with what velocity does zi rtrike the grozund? According to equation (1), v = 32 t. v =32 x 5. v =160 feet. 26. How far will a body fall in Io seconds? According to equation (2), d = 16 t2. d = 16 x 102 = 1600 feet. Witih what velocity will it strike the ground? According to equation (1), v = 32 t. v = 32 x 10 = 320 feet. 27. A body is thrown iujward with a velocity of 192 feet the,irst second, to what height will it rise? Equation (1), v = 32 t. 192 = 3-2 t. t = 6 sec. (2), d = 16 t2. d = 16 x 62=57f feet. 28. A ball is shot ufiward with a velocity of 256 feet;, t what height will it rise? How long will i cottiznuze to ascend Using equations (1) and (2), as in the last problem, we have: t = 8 sec. d = 1024 feet. 30. Are any two plumb-lines parallel? Thev are not, since they point to the earth's centre of gravity. No twvo spokes of a wheel can be parallel.
Page 13 IN 1NATURAL PHILOSOPHY. 1 3 3r. A stone let fallfromi a bridge strikes the water in three seconds. What is the hezght? Equation (2), d = 16t2. d = 16 x 32 = 144 feet. 32. A stonefallsfrom a church steeple in 4 seconds. What is the height? Equation (2), d = 16t2. d = 16 x 42 = 256 feet. 33. How far would a body fall the first second at a hez-ght of I2,000 miles above the earth's surface? (16,000 mi.)2: (4000 mi.)2:: 16 feet: x = 1 foot. 34. A body at the surface of the earth weizghs oo tons. what would be its weight I,ooo miles above?,(5000 mi.)2 (4000 mi.)2:' 100 tons: x = 64 tons. 35. A boy wishing to find the hezght of a steetle les fly an arrow thatjust reaches the toti and then falls to the ground. It is in the air 6 seconds. Required the hezght. Equation (2), d = 1612. d = 16 x 32 = 144 ft. 36. A cat let fall fronm a balloon reaches the ground it io seconds. Required the distance. Equation (2), d = 16 x 10' = 1600 ft. 37. In what time wzll a tpeznduinu 40 feet long make a vzibration? According to the 2nd. law of pendulums, and taking the length of a seconds pendulum as 39 in., we have: lsec.:x:: /39: /40x12in. x= /-g=1 2.:o+ x = 3.5+ sec. -In what time will a tendulunz 52 feet long make a vz; bration? 1 sec.: x:: /3in.: /52x 12 in. - = 4 seC.
Page 14 14 A.NSTI'ERS TO PRA C77CAL QUESTIONS -How long would it take for apendulum one mile in leng'th tA, make a vibration? — How long would it take for a fpendulum reac Itingfrom the earth fto the moon to make a vibration? -Required the length of a pendulum that would vibrate centuries. ( 7 be solved likeprobl/em 20.) 38. Two mneieoric bodies in space are 12 miles apart. They weigh Ioo and 200 lbs. respectively. If they siould fall toaether by force of their mutual attraction, what Plortion of the distance woluld be passed over by each body? The distance passed over by the two bodies is inversely as their mass; hence one moves 8 miles and the oth er 4 miles. 39. I/a body weighs 2,000 lbs. ufpon the surface of the earth, what would it weigh 2,000 miles above? (6000 mi.)2: (4000 mi.)j:: 2000 lbs.: x = 888,/9 lbs. /Low much 500 miles above? (4500 mi.)2: (4000 mi.)2:: 2000 lbs.: x = 1580+lbs. The weight of bodies below the surface of the earth decreases as the distance increases. Ex. Ex. What would the above body weigh if carried 2,000 mziles below the surface? i,ooo lbs. — I,ooo miles belowe? 1,500 lbs. (See Physics, page 5, note.) 40. At what distance, above the sufwace of the earth will a body fall, the frst second, 21 inches? A body falls 16 ft.* (192 inches) at the surface of the earth. 211/3 inches are */9 of 192 inches: Now as the attractioil is inversely as the square of the distance. the distance must be V/, or 4 times that at the surface. Hence the body must be 12,000) miles from the centre, or 8,000 miles from the surface of the earth. The problem may be solved directly by proportion, thus: x2: 40002:: 192 inches: 21'/3 inches. x = 12000 miles (distance from the centre) 12000 miles-4000 miles=8000 miles. 41. How far will a bodyfall in 8 seconds? I,o24 ft. —II t/e 8fz second? 240 ft. —-In Io seconds I, 6o0C ft. —in tht. 3oth second? 944 ft. According to the best authorities tl)e dist,:acte is more exactly 16t1/, f.
Page 15 IN NA TURA L PIHILOSOPIt.. I 5 MOTION. N0. I. Can a rifle-ball befred thr-olgi a handkerchief sus. pended looselyfrom one corner? Yes. The wind of the ball will lift the handkerchief somewhat. 2. A rife-ball thrown against a board standing edg6ewise will knock it down; the same bullet fired at the board vill pass through it without disturbizng its position. Why is this? The ball which is thrown has time to impart its motion to the board; the one fired has not. 3. Why can a boy skate safely over a piece of thin ice, when, if he should pause, it would break under him directly? In the former case there is time for the weight of his body to be communicated to the ice; in the latter, there is not. 4. Why can a cannzon-ball be fred through a ldoor standing ajar, without moving it on its hin-ges? Because the cannon-ball is moving so quickly that its motion is not imparted to the door. 5. Why can we drive on the head of a hammzer by sinuply strikinzg the end of the handle? This can only be done by a quick, sharp blow which will drive the wooden handle through the socket before the motion has time to overcome the inertia of the iron head. A slow, steady blow will be imparted to the head, and so fail of the desired effect. 6. Suzipose )o'u were on a train of cars movin, at the rate of 30 milesper hour: with what force would you be thrown forward if the train were stopped instantly? With the same velocity which the train had, oi 44 feet pet second. Your momentum would be your weight avoirdupois multiplied by this velocity. 7. IZ what line does a stone fall from the nast-head of a vessel in motion? In a curved line, produced by the two forces-gravity and the forward motion of the vessel.
Page 16 L D ANSWERIS TO PRA b'UICAL QUESTION1'S 8. If a ball be droa5i)ed from a hzigh tower' it'ill striev /tIe earth a little east of a vertical line. Why is this? In the daily revolution of the earth on its axis, from vwest to east, the top of the tower moves faster than the bottom, because it passes through a larger circle. When, therefore, the ball falls, it retains that swifter easterly motion and so strikes east of the vertical. 9. If is staled that a suit was once brought by the driver of a light-wagon against the owner of a coach for damcages caused by a collision. The comn laint was that the lattfr was drivingl sofast, that wheln the two carriages struck, fte drivcr Zf the former was thrown-forerard over the dash-board. S'how how his own testimolny pSroved him to have been at f/ullf. WThen the light-wagon was suddenly stopped, its driver went on by his inertia with the same speed at which the wagon was moving. That this threw him forward over the dash-board, proves his speed to have been unusual. io. Supiose a train moving at the rate of 30 miles per hour; on the rear jplaforzm is a cannon ained parallel with the track and in a direction precise/y opposile to the motion of the car. Let a ball be discharged wit/h /e exact speed of the train, where would it fall? In a vertical line to the track. The two equal, opposite motions would exactly destroy each other. t. Su5ppose a steamer in ralpid motion and on its deck a man jumping. Can he jumnpi further by leapigs the w'ay the boat is moving or in the ofpiosile direction? It will make no difference as long as he jumps on the deck. Should he jump off the boat, then the effect would be different. 12. WHhy is a runnlintgjuniz lont er than a standing one? Because the motion gained in running is retained in the jump and adds to its distance. I3. If a stone be dr(ojpped from the mast-head of a vessel in motion, will it strike the same spot on the deck that it would if the vessel were at rest? It will. It falls with the motion of the vessel, and goes just as far forward while falling as the vessel does.
Page 17 IN NA I URAL PHILOSOPHY. 1 7 I4. Coltd a party play ball on the deck of the Great Eastern when steaming along at the rate of 20 miles per hour, without making allowance for the motion of the ship.? They could. The ball would have the motion of the ship, and would move with it in whatever direction they might throw it. I 5. Since "action is equal to reaction," why is it not as dangerous to receive the "' kick" of a gun as the force of the bullet? The striking force is as the square of the velocity; and the velocity with which the gun moves backward is as much less than that with which the bullet moves forward, as the gun is heavier than the bullet. For this reason a heavy gun will kick much less than a light one. I6. If you were to jumZn from a carriage in rapid nZotion, wouldyou leap directly toward the spiot on which you wished to alzghlt? No; because as one jumps from the wagon he has its forward motion, and will go just as far ahead, while leaping, as he would if he had remained in the carriage. He should, therefore, aim a little back of the desired alighting-place. I 7. If you wished lo shoot a bird in swift fzight, would you aim directly at it? No. The bird will fly forward while the bullet is going to it. One should, therefore, aim a little in advance. i8. At what parts of the earth is the centrifugalforce the least? The poles. They simply turn around in 24 hours. 9. What causes the mud tojfy from the wheels of a carriage in rapid motion? The centrifugal force (the inertia of the mud). 20. What proof have we that the earth was once a soft mass? It is flattened at the poles. This effect is produced upon a ball of soft clay by simply revolving it on a wire axis. 21. On a curve in a railroad, why is one track always higher than the other?
Page 18 18 AXSWERS TO PRACTICAL Q Z7ESTIONS The outer track is raised that gravity may balance the cen. trifugal force. 22. I4What is the pirincijple of the sling? The sling is whirled until a strong centrifugal force is generated; the string, the centripetal force, is then released, when the stone flies off at a tangent. 23. The mouth of the Mississzppi river is about 24 miles fulrther from the centre of the earth than its source. What causes its water to thus " run Au hill?" The centrifugal force produced by the revolution of the earth on its axis tends to drive the water from the poles toward the equator. Were the earth to stand still in its daily rotation, the Gulf of Mexico would empty its waters back through the Mississippi to the northern regions. 24. Is it action or reaction that breaks an egg wheen I strike it against the table? The reaction of the table. 25. Was the man philosophical who said "it was not the falling so far but the stofiping so quick that hurt him?" He was. 26. If oneferson runs against another, which receives the greater blow? Action is equal to reaction: hence the blows must be equal. 27. Would it vary the effect if the two persons were running in otbtosite directions? The blow would then be the sum of both their momenta. If they were running in the same direction? The blow would be equal to the diference of their momenta. 28. [eWhy can you notfire a rifle-ball around a hill? Because a single force always produces motion in a straight line. 29. Why does a heavy gun " kic/" less than a light one? See problem I5. 30., ma on on the deck of a large steamer draws a small.
Page 19 IN NATURAL PHIL OdOPHY. 19 boat toward hint. How much does the shipz move to meet the boat? The ship moves as much less distance than the boat, as it'3 heavier than the boat. 31. Suppose a string, fastened at one end, will just sut5p5or a weight of 25 lbs. at the other. Unfasten it, and let two persons pull uipon it in opfilosite directions. How mu, /i can each pull without breaking it? 25 lbs. The second person, in the latter case, can pull as much as the nail did in the former. 32. Can a man standing on a pilatfor;-scale make himself Iighter by ifting uip on himself? He cannot; because action is equal to reaction, and in an opposite direction. As much as he lifts up, so much must he press down. 33. Why cannot a man lift himself by fiulling utp on his boot-straps? See last problem. 34. If ifrom a gun pilaced vertically, a ball were fired into perfectly still air, where would it.fall? It would return into the gun. 35. With what momentum would a steamboat weighing I,ooo tons, and moving with a velocity of I o feet per second, strike against a sunken rock? 1000 tons x 101 = 100,000 tons. 36. With what momentum would a train of cars weighing Ioo tons, and running Io miles per hour, strike against an 7bstacle? The velocity per second is 142/3 ft. 100 tons x (142/3)2 = 21,5111/, tons. 37. What would be the copfiarative striking-force of tzwc hammers, one driven with a velocity of 20feetfer second, ana the other Io feet? 02 = 400. 102 = 100. 400: 10O.: 1: 4. Hence one will strike four times ae ht,rd a blow as the other. This principle is of great impertance in chopping wood, splitting rails, and in all cases where percussion is concerned.'he highest attainable velocity is to be souOg.t.
Page 20 20 AI/' WERS TO PRA CTJCAL QUESTIONS -There is a story told of a man who erected a huge pair of bellows in the stern of his pleasure-boat, that he might alwayi have a faiir wind. On trial the plan failed. In which di rection should he have turned the bellows? In the manner adopted at first, of turning the nozzle toward the sails, the action of the wind against the sails and the reaction of the bellows against the boat just balanced each other. If the man had turned the nozzle backward he could have saved the reaction of the bellows to move the boat. This would, however, have been a most costly and bungling way of navigation. -If we whirl a pail of water swiftly around with our hand, why will the water all tend to leave the centre of the piail? Why will the foam all collect in the hollow at the centre? THE MECHANICAL POWERS. 99. I. Describe the rudder of a boat as a lever. The water is the F, the boat the V, and the hand the P. As the W is between the F and the P, it is a lever of the second class. 2. Show the change that occurs from the second to the third class of levers, when you take hold of a ladder at one end and raise it against a building. At first the ground is the F at one end, the hand the P at the other, and the ladder the W hanging between; hence this is a lever of the second class. After a little, the F remaining the same, the P is applied at one end, near the F, and the ladder is the WV hanging, at the other; hence this is now a lever of the third class. 3. Why is a piinch from the tongs near the hinge more severe than one near the end? Because in the former case the tongs are a lever of the first class-in the latter, of the third. In the first class there is a gain of power, in the third a loss. 4. Two 5ersons are carrying a weight of 250 lbs., hanging.
Page 21 IN NATURAL PH2LOSOPf7l 21 between them from a pole io feet in length. Whe e should it be suspended so that one will lift only 50 lbs.? One lifts 50 lbs.; the other 200 lbs. The proportionate length of the arms of the lever should be the same as the proportionate weights-i. e., 1 to 4. 10 + 5 = 2, the unit of measure. lIence one arm is 2 feet long and the other S feet long. PRooF.-(See Prob. 7, p. 10.) 50 x 8 = 200 x 2. This is the substance also of the equation P x Pd = XV x Wd. 5. In a lever of the first class, 6 feet long, where should the F be fplaced so that a P of I lb. will balance a Woof 23 lbs.? 6 feet = 72 inches. 72 + 24 = 3, the unit of distance. The W must be placed 3 in. and the P 69 in. from the F. PRooF. 23 x 3 = 1 x 69 (Prob. 4). 6. What P would be required to lift a barrel of fiork with a windlass whose axle is one foot in diameter and handle 3 ft. gong. P: W: rad. of axle:: rad. of wheel. x: 200 lbs:: 1/2 ft.: 3 ft.: = 331/s lbs. 7. What sized axle, with a wheel 6 feet in diameter, would be required to balance a W of I ton by a P of Ioo lbs F P: W:: rad. of axle: rad. of wheel. 100 lbs.: 2000 lbs. x: 3 ft. x = /20o ft. = the rad.; hence the diameter = 3/10 ft. 8. WHhat number of movable pzulleys would be required to;ift a W of 200 lbs. with a P of 25 lbs.? W= P x twice the no. of mov. pulleys; hence p-= twice the no. of mov. pul's. 200 + 25 = 8. 8 + 2 = 4 = the no. required. 9. How many lbs. could be lifted with a system of 4 zmovable pulleys, and one fixed pulley to change the direction of the force, by a P of oo lbs.? W= P x twice the no. of mov. pulleys. 100 lbs. x (4 x 2) = 800 lbs. = the W. io. What weight could be lifted with a single horse-15owe, (33,000 lbs.) acting on the tackle-block? (Fig. 62.) This block has 3 movable pulleys, and using the equation of the pulleys given in the last two problems, we have, making no allowance for friction, 33,000 lbs. x (3 x 2) = 198,000 lbs.
Page 22 22 ANSWERS TO PRACTICAL QUESTIONS I I. What distance should there be between the threads oj a screzwe, that a Pof 25 lbs., acting on a handle 3 ft. long, may lift I ton weight? F: W:: Interval: Circumference. 25 lbs.: 2000 lbs. 7: 72 in. x 3.1416. x = 2.83 -in. 12. How high could a P of 12 lbs., movinfg I6 ft. along an indcined plane, lift a W of 96 lbs.? P: W:: height: length. 12 lbs: 96 lbs. 16 ft. x = 2 ft. 13. I wish to roll a barrel of flour into a wagon, the box of which is 4ft. from thegroulnd. l can lift but 24 lbs. How Ionff a plank should I get? P: W:: height: length. 24 lbs: 196 lbs. 4 ft.: x = 322/s ft. 14. The "evenzer" of apair of whifclrees is 3 J. 6 in. loin,, how much must the whifzzetree be ntov'ed to give one horse the advantag-e of a over the other? For every 3 lbs. one horse pulls, the other must pull 4 lbs.: hence 7 represents the proportion in which the load is to be divided. 3 ft. 6 in. = 42 inches. 42 in. + 7 = 6 inches. the unit of measure. Hence one arm of the evener must be 6 in. x3 = 1S in. long, and the other 6 in. x 4 = 24 in. long. Or, if we prefer, we may say 21 in. - 3 in. = 18 in. lonz. and 21 in. + 3 in. = 24 in. long. Pnoon.(See Prob. 4, p. 20.) 18 x 4 = 24 x 3 = 72. 15. In a set of three horse wshiffletrees, haing an "evene"?' 5 ft. long, at what:point should the pfilough-clevis be attached that the single horse may drawv the same as each one of the spfan of horses? For every lb. drawn by the single horse the span should draw 2 lbs.: hence 3 represents the proportion in which the load is to be divided. 60 in.
3 = 2(0 in., the unit of measure. 20 in. x 1 = 2(1 in., and 20 in. x 2 = 40 in. Hence one arm mast be 20 in.. and the other 40 in. long. To give.
advantage? The single horse should draw 3 lbs. and each of the others 4 lhs.: hence the span should draw 8 lbs. 60 in. - 11 = 56/1, in., the unit of measure..6/,l in. x 3 = 164/,l in., and 55/11 in. x S = 437/1, in. I6. What W can be lifted with a P of 0oo lbs. actino cn a screw having threads i of an inch apart and a lAver handle,1 f!. ad a v.
Page 23 IN NATURAL PHILOSOPHY. 23 P:'W:: Interval: Circumference. 100 lbs.: x: 1/4 in.: 96 in. x 3.1416. x = 120,637+ lbs. 17. What is the object of the big balls cast on the ends of the Fandle of the screw used in cohying-firesses? By their inertia and centrifugal force they make the motion more uniform and continuous. I8. In a steelyard 2ft. long, the distancefrom the weighthook to the fulcrum-hook is 2 in. How heavy a body can be weighed with a I lb. weight at the further end? 24in.-2-in.=22in. lib. x 22=221bs.=P. 221bs. -+ 2 = lllbs. = W. i9. Describe the changefrom the Ist to the 3d class of levers, il the ditSerent ways of using a spade. When digging, the ground at the back of the spade is the F; the ground lifted is the W; and the hand at the other end is the P. As the W is at one end, P at the other, and the F between, this is a lever of the ISt class. When throwing dirt, the left hand at one end of the spade is the F; the dirt at the other end is the W, and the right hand between the two is the P. As the P is between the F and the W, this is a lever of the 3d class. 20. W Vhy are not blacksmiths' and fire tongs constructed on the same princihle P The former are of the Ist class, as power is required: the latter of the 3d class, as rapidity only is necessary. 2 i. In a lever of the 3d class, what y will a P of 50 lbs. balance, if one arm is 12 ft. and the other 3 ft. lon? P: W:: Wd: Pd. 50lbs.: x:: 12 ft.: 3 ft. x = 121/2 lbs. 22. In a lever of the 2d class, what IV will a P of 50 lbs. balance, with a lever I2 feet long and W 3 feetfrom the Ff 0 lbs.: z:: 3ft.: 12ft. t = 200 lb*
Page 24 24 AINSSTERS TO PRACTICAL QUtESbl'ONS 23. In a lever of the Ist class, what Wgwill a P of 50 lt.A balance. with a lever I2 ft. long and the F 3 ft. from the W 9 50 lbs.: x:: 3ft.: 9ft. x = 150 lbs. 24. In a wheel and axle, the P= 40 lbs., W= 36o lbs., diameler of axle =8 in. Required the circumference of thu wheel. P: W:: diameter of axle: diam. of wheel 40 lbs.: 860 lbs. 8 in.: x = 72 in. = 6 ft., the diameter of wheel. 6 ft. x 3.1416 = 18.85 ft., the circumference of the wheel. 25. In a wheel and axle the P = 20 lbs., the W= 240 lbJ., and the diameter of wheel = 4ft. Required the circumference of the axle. 20 lbs: 240 lbs:: x: 48 in. x = 4 in. (diameter of axle). 4 in. x 3.1416 = 12.56 in. (circumference). 26. Required, in a wheel andaxle, the diameter of the wheel, the diameter of the axle being IO inches, P= Ioo lbs. and W I to0n. 100 lbs.: 2000 lbs. 10 in.: x = 200 in. = 162/3 ft. 27. What P would be necessary to sustain a weight o0 3,780 lbs., with a system of 6 movable ulleys and one rote Y W = P x twice the no. of mov. pulleys. 3,780 lbs. = P x (6 x 2). P = 315 lbs. 28. Iowr many movable pfilleys would be required to sustain I Wof 420 lbs. with a P of 2 Io lbs.?-Ans. I. HYDROSTATICS. 121. I. Why do housekeepfers test the strength of lye, b) trying whether or not an egg will float on it? The potash dissolved in the water to form lye increases the density of the liquid. When enough has been dissolved to make its specific gravity greater than that of the egg, the egg will float. This becomes, therefore, a simple means of testing the amount of potash contained in the lye.
Page 25 1A AATURAL PHILOSOPHY. 25 2. How much water will it take to make a gallon of strong brine. A gallon. The salt does not increase the bulk of the liquid. 3. Why can afat man swim easier than.a lean one? Because muscles and bones are heavier than fat. The specific gravity of a fat man is therefore less than that of a lean one. 4. Why does thefiring of a cannon over the watersometimes bring to the surface the body of a drowned person.f One answer is given in the Philosophy. It is probable, also, that the firing of the gun produces a partial vacuum, or in some way takes off, for an instant, a part of the pressure of the air on the water. The gases in the body would then expand and bring it to the top. 6. if we let bubbles of air fpass uj5 through a jar of water, why will they become larger as they ascend? The pressure of the water is less as they near the top, and so they expand. 7. What is the pressure on a lock-gate 14 feet high and Io feet wide, when the lock is full of water f 14 x 10 x 7 x 1000 oz. = 980,000 oz. = 61,250 lbs. S. Will a iail of water weigh any more with a live fish in it than without? If the pail were full before the fish was put in, then it will make no difference, since the fish will displace its own weight of water, which will run over. If the pail is only partially filled, then, though the fish is upheld by the buoyancy of the water, since action is equal to reaction, it adds its own weight to that of the water. -If a man and a boy were riding in a wagon, and, on conming to the foot of a hill, the man should take up the boy in his arms, would not that helP the horse? 9. If the water filtering down through a rock should collect in a crevice an inch square and 250 feet high, opening at the bottom into a closed fissure having 20 square feet of surface, what would be the total pressure tending to break the rock? 2.
Page 26 26 ANSWERS TO PRACTICAL QUESTIONS. The pressure is the same on every square inch of the twenty square feet of surface. 250 x 1000 oz. x 20 x 144 = 312, lbs. 144 Io. Why can stones in water be moved so mnuch more easily than on land? Because the water oaoys up about one-half of their weight. I I. Why is it so difficult to wade in the water where there is any current? Because the buoyant force of the water makes us so light that we are easily carried away from our footing. I2. Why is a mill-dam or a canal embankment small at the tofp and large at the bottom? Because the pressure of the water increases with the depth. 13. In digging canals and building railroads, ozught not the engineer to take into consideration the curvature of the earth? Certainly. If he should build on a true level he would find his embankment pointing up to the stars. I4. Is the water at the bottom of the ocean denser than thal at the surface? The immense pressure must condense it very much at great depths. There is a certain point beyond which divers cannot penetrate. I5. Why does the bubble of air in a spzrit-level move as the instrument is turned? Because the air is lighter than the alcohol and rises constantly to the highest point. For this reason, also, the tube is curved upward at the centre. i6. Why can a swimmer tread on glass and other sharp substances at the bottom of the water with ithttle harm? See problem I I. 17. Will a vessel draw more water in salt or in fresh water! In fresh, because its specific gravity is less. 18. Will iron sink in mercury? No. It will float, like a cork on water. 19. The water in the reservoir in New York is about 8ofeel.
Page 27 IN NATURAL PHILOSOPHY. 27 aboe thefountain in the City Hall Park. What is tihe pressure on a single inch of the pi]pe at the latterpoint? (1000 oz. x 80) + 144 = 34.7 lbs. 20. Why does cream rise on milk? Because it is lighter than the milk. 2. Ifa ship founders at sea, to what dei5th will it sink? Until its specific gravity becomes equal to that of the water? 22. There is a story told of a Chinese boy who accidentally dropped his ball into a deep hole, where he could not reach it. He filled the hole with water, but the ball would not quite lat. Hefinally bethought himself of a lucky expedient, which was successful. Can you guess it? He put salt in the water. 23. Which has the greater buoyantforce, oil or water? Water, because its density is greater. 24. What is the weight of 4 cu. ft. of cork.? 1000 oz. = the weight of 1 cu. ft. of water..240 = the spec. grav. of cork. 240 oz. = the weight of 1 cu. ft. of cork. 4 960 oz. = 4 " " = 60 lbs. 25. How many oz. of iron will a cubic foot of corkfloat in water? 1000 oz. = weight of a cubic foot of water..240 = spec. grav. of cork. 240 = weight of a cubic foot of cork. 1000 oz. - 240 oz. = 760 oz., the buoyant force of a cubic foot. 26. What is the specific gravity of a body whose weight ix air is 30 grs. and in water 20 grs.? 30 grs. - 20 grs. = 10 grs. 30 grs. + 10 grs. = 3. The body is three times as heavy as water. 27. Which is heavier, a pail of fresh water or one of salt. atErr? A pail of salt-water is as much heavier than one of freshwater as the weight of the salt added to make the brine.
Page 28 28 ANSWERS TO PRACTICAL QUESTIONS 28. The weights of a piece of syenite-rock in air and tn wa/er were 3941.8 grs. and 2607.5 grs. Find its sjiec. grav. — Ans. 2.954. 29. A sfiecimen of green safifhire from Siam weighed in air 2I.45 grs., and in water I6.33 grs. Required its sjiec. grav.-Ans. 4. I 89. 30. A specimen of granite weighs in air 534.8 grs., and in wuater 334.6 grs. What is the sj5ec. grav.?-Ans. 2.67 1. 31. What is the bulk ofa ton of iron? 1000 oz. = weight of 1 cu: ft. of water. 7.8 = spec. grav. of iron. 7800 oz. = weight of a cu. ft. of iron. 82,000 oz. (a ton of iron) -+- 7,800 (weight of a cu. ft.) = 44/s za. ft A ton of gold? 1,000 oz. = weight of a cu. ft. of water. 19.34 = spec. grav. of gold. 19,340 oz.* = weiht of a cu. ft. of gold. 32,000 oz.* + 19,340 oz. = 1.6, the no. of cu. ft. A ton of coAS5er? 1000 oz. x 8.9 = 8900 oz. 32,000 oz. + 8900 oz. = 3.6 (nearly) the no. of cu. ft. 32. What is the weight of a cube of gold 4 feet on eacA ride? 43 = 64, the no. of cu. ft. 19,340 oz.* (no. of oz. in 1 cu. ft.) x 64 = 77,360 lbs. 33. A cistern is 12 ft. long, 6 ft. wide, and o Jft. deep When full of water, what is the firessure on each side? On one side, 12 x 10 x 5 x 1000 oz. = 600,000 oz. = 37,500 lbs. On one end, 6 x 10 x 5 x 1000 oz. = 300,000 oz. = 18.750 lbs. 34. Why does a deadfish alwaysloat on its back? It has its swimming-bladder located just under the spine; and this is the lightest part of its body, and, of course, comes to the top as soon as the fish dies. * In these solutions the student should notice that avoirdupois weight is used in weighing the gold. To be exact, 1,000 oz., the weight of a cu. ft. of water, should be reduced to Troy weight, and the lb. gold taken as 12 oz. Troy, whenr the ans. would be about 1.36 cu. ft.
Page 29 IN NATURAL PHILOSOPHr. 29 36. A vessel holds Io lbs. of water-: how much n.rcurmy would it contain? Mercnry is 13.5 times heavier than water. Hence the vessel would contain 10 lbs. x 13.5 = 135 lbs. of mercury. 37. A stone weighs 70 lbs. in air and 50 in water [Whal is its bulk? 70 -50 = 20. 20 x 16 oz. = 320 oz., the weight of water displaced. 320 oz. is 8/25 of a cu. ft. 38. A hollow ball of iron weighs Io lbs.: what must be its bulk, to foat in water? 10 lbs. = 160 oz. As a cubic ft. of water weighs 1,000 oz., the ball must displace such a part of a cu. ft. of water as 1,000 oz. is contained times in 160 oz which is.16 cu. ft. HYDRAULICS. 121.. How much more water can be drawn from a faucet 8 feet, than from one 4 feet below the surface of the water in a cistern? = 2gd; hence v = 2 V16 x8 = 2Q.6. v = 2 J16x4 = 16. Hence 6.6 cu. ft. more would flow from one than from the other in each second..2. How much water would be discharged ijer secondfr-om a shortpfipe having a diameter of 4 inches and a depth of 48 feet below the surface of the water? 42=16. 16 x.7854=12.57 sq. inches=.087 sq. ft. (area of the tube). v = 2gd = 2V16 x 48 = 55.4.087 x 55.4 = 4.8 cu. ft. 3. When we pour molasses from a jug, why is the stream so much larger near the nozzle than at some distance from it p Because, according to the law of falling bodies, the further the molasses falls the faster it falls. The stream, therefore, becomes smaller as it moves more swiftly, until, at last, it breaks up into drops.
Page 30 30 ANSWERS TO PRACTICAL QUESTIONS 4. Ought afaucet to extend into a barrel beyona the staves-t No; because cross currents would be produced, which would interfere with the free passage of the liquid. 5. What would be the effect if both the openings in one of the arms in Barker's Mill were on the same side? It would cease revolving. The pressure in each direction would then be equal, and the arms would balance. PNEUMATICS. 148. I. Why must we make two openings in a barrel of cider when we taf it? One to let out the cider, and one to admit the air. 2. What is the weight of ro cubic feet of air? 100 cu. in. weigh 31 grs.; hence 10 cu. ft. will weigh 31 grs. x 172.8 =.7652 lbs. avoirdupois. 3. What is the pressure of the air on one square rod of land? 2721/4 x 144 x 15 lbs. = 588,060 lbs. 4. What is the pressure on a pair of Magdeburg hemispheres 4 in. in diameter, when the air is entirely exhausted? 3.1416 x 42 x 15 lbs. = 753.9 lbs. 5. How high a column of water can the air sustain twhen the barometric column stands at 28 in.? 28 in. x 131/2 = 311/2 feet. 6. If we should add a fressure of two atmospiheres, what.would be the bulk of ioo cu. in. of common air? The pressure is trebled, and according to Mariotte's law, the volume will be reduced in the same proportion; hence it will be 100 cu. in. + 3 =.31/, cu. in. 7. If, while the water is running through the sizphon, we quickly lift the lonlg arm, what will be the effect on the water in the sipthon? It will all run back through the short arm into the vessel. 8. If we lift the entire sipthon? The water will all run out the long arm.'rhe reason of this.
Page 31 IN NATURAL PHILOSOPHIY. 3 difference is, that when we lift the long arm we make it in effect the short arm, and the other arm the long one. 8. When the mercury stands at 29.
in. i'z the barometer, how high above the surface of the water can we place the lower pumf-valve? In theory, 29. in. X xI3 - 398.
in.; in practice, the distance is much less than this. 9. Why cannot we raise water, by means of a sipfhon, to a higher level? There is no power in a siphon; it is only a way of guiding the flow of water to a lower level. Io. If the air in the chamber of a fire-engine be condensed to 1c6 its former bulk, what will be thefiressure due to the ex!pansive force of the air on every sguare inch? —Ans. 240 lbs. I x. What causes the bubbles to rise to the surface, when we put a lump of loaf-sugar in hot tea? The bubbles of air contained in the pores of the sugar rise because they are lighter than the water. 12. To what height can a balloon ascend? Until its specific gravity is the same as that of the air in which it floats. -What weight can it lift? A weight equal to the difference between its own weight and that of the air it displaces. 13. Why is the air lighter in foul and heavier in fair weather? This question is answered in the Philosophy. Another reason may be, that the upward currents of air partly remove the pressure in foul weather. 14. When smoke ascends in a straight line, is it a proof o1 the rarity or density of the air? Of its density, because it shows that the smoke is much lighter than the air, and so rises immediately to the top. I. Why do we notfeel the heavy pressure of the air on out bodies?
Page 32 32 ASNSWERS TO PRACTICAL QUESTIONS Because it is equally distributed within and without our bodies. The pressure on a person of ordinary size is about 16 tons. I6. Is a bottle empSty whenfilled with air? No; because we must empty the air out before we can fll the bottle with anything else. I8. How does the variation in the pressure of the air affect those who ascend lofty mountains? The outward pressure is there partly removed, and the inner pressure remaining the same, the blood is often forced through the ears, nostrils, etc. When one descends into a deep mine the conditions are reversed: the outer pressure becomes in excess of the inner; severe pain is felt in the eardrum, and ringing noises in the head become almost intolerable. These, however, disappear after a time, where the equilibrium between the internal and external pressure is restored. It is said that Humboldt ascended where the mercurial column fell to 14 inches, and descended in a diving-bell where it rose to 45 inches-thus making a variation of 3I inches, or a difference of 3 I,ooo lbs. pressure on his body. -If the atmosphere in a diving-bell were of the same density as that at the surface of the earth, how deep in the water would it be necessary to sink the bell in order to reduce the volume of the air one-half, or, in other words, for the bell to half fill with water?-Ans. 34 feet. How near would the bell be filled at a depth of 1,020 feet. Ans. 29/so. If the bell were then raised, would the water stay in till it reached the surface? The elasticity of the air would cause it to gradually expand and drive out the water as it rose. ACOUSTICS. 184. I. Why cannot the rear of a long column of soldiers keep time to the music.
Page 33 IN NA TURAL PHiLOSOPHY. 33 Because it takes time for the sound-wave to pass down the column, and hence those in the rear do not hear the music as soon as those in front. 2. Three minutes elap5se between theflash and the rejiort of a thunderbolt: how far distant is it? If the air is at the freezing point, the distance is 1090 ft. x 60 x 3 = 196,200 ft. 3. Five seconds expire between theflash and report of a gun: what is the distance.? 1090 ft. x 5 = 5450 ft. 4. Suippose a speaking-tube should connect two villages Io miles apart. How long would it take a sound to pass that distance? 52,800 ft. -+ 1090 ft. = 48.4 (sec.) 5. The report of a pistol-shot was returned to the earfrom theface of a cliff in 4 seconds. How far was it? 1090 ft. x 2 = 2180 ft. 6. What is the cause of the difference in the voice of man and woman? It may be a difference in the length of the vocal chords, or in the power of lengthening and shortening them; but it is not yet fully understood. The difference between a bass and tenor, as between a contralto and soprano voice, is probably that of quality only, like that between different kinds of musical instruments. 7. What is the number of vibrationsfier second necessary to produce the fifth tone ofthe scale of C? (p. 176.) C, = 128 vibrations. G of that scale = 192 vibrations per second. 8. What is the length of each sound-wave in that tone when the temperature is zeroa? 1090 ft.- 32 ft. =1058 ft. 1058 ft. +192=5 ft. 6 + in. (the length of each vibration). 9. What is the number of vgbrations in the fourth tfne above middle C (Cj)? C, = 256 vibrations.36, = (the proportionate no. for the 5th of the scale). 256 x = 384 (the number of vibrations per second). 9*
Page 34 34 ANSWERS TO PRA CTICAL QUESTIONS 10. A meteor of Nov. 13, I868, is said to have exfiloded at a height of 6o miles: what time would have been necessary for its sound to reach the earth? 52SO ft. x 60 = 316,800 ft. 316,800 ft. + 1090 ft. = 290 (sec.) = 4 min. 50 sec. I I. A stone was let fall into a well, and in 4 seconds was heard to strike the bottom. How deep was the well? (See p. 48.) d = 16 x t2. d = 16 x 42 =256 ft. I2. What time would it require for a sound to travel 5 mites in the still water of a lake? 5280 ft. x 5 = 26,400 ft. 26,400 ft. + 4700 ft. = 5.6 (sec.) 13. How much louder will be the report of a gun to an observer at a distance of 20 rods than to one at half a mile? 160rods are8times 20 rods. The intensity of the sound is inversely as the square of the distance = 1/64. Hence the sound is 64 times louder to the observer at 20 rods that to the one at half a mile. 14. Does sound travel faster at the foot or at the tofi of a mnountain? The density and elasticity of the air vary in the same proportion; hence if the temperature were the same on the top of a mountain that it is at the foot, the velocity of sound would be the same, but as it is always colder, the velocity is less. 15: Why is an echo weaker than the original sound? Because the intensity of the sound-wave is weakened at each reflection. i6. Why is it so fatiguing to, talk through a sfieakingtrumpet? Because so much more air must be set in motion by the vocal chords. The column of air in the resonant cavity of the throat is re-enforced by all the air in the trumpet. -— When we hear a goblet omr a wine-glass struck with the blade of a knife, we can distinguish three sounds, the fundamental and two harmonics.* * Is not the ear the most perfect sense? A needlewoman will distinguish by the sound, whether it is silk or cotton that is torn. Blind people recognlze.
Page 35 IN NATURAL PHIILOSOPIY. 35 OPTICS. 224. I. Why is a secondary bow fainter than the jprimary I The primary is produced by one reflection and two refractions; the secondary, by two reflections and two refractions. The additional reflection weakens the ray. Why are the colors reversed? We can understand this by looking at Fig. 159. In one bow we see that the rays enter the drops at the top, and are refracted at the bottom to the eye; in the other, that the rays enter at the bottom, and are refracted at the top to the eye. 2. Why can we notsee arounda house or through a bent tube? The rays of light move in straight lines. 3. What color would a painter use if he wished to represent an opening into a dark cellar Black. 4. Is black a color? No; it is the absence of color. Is white? Yes; it is the presence of all color-i. e., it is the compound effect produced on the brain by seven different impressions. 5. By holding an object nearer a light, will it increase or diminish the size of the shadow? It will increase it, because more rays are intercepted. 7. Where do we see a rainbow in the morning? In the west. the age of persons by their voices. An architect, comparing the length o' two lines separated from each other, if he estimate within the 30th part, we leem very accurate; but a musician would not be considered very precise who only estimated within a quarter of a note. (128-30 = 4, nearly.) In a large orchestra, the leader will distinguish each note of each instrument. Wc recognize an old-time friend by the sound of his voice, when the other senses utterly fail to recall him. The musician carries in his ear the idea of the musical key and every tune in the scale, though he is constantly hearing a multitude of sounds. A tune once learned will be remembered when the words of the song are forgotten. Prof. Pepper tells us that he tuned a fork which corresponded to 64,000 vibrations per second. The first harmonic is produced by one-half the whole cord, the second by one-third, &c.
Page 36 36 ANSVWERS TO PRACTICAL QUESTIONS 8. Can any two sp5ectators see the same rainbow? They cannot, because no two persons can be at the right angle to get the same color from a drop. 9. Why, when the drofps of water are falling through the air, does the bow appear stationary? Because the drops succeed each other so rapidly that they keep a constant impression on the retina. Io. Why can a cat see in the night? Because the pupils of its eyes are larger, and so admit more light. Why cannot an owl see in daylight? The pupils of its eyes are large enough to admit of cleal vision in the night, but they cannot be contracted, and so in daylight the owl becomes dazzled with the excess of light received. I2. Wshy are we blinded when we pass quickly from a dara into a brilliantly lighted room? The pupils of our eyes admit too much light, but they soon contract to the proper dimensions, and we can then see distinctly. When we pass out from a lighted room into the dark street, the conditions are reversed. I3. If the light on a distant planet is only ylog that which we receive, how does its distance from the sun compare with ours? As the light is inversely as the square of the distance, the distance is V ioo = I times greater than ours. 14. If when I sit 6 feet from a candle I receive a certain amount of light, how much will I diminish it if I sit back 6 feet further? As my distance from the light is doubled, the light is inversely as 22, or only i as bright. I5. Why do drops of rain, in falling, appear like liquid [hSoads? The impression the drop makes on the retina remains until the drop reaches the ground. i6, Why does a to-wal turn darker when wet?
Page 37 IX NATURAL PHILOSOPHY. 37 More of the light is transmitted, and less reflected. We see this illustrated in greasing a bit of paper. It becomes semitransparent because more light passes through it, but looks darker itself because less light is reflected to the eye. 17. Does color exist in the object or in the mind of the observer? In the mind. Color in the object can be only a peculiar property whereby a body absorbs some colors, and reflects or transmits others. 18. Why is lather opaque, while air and a solution of soap are each transparent? By repeated reflections and refractions in passing through the unhomogeneous mass of lather, the rays are weakened. The principle is the same as that of deadening floors with tanbark. (Phil., p. i6x.) I9. Why does it whiten molasses candy to jull it? Water is given up both in cooking and pulling. This causes more light to be reflected (Q. i6), while the crystals formed, especially on the surface, hide the impurities. 20. Why does plastering become lighter in color as it dries? Because, as the water evaporates, the mortar transmits less light, and reflects more light to the eye. q I. Why does a photographer iuse a kerosene oil-lamp in the' dark-roomz?" Kerosene oil-flame emits only heat and color, but no actinic rays. Some " dark-rooms" are lighted with yellow glass windows. 22. Is the common division of colors into "cold" and "warm" verified in philosophy? Yes; red contains more heat than violet. 23. I Why is the image on the camera, Fig. I67, inverted? The rays cross each other at the focus of the double convex len. 24. WJhy is the second image seen in the mirror, Fig. 134, bngrtgter hani. e f, r The first is formed by reflection from the glass, and the second from the mercury. As the latter is a beter reflector,
Page 38 38 ANSWERS TO PRACTICAL QUE'STIONS the second image will be brighter. Each image after that will be weakened by the repeated reflection. 27. Which can be heard at the greater distance, noise or music? Other things being equal, music will penetrate much further than noise. Boatmen call to each other, at a distance, in a musical tone. A band is heard above the noise of the rabble. It seems to be a wise arrangement of Providence that all harsh, discordant noises should perish as soon as possible, and only harmonious ones survive. 28. Why are some bodies brilliant, and others dull? Some reflect the light better than others. A piece of stone coal lying in the sun's rays will shine so brilliantly that one will cease to see the coal at all, and will judge it to be a bright metal. 29. Why can a carpenter looking along the edge of a board tell whether it is straight? If the edge is straight, the light will be reflected uniformly to his eye from the whole length. Any uneven places will make dark and light spots. 30. Why can we not see out of the window after we have lighted the lampf in the evening? The glass reflects the light of the lamp back to our eyes, and they adapt themselves to the increased amount. 3 I. Why does a ground-glass globe soften the light? It scatters the rays. 32. Why can we not see through.grozund-glass or painted wvindows? They transmit the light irregularly to the eye, and not uniformly, like a transparent body. 33. Why does the moon's surface appear flat? Because it is so distant that the eye cannot detect the difference between the distance of the centre and the circumference.
Page 39 IN NATURAL PHILOSOPHY. 39 34. Why can we see further with a telescope than with the naked eye? Because it furnishes us more light with which to see a distant object. 35. Why is not snow transparent, like ice? Because it is unhomogeneous. See problem I8. 36. Are there rays in the sunbeam which we cannot see? We cannot see the heat or the chemical rays. 37. (x) Make two marks on a sheet of white paper, at a distance of about three inches from each other. Then closing one eye and looking steadily at one mark (though we can see both), move the paper toward the eye. A point will be reached where the eye can perceive only one of the marks; on coming nearer, both will be seen again. 38. (2) Prick with a pin, through a card-board, two holes:loser together than the diameter of the pupil of the eye. Holding the card pretty near the eyes, look through these holes at the head of a pin. There will seem to be two pin-heads. 39- (3) Press the finger on one eyeball and we shall see objects double. Since an impression is made on the retina of each eye, it would seem that we ought always to see objects double. The nerves from both eyes are so joined, however, before they reach the brain, that this effect is avoided. If, now, we cause the image on the retina to be made on parts of the eye which do not correspond to each other, we shall obtain a double image. 40. Why is a rainbow in the morning a sign of foul, and in the evening of fair weather? In the morning it indicates a formation of clouds when the temperature is rising, and therefore shows a determination to moisture. In the evening it indicates a clearing away when the temperature is falling, and hence shows a determination to dryness. 41. Why is a red, lowering sky in the morning a sign of rain, and a brilliant red sky at night, of fair weather?
Page 40 40 ANSWERS TO PRACTICAL QUESTIONS 42. Why does a distant light, in the night, seem like a star! 43. Why does a bright light, in the night, seem so much nearer than it. is? 44. Why does a ray of light, j5assed through a small hole, of any shape, inz a card, make a round, bright spot? 45. Why are these siots crescent-shaped during an eclipse? 46. VWhat color predominates in artificial lights? Yellow. 47. Why does yellow seem white, and blue green, when seen jby artificial light? Because the white takes on, in the yellow rays. a yellow hue, and the yellow added to the blue gives a green, hence there is no white for comparison. So, also, dark blue becomes purple, and red has a tawny hue. Magnesium light possesses all the colors of the spectrum, and hence all objects retain their natural appearance when illuminated by it. 48. Why are we not sensible of darkness when we wink? Because the impression of the light is retained upon the retina during the brief interval of darkness. HEAT. 258. I. Why will one's hand, on a frosty morning, freeze to a metallic door-knob sooner than to one of porcelain? Because the metal is a better conductor of heat than the porcelain, and hence conducts the heat from the hand faster. 2. Why does a piece of bread toasting curl up on the side toward the fire? The water being expelled from the pores on that side causes the bread to shrink. 3. Why do double windows protect from. the cold? The non-conducting air enclosed between the window-panes keeps in the heat and keeps out the cold. 4. VWhy do fur;nace-men wear flannel shirts in summet to kefie cool, and in winter to