GIFT OF . Prof » M. E« Jarfa Digitized by the Internet Archive in 2007 with funding from Microsoft Corporation http://www.archive.org/details/averysphysicalteOOaverrich AVERY'S Physical Technics AND TEACHER'S HAND-BOOK, TO ACCOMPANY THE FIRST PRINCIPLES OF NATURAL PHILOSOPHY THE ELEMENTS OF NATURAL PHILOSOPHY. CONTAINING SOLUTIONS TO PROBLEMS, DESCRIPTIONS OF INEXPENSIVE AND HOME-MADE APPARATUS, MANY SIMPLE EXPERIMENTS, PRACTICAL SUGGESTIONS, ADDITIONAL PROBLEMS AND OTHER MATTER CONCERNING TOPICS CONSID- ERED IN THE TEXT-BOOKS, ETC., ETC. NEW YORK AND CHICAGO: Sheldon & Company Dr. AVERY'S PHYSICAL SCIENCE SERIES. mn , • ' ISt. •^r^RST PRINCIPLES OF NATURAL PHILOSOPHY 2d. THE ELEMENTS OF NATURAL PHILOSOPHY. 3d- THE ELEMENTS OF CHEMISTRY 4th. THE COMPLETE CHEMISTRY. Containing the Elements of Chemistry, with an additional chapter en Hydro carbons in Series or Organic Chemistry. It can be used in the saiuc ci?*ss w'.^t The Elements of Chemistry. 5th. PHYSICAL TECHNICS. To accompany Avery's Natural Philosophies ; containing Solu**«*w f l Problems, Additional Experiments, Practical Suggestions, etc. 6th. TEACHER'S HAND BOOK. To accompany Avery's Chemistries. Copyright^ 1879, 1886, by Sheldon & Company. Eltctrotyped by Smith & McDougal, 82 Beekman St., New York. TO THE TEACHER. r~ I AHIS little volume has been prepared for your con- -*- venience and not for that of your pupils. It is sent forth by the author with the hope that it may lessen the labor and increase the usefulness of some of his fellow-teachers. You will confer a favor upon him by notifying him of any errors you may find in it, or in the text-books to which it pertains. If, in your class, you use The First Principles of Natural Philosophy, you will find it to your advantage to have a copy of The Elements of Natural Philoso- phy and habitually compare the corresponding topics. As the general arrangement of the two books is the same, the reference will be easily made. Such reference being made, you will naturally refer to the corresponding notes on The Elements, contained in this volume. If your class uses The Elements, you will still find it of advantage to have a copy of The First Princi- ples, to which frequent references are made in this vol- ume. 769793 FIRST PRINCIPLES OF NATURAL PHILOSOPHY.,- CHAPTER I. %9T Tfte full-faced numeral* at the left of the page refer to par- agraph* i a the text-book. 4. "At its ordinary pressure, the atmosphere is not very dense, and its recognition, as a constituent of the world of matter, is quite a modern notion. It would seem that when divided by a million, s« little matter will be left that we may justifiably neglect the trifling residue and apply the term vacuum (§ 187) to the space from which the air has been so nearly removed. To do so, however, would be a great error, attributable to our limited faculties being unable to grasp high numbers. It is generally taken for granted that when a num- ber is divided by a million the quotient must necessarily be small, whereas it may happen that the original number is so large that its division by a million seems to make little impression on it. Ac- cording to the best authorities, a bulb like the one before you (13.5 centimeters in diameter, see Appendix B) contains more than 1000000 000000000000000000 (=10 84 ) molecules. Now, when ex- hausted to a millionth of an atmosphere we still have 1 000000 000000- 000000 (=10 18 ) molecules left in the bulb — a number quite sufficient to justify me in speaking of the residue as matter. "To suggest some idea of this vast number, I take the exhausted bulb and perforate it by a spark from the induction coil (£ 300). The spark produces a hole of microscopical fineness, yet sufficient to allow molecules to penetrate and destroy the vacuum. The inrush of air impinges against the vanes (see Elements of Nat. Phil., Fig. 1 77) and sets them rotating. Let us suppose the molecules to be of such a size that a hundred millions could enter in every second of time. How long, think you, it would take for this small vessel to p't full of air? An hour? A day? A year? A century? Nay, almost an eternity! A time so enormous that imagination itself 6 [First Principles of Natural Philosophy, p. 2.\ cannot grasp the reality. Supposing that this exhausted glass bulb, indued with indestructibility, had been thus pierced at the birth of the solar system ; supposing it to have been present when the earth was without form and void ; supposing it to have borne witness to all the stupendous changes evolved during the full cycles of geologic time, to have seen the first living creature appear and the last man disappear ; supposing it to survive until the fulfillment of the math- ematician's predion >.i tint the sun, the source of energy, four million centuries from its formation, will ultimately become a burnt out cinder ; supposing ail this — a;t the rate of filling I have just described, 4 hundred million molecules a second, this little bulb even then would scarcely have been filled. u But what will you say if I tell you that all these molecules will enter through the microscopical hole before you leave this room. The hole being unaltered in size and the number of the molecules undiminished, this apparent paradox can be explained only by sup- posing the size of the molecules to be diminished almost infinitely, so that instead of entering at the rate of 100 000 000 a second they troop in at the rate of something like 300 003000 000000000000 a second." — WUliara Crookes. It is estimated that a cubic centimeter of air contains about .000 000000 000000 000000 molecules. Then the bulb above de- scribed would contain (13.5 3 x 0.5236 x 1000 000000 000000 000000 =) 1 288252 350000 000000 000000 molecules of air at the ordinary atmospheric pressure. When exhausted to a millionth of an atmosphere, the bulb still contains 1 288252 350000 000000 mole- cules, leaving 1 288251 061747 650000 000000 to enter through the perforation. At the rate of 100 000000 molecules a second, the time required for them all to enter will be 12882510617476500 seconds, or 214708510291275 minutes, or 3578475171521 hours, or 149103132147 days, or 408501731 years. 6. See Daniell's " Principles of Physics," pp. 222-236. [Fvrst Principles of Natural Philosophy, pp. 23-81.] 7 43. See note on § 4. Review Questions, Page 2&, 1. See line preceding Exp. 1. 2. See|§land 8, b. 3. The kinds of atoms. § 3, a. 4. Eight cubic inches. § 19. 6. Float the cork on the water ; surround it with the larger end of the chimney ; cover the smaller end with the fleshy part of the hand and push the glass downward into the water. 7. (a.) An atom, (b.) A molecule. 8. Elementary. §§ 3 (a) and 4 (b). 9. Compound. §§ 3 (a) and 4 (b). 11. Same size. Vaporization is a physical change. § 11 (a). 16. See §§ 7, 30. 19. See § 23. 54. The momenta of the blocks mentioned in Exp. 29 vrill be equal. 8 [First Principles of Natural Philosophy, pp. 35-36.] Exercises, Page 85, 25 x 100 _ Z ' "21T60" ~ ' 3. 1000 + 50 = 20. 4. The canoe, because the momentum of a body at rest u zero. § 49. 5. 5 x 4 = 10 x 2. Their momenta are equal. 6. Reduce the velocities to feet per minute. 5 *B i x m^ x u = 5. n x n x < 4 7. No. 8. (#.) Physical. (5.) Chemical. See Hand Book note on § 634 of Elements of Nat. Phil, (c.) The molecule. (§ 11, a.) 9. Crowded more closely together on the concave side ; palled further apart on the convex side. 10. See § 40 (a) and (b). The velocity with which it strikes will depend upon the distance it has fallen. §§ 79 (1) and 98 (a). 11. The momenta must be the same, for equal forces produce equal effects. Since the momenta are equal the 1100 pounds will move twice as fast as the 2200 pounds. 60. Compare Elem. Nat. Phil, § 100. First Principles or Haturcu Philosophy, pp. M-60.] 9 E xercis e * , Fnge 44. 1. §§ 72, 73. 2. § 73. The base of the sphere is a point. The line of direction will not pass through this point unless the supporting surface be horizontal. 5. Doubling the weight means doubling its attraction (for the earth or anything else). 6. One unit. § 60 (2). 7. To the outermost bounds of the universe. Exercises , Page. 50, 1. S = \gfl = 16.08 x 100 = 1608. 2. v = gt = 32.16 x 4 = 128.64. 3. s = iff (2t - 1) = 16.08 (8 — 1) = 112.56. 4. s = iff (2t — 1) + 25 = 144.72 + 25 = 169.72, the number of feet. 5. In this case, the increment of velocity due to gravity (ff) is 10 feet instead of 32.16 ft, as it would be were this a freely falling body. Use the same formula, giving ff thic new value. v = gt = 10 x 10 = 100. 6. It is 9.81 meters, or 981 centimeters. 7. The first one has fallen for 5 sec. : S=igP = 16.08 x 25 = 402. The other has fallen for 2 seconds : S = igt 2 = 16.08 x 4 = 6132 337 68 8. v = gt. .'. 98.1 = 9.81/. .'. 10 = t. 9. S represents " the distance traversed by a freely falling body during any number of seconds"; \g represents 44 16.08 feet, or 4.9 meters"; t 2 represents "the square of the number of seconds," and the method of writing the factors { g and P represents " multiplied by." 10 [First Principles of Natural Philosophy, pp. 56-65.] Exercises, Page 56. 1. It will vibrate the same number of times. 2. The other is 40 inches long. § 88. 3. They will vibrate at the same rate. § 87. Distinguish between the true length and the apparent length as ex- plained in Exp. 38. See Elem. Nat. Phil. §§ 141, 142. 4. Vl6 : a/64 =1:2. The short pendulum will vi- brate twice as fast as the long one. Ans., 8 times. 5. Make it one ninth as long. 6. It is too long. Lower the bob. 7. Vi : V9 -' 2 ° '*. The short one will make three while the long one is making two. 8. V49 : V64 = 7:8. The time of vibration of the long pendulum will be f that of the short one. (Its num- ber of vibrations in a given time will be only -J that of the short one.) 9. Four times the length of the second's pendulum, or (in this latitude) about 156.4 inches (more than 13 ft). 10. One fourth the length of a second's pendulum, or a little less than 10 inches. Such pendulums are very com- mon in clocks. Exercises, Page 65. , 100 000x198 1A -1 , , ., .. L "33000-^60" = 10 - W ° rk by cancellatlon ' 2000x10x50 500 ■ --j. , . * . , 2 * 33000x2 = W = l0 A ' the nUmber ° f mmuteS * 3. Double it ; the K. E. varies with the square of v. § 98. 4. They are equal. 6. 5 x 20 x 50 = 5000, the number of foot-pounds. 7. (a.) 5000 foot-pounds, (b.) The kinetic energy ex- pended in lifting them to an elevation of 50 ft. was all stored in the bricks at that height, as potential energy. a k. m. = St = ^o_xm ^200 = 40 000 000< 2g 64.32 [First Principles of Katural Philosophy, pp. 66-77.] 11 Review Questions, I*af/e 66, I. Gravitation pulls downward both the cork and the water. But, the water being the heavier, is drawn with the greater force. The water is, therefore, drawn under the cork (it having freedom of molecular motion, § 39) and pushes the cork upward. 3. Because the centre of gravity is lower ; the base is the same ; the line of direction is, therefore, less easily thrown without the base. § 73. 4. At the bottom; to bring the centre of gravity as low as possible. 5. Because the base is broader. § 72. 6. No. There would be nothing to offer any resistance to any effort that he might wish to make. There would be nothing to react on him and put him in motion. § 54. An infinitesimal force from without would move him, but he can not exert even such a force because there is nothing upon which to exert it. 7. Quartered. 9. Because of their freedom of molecular motion. 10. Elasticity in particular. II. Elasticity of the spring. 12. If the nail is smooth, adhesion; otherwise, cohesion aids. 13. To bring the centre of gravity as far below the centre of buoyancy (§ 163, b) as possible, and thus keep the vessel in stable equilibrium. 14. Adhesion. 15. Gravitation, of which gravity is a special kind. Exercises, Page 77* 1. 1000 -r- 100 = 10.— Ans. 2. To put the unloaded lever in equipoise. 3. The two arms are respectively 1 foot and 4 feet long. 7 pounds x f = 28 pounds. — Ans. 12 {First Principles of Natural Philosophy, pp. 77-85.] 4. The two arms are respectively 1 foot and 5 feet long 7 pounds x f = 35 pounds. — Ans. 5. The two arms are respectively 5 feet and 1 foot long 7 pounds x -J = 1 lb., 6f oz. G. Not in the middle, because then the arms would be of equal length and the power would equal the load. As the power is only half the load, the power arm must be twice as long as the weight arm. The fulcrum must be 50'inches from the load and 25 inches from the weight. (This ignores the weight of the lever itself, or assumes it to be in equipoise about the fulcrum placed as described.) 7. (a.) 18 ft. (b.) 12 ft. (c.) 12 ft. 9. The power (applied at c) moves 10 inches. The load (applied at b) moves \ inch. As the power moves 20 times as far as the load, the load will be 20 times as great as the power. § 108 (2). 100C lb. x 20 = 20000 lb. Exercises, Page 85, 1. 5 : 1 = 125 : 25. 2. The power (applied at the handle) moves 9 ft. while the load (suspended from the rope) moves 3 ft. As the power moves 3 times as far (or 3 times as fast) as the load, the load must be 3 times as great as the power when the machine is in equilibrium. § 108, (2) and (3). 3. The radius of the wheel is 8 ft; that of the axle, 1 ft. Therefore, the power will be \ of the load. 4000 lb. -$•..8 = 500 lb. This power being furnished by 4 men, each man pushes (or ought to push) with a force of 125 lb« 500 -*■ 4 = 125. 4. (a.) 10 1b. (b.) 20 1b. (c.) 60 1b. (d.) 30 1b. 7. 2 * [ Z ll i" [First Principles of Natural Philosophy, p. 93.] 13 i;.ierrisrs, I'(ff/r U'.i. 1. The weight of the plunk is practically at its centre of gravity, 10 ft. from either end. Lifting this weight at one end of the plank, the boy is using a lever of the second class with arms of 10 ft. and 20 ft. respectively. Hence he lifts only 62£ lb., the rest of the weight of the plank being carried by the fulcrum (the ground), (b.) The length of the inclined plane is 4 times its height 196 lb. -7- 4 = 49 1b. 2. 10 ft. x ft = 30 fa—Ans. 3. 15 lb. x 6 = 90 lb.— Ans. 4. The power moves 40 inches while the weight moves i inch. 40 -T- 1 = 160. 1600 Kg. -T- 160 = 10 Kg. 5. 30 lb. x 160 = 4800 lb. 4800 lb. — 480 lb. = 4320 lb. Or we may deduct the ^ from the 30 lb. and say 27 lb. x 160 = 4320 lb. 14 [First Principles of Natural Philosophy, p. &£.] Review Questions, Page 94. 1. By thus raising the centre of gravity above the point of support, he may put the boat in unstable equilibrium. §§ 163 (b.) and 69. 2. § 144. 7. § 21. (a.) The pupils will enjoy your reading to them this poem of Shelley's. 10. The momentum of the " run" adds its effect to the muscular effort of the " jump." 11. (a.) The effect of gravity is less 1000 miles above the surface of the earth than it is at the surface (§63). Con- sequently at that elevation it would take a larger lump to pull down the spring of the balance as far as a pound would pull it here. (J.)- The elasticity of the spring would, probably, not be affected by its greater distance from the earth's centre, but with the lever balance, the weight and counter weight would be equally affected. In one case, the standard is constant ; in the other, it is changeable. 12. Cohesion. §§ 7, 30. 13. Cohesion. 14. Cohesion. 15. See Hand-Book note on that exercise. P is at one end of the plank ; W, at the middle ; F, at the other end which rests on the ground. 16. (a.) Adhesion, (b.) Grease the outside of the jar at the part over which the water is poured. 17. 10 lb. x {m = U K>.—Ans. 18. § 73. 20. K. E. = £ = 1Q ° X 1°Z X J00 ° = 6218905.47, 2g 64.32 the number of foot-pounds. [First Principlt* of yat'tra' Phi osophy, pp. MJ-112.] 15 Ej-erriscs. Pa /r Ht<>. 1. 100 lb. x V- X -^P* = 10 000 000 11). 2. In the basement, because the "imaginary column* will be higher, i.e., the head (§ 171) will be greater. 3. The exposed surface is 250 sq. ft. (§ 158.) The imaginary column is 5 ft. high and has a volume of L250 cu. ft. Such a volume of water would weigh 62.42 lb. x 1250 = 78025 lb. 4. 6 x 8 x 4 = 192, the number of cubic feet. 62.42 lb. x 192 = 11984.64 lb. 5. 2 x 3 x 1.5 = 9, the number of cubic meters. Each cubic meter equals 1000 cu. decimeters or liters. (Ap- pendix B.) Each of the 9000 liters of water weighs 1 kilogram (for each liter contains 1000 cu. cm., and each :u. cm. of water weighs one gram). Exercises, Paffe 112. 1. In the valley, because the pressure will vary with the depth below the surface of water in the reservoir. 2. 50 lb. § 163. 3. 1 cu. ft., which will weigh 62.42 lb. 5. Consult biographical dictionary or cyclopaedia. 4. It will displace 1 cu. ft. of water and, therefore (§ 162), lose 62.42 lb. of its weight. 6. (a.) Its own weight, (b.) Its own volume. 7. When its centre of gravity is below its centre of "buoyancy. It may be necessary for the boat to carry ballast to keep it there. 8. Because, while it is in the water, it is buoyed up with a force equal to the weight of its own volume of water ; after that, the buoyant effect is only the weight of its own volume of air. !». Because you displace a volume of water that weighs nearly as much as you do. Thus, you are nearly lifted from the ground. 16 [First Principles of Natural Philosophy, pp. 116-121.] Exercises, Page 116. 1. It loses 50 lb. in water. Its volume of water weighs 50 lb. The body is three times as heavy as its own volume of water. This means that its specific gravity is 3. a W 150 150 *■ ^ == WW = 150^100 = To" f d '~ Ans - 2. 75 oz. — 60 oz. = 15 oz.— Ans. 3. No ; it will float. Try it before the class if you can. 4. It will lose 1.8 times as much weight in the acid. 5. In fresh water. The buoyancy of the salt water will be the greater. 6. It is well known to be easier to swim or float in sea water than it is in fresh water. 7. The volume of the overflowing water was equal to the volume of the brass. 41.9 oz. -f- 5 oz. = 8.38. 8. The bottle will hold (1000 cu. cm.) 1000 grams of water. The same volume of water weighs (800 grams -=- 1000 grams = ) 0.8 as much. That is, the sp. gr. of alco- hol is 0.8. Eemember that the weight of an equal volume of water is always the divisor. Mevietv Questions, Page 121. 1. § 146. 2. § 152. 3. § 148. 4. §§ 150, 111. 5. Solids have permanency of form ; liquids have not. Liquids have freedom of molecular motion ; solids have not. 6. One second. § 86. 7. The nutcracker is a double lever of the second class (§ 109). F is at the hinged end ; the resistance of the nut is W; P is at the hand. 9. In no direction ; they transmit pressure equally in all directions. [First Principles of Natural Philosophy, pp. 1S1-12S.] 17 10. § 147. 12. The lev is an abstract number. It simply means ten times as heavy as water. All multipliers are abstract numbers. 16. The centre of gravity is thus brought lower. As shown in the figure, the apparatus is still in unstable equilibrium. The knives might be brought low enough to bring the centre of gravity below the point of support, and thus put the apparatus in stable equilibrium (§§ 73, 66). Exercises, Page 128. 1. Because the upward atmospheric pressure is as great. 2. Water would rush in. The tension of the air in the bottle would be only that of the atmosphere at the mount- ain top, and this is less than atmospheric pressure at the sea level. 3. The exposed surface is 1728 sq. in. 15 lb. x 1728 = 25920 lb. • 4. The exposed surface is (100 x 200 = ) 20000 sq. cm. The pressure is a kilogram for each sq. cm. Arts., 20000 Kg. 5. To prevent the downward pressure of the atmosphere on the top of the mercury column. 6. To permit the atmosphere to act upon the bottom of the mercury column and thus to support it. 7. The mercury is 13.6 times as heavy as water. 28 in. x 16.6 = 380.8 in. = 31 ft, 8$ in. 8. The boiler was subjected to an internal pressure of 150 lb. per sq. in. This test might have been hot or cold ; steam may have been generated in the boiler until the steam gauge recorded a pressure of 150 lb., or the boiler may have been filled with water and hydrostatic pressure applied (§ 150). The cold test is considered the more severe. 18 [First Principles of Natural Philosophy, pp. 137, 138.] Exercises , Page 137, 1. The cube has six faces. Its total surface is 6 sq. in. 15 lb. x 6 = 90 lb.— Ans. 2. 28 ft. = 336 in. 336 in. -f- 13.6 = 24|f m.—A?is. 3. By placing the pump within 28 ft. of the surface of the water and extending the spout (Fig. 70) to the top of the well. The cylinder of the pump may be a tube ex- tending to the top of the well, the piston rod running down the inside of such long cylinder. 4. The tension of the air, when you blow in at /, lifts the water to h and fills the tube. The tube then consti- tutes a siphon and continues to deliver water into g. The rising of the water in g reduces the air space and thus increases the tension of the air in g, i and a. This in- creased pressure exerted by the air on the surface of the water in a is transmitted to the water contained in a and forces it out in a jet at n. 6. Atmospheric pressure. 7. 1728 cu. in. -5- 8 = 216 cu. in. Review Questions, Page 138. 1. (a.) The bottle contains air. § 19. (b.) The air is compressed by the liquid pressure. 2. (a.) §§ 22, 49. (b.) Chiefly, the friction of the water against the sides of the hull. 3. Because of the continued action of gravity. 5. The Third Law of Motion. The particles that first hit the target are stopped, but other particles press forward, overcoming the force of cohesion until they are stopped by the target. 6. Because of the continued action of gravity, the force that produces the velocity. 7. Much of it is stored up in the pyramids as potential energy. [First Principles of Natural Philosophy, pp. /::>-?o5.] 19 8. A double lever of the first class. P is at the hand; F, at the rivet ; W, at the cord. a 3 iG7. 10. Once a second. § 87. 12. §§ 79 (3), 82. 14. § 161. Exp. 9S. The clapper is polarized, attracted, charged, repelled, discharged, polarized again, etc. Exp. 97. After the leaf is charged by touching the rod, the similar charges repel each other (§ 214). Exp. 98. The pupil being charged by conduction, polarises and attracts the yard-stick (g 225). Exp. 99. When the cover is lifted from the plate, the bound electricity is set free and then similarly charges and repels the paper bits. See Elem. Nat. Phil, § 338 (6-). Exp. 103. See § 240. The repulsion of the air par- ticles for the similarly charged arms of the whirl produces the motion. This is not a case of the mere reaction of the repelled air particles. See § 54. Exercises, Paye 179. 1. Because they produce opposite effects when presented to a third charged body. See § 211. Also Eton. Nat. Phil, § 322 and Exp. 22, p. 194. 3. Electroscope. 4. See § 214. 5. To prevent the condensation of atmospheric moisture. 6. (b.) § 224. (c.) Opposite. Exercises, I'at/e 205. 1. The greater action is upon the zinc. See § 249 aud Fig. 102. 2. (a.) By making the plates larger ; by bringing them nearer each other ; by preventing, by mechanical or chem- 20 [First Principles of Natural Philosophy, p. 205.\ ical means, the accumulation of hydrogen upon tbe negative plate. The internal resistance of a battery may be lessened by joining the cells parallel, (b.) By in- creasing the E. M. F., or by reducing the circuit resist- ance. §§ 252, 265, 266. 3. See § 254. 4. 3.02 : 22.65 = 18.12 : 135.9. Ans., 135.9 yd. 6. §§ 273, 260. 1.079 volts is less than the E. M. F. of the ions (1.45 volts), while 2.158 volts is greater. 7. Assume any number of volts, as 1 volt, as the inter- nal resistance of the Grove cell, and find the current strength of the two cells for comparison. W 1 73 C = -= = ~~ 'Ht 1.73, the number of amperes with Grove cell. Tjl -t f\Q O = -„■ = -V- = 0.216, the number of amperes with Daniell cell. 1.73 -T- 0.216 = 8 + To make the solution more general, call the internal resistance of the Grove cell, a ohms. 1.73 Grove current = — — a Daniell " = ^~ 5a 1.73 1.08 1.73 5a „ „. ., . '- -z — = X =-x^. By cancelling the fao* a 5a a 1.08 J b tor, a, in numerator and denominator, we have : 1.73 5 _ 8.65 _ Q 1 X 1.08 - 1.08 " + * [First Principles of Natural Philosophy, p. 205.] 'i\ 8. (a.) The E. M. F. will be 6 times that of a single cell. (b.) The internal resistance will be J that of a single cell. ET 200 9 - («•> C = R = 25 + 1000 = °- 195 + - ( In 8erieS -) W C = 1 = 0.0025 + 1000 =0 -° 019 + - ( AbrcaSt -) 10 " « C = I = 0.0025 + 0.001 7 571A ( AbreaSt ) <»•) c = i = sstSm = m F**^ 11. Single celL = § = -^^ = 7.96a XT -i nrv 50 cells. C = _ = ___ = 7 .999. With a small external resistance, there is but little gain from joining cells in series. Joining more cells in series will multiply numerator and denominator by the same number and will not change the quotient, which will continue to indicate a current of 8 amperes. 22 [First Principles of Natural Philosophy, pp. 226-243.'] Exercises, Page 226. 2. No ; you have two magnets. 6. It can not be done. 7. Make the experiment. 8. Put the magnet in a hollow iron sphere. 9. See Mem. Nat. Phil, § 437. 10. See Exp. 133. 12. Make the experiment. Exercises, Page 242. 1. Use the power to operate the dynamo, extend the line wire to his residence and use arc or incandescence lamps, or both. 2. § 308. 3. (a.) The electric light, (b.) The 3468 cu. ft. of gas per hour would cost $6,936, showing a saving of $4.73 each hour, (c.) $14208. Review Questions, Page 243. 2. Second class. 3. Wedge. 4. Weight, height, time. 5. By sucking at b, a partial vacuum is formed in /. Atmospheric pressure on the surface of the water in a, forces the liquid up the tube and forms the jet. As b is lower than the surface of the water in a, gravity draws the water downward through it, maintaining a partial vacuum in the closed flask, into which vacuum water con- tinues to be forced. In fact, the apparatus is a siphon with an enlarged portion at its highest point. 7. Make the experiment. 8. The lightning flash. 9. Impenetrability. 10. The tendency of the molecules to cling together in one case, or to separate in the other. Both are fluids. [First Princip 'iral Philosophy, p. 24S.] 28 12 C- £ - 839 - ^- 9 - 10 i? "" (4.56 x lg) + 10.54 + 0.4 ~~ 8.39 " Ans. 9 10 amperes. 13. Neither ; they are developed simultaneously. 14. See § 231. 16. (a.) v = gt = 32.16 ft. x 5 = 160.8 ft.— Ans. \b.) S = W 2 = 16 - 08 ft - x 25 = 402 ft.— Am. 17. See Exp. 111. If convenient, use fine platinum wire instead of the iron wire. 18 - c = i = ( WxTO)+io = is= - 39 -^- 19. Make the experiment. 20. Remember that the glass rod was positively charged. If you noticed attraction, the paper must have been neg- atively charged. If you noticed repulsion, the paper was positively charged. 21. It is the difference between conductors and non- conductors. In other words, it is a matter of resistance. The brass carried the electricity, as fast as it was developed, to the hand and allowed it to escape through the body. The resistance of the sealing-wax prevented such an escape. 22. s = \g (21 — t). See § 82. 337.68 = 16.08 (2t — 1). Dividing by 16.08: 21 = 2t — 1. Adding 1 to each side of equation. 22 = 2/. .-. 11 = t. Ans., 11 sec. 23. The imaginary column of water (§ 157) contains : (42 x 6 =) 252 cu. in., or ^ ff cu. ft. 62.42 lb. x tWj = 9.1 lb.— Ans. 317. The teacher is referred to TyndalPs Lectures on "Sound"; Helmholtz's "Sensations of Tone" and Mayer's " Sound," mentioned in § 320, a. 24 [First Principles of Natural Philosophy, pp. 258-279.] Exercises, Page 258. 2. The temperature is 0°C. § 325. Ans., 1090 ft 3. § 321. 1280 ft. -f- 256 = 5 it.— Ans. 4. 1090 ft. -f- 218 = 5 ft.— Ans. 5. § 325. 332 meters -f- 1 meter = 332. § 321. Ans., 332 vibrations per second. 6. The temperature is 20 centigrade degrees above freezing. §326. 2ft.x20=40ft. 1090 ft. + 40 ft. =1130 ft.— Ans. 7. 1126 ft. - 1090 ft. = 36 ft. 36 ft. -7- 2 ft. =18, the number of centigrade degrees above freezing, or above the centigrade zero. Ans., 18°C. 36 ft. -T- 1.12 ft. = 32.14, the number of Fahrenheit degrees above freezing or above 32°F. 32 + 32.14 = 64.14. Ans., 64.14°F. The increments mentioned in § 326 are only approxima- tions. The temperature, 18°C, is really equivalent to 64.4°F., instead of 64.14°F. Exercises, Page 279. 1. (a.) The first. (J.) The second. 2. 1120 ft. -^ 280 = 4 ft— Ans. 4. 254 or 258. § 345. 5. Vibratory. 6. In the first, the particles vibrate in the line of propa- gation of the motion, as in a sound wave. In the second, the particles vibrate across the line of propagation, as in a water wave. 7. Zero. § 324. 8. The rapidity of vibration of the sounding body. [ First Principles of Natural Philosophy, p. 280.] 1!< ri< tr Que#tioti8, Page 280. 25 1. (a.) By changing its tension by means of the pegs, or by changing its length by fingering. (b.) Both electricities are in the body, but they are sep- ;u;ik(l, one being attracted and the other being repelled by the charge of the polarizing body. 2. Imagine the weight of the door concentrated at its centre of gravity. Fulcrum, at the hinges; H r , at middle of door; P, between Hand F; 3d class. 3. Place c in the acid ; close the opening in b ; suck at a until the acid runs into b ; remove the stopper from b. 4. Transverse waves moving outward in concentric circles from the centre of disturbance. 5. Longitudinal waves moving outward in concentric spherical shells from the bell as a centre. 9. § 167. 10. § 272. 11. § 321. 12. (a.) 10900 ft, or 3320 m. (b.) That I may know the velocity. § 326. 13. Electro-magnet. 26 [First Principles of Natural Philosophy, pp. 288-296.] Exercises, Page 2 88. 1. 15° x 1 = 27° 27 + 32 == 59. Ans., 59° F. 2. 59° — 32 = 27. 27 x f = 15. Ans., 15° C. 3. 273 + 15 = 288. Ans., 288° C. (absolute). That the temperature in question is 288 centigrade degrees warmer than that at which there are no molecular motions constituting heat. 4. By rubbing a brass button on the floor, or by any other means of producing friction. 5. §§363,364. E&ereises, Page 296. 1. At the same temperature, 115° C. § 368 (1). 2. §§ 370, 371. 3. By heating it in a closed vessel so that the pressure of its own vapor is exerted upon the liquid. E. g. , the water in a steam boiler under a pressure of 10 atmos- pheres is 356.6° F., instead of 212° F. 4. See Elem. Nat. Phil, §§ 571, 572. 5. Steam is invisible. 6. § 374. 7. By distillation. Most naval vessels and ocean steam- ers are provided with distillation apparatus for use in emergency. 8. 0° C, or 32° F. § 368 (2). 9. (a.) About 1700 cu. ft. (b.) About 850 cu. ft. [First Principles of Natural PKUowphy, pp. Jo;- j J? I.i rrrisrs. I'tlt/r .iO}. 1. § 382. 2. Yes ; by the withdrawal of heat to do the work of vaporizing the liquids on the tongue. 3. To cool it by the abstraction of the heat used in the work of vaporization. 4. § 384. 144 x 3 = 432. 5. The increase of temperature is 212 — 32 = 180. '80x3 = 540. 6. § 385. 537 x 3 = 1611, the number of lesser calories. 7. To melt the ice (144 x 3 =) 432 units. To warm the water from 32° to 212° (180 x3=) ' 540 " To vaporize the boiling hot water (967x3=) 2901 " Total, 3873 " 8. 1 kilogram = 1000 grams. To warm the ice to 0° C, 5000 lesser calories, To melt the ice, 80000 " To heat the water from 0° 0. to 15° C, 15000 " " Total, 100000 " Or 100 calories. See Elem. Nat. Phil, § 579, a. 722,000 lesser calories would convert the ice into steam. Exercises, Page 316, 1. Because a moist atmosphere is a better conductor of heat than a dry one. 2. Because the bodily heat is carried away in part by convection. 28 {First Principles of Natural Philosophy, pp. 316-334.] 3. Because some are better conductors than others. In a cold room, the good conductors carry heat from the person with rapidity and thus give us the sensation of cold. 4. (a.) A non-conductor, (b.) A non-conductor. 5. By conduction. 6. For radiation. § 404. Exercises, Page 324, 1. 424 m., or 1390 ft. § 413. 2. The given amount of heat will do the same amount of work as in the former case and lift twice the weight just half as high. § 95. 3. 212 ra., or 695 ft. 4. 424 m., or 1390 ft. 5. It will lift its own weight (10 lb.) 424m., or 1390 ft, or half that weight twice as high. 6. It will lift its own weight 424 m., or 1390 ft., or twice its weight to half that height. Ans., 212 m,, or 695 ft. 7. One heat unit (pound-Fahrenheit). 8. Two heat units (pound-Fahrenheit). 9. One unit for each gram so raised. Ans., 1000 units. 10. This work is twice as great as that mentioned in the last Exercise. It will, therefore, take twice as much heat. 11. We have placed at our disposal 34462 heat units (gram-centigrade). § 411, a. Each gram of water will require 100 units. 34462 -f- 100 = 344.62, the number of grams. 12. We now have 8080 units. 8080 + 100 = 80.8. 14. Nearly 1£ times as much ; -^^ times as much. § 411, a. 15. Heat can, by being converted into some other form of energy. Energy cannot. [First Principles of Saturn! Philosophy, p. 325] 29 Retrteu) <>m stinns. I'atjr :;?.>. 1. Weight, length and tension. 2. (a.) Yes. (b.) No. § 894. 3. Perhaps a little mercurial vapor. Otherwise it should fje a vacuum. 4. Amplitude of vibration. § 330. 5. To provide for expansion in warm weather. G. Because the alcohol that fills the gallon measure iu winter expands with summer heat so that only a part of it will go into the same measure. The measure will hold a greater number of alcohol molecules in January than it will in August. The gallon measure is supposed to have a capacity of a gallon, or 231 cu. in. in each case. 7. No. There is no atmospheric pressure to lift the liquid against the force of gravity. 8. Very little, for want of sufficient pressure on the surface of the water in the cistern when a little is removed. The water would give its vapor to the space thus made vacant, but its tension would not be sufficient to lift the water to any considerable height. 9. Yes ; on account of the tension of the confined air. 10. Close a bottle full of water with a cork perforated by a glass tube dipping into the water. Try to suck out ■ome of the water and you will fail. Repeat the experi- ment with a bottle half full of water and you will succeed. 11. A windy day. Loss of bodily heat by convection. 12. Much greater. § 390. 13. No. § 363. U. See answer (in this Hand-Book) to Ex. 3, p. 296. 15. Solids and liquids have different rates of expansion. A.11 gases expand at practically the same rate. See Elem. Nat. Phil, % 557. 16. Third class. F is at the bend of the tongs ; P is where the fingers are applied; W is at the lump held in the tongs. 80 [First Principles of Natural Philosophy, p. 325.'] 17. Heat is withdrawn from the body for vaporization. 18. 50° C. 19. (a.) When drops fall from c, the space occupied by the quantity of air confined iu the bottle is increased ; this lessens the tension of the air thus confined, soon bringing it so low that atmospheric pressure at a forces air inward, overcoming the pressure of the water at the lower end of the tube. This pressure of the water is due to its own gravity and to the pressure exerted upon its surface by the confined air. (b.) When air can no longer enter at a, the tension c the confined air diminishes with the fall- ing of each drop at c and the consequent increase of the air space in the bottle. Soon this tension becomes so small that it and the weight of the water are together less than the upward atmospheric pressure at c. 20. Sound waves. The vibrations of the ball are longi- tudinal. 21. (33 x 1.8) + 32 = 91.4. Ans., 91.4° F. 1.8 = |. § 360. 22. By the boiling away, the lower end of the tube is un- covered. Air then enters the bottle. Water from the bottle raises the liquid surface in the basin until the end of the tube is sealed against the further admission of air. The water will be kept at that level as long as there is any water in the bottle. 23. See § 189. 24. See § 332. 25. See § 363. 26. See § 366. 27. (a.) The atmosphere, (b.) The luminiferous ether. §396. 28. See § 153. 29. See § 272. 30. See § 82. v = gt + 20 = (9.81 x 4) + 20 == 39.24 + 20 = 59.24. Am., 59.24 m. 31. The First Law of Motion. §§ 51, 52. 32. See § 326. 33. See § 11, a. [First Principles of Natural Philosophy, pp. 335-346.] 31 EjCirrisrs, I'tHJC 3M< 1. Less. Water waves are transversal like luminous waves ; sound waves are longitudinal unlike luminous waves. 2. § 420. 3. A collection of rays emitted by the sun. Owing to the great distance of the sun, the rays that come to any place on the earth are practically parallel. § 424. 4. See § 426. 5. Eight minutes and eighteen seconds. § 427, a. 6. It would be one fourth as intense. § 428. 7. (a.) Neither, (b.) The more distant one has four times the luminous power of the other. 8. See§ 421, 12 inches = 1 foot. The wall is 100 times as far away as the screen. Each side of the shadow will be 100 times the length of one side of the screen, i. e., 300 inches. Therefore, the area of the shadow will be (1 sq. in. x 300 X 300 =) 90000 sq. in. See Exp. 210 and § 428. 10. The lamp gives an equal illumination at three times ihe distance. 3 2 = 9. The lamp is of 9 candle power. Il.nrciscs, i'ttf/c 340. 1. Locate the three points on the paper and letter them. Draw the lines, A C and B C. Bisect the angle, A C B, by the line, CD. Through 6', draw the line, m n, perpen- dicular to CD. This line, m n, indicates the position of tlie mirror. The angle, A C D, is the angle of incidence. Yh? angle, B CD, is the angle of reflection. They were < (jual in accordance with § 431. .' Because the spot transmits more light to the eye than does the rest of the piper. 3. Because, as the spot transmits more light than the rest of the paper, it reflects less to the eye. 4. See § 440. 5. See § 434. 6. See § 434. 32 [First Principles of Natural Philosophy, p. 364.] Exercises, Page 364. 2. (b.) See § 542, a. 4. See the secondary axes, A a and B Ob, m Fig. 220 5. See § 456. C. A straight line passing through the centre of a circle. 7. Draw the chord of a circle (other than a diameter) to i-3present the path of the wave through the glass. From the ends of this chord, draw straight lines representing the paths of the wave before and after refraction. These lines gradually approach the prolongations of a diameter parallel to the chord first drawn. 8. See the line, L a b c, in Fig. 214. 9. Draw an isosceles, right-angled triangle. From any point on the hypothenuse, draw lines cutting the other two sides perpendicularly. Prolong these lines. These two lines form a right angle at the hypothenuse and rep- resent the path of the ray. See § 444 (1). The ray is reflected (§ 445) at the hypothenuse because the incident angle (45°) exceeds the critical angle for glass. See Ehm. Nat. Phil, § 682. 10. (a.) See Fig. 219 (1). (b.) See Fig. 218 (2). (c.) The rays will converge on the other side of the lens, on the principal axis, between the principal and secondary foci. See Fig. 218 (1). (d.) See Fig. 219 (2). [First Principles of Natural Philosophy, p. S72.] 33 Exercises, Page 372. 1. The first is an effect of reflection (§ 432) ; the second ii an effect of refraction (§ 468), 2. When the body sends red rays to the eye. 3. Violet, indigo, blue, green, yellow, orange, red. § 462. 4. Pitch, both being determined by rate of vibration or wave length. 5. Because the glass transmits green rays and absorbs or reflects the others. 6. No. Color is a property of light and not of matter. 7. (a.) One second. (b.) See §467. 39000 waves per inch. 39000 x 12 " " foot. 39000 x 12 x 5280 " " mile. 39000 x 12 x 5280 x 186000 = the number of wavea — Am. (c.) 39000 x 12 x 5280 x 186000 = the number of waves. A 71S. 8. (a.) Yes. (b.) Because it is visible. See § 425, a. (c.) Red. See § 465. (d.) They are absorbed and warm the ribbon. 9. Converging lenses are represented in Fig. 215 (1), (2) and (3). They render parallel incident rays, converg- ing ; make converging rays more converging, and diverg- ing rays they make less diverging. Diverging lenses are represented in Fig. 215 (4), (5) and (6). They render parallel incident rays diverging; make diverging rays more diverging, and converging rays they make less converging. 10. Refraction^ reflection, dispersion. 34 [First Principles of Natural Philosophy, p. 384.] General Review, Page 384, Suggestion. — Use the index freely. 5. Multiply the velocity of sound at the observed tem- perature (§§ 325, 326) by the number of seconds that intervene between seeing and hearing in cases like those mentioned in § 325. 7. In passing through the earth's atmosphere, they are continually refracted in accordance with § 444 (2), for the atmosphere is continually increasing in density from its upper to its lower limit. As the ray is continually re- fracted, it changes its direction at every point, i. e., it is curved. 11. The reflected, as well as the incident, rays will be parallel. 12. No. § 444 (1). 13. See Fig. 207. If the eye be directly above the stick, it will not appear bent at the surface of the water, because the rays that enter the eye and picture the stick upon the retina are not refracted in passing from one medium to another. § 444 (1). 14. See § 457. 15. On account of expansion by the summer heat. 16. See § 8, c, and § 24, b. 18. See § 384. 19. Yes. § 53. 20. The lamp is 4 times as far away. Its illuminating power is (4 2 =) 16 times that of the candle. § 428. 21. No. See Fig. 224. 22. A pound of ice. Every one knows that ice will float on water, t. e., that it is lighter than water. 23. See Exp. 180. 25. It changes the intermolecular distances ; not molec- ular sizes. » 29. See § 82. S = igt 2 = 32.16 ft. x 10* = 3216 ft— Ans. [Ftr*t Principles of Natural Philosophy, pp. J84-391.] 35 30. Fluid. 31. See § 108. 1 •.'. In no way. 39. See Mem. Nat. Phil, § 301. 42. See §§ 363, 364, 394, and Epxs. 199, 200. 47. So that the external and internal resistances shall be equal In other words, it depends on the work to be done. § 267. 48. See § 425, a. Exercises, Page 391. 1. A kilogram, or 1000 grams. 2. 1.8 kilogram, or 1800 grams. 3. 1250 cu. cm. of water weighs 1250 grams. That quantity of alcohol will weigh 1250 g. x .8 = 1000 g., or 1 Kg. 4. One quarter. 5. A cu. dm. is a liter, or 1000 cu. cm., and weighs 1000 g., or 1 Kg. 6. 1 /. of water weighs 1000 g ; 1 dl, therefore, weighs 0.1 as much, or 100 g = 1 Hg. Note. — The denomination, bektograin, is not often used. Rather say 100 g. ELEMENTS OF NATURAL PHILOSOPHY. CHAPTER I. |?P" The numeral* at the left hand side of the page refer to para* graphs in the text -book. Introductory. — " The ultimate basis of all our knowledge is experience. When a natural phenomenon arrests our attention, we call the result an observation. Simple observations of natural phenomena seldom lead to such complete knowledge as will suffice for a full understanding of them. An observation is the more com- plete, the more fully we apprehend the attending circumstances. We are, generally, not certain that all the circumstances that we note are conditions on which the phenomenon in a given case depends. In such cases, we modify or suppress one of the circum- stances and observe the effect on the phenomenon. If we find a corres|K>nding modification or failure with respect to the phenom- enon, we conclude that the circumstance, so modified, is a condition. We may proceed in the same way with each of the remaining cir- cumstances; leaving all unchanged except the single one purposely modified, at each trial, always observing the effect of the modifica- tion. We thus determine the conditions on which the phenomenon depends. In other words, we bring kxpkkimknt to our aid in dis- tinguishing between the real conditions on which the phenomenon dependl and the merely accidental circumstances that may attend it. " But this is not the only use of experiment. By its aid we may frequently modify some of the conditions, known to be conditions, in such ways that the phenomenon is not arrested, but is so altered in tin- rate with which its details pass before us that they may be easily observed. (See § 122.) " Again, experiment often leads to new phenomena and to a knowledge of activities l)efore unobserved. Indeed, by far the greater part of our knowledge of natural phenomena has been 38 [Elements of Natural Philosophy, pp. 1S?\ acquired by means of experiment. To be of value, experiments must be conducted with system, and so as to trace out the whole course of the phenomenon. " Having acquired our facts by observation and experiment, we seek to find out how they are related, i. e., to discover the laws that connect them. The process of reasoning by which we discover such laws is called induction. As we can seldom be sure that we have apprehended all the related facts, it is clear that our inductions must generally be incomplete. Hence, it follows that conclusions reached in this way are, at best, only probable ; yet their probability becomes very great when we can discover no outstanding fact, and especially so when, regarded provisionally as true, they enable us to foresee what will occur in cases before unknown. "In conducting our experiments and our reasonings, we are often guided by suppositions, suggested by previous experience. If the course of our experiment be in accordance with our supposition, there is, so far, a presumption in its favor. So, too, in reference to our reasonings ; if all our facts are seen to be consistent with some supposition, not unlikely in itself, we say that it, thereby, becomes probable. The term hypothesis is usually employed instead of supposition. "A law of nature can not be demonstrated in the sense that a mathematical truth is demonstrated. Yet so great is the constancy of uniform sequence with which phenomena occur in accordance with the laws which we discover, that we have no doubt respecting their validity. " When we would refer a series of ascertained laws to some com- mon agency, we employ the term theory. Thus, we find in the 1 wave theory ' of light, based on the hypothesis of a universal ether (§ 608) of extreme elasticity, satisfactory explanations of the laws of reflection, refraction, diffraction, polarization, etc." — Anthony and Brackett. See Deschanel's " Natural Philosophy " (published by D. Appleton & Co.), §§ 1-5. The teacher can ill afford not to own this book. § 5. See First Principles of Nat. Phil, §§ 4, 6. Also Hand-Book note on § 4 of First Prin. Nat. Phil § 6. The several divisions of matter may be defined as follows : [Elements of \nturdJ Philosophy, p. 8.] 39 (a.) A mass is any portion of matter that is divisible without destroying its identity. (b.) A molecule is a portion of matter so small that it cannot be divided without destroying its identity. This definition is chemical in its bearings. (c.) For the sake of simplicity, let us consider the mole- cules of matter in a gaseous condition. Then we may say that a molecule is that minute portion of the substance that moves about as a whole so that its parts (if it has parts) do not part company during the motion of agitation of the gas. This definition is dynamical in its bearings. (d.) An atom is a portion of matter supposed to be in- capable of division into parts. (Etymologically, atom means something that cannot be cut.) In some works written by eminent physicists, the word atom is used as if it were synonymous with molecule, but during the last few years usage has been growing more uniform. The distinction is now generally maintained. Concerning molecules, the teacher may find information in Todhunter's !" Natural Philosophy for Beginners," Part I, Chapter LXI. Concerning atoms, he is advised to read Lecture XII, of Tait's " Recent Advances in Physical Science." Also read Chapter XXII of Maxwell's "Theory of II. at ■ and pp. 5, 6, of this Hand-Book. Molecules may be elementary or compound (». e., composed of a single element or of two or more elements) ; atoms are necessarily elementary. It is considered certain that oxygen, hydrogen, chlo- rine, nitrogen, bromine, iodine, sulphur, selenium and tellurium are diatomic (i e., huve two atoms to the molecule) ; that phosphorus and arsenic are tetratomic (four atoms), and that cadmium and mercury are monatomic (one atom). It is very probable that potas- sium is diatomic. Concerning the atomicity of the other elements, nothing is known. See Elements of Chemist ri/. While it is practically impossible to isolate a molecule, it may be urged that, as a mmtu ! feat, it is possible to divide a molecule of phosphorus into four atoms of phosphorus, which would leave the identity of the substance unchanged. Still, tin- theoretical concep- tion is that, in the free or uncombined state, the elements exist as molecules and aggregations thereof ; th it when they enter into chemical combinations, they do so as atoms rather than as molecule* 40 [Elements of Natural Philosophy, p. 3.] This whole matter (which pertains to chemistry rather than to physics) is so -largely theoretical that it would not be wise to puzzle the minds of ordinary pupils by dwelling at any length upon these points. It is said that the smallest living being visible with the aid of the microscope contains not more than a million organic molecules and a million molecules of water. It has been estimated by Sir W. Thomson and others that about two million molecules of hydrogen placed in a row would occupy the space of one millimeter (§ 26), and that about two hundred million million million of them woul;l weigh one milligram (§ 35). While these are mere ap- proximations to accurate determinations, they indicate that the determination of the size and weight of a mole- cule is a legitimate object of science and that they are not immeasurably small. Much has been written concerning the ultimate identity or fundamental diversity of atoms. The common view is that there are as many kinds of atomic matter as there are elements, i. e., sixty-six or more. But some able physi- cists believe that all of these apparent diversities result from the forms of atomic motion, or, as Herbert Spencer says, from "the compounding and recompounding of ultimate homogeneous units." Says Thomas Graham : " It is conceivable that the various kinds of matter now recog- nized as different elementary substances may possess one and the same ultimate or atomic molecule [the meaning is evident though the expression is unfortunate] existing in different conditions of movement." Probably every teacher and pupil has seen the rings produced by some tobacco smoker, or sent upward from the smokestack of a railway locomotive. See Tait's "Recent Advances in Physical Science," p. 292. Such rings have a peculiar " vortex" motion by virtue of which they keep their form distinct from the air through which [Elements of Natural Philosophy, pp. 3-6.] 41 they are passing. Whatever the translatory motion of the ring, every smoke particle on the inner side of the ring is moving forward, and every such particle on the outside of the ring is going backward, bo that all of the smoke is turn- ing round and round its linear, circular core. If the air were a perfect fluid (i.e., if there were no fluid friction in the air), such vortex rings would go on moving and pre- serving their form forever. Sir William Thomson has offered a hypothetical atom consisting of vortex rings of a universal, perfect fluid. Such a vortex ring might exist with any number of knots ami windings upon it. If two such rings were linked together, they never could be sepa- rated, and if they were knotted upon themselves, they never could be untied. Each would preserve the form given to it at the time of its creation. The conjecture of Sir W. Thomson is that the different forms of vortex rings com- posed of one homogeneous, incompressible, perfect fluid, constitute what are generally called atoms and that differ- ence in form of rotation is the basis of difference in the properties of matter. At first sight, this may seem very fanciful, but to some of the leading physicists of our day, " it appears to be, by far, the most fruitful in consequences of all the suggestions that have hitherto been made as to the ultimate nature of matter. " See Ninth Edition of " Encyclopaedia Britannica," Vol. Ill, p. 43. § 8. See First Prin. Nat. Phil, § 8. § 11. Dissolve a tablespoonful of white sugar in a little hot water, making a thick syrup. Place a teacup, con- taining the syrup, in a large platter and pour upon the syrup two or three times its bulk of strong sulphuric acid. The sugar molecule is represented by the formula. C,2H 2 20|,; i.e., it consists of twelve atoms of carbon, twenty-two of hydrogen and eleven of oxygen. The quantity of hydrogen and oxygen in this one molecule is just equal to that constituting eleven molecules of water j 1 1 [Elements of Natural Philosophy, pp. 5-9.] (11 H 2 = H 22 0,,). Sulphuric acid has a very great avidity for water. In this experiment, the acid robs the sugar of the elements of water and leaves the carbon as a black, bulky, spongy mass. This is a chemical change, for the molecule has been changed from sugar to carbon (or charcoal). Dissolve a " heaping teaspoonful" of calcium chloride (not chloride of lime) in a teaspoonful of warm water. In another wine glass, add half a teaspoonful of sulphuric acid to two teaspoonfuls of water. Pour the diluted acid into the calcium chloride solution. The two liquids make solid plaster-of- Paris (calcium sulphate). These experiments (or either one of them) will interest the class and be sufficient for the purpose intended. Many more may be found in the Elements of Chemistry. § 24. You can get any desired information concerning the metric system or metric apparatus by addressing the weighs (water) 1 American Metric Bureau, 32 Hawley Street, Boston. Enclose a postage stamp for reply. The supply depart- ment of the Bureau distributes the metric weights, meas- ures, apparatus, etc., at wholesale prices. The following is an extract from the Constitution of the Bureau: "The object of this Bureau shall be to disseminate information concerning the Metric System ; to urge its early adoption ; and to bring about actual introductions wherever practicable. To this end, it will secure the delivery of addresses ; publish articles ; circulate books, pamphlets and charts ; distribute scales and measures ; in- J [Elements of Natural Philosophy, pp. D-u.] 43 joduce the practical teaching of the system in schools ; and in nil proper ways, as far as the means at its disposal will allow, the Bureau will urge the matter upon the attention of tin* Americas p eopl e ! I'M tne y shall join the rest of the world in the exclusiw BM of the International Decimal Weights and Measures," §25. It is now known that the meter is not exactly 0.0000001 of a quadrant of the meridian of Paris. Such a quadrant is about 10,000,850 meters. The meter is, therefore, an arbitrary standard. It is represented by a certain platinum bar at Paris. § 31. See Danieirs " Principles of Physics," p. 203. §32. Porous corks maybe made air and water tight by holding them for five minutes beneath the surface of melted parafrine wax. The paraffine may be had at the druggist's. The corks may be held down in the liquid by a perforated cover or wire screen. A simple experiment to illustrate the impenetrability of air is to invert a tumbler in a basin of water. It can be seen that the water does not fill the tumbler. Of course it will compress the air. (£§ 227, 284.) Then thrust a wad of coarse brown (or filter) paper into a glass tube, asalamp-chimnev, close one end with the hand and immerse the tube in water, holding the open end downward. That the water does not enter the tube while the hand closes the up]K?r end may be seen directly, or from the fact that the paper wad remains dry. See First Prin. Nat. Phil, Fig. 2. 44 [Elements of Natural Philosophy, p. 14.] Exercises, Page 14. 1. A liter = 1 cu. dm. = 1000 cu. cm. One cu. em. of pure water weighs 1 gram ; 1000 cu. cm. weigh 1000 grams, or 1 Kg. 2. 1000 g. x 1.8 = 1800 g. 3. 1250 cu. cm. of water weigh 1250 g. 1250 g. x .8 = 1000 g. or 1 A#. 4. Since a liter of water weighs 1000 g., 250 #. of water is J of a liter of water. 5. 1 cu. dm. p 1000 cu. cm. 1 cu. dm. of water, there- fore, weighs 1000 g. = 1 A#. 6. 1 liter = 1000 cu. cm.; 1 dl. = 100 ew. cm. 1 e#. of water weighs 100 times 1 g. = 100 g. = 1 J^r. The following is well calculated to show the great con- venience of the metric system of weights and measures: Required to find the capacity of some small, irregular cavity in a solid. Weigh the solid. Then fill the cavity with mercury and weigh the solid again. The difference between the two weights will be the weight of the mer- cury. This weight, in grams, divided by 13.6 [§ 253 (2)] will give the number of grams that the same bulk of water will weigh and. therefore, the capacity of the cavity in cubic centimeters (§ 36). § 37. When a candle burns, it disappears. To show that the matter of the candle has not been destroyed, support a tin basin of water containing ice above the flame so that the tip of the flame shall just touch the middle of the bottom of the basin. Protect the flame from disturb- ance by air currents. In about 10 minutes, examine the bottom of the basin. Whence the carbon (soot) and the water ? The carbon came from the candle. Part of the water (H 2 0) came from the same source, the hydrogen of the candle uniting (in a chemical process, § 11) with the oxygen of the air to form steam. This steam was con- [Memento of Natural Philosophy, pp. 1M&] 45 densed to water by the cold metal with which it came in f o contact See EbmenU of Chemistry, Exps. 57, 169-171 and *• Popular Science News," Vol. 20, p. 92. § 41. Opposed to the commonly accepted theory that bodies arc made up of atoms is the theory of the homo- geneity and continuity of bodies. This asserts thai as a drop of water (or other inorganic body) may be divided into two parts each of which is a drop of water, so these smaller drops may be again divided and that there is nothing in the nature of things why this process of* divi- sion may not be repeated again and again, times without end. This theory of the infinite divisibility of bodies is in direct contradiction to the atomic theory. It is not evident how the former can be reconciled with the ob- served facts of the compressibility and interpenetrability of bodies, which properties of matter are easily explained on the theory of intermolecular spaces occupied by a highly elastic medium called the ether. § 42. See First, Prin. Nat. Phil, Exps. 15, 16, aud Deschanel's " Natural Philosophy," §§ 21, 22, 23. § 44. See First Prin. Nat. Phil, Exp. 17. § 45. See First Prin. Nat. Phil.. Exp. 18. § 46. See First Prin. Nat. Phil, Exp. 19. § 47. See First Prin. Nat, Phil, Exp. 20. § 51. See First Prin. Nat. Phil, Exp. 21. § 54. All solid, unorganized bodies are crystalline or amorphous. Crystalline bodies are characterized by reg- ularity of form ; amorphous bodies exhibit no such reg- ularity. Freedom of molecular motion is necessary for the formation of crystals. When crvstallizable bodies slowly solidify from the liquid or gaseous conditions, the molecules arrange themsi -Ives, under the influence of the mysterious structural forces, according to one of six min- 46 [Elements of Natural Philosophy, pp. 21, 22. ~\ eralogical systems of crystals. Such molecular motion and arrangement sometimes take place in solids, under the influence of friction, percussion, etc. Thus the jarring of continued use often renders railway car axles, crystal- line and brittle. Such facts lead us to ascribe a definite structural form to such molecules, determining special points of application for the molecular forces. Amorphous bodies' that cannot, under any known circumstances, assume the crystalline form are called colloids. § 55. Thomas Young has shown that a liquid may be treated as if it were covered at the bounding surface with a stretched membrane with a constant tension tending to contract it. Hence, every free liquid moves so that its bounding surface shall be as small as possible ; i. e., it assumes the spherical form. This is familiarly shown in drops of falling water and in globules of mercury. Pla- teau illustrated the same fact on a larger scale by placing a mass of oil in a mixture of alcohol and water, carefully adjusted to have the same specific gravity as the oil. The oil then had no tendency to translatory motion under the influence of gravity, but was left free to arrange itself \mder the free action of the molecular forces. The freely floating mass at once assumed the spherical form. § 59. It is proper to add that there is no sharp line of distinction between the three conditions of matter such as our definitions imply. Bodies present all forms of molec- ular aggregation and often pass from gas to liquid or from liquid to solid by imperceptible gradations. (a.) Oxygen was liquefied at a temperature of — 140° C. (§ 546) arrl under a pressure of 320 atmospheres (§ 277). When a jet of this liquid escaped into the air, it was partly solidified. Hydrogen was similarly liquefied under a pressure of 650 atmospheres. For full accounts of the liquefaction of "the permanent gases," see "The Popular Science Monthly," "The Scientific American," or the English paper, " Nature," for the year 1878. (&.) See First Prin. Nat. Phil., § 43 (a). Also, Exp. 25. [Elements of Natural Philosophy, p. 24.] I j § 62. The colliding molecules of a gas are supposed to act on each other only within very short distances and for MTv short times before and after collision. Their motions are free and, therefore, rectilinear in the intervals. The average distance between such actions is called the mean free path of the molecule. These paths lie in all conceiv- able directions. The intervals of time between the en- counters are indefinitely long in comparison with the duration of tbe collisions. Three kinds of experiments indicate that, at a pressure of one atmosphere and at the temperature of melting ice, the mean free path of a hydro gen molecule is about 0.0001 millimeter, or about 0.2 the length of a wave of green light (§ 717). The mean free path of other molecules is less than that of hydrogen. In the introductory paragraph of this Hand-Book, we have considered the definition of hypothesis. It may be well, right here, to ask ourselves, What is an explanation t " Every act of explanation consists in detecting and pointing out a resemblance between facts or in showing that a greater or less degree of identity exists between apparently diverse phenomena. — J> cons. " When a new phenomenon presents itself, the question arises in the mind of the observer : What is it? This question means: Of what known, familiar fact is this apparently strange, hitherto un- known fact, a new presentation,— of what known familiar fact or facts is it a disguise or complication? All explanation, including explanation by hypothesis, is, in its nature, classification." — Stallo. "The business of science is simply to ascertain in what manner phenomena coexist with each other or follow each other, and the only kind of explanation with which it can properly deal is that which refers one set of phenomena to another set."— Fiske. CHAPTER II. The teacher will probably find that the section on Force and. Motion, at the beginning of this chapter, is difficult for the pupils at this stage of their progress. The author would have placed it in the latter part of the book, had not its very nature demanded, that it be placed, where it is. He would advise that it be taken in course, but that its complete mastery be not insisted upon until the review. Such a review should be had before Chapter III is begun. " The advance in knowledge which an individual student obtains by the devotion of time and attention to a science, is similar in character to the progress which the science itself makes in the course of ages ; the student can trace his way backward to a clearer view of the first principles, and forward to more extensive developments and appli- cations. " § 63. " Dynamics is the science which treats of the action of force. The name is derived from the Greek word dynamis, meaning force. Within the last twenty years, many improvements have been made in the nomenclature employed in this science. The name Mechanics, which properly denotes the science of machines, and was used by Newton in that sense, came for a time into use, instead of the appropriate word, Dynamics, for the science which treats of force ; and under that name there was a peculiar ' cross-division of the subject into Statics and Dynamics, in which the proper signifi- cation of the latter name was altogether departed from.' The change to a better nomenclature has recently been made. " — Bottomley. Physical science accepts a dynamical interpretation as the best explanation of all physical phenomena. " The object of the natural sciences is to find the motions upon which all other changes are based and their corresponding motive forces." — Helmholtz. [Elements of Natural Philosophy, pp. 25-20.] 49 " When a physical phenomenon can be completely described as a change in the configuration and motion of a material system, the dynamical explanation of that phenomenon is said to be complete. We cannot conceive any further explanation to be necessary, desir- able or possible, for as soon as we know what is meant by the words configuration, mass and force, we see that the ideas which they represent are so elementary that they cannot be explained by means of anything else." — Clerk Maxwell. "Physical science is a resolution of the phenomena of nature into atomic mechanics. It is a fact of psychological experience that, whenever such a reduction is successfully effected, our craving for causality is, for the time being, wholly satisfied."— Emil du Bois Beymond. Stallo speaks of the claim that "modern physical science is throughout a partial and progressive solution of the problem of reducing all physical phenomena to a system of atomic mechanics." The kinetic theory of gases, for example, is valuable and satisfactory, chiefly because it affords consistent ground for the dynamical interpretation of the phenomena to which it relates. The " action at a distance " explanations &f gravitation and electric attraction are unsatisfactory chiefly because they do not thus deal with the phenomena to which they pertain. See DeschanePs "Natural Philosophy," § 6. § 64. See Tait's "Heat," Chap. 3. § 69. The force that, acting for one second on a mass of one pound, produces a velocity of one foot per second, is called z, poundal. As the increment of velocity due to gravity (§ 127) is 32.16 ft., the weight of a pound-mass equals 32.16 poundals. In the text and here, when we use the word "weight," we mean the force exerted by the force of gravity on the mass in question. 50 {Elements of Natural Philosophy.} Exercises, Page 30. 1. 500 X 500 == 250,000. 2. 321.6 x 200 = 64,320. ■■\ .„ X ^ ^ !• Their momenta are equal 10 x 2 = 20 J * 4. Gee § 67 (a.) and § 68. 32.16 x 10 = 321.6. 5. There are 5280 ft. in a mile. 5 280 x 15 x 1 _ 1320 x 12 The momentum of the ball will be 5 times that of the stone. n ( 50,000 x 2 = 100,000 ) mi • i i 6. 1 * ™" *1 .L\™ r Their momenta are equaL ( 10,000 x 10 = 100,000 J M 7. 25 x 60 = 1500, the momentum of the first, and, consequently, of the second. 1500 -=- 40 = 37.5. The velocity of the second is 37.5 ft. per second. 8. 100 x 20 = 2000. 2000 -r- 500 = 4. Velocity = 4 m. per second. 10. See § 69. 12 x 6 = 72, the number of dynes. 12. We must consider the attracting force to be uni- formly y^ dyne. As a matter of fact, this would not be true. See § 100 (2). A force of 1 dyne would give to the body weighing 1 gram, a velocity of 1 cm. per second. (§ 69.) Then a force of y^ dyne would give it a velocity of yJ ¥ of 1 cm. = .1 mm. A body 100 times as heavy would be moved by the same force with yfg- of this velocity, or .001 mm. [Element* of Natural PhUog.yhy, pp. 51 § 73. " If we conceive of a body moving in empty space, we can think of no reason why it should alter its path or its rate of motion in any way whatever." — Anthony and Brackett. § 74. See Frick's " Physical Technics/' pp. 58-61, and Deschanel's Nat. Phil., §§ 49-51. § 84. See Frick's " Physical Technics," pp. 58-61. § 86. Two equal forces acting in opposite directions along parallel lines cannot be balanced by any single force. They constitute what is called a couple. The moment of a couple is the product of the numbers representing respect- ively the magnitude of one of the forces and the perpen- dicular distance between the lines ^^____^^ of the two forces. Two couples ap- /ffy\ ^^***v plied to the same rigid body will / t \^ g\ balance if their planes are coinci- t A \ """.'' J dent or parallel, their moments are \. \/^/^ equal and if they are applied so as ^ y to turn the body round in opposite directions. Thus, the couple composed of the forces, F and / will balance the couple G and g, if F x A B = G x C I). The direct tendency of a couple is to produce rotation of the body to which it is applied. The turning of a key in a lock affords a familiar example of a couple, the shaft of the key serving to transmit the effect of the couple acting on the handle. See § 171. § 92. See Deschanel's " Natural Philosophy,'' § 16. § 93. " When two bodies interact so as to produce, or tend to produce, motion, their mutual action is called a stress. If one body be conceived as acting and the other as beinjr, acted on, the stress, regarded as tending to produce motion in the body acted on, is a force. The third law of motion states that all interaction of bodies is of the nature of stress and that the two forcrs into which the stress can be resolved are equal and oppositely directed. From this follows directly the deduction that the total momentum of a system is unchanged by the interaction of its parts ; that is. the momentum 52 [jileme?Ui* of Natural Philosophy, pp. 42, 4$.] gained by one part is counterbalanced by the momentum lost by the others. This principle is known as the conservation of momentum," —Anthony and Brackett. § 95. See First Prin. Nat Phil, Exp. 32. [Elements of Natural Philosophy.] 53 Exercises , Page 44. 1. Adopt any convenient scale, as 1 mm. to the lb. Then would the force of 100 lb. be represented by a line 10 cm. long, and the other force by a line 15 cm. long. See § 80 (1). The resultant would be represented by a line 25 cm. long. & See § 80 (2). The resultant would be represented by a line 5 cm. long (if we adopt the same scale as above) ; motion will be in the direction of the greater force. 3. Suppose we adopt the scale of an inch to the mile. Draw a horizontal line 4 inches long to represent the force of the oars. From one end of this line, draw a vertical line 3 inches long to represent the force of the current. Join the free ends of these lines ; the hypothenuse thua formed will represent the resultant of these two forces. 3 2 + 4 2 = 25. a/25 = 5. See § 85. The boat will move in the direction indicated by the hypothenuse and with a velocity of 5 miles per hour. Of course, the problem means that the boat is headed directly across the stream. 4. Draw a vertical line, 64 units (as mm., or 16ths of an inch) long. From the foot of this line draw a horizontal line 24 units long. (Use the same kind of units that you adopted for the vertical line.) Join the free ends of these lines. The hypothenuse will be the graphic representa- tion of the resultant. 642 -f 242 = 4672. \/4672 = 68+. 5. Draw, as before, a vertical line (3 x 20 =) 60 units long, and a horizontal line (12 x 20 =) 240 units long. Draw the hypothenuse. 60 s + 2402 = 61200. \/61200 = 247+. 54 [Elements of Natural Philosophy, p. 45.] 6. See § 68 (a). 804 kinetic units = 25 gravity units, Draw BN = 10 units of length. From B, draw BE at right angles to BN and make it 15 units long. Complete the parallelogram and draw the partial resultant, Br. From B, dfaw BS at an angle of 45° from BE and make it 25 units long. Complete the parallelogram and draw the diagonal, BR, which will represent the complete resultant. The line, BN, being taken 2 cm. long, the scale here adopted is 2 mm. per pound. The line, BR, being 67 mm. long, represents a force of 35^ lb. or 1141.68 absolute units. Some weight may be assumed for the ball. The resultant must be assumed to act for some definite time, say one second. Dividing the number of absolute units (1141.68) by the number of pounds, gives us the velocity imparted to the ball by the resultant force in one second. This velocity multiplied, in its turn, by the same number of pounds, gives us the momentum. As, in this operation, we use the weight successively as divisor and multiplier, its value is of no account in the solution of the problem, [Elements of Xatural Philosophy, p. 45.] 55 as it would be if velocity and not momentum were called for. The greater the weight, the lest* the velocity and versa, their product (momentum) remaining the same. The number of absolute units represents the momentum also. 7. See § 72 (3). The momentum of the gun is equal to the momentum of the projectile. As the gun is heavier than the projectile, its velocity must be less than that of the projectile, in order that the products of the numbers representing the weight and velocity in each case may be equal 8. The width of the river is represented by a line 4 units long ; the actual course of the boat by a line 5 units long. If the 4 units represent 1 mile, the 5 units will represent 1 j miles, the distance that the boat moves. It takes no longer. See § 78. 9. See Fig. 55, in which LM represents the plank and MN, the distance that one end of it is raised. A C repre- sents the gravity or weight of the cask. (Gravity acts in a vertical direction.) From A, draw AD perpendicular to LM. From C, draw CD parallel to LM. Complete the parallelogram, A BCD. The force of gravity represented by A C may be resolved into two components, represented by AD and AB. AB represents the force with which the rask tends to roll down the plank. This tendency may be successfully resisted by a force represented by AB', equal to AB and opposite in direction. AB = \AC, as may be seen by direct measurement or as may be proved geometrically, the triangles ABC said LNM being similar. il' nee, the muscular force needed is 25 lb. 10. See § 68. 32.16 x 60 = 1929.0, the number of F. I\ S. units. 11. See § 69. 60 Kg. — 6000 g. 980 dynes x 6000 = 5880000 dynes. 56 [Elements of Natural Philosophy, p. 46.] §98. Whether this "attractive force" is a property inherent in matter or is a secondary phenomenon, a result of unexplained action of some kind, is a theme on which much has been ably written. The latter is probably the fact. " All physical action is by impact ; action at a distance is impos- sible ; there are, in nature, no pulls but only thrusts." The reduction of the phenomena of celestial motion to the principle of universal gravitation was first made by Sir Isaac Newton. But Newton himself did not believe the mutual attraction of bodies to be an attribute of matter, essential thereto and inherent therein. He says : " The reason of these properties of gravity I have not, as yet. been able to deduce, and I frame no hypotheses." Again: "That gravity should be innate, inherent and essential to matter, so that one body may act on another at a distance, through a vacuum, with- out the mediation of anything else by and through which theii action may be conveyed from one to another, is to me so great an absurdity that I believe that no man who has a competent faculty oi thinking in philosophical matters can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws, but whether this agent be material or immaterial I have left to the consideration of my readers." Newton comes very near framing a hypothesis when, in speaking of the luminiferous ether, he asks : " Is not this medium much rarer within the dense bodies of the sun, stars, planets and comets than in the empty celestial spaces between them ? And, in passing from them to great distances, doth it not grow denser and denser perpetually and thereby cause the gravity of those great bodies towards one another and of their parts towards the bodies, every body endeavoring to go from the denser parts of the medium towards the rarer ? " [Elements of Natural Philosophy, p. /,';.] 57 One of Newton's contemporaries said that the two sup- positions of an attractive faculty and a perfect void are "revolting"; others were equally emphatic. D'Alembert attributed the phenomena to that class of motion-pro- ducing causes the real nature of which is unknown in contradistinction to action by impact of which we have a clear mechanical conception. James Croll affirms that no principle will ever be generally received that stands in opposition to the old adage, " A thing can not act where it is not," anymore than it would were it to stand in oppo- sition to that other adage, "A thing can not act before it is or when it is not." " It is impossible to conceive what is called an attractive force in the strict sense of the terra, that is, to imagine an active principle having its seat within the molecules and acting without a medium through an absolute void. This amounts to an admission that bodies act upon each other at a distance, i. e., where they are not ; an absurd hypothesis— equally absurd in the case of enormous and in that of very small distances." — Secchi. Numerous hypotheses have been framed in which gravi- tation is referred to a wave motion of an elastic, interstel- lar and interatomic fluid, similar to the luminiferons ether or identical with it. " All attempts yet made to connect gravitation with the luminif- erous ether or the medium required to explain electric and magnetic distance-action have completely failed, so that we are apparently driven to the impact theory as the only possible one." — Stewart and Tail. J. B. Stallo says that the only impact theory seriously discussed by modern physicists and astronomers is that of Le Sage, and this, on account of "the extravagance of its assumptions," he character- izes as " a survival of the fancies of an age in which the functions of a scientific theory were imperfectly understood." He states Le Sage's theory thus : " Space is constantly traversed in all directions by streams of infinitely small bodies moving with an almost infinite velocity and coming from unknown regions of the universe. These bodies are termed 'ultramundane corpuscles.' By reason of th«ir minuteness, they rarely if ever collide and the greater part of them 58 [Elements of Natural Philosophy, p. 46.] find ready passage through ordinary sensible bodies so that all parts of these bodies — those on the interior as well as those on the sur- face — are equally liable to be struck by the corpuscles, the force of the impact being thus proportional, not to the surfaces but to the masses of the bodies. A single body or particle would be equally battered by these corpuscles on all sides ; but any two bodies act as mutual screens, sr> that each receives a less number of impacts on the side facing the other. They are, consequently, driven toward each other. The motion of the corpuscles being rec- tilinear in all directions, the diminution of pressure thus resulting is inversely as the squares of the distances between the bodies affected." In the Ninth Edition of " Encyclopaedia Britannica," Vol. Ill, p. 47 which see), J. Clerk Maxwell, speaking of Le Sage's theory, after pointing out its inability to account for the temperature of bodies remaining moderate while their atoms are exposed to this corpus- cular bombardment, as well as other important shortcomings, says : u This theory is ingenious and is the only theory of the cause of gravitation that has been so far developed as to be capable of being attacked and defended." We have thus considered the difficulty in the way of accounting for the phenomena of gravitation at consider- able length on account of its own immediate importance and, not less, for the reason that it opens up to view several of the more important concepts and theories of modern physics. With these, it is important that the teacher become as familiar as the time at his disposal will permit, but he must exercise good judgment in the matter of opening up such polemical topics to his classes. Most young pupils would have their ideas beclouded rather than clarified by the attempt to give intelligent consid- eration to such themes. {Elements of Natural Philosophy, pp. 47, 48.] 59 § 102. See Deschanel's "Natural Philosophy," §§52,53. § 103. It is demonstrable that, considering the earth as a hollow sphere, a body would be in equilibrium unij- where within the shell ; the attraction in all directions would be equal, whether the body be at the centre or not. The subterranean investigations recorded by Ed wan I Everett Hale, in his story of "John Whopper, the News- boy,* are consistent with the facts of gravitation. § 104. It is to be borne in mind that this paragraph B881 lines "the earth's density to be uniform." The den- sity of the earth as a whole is believed to be twice that of an ordinary mountain upon its surface, or about 5£ times that of water. The interior parts of the earth certainly are more dense than the exterior parts. Bodies actually weigh more as we descend for some distance below the earth's surface. The full and mathematically accurate treatment of this subject would be beyond the province of an elementary text-book. A brief presentation of the subject will be found in Anthony and Brackett's " Physics, " Part I, page 82. 60 [Elements of Natural Philosophy.] Exercises, Page 49, The teacher will be particularly fortunate who finds that all of his pupils are able to handle a proportion intelligently and easily. Be sure concerning this ability before going any further ; secure it if possible. Frequently vary the form of the statement from a :b = c : d to - = - . o a 2. 4000 — 3000 = 1000, the number of miles from the earth's centre. w: W :: d : D. w : 550 :: 1000 : 4000. /. w = 137J. 3 75* _ 5625 _ 502 - 2500 "~ *' 4. If the first and second were at equal distances from the third, the first would have, on account of its lesser mass, only f or | as great an attraction as the second. But being only half as far distant, its attraction is four times as great as it would be if it were at an equal dis- tance, f x 4 = f . The smaller ball exerts 2f as much force upon the third ball as the larger one does. /6 50 2 8 , (9:6), 8\ \9 X W> = r° Tl:X:: 1252:504' ?> me t*=l} 5. w : W :: D* : d 2 . w,: 900 :: 4000 2 : 12000 2 . .% w = 100, the number of pounds. Or, the distance from the earth's centre being increased threefold, the weight will be divided by 3 2 or 9. 900 lb. -f 9 rs 100 lb. 6. w : W : : D 2 : d 2 . 1 : 16 :: 4000 2 : d 2 . /. d = 16,000, the number of miles from the earth's centre. 16,000 — 4,000 = 12,000, the number of miles from the earth's surface. [Elements of Natural Philosophy, p. 49.] 61 7. w : W. = D> : dK w : 200 lb. = 4000 2 : 7000 3 . w' : 100 lb. = 4000* : 7000*. .-. w = 65.3 lb., the man's weight. .-. w = 32.65 lb., the boy's weight. Difference in their weights = 32.65 lb. 8. Answers, (a.) 80 1b. (b.) 90 1b. 9. Work as in preceding examples, or as follows: 50 lb. x H = 32 lb -> tne weight 1000 miles above the surface. 50 lb. x I = 37J lb., the weight 1000 miles below the surface. It would weigh 5 £ lb. more when below the surface. 10. It would be i as great in either case. See § 100 (2) 11. Work as in preceding cases, or as follows : 4000 miles xj} = 3750 miles. H ** 1?29 - ( 4Q00 ) 8 W ~ d* '"' 2700 ~ d* ' m 4 _ 4000 x 4000 , 1 1000 x 4000 *' 9 " cP '*' 9 " ~«P .-. d* = 36000000. d = 6000. 6000 — 4000 = 2000. 13. It would increase the weight fourfold [§ 100 (1)]. § 107. See Daniell's " Principles of Physics," p. 107. 62 [Elements of Natural Philosophy, pp. 60-52.] § 108. See First Prin. Nat. Phil, Exp. 34 and Picker, ing's " Physical Manipulation," p. 66. § 111. See First Prin. Nat. Phil, § 68, a. With the point of a pen-knife blade, make a hole of 2 or 3 mm. diameter in the large end of an egg. In the small end, prick a pin-hole. Blow the contents of the shell out through the larger hole. Rinse and dry the shell. Drop a little pulverized rosin or melted sealing-wax through the larger hole into the smaller end of the egg. Support the egg in a small tin can (that may be obtained from any kitchen) or in any other convenient way, and pour a few grams of melted lead through the larger hole and into the smaller end. The lead will not run out through the pin-hole even if the rosin or sealing-wax be not used. The larger hole may be neatly concealed with a piece of thin paper put on with flour paste. You have a " magical egg " that persists in standing on its smaller end. Prepare an A-shaped frame, like that shown in the figure, making the stick, B D, jfc^' 2 or 3 feet long. Place the ■'- ^^i,,,,,,,,,,,,,,,,,,, „ utl „ir» ll „„ l , l „, l „„, u ,„„ l „ iiP le & -P* u P on a snelf or table, - ^^^^^ Zl^K^^ as shown, and hang a pail of JUiM!lll\jlMlffllB|M ^^^^^ water or other weight at E. I! |jy E The centre of gravity will fall II B below the point of support and the frame and its load will be in stable equilibrium. The apparatus may be rocked up and down, like the cavalryman mentioned in the text-book. If the weight be removed from E, the frame will fall to the floor. Instead of the cross-bar at G, a stout cord or wire may be used. You may sim- plify the apparatus (and thus increase the probability of pupils trying the experiment at home) by cutting a notch on the under side of the stick, B D, near the end, touts of WtdurrU Pid'oHophy, pp. :,:->, ,;.\ 03 to receive the tapered end of the stick, ED. The end at E is thrust into a pail of water. A stout cord extends from the handle of the pail to a point on B D, near <\ the cross-bar being wholly omitted. The length of this eon! may be so adjusted that the pail will he supported to low B. Exercises, Paf/e 56. 1. First answer, 600 lb. Second answer, 300 lb. 2. u a 3000 miles. " (C 2000 miles. 3. a a 200 lb. tt 128 lb. 4. a tt 112J lb. a 96 1b. 5. a a 3000 miles. " ft 4000 miles. 6. (1 a 1000 lb. a 250 lb. 7. Second I" 200 lb. First a 120 lb. 8. First a 3500 miles. Second tt 4000 miles. 9. a a 90 lb. tt 213J lb. 10. a t( 3200 miles. " tt 8000 miles. 11. a tt 1500 miles. " tt 16 lb. 12. tt tt 576 lb. it 20000 miles. 13. Second L w 1024 lb. First tt 3000 miles. 14. First n 3750 miles. Second tt 20000 miles. 15. Second a 13520 lb. First a 2704 lb. § 118. The statement that "the force of gravity is a constant force," is sensibly true for all attainable distances from the surface of the earth. But if we were able to drop a body from a point several hundred or thousand miles above the surface of the earth, the force of gravity would sensibly increase as the body approached the earth. (§ 100 [2]). The velocity would not be an uniform^ accelerated velocity. ^ 1 22. See Deschanel's " Natural Philosophy," §§ 34-37. ^ 1M4. See Pickering's "Physical Manipulation," p. 84. 64 [Elements of Natural Philosophy, pp. 63-67.1 § 127. The value of g is computed by the formula 7T*l iu which n represents the ratio of diameter to circumfer- ence (3.14159) ; I, the length of a given pendulum and t, the time (in seconds) of its single vibration. By measure- ment, the value of I is determined (§ 142). By counting the number of vibrations for, say 30 minutes, and dividing the number of seconds (1800) by the number of vibrations as counted, the value of t is determined. See Deschanel's " Natural Philosophy," §§ 44, 47, 48. At the earth's equator, g = 9.781 m. or 32.0902 ft. At the poles, g == 9.831 m. or 32.2549 ft. Hence, the force of gravity, per gram, varies from 978.1 to 983.1 dynes (§ 69). In latitude, 45°, g = 9.806 m. Exercises, Page 67 '. 4. Answer, 80.4 ft. 6. S = \gt\ S = 16.08 ft. x (i) 2 = 16.08 f t. x i = 4.02 ft. 7. Substituting in the same formula, 8 = 16.08 ft. x {li) 2 sr 36.18 ft. 8. S = 16.08 ft. x (12J) 2 = 2512J ft. Note. — Remember that the body is supposed to be falling freely ; the resistance of the air is disregarded. 9. S = \gt\ 787.92 = 16.08*2. 49 = t\ .-. 7 = t. 10. Answer, 225.12 ft. (v = VfyS See § 254.) 11. Answer, 498.48 ft. 12. 6£ oz. + 6-J- oz. -f- 2 oz. -f 1 oz. == 16 oz., the total weight to be moved. To move this weight, we have the gravity of the rider, a force of 1 oz. This force can give to an ounce of matter a [Elements of Natural Philosophy, p. 67.] 65 velocity of (g =) 32. 1G ft. per second ; the same force can give to 16 oz. of matter only ^ of this velocity. 32.16 ft -^ 16 = 2.01 ft. 13. S=igfl. (See §136.) 257.28 = 16.08/ 2 . /. / = 4. The ball will reach the ground at the end of 4 seconds. During that time it will move from the tower (60 ft x 4 =) 240 ft. 14. During 4 seconds it will fall 257.28 ft. During 6 seconds it will fall 578.88 ft During the 5th and 6th seconds it will fall 578.88 ft. — 257.28 ft = 321.6 ft. Or we may say that its average velocity during these two seconds will be that attained at the end of the 5th second, which is 160.8 ft. Moving at this average rate for two seconds, it will move (160.8 ft. x 2 =) 321.6 ft. 15. See § 132. It can rise for 2 J seconds. At the time specified it will have been falling \ second, and will have a velocity of 16.08 ft 16. Fl represents the distance that gravity will move the body during the first second. Fa represents the velocity due to the horizontal impelling force, or the dis- tance that force would move it in the first second. Aa represents the amount of deviation from a horizontal plane, as a consequence of the pull of gravity during the first second. It is equal to Fl. Fc represents the hori- zontal distance the projectile will move in 3 seconds. It is 3 times the initial velocity. Dd represents the total pull of gravity for four seconds from starting. 17. S = igP. (See §131.) S ss 16.08 ft. x 16 = 257.28 ft. This is the distance the body would have moved in the given time if it had had no initial velocity. But it moved (357.28-257.28=) 100 ft further in the 4 seconds. 06 [Elements of Natural Philosophy, pp. 67, 68.] The initial velocity must, therefore, have been (100 4*4 ±±) 25 ft. 18. During that time, gravity alone moved it 2512.5 ft. The additional force moved it (35 x 12£ =) 437.5 ft. Together they moved it (2512.5 + 437.5 =) 2950 ft. Its final velocity due to gravity is (32.16 x 12.5 =) 402 ft., to which we must add the initial velocity, making a velocity of 437 ft. 19. (a.) 3216 -r- 32.16 = 100, the number of seconds. See § 132. (b.) The end of the 4th second of the ascent corresponds to the end of the 96th second of the descent. v = gt = 32.16 ft. x 96 = 3087.36 ft. Do not forget that this result disregards the resistance of the air ; that it is true only for a freely falling (or rising) body. (c.) The end of the 7th second of the ascent corresponds to the end of the 93d second of the descent, v = 32.16 ft. x 93 = 2990.88 ft. 20. The ball has to fall from a height of 257.28 ft. Whether the force of gravity draws it vertically downward as a freely falling body, or acts with the projecting force to produce a curved path, it will reach the ground in the same time. (§ 78.) It would fall this distance in what time? S = igt 2 ; 257.28 = 16.08^; 16 =t*; ^ — t. If it would take 4 seconds to fall from the highest point reached, it would require 4 seconds for it to rise to that height; it would be in the air 8 seconds. (§136.) During each of these seconds it has a horizontal motion of 1000 ft. 21. S= \gt % = 16.08 ft. x 25 = 402 ft., the distance [Elements of Natural Philosophy, pp. 67, 68.] 67 that the force of gravity would move the body in 5 seconds. The force with which it was thrown moves it 10 ft. t-acli second, or 50 ft. during the 5 seconds. 402 ft. 4- 50 ft. = 452 ft. (§ 131.) 22. v = gt = 32.16 f t. x 5 = 160.8 ft. 160.8 ft. + 10 ft. = 170.8 ft. 23. See §125. (a.) The value of each space is 7 ft. In 5 seconds it will pass over (t 2 =) 25 such spaces, or 175 ft. (b.) Its final velocity will be (2* =) 10 times 7 ft. = 70 feet. See § 125. 24. (a.) See §§ 124, 125. The distance passed over in the first second will be half the velocity acquired during the first second. Hence, the value of the spaces traversed in this case is 10 ft. In 10 seconds it will pass over (t 2 =) 100 such spaces, or 1000 ft. Or we may say that the increment of velocity (g) under these circumstances is 20 ft., instead of 32. 16 ft. Then, S = \gt 2 = 10 ft. x 100 = 1000 ft. (b.) See §130. The ratio between the height and length of the plane is the same as that between 20 ft. and 32.16 ft. 20:32.16 :: 800 ft. : 1286.40 ft. 25. See § 132. (a.) It would take just as long to rise 1302.48 ft. as it would to fall that distance. Then, 8 as \gt 2 ; 1302.48 sa 16.08/ 2 ; 81 = fi ; 9 = i. (b.) The initial velocity of a body that can rise for 9 seconds, is the same as the final velocity of a body that has fallen for 9 seconds. Then, v=gt = 32.16 ft. x 9 = 289.44 ft. 26. During 7 seconds, gravity would give it a velocity <>f (gt as 32.16 ft. x 7 =) 225.12 ft. But as its velocity is 235.12 ft, it must have had an initial velocity of (235.12 — 68 [Elements of Natural Philosophy, pp. 67-73.] 225.12 =) 10 feet During 4 seconds, gravity would move it (yt 2 = 16.08 ft. x 16 =) 257.28 ft. But during each of these 4 seconds, the force of the throw moves it 10 feet more. This amounts to 40 additional feet during the 4 seconds. 257.28 ft. + 40 ft. = 297.28 ft. 27. S = \g&\ 787.92 = 16.08* 2 ; 49 = P ; 7 = t This is the time that the second body was in falling 787.92 ft. But the first body fell 3 seconds more, or 10 seconds. During 10 seconds it would fall 16.08 ft. x 100 = 1608 ft. [Elements of Natural Philosophy.] 69 § 146. See First Prin. Nat. Phil, Exp. 39. Formulas f«»r tli is law may be given as follows: I : L = P : T\ L:l = n*:N*. The Fourth Law of the pendulum is as follows : The time of vibration varies inversely as the square root of the accelerating force, or as VI- § 147. FoucauWs Experiment, in which the persistence of the pendulum in its plane of vibration is used to prove the rotation of the earth on its axis, is described in Frick's "Physical Technics," p. 143 (§ 120). For the use of the pendulum to determine the value of g, see the Hand-Book note on § 127. It is interesting to notice that the length of the second's pendulum is very nearly a meter. Exercises, Page 75. 1. (b.) Time is 3 seconds. (a.) 39.1 inches x 9 = 351.9 inches. (See § 146.) 2. (b.) Time is 2 seconds. (a.) 39.1 inches x 4 = 156.4 inches. 3. We have two pendulums to compare ; the second's pendulum, the length and time of which are known (§ 147), and the given pendulum, the length of which is 30 inches, but the time of whose vibration we are to find. From § 146, we have the formula, L : I = T* : t*. Let the capital letters refer to the second's pendulum. Then we may substitute as follows : 39.1 : 30 = 1«: fc .-. P = 0.7672 .-. t a= 0.87. Since the time of one vibration is 0.87 seconds, there will be as many vibrations in 60 seconds as .87 is contained times in 60, which is 68.9. Hence the number per minute is 69 nearly. 4. 39.1 : 16 = l 2 : rf 2 . .\ t = 0.64—. The number of vibrations is 93.7 -f-. 70 [Elements of Natural Philosophy, p. 75.] 5. (b.) 60 -j- J = 240, the number of vibrations per minute. (a.) 39.1 : Z :: 1> : (J) 2 . .\ Z == 2.44+ inches. Or we may say that, as the time is J that of the second's pen- dulum, the length will be-^ that of the second's pendulum, or 2.44+ inches. 6. (b.) 60 sec. -f- 15 sec. = 4, the number of vibrations per minute. (a.) 39.1 : I :: l 2 : 15 2 . Or since the time is 15 times that of the second's pendulum, the length will be (15 2 =) 225 times the length of the second's pendulum. 7. 39.1 : 39.37 : : l 2 : t\ .\ t = 1 + seconds. Notice how closely the meter corresponds to the length of the second's pendulum : (39.37 in. — 39.1 in. = 0.27 in.) 8. (b.) Time of 1 vibration = 6 seconds. (a.) 39.1 inches x 36 = 1407.6 inches = 117.3 ft. 9. 39.1 : 10 :: l 2 : t\ .*. t = ± + . 10. The time = 60 seconds. The length = 39.1 inches X 3600 sb 11730 ft., or more than 2£ miles. 11. The length of this pendulum is that of the second's pendulum. Hence the number of vibrations is 1 per second, and the time is 1 second. (1000 mm. — 993.3 mm. = 6.7 mm.) 12. (a.) 99.33 cm. x ± = 397.32 cm. — 3.9732 m. 13. (a.) 99.33 cm. x 120 2 = 1430352 cm. se 14303.52 m. = 14.3+ Km. [Elements of Natural Philosophy, p. 75.] 71 14. U>.) 99.33:24.83 :: l 2 : P. 15. (b.) Time = -J second. (a.) Length = 993.3 trim, x (i) 2 = 15.52 mm. 16. (b.) 99.33 : 397.32 :: l 2 : Z 2 . .\ t = 2. 17. (A.) 99.33 : 11.03 :: 1»: Z 2 . .•.*==$ nearly. 18. (a.) 99.33 cm. x 100 = 9933 cm. = 99.33 rn. 19. (£.) 99.33 : 2483.25 :: l 2 : Z 2 . .\ t = 5. Suggestion. — Divide the 1st couplet by 99.33. 20. (a.) 99.33 cm. x 16 = 1589.28 cm. = 15.8928 m. 21. X:Z :: T* : Z 2 . .-. 4:49 :: T 2 : /*. /. 2:7 :: T: t 22. L:l :: n*:N*. (See §146.) .-. L\l :: 4900:6400. 23. The time of the longer pendulum will be twice that of the shorter one. 24. 39.1 inches x (\) 2 = 1.564 inches. 25. (a.) 39.1 inches x 64 = 2502.4 inches, or 99.33 cm. x 64 = 6357.12 cm. = 63.57+ m. (b.) 39.1 inches -=- 64 = 0.61 inches, or 993.3 mm. x & = 15.5 mm. 26. 39.1 in. x (3.5) 2 = 478.975 in., nearly 40 ft. 27. Time of vibration = .8 seconds. 39.1 in. x (0.8) 2 = 25.02 + in. 28. L : / : : n» : NK :. 60 in. : 60.5 in. :: n* : 400 2 . .-. n = 398 + . 72 [Elements of Natural Philosophy, pp. 78, 79.] § 150. Be sure that your pupils understand that work is the product of two factors ; viz., force and resistance through space. If either factor is zero, the product is zero and no work is done. A planet or a comet imagined as moving without resistance must be conceived as doing no work. Similarly, a pillar supporting a weight does no work. § 154. The work of lifting 1 gram to a height of 1 cen- timeter is 980 ergs. The work of lifting a kilogram to that height is 1,000 times as great, or 980,000 ergs. The work of lifting a kilogram 100 times as high (100 cm. = 1 meter) is 100 times as great, or 98,000,000 ergs. But the work of lifting a kilogram to a height of a meter is a kilogrammeter. Hence, a kilogrammeter is equivalent to 98,000,000 ergs. § 156. See First Prin. Nat. Phil, Exp. 40. § 157. Force (the cause of motion) is properly meas- ured by the acceleration it produces in the velocity of unit of mass. Thus, force and mass are measured by each Dther. Two forces are equal when they produce equal accelerations in equal masses ; two masses are equal when they are equally accelerated by equal forces. The velocity (v) is directly as the force (/) and inversely as the mass (m). When the force is constant, velocity is proportional to the time of action (t) also. That is, f v = — x t .'. mv = ft. (1.) The space (S) through which a body moves under the action of a constant force is also directly as the force and inversely as the mass. But we learn from § 128 (3), where the particular constant force is represented by g, that the [Elements of Natural PhUowphy, p. 79.] 73 space is proportional, not to the time (as velocity is ; v=gt but to half the square of the time ( S=g ^ I . Consequently, Substituting the value of f* given in equation (2), / Multiplying both members of this equation by fS=imv>. (5.) But the product of the force acting and the space through which the body is moved measures the work (§ 150) done on that body and, consequently, the energy required to do the work. In other words, the product, f S, represents kinetic energy and equation (5) becomes K. E. = i mv>. 74 [Elements of Natural Philosophy.'] Exercises, Page S3, 1. See § 155. tt _ No. of feet x No. of lbs. _ Foot-pounds orse-powei — 33000 x No. of minutes ~ 33006~m.~ 176 x8250 L-V'i; \ ^ -OQQQQ r = 11* the number of horse-power. Suggestion. — Reduce by cancellation. o /a g -. ^ x 192.96 x 10000 l Jj^- 2. (See§lo7.) — ^- = 30000. 3. The direction makes no difference (§ 156). 50 x 19.6 x 19.6 ^ r j. 2xk8 * 5 ° X 19 - 6 * 980 ' the number of kilogram-meters. K. E. ~ w ( — ^-1 . See V8.02/ page 66, following. 4. See §132 (a). Gravity will diminish the velocity 32.16 ft. each second. (a.) In 3 seconds it will diminish it 96.48 ft. The velocity at the end of 3 seconds will be 225.12 ft. - 96.48 ft. == 128.64 ft. (§ 157.) K.E. = 10xl f°j*f 8 - 64 = 2572.8, the number of foot-pounds, (v = VfyS.) (b.) v = gt = 32.16 ft. x 4 = 128.64 ft. (§ 128.) The weight and velocity being the same as before, the X. E. will be the same, i. e., 2572.8 foot-pounds. K 40x8£x8J 2x9.8 141f£f-, the num. of kilogram -meters. * /B1KK x 1500x2376 _ . , , _. 6. (§155.) — —=36, the number of horse-power 00UUU X o„ \EUment% of Natural Philosophy, p. 83] 75 7. That quantity of water weighs about (62.51b. x 300=) 18750 pounds. 62.5x300x132 • 33000 ~ ' the number of horse-power necessary. 8. A velocity of 20 miles per hour is one of 29 J ft. per second. v „ 100 x 204 x 29^ _ , , , _ K. E. = — ^ * = number of foot-pounds. 64.32 9. (a.) 6000 x 50 = 300000, the number of foot-pounds. (b.) 300000 -r- 16500 = the number of horse-power. (§155.) 10000x100 10 - *~ teboom • •••™ = 15 A> the number of minutes. the number of feet. 12. 1650000 -r- 33000 == 50, the number of horse-power 2376 x 1000 oa ,, , _, 13. ^/x/v/x -r- = 36, the number of horse-power. 33000 x 2 r K.K = ^«> = 1 25 0, the number of foot-pounds that the moving sphere can perform. This working power is the exact measure of the work performed upon it. Hence, the answer is 1250 foot- pounds. (§ 162.) 15. A resistance of 8 pounds per ton signifies that to move a ton one foot on the mils involves as much work as to lift 8 lbs. one foot high, or 8 foot-pounds. To move 10 tons 50 feet on the rails would require 4000 foot-poum'.-. The additional work done in giving kinetic energy (or /6 [Elements of Natural Philosophy, pp. 83-85.] velocity) to the car will be measured by the kinetic energy of the car. The velocity of the car is 4.4 ft. per second. 20000 x 4.4 x 4.4 _ KE '- 6452 - 6019 + > the number of foot-pounds that the car can perform, or the amount of work done in giving the car the velocity specified. 4000 foot-pounds + 6019 + foot-pounds = 10019 + foot-pounds, the whole amount of work done. Heview Questions, Page 84* 4. (a.) See §21. 8. (a.) Gravity is a variety of gravitation ; the latter includes the former ; the latter is of universal application ; the former is (as generally understood) confined to the earth and bodies thereon. 10. (a.) See § 120. (c.) Galileo was Professor of Mathe- matics at the Universities of Pisa and Padua, Italy. He was born A. D. 1564, and died in 1642. 12. (/.) Its isochronism. This property of the pen- dulum is said to have been discovered by Galileo, by observing the swinging of the chandelier in the cathedral at Pisa, in 1582. 13. Refer to Fig. 9. In this case the parallelogram will be a rectangle. Make AB = 8 cm. and AC = 6 cm. Complete the rectangle. Draw the resultant, AD. The line AD is the hypothenuse of the right-angled triangle ABD or A CD, and its numerical value is 10. It therefore represents a force of 10 pounds acting from A toward D. Its equilibrant would be a force of 10 pounds acting in the opposite direction, or from D toward A. 17. (a.) To discover or to illustrate physical truths. [Elements of Natural Philosophy, p. 85.] 77 18. The first ball has a momeDtum of 300. (§ 70.) After striking the secoud ball, since they are inelastic (§ i>4), they will move together, but the momentum will be uuchanged. Since the weight is now 12 (= 5 + 7) and the momentum is 300, the velocity is (300 -=- 12 =) 25 feet per second. After the second impact, the momentum is still 300, but the weight is (5 + 7 + 8 =) 20 pounds. The common velocity will therefore be (300 -r- 20 =) 15 feet per second. 19. See § 68 (a). 32,10 x 9 = 289.44, the number of F. P. S. units. 20. See § 69 (a). 9 Kg = 9,000^. 980 dynes x 9000 = 8,820,000 dynes. 21. K. E. = \ mv> = i x 50 x 60*= 90,000. 22. K. E.= i mv* = $ x 30 x 40,000 2 = 24,000,000,000= 24 x 10». CHAPTER III. § 163. " Any arrangement of the mechanical powers designed tn transmit work undiminished is called a machine. The more nearly this design is realized in actual combinations of materials, the more closely the machine approaches perfection. The elasticity of the materials we are compelled to employ, friction and other causes which modify the conditions required by theory, make the attain- ment of such perfection impossible. The ratio of the useful work done to the energy expended is called the efficiency of the machine. Since, in every actual machine, there is a loss of energy in the trans- mission, the efficiency is always a proper fraction/' — Anthony and Brackett. § 168. See Frick's " Physical Technics," p. 69. § 170. See First Prin. Nat. Phil, Exps. 42, 43. § 175. See Deschanel's * Natural Philosophy," §§ 54-57. " In the balances usually employed in physical and chemical in- vestigations, various adjustments are provided by means of which all the required conditions may be secured. The beam is poised on knife edges and the adjustment of the centre of gravity of the beam is made by changing the position of a nut which moves on a screw placed vertically, directly above the point of suspension. Perfect equality in the moments of force due to the two arms of the beam is secured by a horizontal screw and nut placed at one end of the beam. The beam is a flat rhombus of brass, large portions of which are cut out so as to make it as light as possible. The knife edge on which the beam rests and those upon which the scale-pans hang are arranged so that, with a medium load, they are all in the same line. A long pointer attached to the beam moves before a scale and serves to indicate the deviation of the beam from the position of equilibrium. If the balance be accurately made and perfectly ad- justed and equal weights placed in the scale-pans, the pointer will remain at rest or will oscillate through distances, regularly di- minishing on each side of the zero of the scale." — Anthony and Brackett. [Elements of Natural Philosophy.] Exercise* , l*ayv ft 4. n I fHQ ^ « « CO - 1-< »9 - ot eo qj3ayi d o d M 9* j IN 96 d £ d £ d d o o iq*l94t i s" M 3 £ ft jtj 1*1 5 IB i J3.VlOd s 3 i a 8 : • T4 £ £ 9 i-i 8 2 ^ j § i auv-m^PM 11 8 i d to 55 d d 'UUV-J3M0,{ d to i - * i d 00 si 5; * <* -*• & 1-H 2 77 -* w to «o t- ■ 2 i iqSia^ i 1 ** ^ £ 1 i 35 2 < — 3 eo © •J3MOJ 8 s 9* — 9 — on * 5? S •uuv-»q3t3M O* d d ■# i 5 s v d nuy-aaMoj; d d o 5 i d 2 £ 1! 1 m ?' eo * to £ I + s .s : m a 9 t- j.-: •e + i a 2: •- 1 iH 2 K o k 1 j 1 B ■* 5(5 : 1 b. ft Q i E ? 1 i ; ! £ p '• s ^ )' 1 ce : «o *" Bq 1* > 6 1-" 1 eo K > fit ■j £ * X i kj '< ^ & x * £ Ttifta/A * * * • i c 1 3 > eg s 8 2 9 8 \ N i 1 1 s s £ < ,c i i g s s •J8M0J 3 1 I °> 5 c 1 * ee ©* en K > eo •raa[qoj < £ H O M 5 ■* IQ C > t- a > os o jo -ok 11. 78.74 inches = 2 meters = 200 cm. The circum- ference of the wheel being 20 times that of the axle, the weight supported will be 20 times the power employed ; 20 times 13 oz. = 260 oz. == 16 J lb. Or (§ 182), P : W :: c : O. Then, 13 : i :: 10 : 200. .-. x = 260. 12. P : W : : d : Z) ; a? : 180 : : 6 : 36. .-. $ = 30. Any power greater than 30 lb. w T ill move the rudder. 13. (§ 182.) x : 2000 : : 8 : 80. .'. x = 200. 200 -7- 4 = 50. Ans. 50+ lb. [Elements of Natural Philosophy, p. 102.] 87 14. See Fig. 49. P:W::d:D; x : 1100 :: 1 : 10. .-. x = 110 ; 110 -j- 4 = 37f Ans. 2:W::d:C; P : W :: 1} : 12 x9 x 3.1416. Dividing the second couplet by 1}, P: W :: 1:271.4 + 18. 1 -r- i = 8. 15 lb. x 8 = 120 lb. Arts. 19. The power being given, it is more convenient to begin with the power. (See § 182.) P:W:: r: R. 25 : W : : 4 J : 30. .-. W= 166}. The boy could support a load of 166| lb. with the wheel and axle, without the aid of the inclined plane. With the inclined plane, he could support 20 times as great a load, or 33334 lb. He could lift anything less than 3333| lb. 20. (§ 167 [2].) The threads of the screw being an inch apart, the teeth on the wheel must be an inch apart, i. e. y the wheel must have 60 teeth. 25 lb. x 72 x 60 = W x 10. .\ W = 10800 lb. (This computation, so far, considers only the endless screw in action while its axle turns around once.) The jx»wer at the crank produces a tension of 10800 lb. on the rope of the pulleys. Supposing that there are 6 cords to the pulley (S 197), the pullev would exert a power of (10800 lb. x 6 =) 64800 lb. on the wheel and axle. The wheel and axle increases this intensity of power eight-fold, making it 518400 lb. Deduct J of this for loss by friction, and we have 345600 lb. for the answer. %h (§ 167 [2].) 75 x 120 x 81 = 18 W. /. W = 40500. 94 [Elements of Natural Philosophy, pp. 114, 115.] ^ 500 1b. x 7x3x12x6 _ 45818181b _ Deducting J of this for loss by friction 11454.541b. We have, for the force exerted ~ 34363.64 lb. Exercises, Page 115. 2. (c.) See §§ 171, 181. P x R = Wx r. 3. (b.) See Fig. 41. 4. Second class ; the power-arm is the whole length of the lever. 5. The compound lever. See §§ 178, 181, 185, 186. 6. Same amount of work. When the inclined plane is used (h = 4, I = 12), only % as great a power is needed, but the power has to move 3 times as far. (§ 152.) 7. (c.) See problem 17, p. 108. 8. (a.) Fasten one end of the cord to the movable block ; the cord will be divided into 9 parts by the mov- able pulleys. (b.) See § 167 (2). Consider the distances described by the power and weight respectively while the screw turns around once. Then Px C= Wxd. .'. P:W :: d : C. See § 167 (3). Suppose that the screw turns around once in a second. Then P x C= Wx d, .\ P:W:: d:C. 9. (a.) Loss of power, (b.) The fibres of the rope are thus held together ; were it not for friction, the rope would fall to pieces of its own weight. 12. (a.) 20 foot-pounds. (§ 164.) (b.) 5 ft. [Elements of Natural Philosophy, p. 115.] 95 13. See § 201. 14 (ar to require daily of each pupil written solutions of three or four problems as review work. For instance, tell the class, on Friday, to bring to the recitation on Monday, solutions (written in ink and neatly arranged) of the following problems: 2d on p. 14; 1st on p. 44 ; 1st on p. 56. On Monday, tell them to bring to the recitation oi Tuesday solutions of the following problems • 3d on p. 44 ; 10th on p. 67 ; 1st and 2d on p. 75. To indicate (not to correct) every error of any kind on all of these papers will require patient work on the part of the teacher, but if the time can be secured, its investment here will pay. Papers notably poor should be rewritten until they are satisfactory. Pupils can soon be made to see that it is economy to do the work well the first time— a vei'y important lessen. Needed drill in penmanship, orthography, syntax, rhetoric, and physics is thus provided Any newspaper editor can testify that but very feu adults can prepare an article for publication so that its literal ren- Aering in print would not bring a blush to the cheek of the author. CHAPTER IV. § 216. The " Cartesian Diver," a pretty piece of appa- ratus, is represented in the accompanying cut. It consists of a figure suspended from a hollow glass globe or balloon, which has a small opening m its lower part. The tall glass vessel is nearly filled with water, in which is floated the figure. In trying the experiment, be sure that the figure will just float, L e., that the weight of the figure with its balloon and the contents of the balloon is a little less than that of an equal bulk of water. If the appa- ratus be too light, warm the balloon gently to expel part of the air therefrom, and, while yet warm, immerse it in water. Water will thus be forced into the balloon and increase the weight of the apparatus. If this first attempt render the apparatus too heavy, hold it so that the contained water rests over the opening in the balloon ; then warm the bal- loon gently, until a drop or two of water is driven out. If the first attempt did not render the apparatus heavy enough, hold it so that the water already forced in will be under the opening instead of over it, heat gently, and immerse as before. The beauty of the experiment depends largely upon the nicety with which the weight of the apparatus is adjusted. The top of the vessel is then closed by snugly tying over it a piece of elastic rubber cloth. When the finger is pressed upon the cloth, the air-space at the top of the jar is diminished, the tension of the air there is increased, the increased pressure thus exerted upon the surface of the water is transmitted by the water to the air in the balloon, the air space in the balloon is thus reduced, more water enters and thus increases the weight of the apparatus, rendering its specific gravity greater than [Elements of Natural Philosophy, p. I Hi] 97 that of water. The figure thru rink* When the finger is removed, the tension of the air in the balloon being greater than that of the air at the top of the jar, expels a part of the water from the balloon. This reduces the specific gravity of the apparatus below that of the water. The figure then risen. A pleasing alternation of sinking and rising may thus be produced. The experiment illustrates Pascal's (§ 217) and Mariotte's (§ 284) Laws and Ar- chimedes' Principle (§ 238). The figures are often given fantastic shapes and called "Bottle Imps." A small inverted " test-tube " or vial carrying a proper weight sus- pended from its mouth answers well for the experiment Lead the pupils by questions to see that when the finger is removed from the cloth, the tension of the air in the bal- xoon and in the jar is equal to the atmospheric pressure: that when the finder is pressed down, the tension of the air in the balloon and in the jar is greacer than the atmos- pheric pressure. The jar may be closed with a piece of bladder instead of sheet rubber. A common fruit jar may be used with a syringe bulb attached by a short tube to the perforated cover of the jar. Squeezing the bulb, increases the pressure on the surface of the water in the jar and causes the image to descend. A glass bulb about 2 cm. in diameter with a little tube ending with a tine aperture gives a better illustration than the more elaborate figures made of opaque and colored glass. On the whole, it is well to interest (and perhaps mystify) the class with the colored images first and thin to use the inverted test tube for observation and explana- tion. The images do not cost much, and may be had of Jas. W. Queen & Co., 924 Chestnut St., Philadelphia. 98 [Elements of Natural Philosophy, pp. 123-127.] Exercises, Page 123* § 225. (a.) Into a £7" tube pour enough mercury to fill each arm tc the depth of 3 or 4 cm. Place the U tuba upon a table and hold it upright by any convenient means. Back of it and resting against it, stand a card having a horizontal line drawn on it to mark the level of the mercury in the two arms of the tube. To one ann attach the neck of a funnel by means of a bit of rubber tubing. The funnel may be held by the ring of a retort stand. Pour water slowly into the funnel until nearly full, and mark the level of the water by a sus- pended weight or other means. In one arm the mercury will be depressed below the line marked on the card ; in the other arm it will be raised above it an equal distance. Mark these two mercury levels by dotted horizontal lines on the card. Remove the funnel and re- place it by a funnel or " thistle " tube, making the connection by means of a perforated cork. Pour water into the funnel tube until it stands at the level indicated by the suspended weight, being careful that no air is confined by the teater in the tubes. Although much less water is in the funnel tube than was in the funnel, it forces the mercury into the position indicated by the dotted lines on the card The down- ward pressure of the water in each case is measured by a mercury column with a height equal to the vertical distance between the two dotted lines. See First Prin. Nat. Phil., Exps. 45, 47. Exercises, Page 127 » 1. (See § 231.) The imaginary column has a base of 30 x 20 and an altitude of 10 ft. Cubic contents = 6000 cu. ft. The weight of 6000 cu. ft. of water is (§ 226, note) 62.42 lb. x 6000 = 374520 lb.— Ans. Suggestion.— Allow the pupil to use 62| lb. as the weight of a cu. ft. of water, if he prefers to do so. That value is more easily re- membered, and nearly enough accurate for non -professional purposes. 2. Bulk of imaginary column = (6 x 10 x 3 =) 180 cu. m. = 180 Kl. = 180000 liters. (§ 29.) Each liter of water weighs 1 Kg. (§ 36.) Hence the pressure is 180000 Kg. 3. 5 x 12 x 6 = 360, the number of cu. ft. 62.42 lb. x 360 = 22471.2 lb.— Ans. 4. 2 x 4 x 2 = 16, the number of cu. m. 16 cu. m. — 16,000 I, which weigh 16,000 Kg.— Ans, [Element* of Xuturul Philosophy, p. 127.] 99 5. (See § 226.) 2 cu. yd. = 54 cu. ft. 62.43 lb.x54 = 3370.08 lb.— Am. 6. 2cu.m. = 2000 I 2000 /. of water weigh 2000 Kg.— Am. 7. (See § 228.) 25 cu. ft. of water weigh (62.42 lb.x 25 =) 1560.5 lb.— Am. 8. 30 x 30 x 800 = 720000, the number of cu. cm. This quantity of water weighs 720000 g. or 720 Kg.— Am. 9. 3 x 3 x 7 = 63, the number of cu. ft. 62.42 lb. x 63 = 3932.46 lb.— Am. 10. The dimensions of the vessel are 12 x 12 x 12. The acid stands 8 in. deep. 12 x 8 x 4 = 384, the number of cu. inches in the imaginary column. This is f of a cu. ft. If the imaginary column were of water, it would weigh f of 62.42 lb. = 13.871+ lb. Such a column of acid would weigh 1.8 times 13.871+ lb. = 24.9678+ lb.— Am. 11. 237 x 35 = 8295, the number of cu. cm., and conse- quently the number of grams. 12. 237 x 35 = 8295, the number of cu. in. 62.42 lb. x fffrl = 299.7 Ik— Am. (See § 24.) 13. The water must stand (V =) H * k deep. The sides subjected to lateral pressure hare an area of (10 x 4£ = ) 45 sq. ft. 45 x 2J=101J, the number of cu. ft. in the imaginary column producing lateral pressure. There are 27 cu. ft. (2 x 3 x 4~£) in the column producing pressure on the bottom. 101.25 + 27 = 128.25. 62.42 lb. x 128.25 = 7999.365 lb.— Am. 14. If the lever of the press be of the second class, as ibowu in Fig. 70, the piston of the pump will ' * I'hilomphy, pp. MO-lty.] 101 rnstalloids and colloids is called dia For instance, if the liquid contents of the stomach |jf I dead a;>i.c;d poisoned with arsenic or strychniiu .be. placed in a '//< ua\ing a parehincui. bottom | avid - i][opteA*.pft; water, the poisonous crystalloids will pass through into the water and may thence be easily obtained. The albu- minous contents of the stomach (i. e., the colloids) will be held back by the septum. § 239. See Pickering's " Physical Manipulation," p. 89. § 240. See First Prin. Nat. Phil, Exp. 52 and § 163. I .n irises, Page 134. 1. It will lose the weight of I cu. dm. of water. (§ 238.) This is the weight of a liter of water, 1,000 g. or 1 Kg. 2. It would lose the weight of 1 cu. dm., or 1 liter of the lie pi id (mercury), which would weigh 13.6 times 1 Kg., or 13.6 Kg. = 13,600 g. 3. The iron is supposed to be immersed in the mercury. The mercury pushes it up with a force of 13,600 g. Grav- ity ] ml Is it down with a force of 7,780 g. It must be held down by an additional force of 5,820 g. It can carry a load of 5,820 g. If the iron be allowed to float on the mer- cury, it will displace only 7,780 g. of mercury, thus losing its own weight. (§ 240.) 4. The weight of a cu. ft. of water, or 62.42 lb. (§ 238.) 5. It will displace 100 cu. cm. of water. (§ 237.) It will therefore lose 100 g. in weight. (§§ 36, 238.) The re- maining weight will be 1,035 g. 6. It loses 10 g. in weight when placed in water. It therefore displaces 10 g. or 10 cu. cm. of water; its own bulk is 10 cu. cm. 7. It loses 10 oz. in weight when placed in water. It therefore displaces 10 oz. of water. 10 oz. of water is ( T Jfl T =) -^ of a cubic foot of water or 17.28 cu. inches, (See §226, note.) 102 [Elements of Natural Philosophy, pp. 134-141.] § 250. To prevent the instrument from sinking so as to wet; the pan/tt, ilirtl te keep the hydrometer from touching the side of the jar, it is well to place a wire fork on top of x\vs ia;y^ that its two prongs shall embrace the rod sup- porting a. For a cheap substitute for this instrument, see Frick's " Physical Technics," Fig. 145. § 252. Make a pine rod about a foot long and exactly half an inch square. Graduate it to quarter inches. In the end of the rod (at which your scale begins), bore a hole just large enough to allow lead bullets to enter snugly. Drive enough bullets into this hole to make the rod sink in water to the 8 inch mark on the scale. Dry the rod and dip it for a few moments in melted (very hot) paraffine wax to prevent it from again absorbing water. Adjust it by loading or cutting away at the upper end until, in vvaterv it will sink exactly to the 8 inch mark. It will then displace 2 cubic inches of water, or the rod weighs as much as 2 cubic inches of tvater (§ 240). Next, place it in alcohol. Suppose that it sinks to the 10 inch mark. Then it displaces (*£■ =) 2.5 cubic inches of alcohol, or the rod weighs as much as 2.5 cubic inches of alcohol. Therefore, 2.5 cu. in. of alcohol weighs the same as 2 cu. in. of water, for they both weigh the same as the rod. 2 Then the alcohol, bulk for bulk, is — times as heavy as water. This means that the sp. gr. of alcohol is / 2 =)», p- •* Note. — A source of frequent error in using hydrometers is stated in Daniell's " Principles of Physics," p. 257. The subjects of surface tension and surface tenacity or viscosity and the relation of the former to capillary attraction, as well as of osmose and dialysis are treated on pp. 252-256 of that work. A valuable article on capillary attrac- tion may be found in " Nature," Vol. 34, p. 270. [Element* of Natural Philosophy.] 103 isrs, Ptujv 142. Note. — If you have kept up the written reviews recommended on p. 39 of this Hand-book, you may have found that some of the pupils have frequently forgotten or failed to do the work. Allow no such case to escape your careful notice. Require the performance of the work, unless for -eery go*>d reason. If the pupil cannot solve any given problem, give him the needed help and then require tbt written $oiutim. When the indolent pupil finds that he cannot escape this work, he will cease to try to escape. If a pupil needs help, he should get it from the teacher in time to have his written solution ready when it is due. Analogy : When a bank note is not paid before the close of banking hours on the day of maturity, the note goes to protest. The matter cannot be settled by handing in the money "the next morning," without an additional payment for the cost of the protest, as a penalty. Even then, the business credit of the delinquent has suffered. For examples t to 10, see table on page 43. Suggestions concerning the above exercises : (1.) First fill blank in column marked (c); 1500—1000 = 500. Then fill blank in (o T-i t-5 B» CO i * X © 02 O 3£ £ e» © cs K5 *5 X. <* 5 «c tt n A a H Ci »i © i * iq © © *, en *s § ^ © s i 00 -~ O is C: © © *: © 00 © 3 ** 3 5 M r Ok © © © 8 § (5.) That volume of water would weigli 300 #. This body will weigh 7.5 times 300 g. = 2250 g., the answer for (a.). It will dis- place 300 cu. cm. of water, and, consequently, lose 300 g. when weighed in water. This is the answer for (c). Find the answer for (&.). Multiply (c.) by 2.5, and subtract the product from (a.) for the value for (g.). (6.) Solve in the same manner as the 4th. [Elements of Natural Philosophy, pp. 14S, 14S.] 105 (7.) 62 \ lb. x8 = 500 lb., the value for («.)• 5001b. x 13.6=6800 lb, the loss in the heavy fluid (mercury). 6800 lb. +2700 lb. = 9500 lb., the value for (a.). (8.) From (e.) we see that the value for(c.) is 5000 #. Multiplying this by 6.80, we have 34300 g. for (a ). The loss in water x 13.6 = 68000 g., the loss in mercury. Hence, the body will support a load of 33700 g. on mercury. (9.) Sp. gr. being unity, the body is water or something equally heavy. (10.) Fill the blanks in this order : (&), (a.), (6.), (g.). 11. 6.6 oz. — 2.6 oz. = 4 oz. 6.6 oz. -r- 4 oz. = 1.65, the sp. gr. 12. 453 g. — 429.6 g. = 23.4 g. 453 #. -T- 23.4 g. — 19.36, nearly.— Ans. 13. 52.35 g. + hg. = 10.47, the sp. gr. of silver. (§ 253.) 14. (a.) 695 g. -±%Zg. = 8.37+, the sp. gr. of brass. (b.) 83.^.x. 792 = 65.736 g. 695 g. — 65.736 g. = 629.264 g.—Ans. 15. 708 gr. -r- 1000 gr. = .708, the sp. gr. of the benzo- line. 16. 2.4554 oz. - 2.0778 oz. = .3776 oz. 2.4554 oz. -T- .3776 oz. = 6.5 + .— Ans. 17. 4.6764 oz. -r- .2447 oz. = 19.11, the sp. gr. of the gold. 18. (§ 247.) 970 gr. — 895 gr. = 75 gr. 970 gr. — 910 gr. = 60 gr. 60 gr. -=- 75 gr. = .8.— Ans. 19. (§ 247.) 23 gr. -f- 25 gr. = .92, sp. gr. of the oil. 19 gr. -r- 25 gr. = .76, sp. gr. of the alcohol 20. 1536 g. — 1283 g. = 253 g. 1536 g. + 253 g. = 6.07.— Ans. 106 [Elements of Natural Philosophy, p. 1Ji$.\ 21. Subtract the weight of bottle from the other two weights. 4.2544 g. -~ 4.1417 g. = 1.027 + .— ^4 w*. 22. (1.) Weight of wood and sinker in air, 14= g. (2.) " " " " water, 8.5 g. (3.) " " water displaced by both, 5.5 g. (4.) " " " " sinker (10^.^-16.5=) .954: g. (5.) Weight of water displaced by wood, 4.546 g, (6.) Sp. gr. of the wood (4 g. -*- 4.546 g. =) .897 23. Sp. gr. of metal is 1.73 ; of the unknown liquid, 0.67. 24. 2160 gr. — 1511.5 gr. = 648.5 gr. 2160 gr. <*! 648.5 gr. = 3.33 + .— Ans. 25. (1.) Weight of ice and lead in air, - - 24 lb. (2.) " " " " water, - 13.712 lb. (3.) " u water displaced by ice and lead, 10.288 1b. (4.) Weight of water displaced by lead, 1.4 lb. (5.) " " " " ice, ~~&888 1b. (6.) Sp. gr. of ice (8 lb. 4- 8.888 lb. =) .9+. 26. (a.) 600 g. — 545 g. = 55 g. 600 g. -£- 55 g. = 10.9 + .— Ans. (b.) 600 g. — 557 g. = 43 g. 43 g. -r- 55 g. — .78 + . —Ans. (c.) 600 cu. cm. -T- 10.9 = 55+ cu. cm. — Ans. 27. The simple question is, " How much does that stone weigh in water ? " (§ 244.) 2.5 = 3o^ r ,- .< W = 180 Vo.-Am. 28. An equal bulk of water weighs 1000 g. 870 #.-r-1000#. = .87, the sp. gr. of the turpentine. 29. The volume of the fragments was 1000 cu. cm. — 675 cu. cm. = 325 cu. cm. The fragments weighed [Bkmenit of Natural Philosophy, pp. W, 1U-] 1°? 1487.5 g. — C75 g. = 812.5 g. An equal bulk of watei would weigh 325 g. 812.5 g. -T- 325 g. = 2.5, the sp. gr. of the mineral 30. (See § 29.) The 800 cu. cm. of water weigh 800 g. The 200 cu. cm. of sand weigh 1350 g. — 800 g. = 550 g. An equal bulk of water weighs 200 g. 550 g. -r- 200 g. ss 2.75, the sp. gr. of the sand. 31. Sp. gr. ss jstt — = 8 > tne 8 P- £?• °? tne DraS8 - (§ 250.) o^ ci 2000 -f- 3400 l _ , , - ,, 32. Sp. gr. = 2000 + 1000 = L8 ' the **' &' ° f the acid. (§251.) 33. The given body weighs 10 g. It displaces 2.5 g. of Water (an equal bulk of water weighs 2.5 g.). 10 g. ■+■ 2.5 g. = 4, the sp. gr. 34. 1 cu. Km. = 1000 cu. Hm. = 1000000 cu. Dm. — 1000000000 cw. m. = 1000000000000 cu. dm. or liters. Then, 1 cu. Km. of water would weigh 1000000000000 Kg., and 1 cu. Km. of earth of the assumed density would weigh 5660400000000 Kg. (56604 x 10 8 .) Multiply the weight of 1 cu. Km. by the number of cu. Km.: (56604 x 10 8 ) Kg. x 1082842 x 10»= (61293188568 x 10 1 ') Kg. Suggestion. — To multiply by 10 17 , add 17 ciphers. 35. 427.40 mg. -7- 2545 mg. = 16.793 + . This means that mercury is 16.793+ times as heavy as alcohol. But alcohol is .8095 times as heavy as water. Hence mercury is (16.793+ x .8095 =) 13.59+ times as heavy as water. Sp. gr. of the mercury = 13.59 + . Dividing 5829 mg. by 2545 mg. f we find that the acid is 2.29+ times as heavy as alcohol. Multiplying this 2.29 + by .8095, we find that the acid is 1.853 + times as heavj as water. Sp. gr. of the sulphuric acid = 1.853 + 108 [Elements of Natural Philosophy, p. 144-] 36. (1.) Weight of both in air, 41.2 # (2.) " « " water, 2C.2 g. (3.) " lost by both in water, - - - 15 g. (4.) « " iron " " - - - 5 g. (5.) * * cork " * ... 10^. (6.) Sp.gr. of cork (2.3 -*- 10 =) - - - .23. 37. (*) (See §244.) Sp.gr. = jf^gr - ^ = 60&' .'.r- 547.13+. The lead weighs 547.13+ gr. in water. (b.) (1.) Weight of both in air, - - - 900 gr. (2.) " " " water, - - 472.5 gr. (3.) " lost by both in water, 427.5 gr. (4.) « " lead " 52.87 gr (5.) * " wood " 374.63 gr (6.) Sp. gr. of wood (300 gr.-^374.G3 gr. = ) .8 + 38. 111.7050 g. 14.1256 #. 111.1370 #« 14.1256 #. 97.5794 #. ~ 97.0114 ^ = 1.0058 + .— -4*w. 618 gr. 31 gr. 618 gr. 93 gr. 649 gr. -7- 711 gr. =; .9 + .— Ans. 40. (a) 330 g. — 315 #. = 15 g. 330 g. -^ 15 g. = 22.— Ans. (i.) 330 g. — 303 f. = 27 0, 27 jgr. -+ 15.gr. = 1.8.— 4*w. (§ 247.) (c.) It displaces 15 g. or 15 cw. cw. of water. Its volume is 15 cu. cm. 41. Its volume must be at least that of 1 Kg. of water. (§ 240. ) The volume of 1 Kg. of water is 1 liter, 1 cu. dm., or 1000 cu. cm. [Elements of Natural Philosophy, pp. 144. 145.] 109 42. The lead will displace 10 cu. cm. of water, and con- sequently lose 10 g. in weight. If both lose 159 g. in water, and the lead loses 10 g., the cork will lose 149 g. 30 g. -r- 149 g. = .201, the sp. gr. of the cork. 37 43. (See § 244.) 2.8 = ^ _ W > ' /. W = 23.785+ g.—Ans. Or, we may say that the body being 2.8 times as heavy as water, an equal bulk of water would weigh ~ grams = 13.2142+ g. This is what the body would lose in water. (§ 238.) 37 g. — 13.2142+ g. = 23.785+ g.—Ans. 44. The coal would weigh 2.4 times as much as a cubic foot of water or (62.5 lb. x 2.4 =) 150 lb. It would dis- place 1 cu. ft. of the solution, which would weigh (62.5 lb. x 1.2 =) 75 lb. It will lose 75 lb. weight when in the saline solution. 150 lb. — 75 lb. = 75 lb — Ans. Or, we may say that the coal will weigh as much as 2.4 cu. ft. of water, and that the solution displaced by it will weigh as much as 1.2 cu. ft. of water. The weight less the loss by buoyancy will be the weight of (2.4 cu. ft. — 1.2 cu. ft. =) 1.2 cu. ft. of water, or 75 lb.— Ans. 45. The loss of weight in water will be -^ g. The loss of weight in mercury will be *$£■ g. x 13.6 = 185.45+ g. 300 g. — 185.45+ g. = 114.54+ g.—Ans. 46. With a force equal to the weight of the iron. (§ 240.) 500 g. x 7.8 = 3900 g. 47. (See § 249.) v, the volume of water displaced, weighs 600 gr. &v, " " acid " « 600 gr. In order to compare the sp. gravities of these two liquids, we must find the weights of equal volumes. Thus, we may find the weight of a volume of the acid equal to v, the given volume of water, or we may find the weight of a 110 [Elements of Natural Philosophy, pp. 145-153. ,] volume of the water equal to -ftv, the given volume of the acid. Suppose we try the latter method. ft-v of acid weighs 600 gr. -ft-v of water weighs (ft of 600 gr. =) 337| gr. (See § 243.) 600 gr. -j- 337£ gr. — 1.8, nearly.— Ans. As a matter of fact, the weight of the areometer is not an essential part of the problem, for, inasmuch as it takes only ft^ as much of acid as it does of water to equal the (unknown) weight of the areometer, the acid must be -^ as heavy as the water. *$■ =s 1.8, nearly. Note. — In keeping up the written reviews, you may have noticed that the pupils * ' work together," or help one another. If you have not noticed it, look for it. If you find that the practice prevails in your class, try to have each pupil do his work independently. Show the pupil kindly that in this way only can he get the greatest possi- ble good from the study ; that it is not so much what another does for him as what he does for himself that gives him mental strength. Show him that what you recommend is the honest course for him to follow. He should not deceive you, even unintentionally, into the belief that he is strong enough to do the work of the class when he is not. Show bim that here, as elsewhere, honesty is the best policy, because, judging from his satisfactory papers, you think that he does not need your special attention, which is, consequently, given else- where. Show him that the course from which you would lead him is unmanly ; that asking a classmate for help or accepting his help, is a confession of mental inferiority, while the proffering of unasked assistance is (essentially) an insulting assumption of supe- riority. [Moments of A WUmpkg, pp. 153, /•*;.] 111 ■>4 (e). See Ex. 6, p. 154 of text-book. The teacher will find a pretty Experiment at the bottom of page 282 Of Darnell's u Principles of Physics." § 267 (a). The u hydraulic nun " will be easily under- stood from the accompanying figure. The water-supply is represented by the reservoir, A. The valves at S and 8' being down, S is open and S' closed, as shown in the cut. The water from A, flowing through //and escaping at S, soon acquires sufficient velocity (see § 156) to overcome the gravity of S and close the valve. The weight of S is adjusted for this purpose. The water, thus suddenly checked in its flow, opens the valve, S', and enters the air- chamber at r, covering the lower end of the delivery-tube, T, and compressing the air in the air-chamber (§ 297). The water in H, having lost its motion, is uo longer able to support the properly weighted valves; S and S' are both drawn down by the force of gravity. S being now open again, the water begins to flow along H and again to escape at C, the water in the air-chamber being prevented Dy & from returning. As the velocity of the water flow ing through H increases, the valves are again lifted and the process repeated. The air in the air-chamber being greatly compressed, forces the water out, through the delivery-pipe, to a height greater than that of A, 112 [Elements of Natural Philosophy, pp. 154, 155^ [Element* of Natural Philosophy.] 113 Ejrrrrists, Vtujv 153. 1. v = 8.02^169=8.02 x 13 = 104.26, the number of ft. 2. v = 8.02 Vl2 = 8.02x3.46 = 27.75. 27.75 ft. = 333 in. 333 x ^ X 60 x 60 = 119,880, the number of cu. in. 119,880 -i- 231 ss 519—, the number of gallons. 3. v = 8.02V25 = 40.1. 40.1 ft = 481.2 in. 481.2 cu. in. x 2 x 60 x 60 = 3,464,640 cu. in. = 14,998-f gal. or 2,005 cu. ft 4. 96.24 = 8.02v^; 12 = : d* (c.) -^ = 583.02, the number of foot-pounds. [731 w : 1470 :: 4000* : 14000*; ■w = 120 1b. (§106.) 5. (a.) 112.56 ft. (b.) 257.28 ft. (c.) 128.64 ft. (a.) 34.3 m. (b.) 78.4 m. (c.) 39.2 m. (§§127,128.) 6. «^*l»^2L* _ 5 8 3 000 lb# Deducting J of this for the loss by friction, we have left 388800 lb. — Ans. (§ 2H-) Note. — The pulleys may be arranged so as to give seven parts to the cord. (§ 197.) In such a case, substitute 7 for the factor 6 in the solution above, or, to the answer above, add £ of itself. 7. I : L :: N* : n\ (§§146,147.) (a.) 39.1 : L :: 625 : 3600. .: L = 225.21 inches. Or, 993.3 : L :: 625 : 3600. .\ L = 5721.408 mm. =. 5.7214+ m. (b.) 39.1 : 25 :: iV 2 : 3600. /. N= 75.03. [Elements of Natural Philosophy, pp. 154, 155.] 115 8. (c.) The engine can do GG000 foot-pounds of work per minute. (§155.) It throws to the top of the steeple 528 lb. of water each minute. 60000-^528 = 125. Hence, teeple is 125 feet high. (§§ 152, 15:5.) 9. Figure the lever. Represent the length of the short arm (WF) hy x. Then will the length of the lever and of the bag arm (PF) be 18 + z. 40fe = 4£(18+z). /. x = 2± ; 18 + z = 20J. The length of the lever is 20J inches; that of the short arm is 2^ inches. 10. 150 lb. x V = 1500 lb.— Ans. 11. (a.) See the figure on p. 32 of this Key. (b. ) § (90 x 5) = 300. Any weight less than 300 lb. can be raised. 12. (a.) Figure the lever under both conditions. In the first case the arms will be 24 and 36 inches. 24 x 12 = 36 x 8. In the second case the arras will be 25 and 35 inches. 25 x 14 = 35 x 10. The fulcrum must be moved 1 inch. See the solution of the 32d problem on the 90th page of the text-book. 13. The diameter of the circle traversed by the power is 14 ft., just 12 times the diameter of the capstan barrel There are four men, the energy of one being used to overcome friction. The other three exert a power o! (42 lb. x 3 =) 126 lb. The effect = 126 lb. x 12 = 1512 lb. Or we may proceed as follows : P :W:: d : D. (§182.) 168 : W :: 14 in. : 14 ft. .-. W = 2016 lb. Deducting } of this for friction, 504 lb. The effect produced is 1512 lb. CHAPTER V. § 271. The impenetrability compressibility, and elasticity oi air may be shown by inverting a tumbler over a cork floating on water, and then lowering and raising the glass. The experi- ment also illustrates the principle of the diving-hell. § 272. The figure below illustrates a convenient form of apparatus for this purpose. The balance is also admira* bly adapted to experiments in specific gravity. § 273. See First Prin. Nat. Phil, Exps. 53-60. {Element* of Natural Philosophy, pp. 156-160.] 1 1 ? § 274. See Frick's " Physical Technics," p. 108 (§ 96). § 275. Fill a hydrometer jar (Fig. 272) with watt r and invert it over a water bath. Atmospheric pressure above the contained water column Is sustained by the rigid glass bottom of the inverted jar and the column is supported by the pressure of the atmosphere on the exposed BUrface of the water in the bath. Tie a piece of sheet robber over one end of a lamp chimney or other large tube. Fill this vessel with water and invert it as before. The down- ward pressure of the atmosphere above the liquid column forces the rubber inward until the atmospheric pressure Irom above plus the weight of the supported liquid column equals the atmospheric pressure transmitted from below plus the tension of the rubber diaphragm. § 278. See Deschanel's "Natural Philosophy," §§ 105-110. 118 [Elements of Natural Philosophy. ] Exercises, Page 162. 1. 15 lb. x 144 x 14£ = 31320 lb.— Jins. 2. ttB* = 3.1416 x 16 = 50. 2G56, the number of square inches of surface. 15 lb. x 50.2656 = 753.984 lb. — Ans. 3. The room contains 6000 cu. ft. or 10368000 cu. in. of air. This weighs (.31 gr. x 10368000 =) 3214080 gr., or 459.154 lb. Avoirdupois. 4. If the barometer- tube had a sectional area of 1 sq. cm., the atmospheric pressure per sq. cm. would support a mer- cury column containing 76 cu. cm. Such a column of water would weigh 76 g. ; such a column of mercury would weigh 76 g. x 13.6 == 1033. 6 g. Each side of the cube has a surface of 100 sq. cm. The six sides have a surface of 600 sq. cm. The atmospheric pressure being 1.0336 Kg. per sq. cm., the total pressure is 1.0336 Kg. x 600 = 620.16 Kg.— Ans. 5. It loses the weight of 1728 cu. in. of air, or 535.68 gr. (§ ^38.) 6. (a.) The trunk has a horizontal section of (2 \ x 3J=) 8J sq. ft., or 1260 sq. in. 15 lb. x 1260 = 18900 lb., the downward pressure on the top of the trunk. If the trunk have aflat top, its area will be the same as that of the hori- zontal section (or bottom) of the trunk; if it have an arched top, the total pressure on the upper surface will be more than here given, the excess being lateral pressure, which would not at all interfere with opening the trunk, even if the air were exhausted from it. The downward pressure would not be affected by the shape of the top. (b.) The upivard pressure on the under surface of the trunk top is equal to the downward on the upper surface. 7. The solution of this is involved in the solution of the fourth above. [Elements of Natural Philosophy, p. 163.] 119 8. (a.) The capacity of the room is 320 cu. m. oi 390000 /. (§§ 28, 29.) 1.293 g. x 320000 = 413700 g., oi 413.T0 Kg. (§272.) (b.) and (c.) The surface is 80 sq. m., or 800000 sq. cm. The atmospheric pressure being about 1 Kg. to the sq. cm., the pressure on each of these surfaces is about 800000 Kg. ((/.) The surface is 32 sq. m., or 320000 sq. cm. The pressure on each of these surfaces is 320000 Kg. (e.) The surface is 40 sq. m. or 400000 sq. cm. The pressure on each of these surfaces is 400000 Kg. (/.) The total surface of the room is 3040000 sq. cm. The total pressure is 3040000 Kg. (g.) The outward pressure from within is counter- balanced by the inward pressure from without. 9. A liter of hydrogen weighs .0896 g. ; 10 liters weigh .896 g. The balloon and hydrogen weigh 5.896 g. The 10 /. of displaced air weigh 12.93 g. (§ 272.) ' 12.93 g. - 5.896 g. = 7.034 g.—Ans. 120 {Elements of Natural Philosophy, pp. 163-167.] § 282. When definite quantities of different gases or vapors are mixed in a closed vessel, the pressure of each is added to that of the others ; the pressure of the mix- ture is the sum of the pressures of the separate gases. This fact shows that the molecules act with entire inde- pendence and that, as a consequence, no internal work needs to be done to expand a gas. This conclusion was experimentally demonstrated when Joule showed that a gas is not cooled when it expands without doing external work. The words pressure, tension and elastic force are often used interchangeably. Exercises, Page 167 > 1. (a.) Under a pressure of two atmospheres. (b.) Under a pressure of half an atmosphere. 2. Under ordinary circumstances (§ 272), the air would weigh 3.1 grains. To get 10 times as much air into this same space of 10 cu. in., it must be subjected to a pressure of 10 atmospheres. 3. (a.) 500 cu. cm., or £ liter. (b.) 500 cu. cm. It makes no difference what gas is used. 4. Half of it. 5. (See § 282.) (a.) 20 lb. to the sq. inch. (b.) 15 lb. 4- 5 lb. + 10 lb. = 30 lb., the tension per sq. inch. 6. (a.) In the short arm. The rising of the barometer indicates an increase of atmospheric pressure. This in- crease of pressure will push down the mercury in the open air, and, consequently, push it up in the closed arm. [Element* of I />/<;/, />p. 168-170.] KM 7. If the tension were unchanged, the 11 gr. would occupy ^ as much space as the 8 grains. When all oi this air is forced into the rigid vessel, its volume is only -^ r what it was under a tension of KiJ lb. The volume being •j 8 !- of the original volume, the tension will be *£■ of the original tension ; -y- of li\\ lb. = 22 lb. 11 oz. § 288. The accompanying figure illustrates the con struction of the valves, etc., in Ritchie's patent air-pump. The lower valve is conical, held in place by a triangular stem fitting the tube; it is raised by the valve-rod passing up through a stuffing-box in the piston. The attachment is made so as to allow a motion of the rod side- fcrise, so that any slight change of form of the packing of the piston, or stuffing of the rod, cannot prevent the valve from shutting properly. The cone of the valve is ground to a per- fect tit to its seat; but the valve is also furnished with a disk of oiled silk, which projects just beyond its outer edge, and touches the flat surface of the valve-seat; the valve rod extends up, and is secured in a hole drilled la the upper plate, of depth to allow motion vertically to open the valve. The piston is of thick brass, made in two parts ; the upper ptea has a conical bearing, ground to fit a cone on the piston-rod, which forms the piston-valve ; a series of channels gives free passage for the air ; the lower plate covers the end of the rod, allowing motion to open the valve. A third valve, made of oiled silk, is placed out- side the cylinder. In the thickness of the upper plate of the cylin- der is inserted n steel lever, one end of which covers the valve-rod ; the other end, when the lower valve is closed, is flush with the plate; but when the valve is raised, it projects into the cylinder. In action, the first motion upward of the piston-rod closes the 122 [Elements of Natural Philosophy, p. 170.] piston-valve ; the first motion of the piston opens the lower valve ; as the piston ascends, the air above it is forced out through the upper valve and air from the receiver flows uuobstructedly into the cylinder. The piston strikes the end of the lever and, at the instant of arriving at the top, closes the lower valve. The first downward motion of the piston-rod opens the piston-valve ; the air, in the inter- stices above the piston, which is then of normal pressure, distributes itself throughout the cylinder, but none can pass the lower valve back into the receiver. In selecting an air-pump, remember that a brass plate for holding the receiver is objectionable as it is so easily scratched or indented. Ground glass plates are often furnished, but in school laboratories they are likely to be broken. On the whole, an iron plate is, probably, prefer- able. The oil used will generally protect it from rust. A little lard, sperm or sweet oil should be occasionally poured into the cup at C (Fig. 103) and into the hole in the plate. The oil will be drawn to the parts needing lubrication as the pump is worked. The edge of the receiver should be kept scrupulously free from dust. Before placing the receiver on the plate rub its edges well with tallow, then put it into position, pressing it downward with a rotary motion. Renew this rotary motion after a few strokes of the piston to be sure of an air-tight joint. When the receiver is removed from the plate, set it on a sheet of clean paper. In using the pump, work the handle up and down as far as possible with a motion quick but steady and free from all jerking. See Pickering's "Physical Manipula- tion," p. 103. The following description of an easily made air-pump, written by Mr. Geo. M. Hopkins, is copied from the Scien- tific American, with the consent of its publishers, Munn & Co., 37 Park Row, N. Y. [Elements of Natural Philosophy; p. 170.] 123 The engraving (page 124) shows in perspective in Fig. 1, and in section in Fig. 2, an air-pump which may be readily made. The base, .Lis a perfectly plain board, 8 inches wide, 1> inches long, and 1 inch thick. A ■} -inch hole is bored longitudinally through the cen- ter, and near one end, two /,. inch holes are Ixm-d into the longi tudiual hole at a, J inch apurt. Another ,^-iuch hole is made at 6, and another one at c. The board may be of any well seasoned wood that is not liable to warp. Alter boring, it should receive several x>ats of good alcoholic shellac varnish on all sides and in the holes. When the last coat is applied, a G-inch disk, J, of elastic packing rubber, having a small central aperture, and crbich has p;eviously received a coat of the same kind of varnish, is placed varnish Bide down upon the board, with its central aperture coincident with the hole, r, in the board, and it is kept in position under slight pressure until the varnish dries, which will take a considerable time (a day or so), being confined between the two surfaces. To the base, A, two wooden standards, B, are secured, each 6i inches high and about 2 inches wide at the narrower end and -*■ inch thick. They are two inches apart, and are connected at the top by a cross-piece, G. The base, A, standards, B, and cross-piece, C, should be fastened together with long screws. The pump-barrel, I), is a piece of glass tubing 1 J inches internal diameter, and 6 inches long. A piece which is as nearly true and straight as possible should he selected, it may be cut from a long piece by turning it in a heated loop of heavy iron wire which half encircles the tube. The tube should be turned back and forth at first, until it begins to crack, When it should be turned slowly round in one direction until it cracks entirely around. If the ends need to be squared up, they may be readily ground upon an ordinary grindstone, or by moving it with ■ : an oblong aperture, also a small circular one, as seen in Fig. .">. The oblong aperture is placed over the right-hand hole at a ; the small aperture over the left-hand hole. A disk, F. Fig. 4. of hard rubber, brass, or other suitable material, having its edge grooved, and having two small apertures (,',, loch), which coincide with the holes at a, is covered on its under side with oiled silk, which is drawn over its edges and fastened by a stout thread wound in the groove. Two slits are cut in the oiled silk, one 124 [Elements of Natural Philosophy, p. 170.] [Elemi'iita of PkHowpkg, p. 170.] ir> upon each side of the right-hand hole, making a valve which wort in the little chamber formed by the oblong hole in the packing disk, E\ the oiled silk is removed around the left-hand hole. The upper valve, which is shown in V\g. '•>, consists of a strip of oiled silk. which covers the left-hand hole, and is fastened by a thread arounc' the edges of the disk, as in the other case. The disk. F, is placed upon the packing disk, K, and secured Lj four small screws that pass through both into the base. The piston, I/, Consists of two disks of wood, which have been in melted paraffin to prevent them from absorbing moisture. The lower one nearly fill the barrel ; the upper one is small enough ceive between it and the barrel a leather packing, which is turned upward in the same manner as the packing of an ordinary (4,in pomp. The piston is fastened to the end of the wooden piston-rod, I, by means of a long wood screw. The piston-rod i upward through a hole in the cross-piece, C, and is provided with a suitable handle. A rubber stopper is forced into the longitudinal hole in the bee sen the two holes at a, and another rubber stoppei rite end of the hole. An oiled silk or flexible rubber flap or valve covers the hole, b. The piston should be greased with lard. By adding to the piston a second packing, turned downwaid the pomp may be used for the compression of air. Any of the experiments performed with other air-pumps may bs repeated with this. A bottomless glass jar is shown in the present ipon tin- soft rubber disk, J! It has a thin piece of elastic rubber stretched over its mouth, and tied. When the air is exhaust- ed, external air-pressure forces the elastic rubber downward. By substituting a piece of bladder for the rubber, it will burst with a loud report. By placing the hand over the mouth of the jar and exhausting the air, the fact that the air has weight will at once be realized. [§ 293, (6.) and (7.).] A strong common fruit-jar may be used as a receiver, and to in sure a perfect joint with the rubber disk, a packing-ring of very soft rubber may be interposed between the mouth of the jar and the rub be? disk, J, and in any case the rubber disk, and whatever is placed on it, should b • greased with lard to make a joint. The fountain in vacuo [§ 293, (9.)] requires no expensive appa ratus. All that is n< eded is a small tube or jet. which may be eithei of metal or glass, a piece of stiff rubber tubing, and two good corks or rubber stoppers. One of the corks is Inserted in the lw>tth- sod the jet is inserted in the cork, the rubber tube is slipped over the 126 [Elements of Natural Philosophy, p. 170.] outer end of the jet tube and is fitted to a hole in the second coik, as seen in Fig. 6. To exhaust the air from the bottle, stop the hole, c, insert the cork that is on the end of the rubber tube, in place of the stopper in the end of the bed. Work the pump, and when the air is exhausted bind the rubber tube, as indicated by the dotted lines, so as to close it ; raise the valve from the hole, b, to admit air to the passage in the bed, and remove the cork on the rubber tube from the hole in the bed, and dip it in a vessel of water, at the same time allowing the rubber tube to straighten out. To illustrate the principle of the Magdeburg hemispheres (£ 293, [13}). make a ring of wood a little larger than I M § 289. Air-pumps of the better class are provided with manometers, for the purpose of showing the degn exhaustion attained at any given time. The figure shows one form of the manometer. Over a mercury batli are inverted two glass tubes. The tube at the left is a barometer-tube (§278), with a Torricellian vacuum (§ 274) at the closed or upper end. The upper end of the tube at the right is connected with the receiver or tube of the air-pump. As the air is exhausted, the mercury rises in the second tube, being forced up by atmospheric pressure. When the vacuum in the receiver is as perfect as the Torricellian vacuum, the mercury will stand at the Bflme height in the two tubes. Of course, the mer- cury cannot rise higher in the second than in the first tube. (§ 275.) When the mercury column in the second tube is -fo of an inch shorter than that in the first, we say that the tension of the residual air has been reduced to fo of an inch of mercury. Such an attachment is unsatisfactorily represented in Fig. 103 of the text-book. In the air-pump represented on page 61, a more compact form of manometer is shown. A glass receiver, M, is connected by a stop-cock with the tube t Within M is a bent tube, closed at one end, and a lit tk more than half filled with mercury. The length of the closed arm of this bent tube being less than that of the barometer column, under ordinary atmospheric pressure, 128 [Elements of Natural Philosophy, p. 170.] the mercury is forced to the top of the closed arm. Aa exhaustion proceeds, the pressure upon the mercury in the open arm diminishes. Soon, the tension of the air in M becomes too feeble to support a column of mercury equal to the vertical distance between the mercury surfaces in the two arms. Then the mercury begins to fall in the closed arm and to rise in the open one. When the ex- haustion is complete, the mercury stands at the same level in the two arms. (§233.) At any instant after the mer- cury begins to move, the vertical distance between the two mercury surfaces measures the tension of the air in M 9 J?, and t. [Elements of Natural Philosopfty, pp. m-179.] 129 §293. See Prick's ■■ Physical Ti-Hmifs/' p. 119 (§17) and Deschanel's "Natural Philosophy" £S 109, 170, 174. Make a small hole (2 or 3 mm. across) in the small end of an egg. Place the egg, perforated end downward, in a wine-glass so that the egg shall come within about 1 //////. <»t* the bottom of the glass. Place the glass under the receiver of an air pump and exhaust the air therefrom. The tension of the air within the egg will drive some of the contents of the shell into the wine glass. On the re- admission of air to the receiver, atmospheric pressnre will generally drive the fluid back into the shell. Pass a glass tube through the stopper of a good sized bottle. Slip the end of a snugly fltting rubber tube over the outer end of the glass tube. All of the joints should be air-tight. Suck as much air as you can from the bottle, pinch Che rubber tube close and place ii- ebd in water. On releasing the tube, atmospheric pressure will force water into the bottle. If the inner end of the glass has been drawn out to a small jet (see Mem. Chemistry, Appendix 4 [c]), you will have a pretty little fountain. § 298. See Frick's " Physical Technics," p. 118 (§ 14) and p. 124 (§ 104). Exercises, I*€ige 179, 1. 30 in. x 13.6 == 408 in. = 34 ft— Ans. 2. 28 ft. ~ 0.8 = 35 ft.— Ans. 3. (See § 274.) 76 cm. x 13.6 = 1033.6 cm. = 10.336 m^ the height to which atmospheric pressure will lift water. (a.) It cannot, because atmospheric pressure is not suf* fkrieat to force the water up to that height. 130 [Elements of Natural Philosophy, p. 180.] (b.) The same as for (a). [c.) It can, because the water is lifted by muscular or some similar form of energy not subject to the limitations placed upon atmospheric pressure. 4. 755 mm. x 13.6 ~ 2.96 — 3,468.9 mm. = 3.4689 m.—Ans. 5. 34 ft. -r-1.8 = 18.8+ ft,— Ans. 6. 15 lb. x 15 = 225 lb.— Ans. 7. (a.) See § 289. (*)* = £f§. (b.) Iff as great. (§ 287.) There being only £f£ as much air in the receiver as there was at the beginning, when its tension was the same as that of the external air, its density and, hence, its tension is only -§-|f as great as that of the external air. See § 62. 8. 29.5 in. x 13.6 -+- 1.35 = 223.11 in.— Ans. 9. 69 cm. x 13.6 = 938.4 cm. = 9.384 m.—Ans. 10. (a.) 15 lb. x 3.1416 x 2 2 = 188.496 lb.— Ans. (b.) 1 Kg. x 3.1416 x 4 2 = 50.2656 Kg.— Ans. Review Questions, Page ISO. 3. (c.) 500 x 60 = 30000, the momentum. ,' x w& 500 x 3600 OWrtOK t ,. . (d.) -— = — — — - — — 27985+, the number of iig t>4:.0/S foot-pounds. Note. — A modification of the formula given in § 157, which is often a practical convenience, may be obtained as follows : _ _ w& I u* \ / v Y K - E - = ^= w W 3 ) = w U:o2)- Using this formula, the solution of the problem above is as follows : W {mf = 50 ° {w&f = 50 °( 7 - 481 ) 2 = 500 x 55.965+ = 27982 + (e.) Each would be doubled. [Elements of Natural Philosophy, pp. 180-182.] 131 (/.) The momentum would be increased twofold; the eiu-rgy, fourfold. 4. (c.) See § 106. w : W :: IP : (P; 90 : 1440 :: 4000 2 : d*. d = 1G000; 16000 — 4000 = 12000, the number of miles from the cen tre of the earth. Or, we may proceed as follows: The weight is to be divided by 16 ; then its distance from the centre of the earth must be multiplied by (ViG = ) 4. If its distance from the centre of the earth is to be 4 times the radius of the earth, its distance from the surface of the earth will be 3 times the radius of the earth ; 3 t»mes 4000 mi. = 12000 ml (d.) w : W :: d : D; w \ T440 :: (4000 — 2200) : 4000. /. w — 648, the number of pounds. 7. J of 39.1 he. is 4.34+ in. Or, i of 9'<3.3 mm. is 110.36+ mm. = 11.036 cm. IT. (2J)2 = 635; 39.1 in. x 6.25 = 244.375 in. Or, 993.f, mm. x 6.25 = 6208.125 mm. = 6.208125 m. 13. See § *»74, and the solution of Prob. 34, on page 96 n' text-book. (Page 84 of Hand-book.) 14. <*) v=zgt h J= ^ ;eUi . (d.) 8 aa yfl; 5280 = 16.08/2; .-. t = 18.12. {e.) v = gt; v = 32. 16 ft. x 18.12 = 582.739 ft. 4 . B» sure that the pupil understands that this disregards the resist- tnce of the air, considering tl lf > b, K iy as a / r , Y / y f a ]lin«r body. The resistance of the air would make a very considerable difference in the **sult. 132 \Elements of Natural Philosophy, pp. 1S0-182.~\ 15. (a.) S = igt 2 + 35t = (16.08 x 12.5 x 12. 5) + (35 x 12.5) = 2950, the number of feet. (i.) v=gt + 3o ft. = 32.16 ft. x 12 J + 35 ft. =437 ft 16. (a.) 170 + (7 x 20) = 310 ; 310 x 30 = 9300, the number of foot-pounds. (b.) 158100 -7- 9300 = 17, the number of trips per day. 20 bricks x 17 = 340 bricks. 18. See § 238. The body will displace 1 cu. m., op 1000 cu. dm. (which is only another name for 1000 liters) of each gas. (a.) See Appendix G. One liter of hydrogen weighs .0896 g. ; the 1000 liters displaced will weigh .0896 #. x 1000 = Sd.6g.—Ans. (b.) See § 272. One liter of air weighs 1.293 g. ; the- 1000 liters displaced will weigh 1.293 g. x 1000 = 1293 g. = 1.293 Kg.—Ans. (c.) See § 253, (3.). Carbonic acid gas being 22 times as heavy as hydrogen, a liter of it weighs 22 times .0896 #.> or 1.9712 g. Then a cubic meter of it will weigh 1.9712 #. x 1000 = 1971.2^., or 1.9712 Kg.— Am. 19. Place it under the receiver of an air-pump. The vertical distance from the level of the mercury in the bath to that of the mercury in the tube, measures the tension of the residual air. In a perfect vacuum, the two mer- cury surfaces would be at the same level. 20. See § 231. 5x12x6 = 360, the number of cu. ft in the imaginary column of water. 62.42 lb. x 360 = 22471.2 lb.— Ans. 22. See § 273. "I Kg. to the sq. cm." 16000 Kg.— Ans. [Elements of Natural Philosophy, pp. 180-18S.] 133 23. The balloon contains 1000000 liters of gas. See § 11i. That much uir weighs 1.293 g. x 1000000 = 1000 g. or 1293 Kg. One half of this, or 646.5 Kg., represents the weight of the gas and also the buoyant effort of the gas. From this buoyant effort of 646.5 Kg., subtract the weight of the balloon. 646.5 Kg. — 25 Kg. = 621.5 Kg.—Ans. 8 1. 38 g. — 28 g. = 10 g., the weight of an equal bulk of water. 38 g. — 20 g. = 18 g., the weight of an equal bulk of acid. 18 g, -f- 10 g. = 1.8, the sp. gr. of the acid. 26. (c.) To bring the center of gravity low, and thus to increase the stability. See § 117. 27. The volume of 150 g. of water is 150 cu. an. As the lead is 11 times as heavy as water, the volume of 150 g. ot iead will be ^ of 150 cu. an., or 13.63 cu. cm. The lead will displace 13.63 cu. cm. of acid. 1 cu. cm. of acid weighs 1.75 //. (See note at foot of page 141, text-book.) The acid displaced will weigh (1.75 g. x 13.63 =) 23.8525 #. The lead will weigh in the acid (150^.-23.8525^. =) 126.1475//.— Ans. 28. It is to vibrate f-g- or f times as fast. Then it must be (|) 2 or J times shorter, or $ as long. $ of 1 m. = 444. 4 -f mm. — Am. 29. We must assume the perfect pump. If atmospheric pressure lifts mercury 29.5 in., it will lift water 13.6 times as high, or 401.2 in. If it lifts water 401.2 in., it will lift the given liquid ~^ in., or 297.185 + in. — Ans. 30. See Fig. 102. (e.) The tension of air in air-chamber. 31. r = 8.02 a/A = 8.02 x 5 = 40.1. S = igt* ; 144.72 = 16.08A .-. t = 3. 40.1 ft x 3 — 120.3 ft.— Ans. 32. See Recapitulation on page 24 of text-book. Just the same. In either case, the wood is 0.9 as heavy as an equal hulk of water. CHAPTER VI. § 302. The following recipe for the preparation of the amalgam mentioned in sub-paragraph (a), is said to be good: " Melt together 5 parts of zinc and 3 parts of tin and, on the melted mixture gradually pour 9 parts of heated mercury. The whole is shaken briskly till cold in an iron or thick wooden box. It is then finely pulverized in a mortar, sifted through muslin and mixed with sufficient lard to form a paste. This paste is to be spread evenly, and any excess that does not adhere to the rubber should be wiped off with paper." As a general thing, it will be better to send to Jas. W. Queen & Co., 924 Chestnut St., Philadelphia, for such supplies. §313. "The unsolved question, ' What is electricity?' we shall not attempt to touch upon. When a body exhibits certain proper- ties, it is said to be electrified. We know how to produce, this state at will but we know next to nothing of its nature. * * * We have no conception of electricity apart from the electrified body ; no experience of its independent existence." The above is from pp. 3 and 4 of J. E. H. Gordon's " Four Lectures on Electric Induction," published by D. Van Nostrand, N. Y. It is well worth while to get this little book. See Hand-Book notes on §§ 316, 352. § 315. The teacher will find much information that will be of immediate value to him in Frick's " Physical Tech- nics," pp. 253-310. §316. "We cannot make or destroy electricity. We can only strain bodies so that their two ends shall show opposite electrical [Elements of Natural PhVwtphy, pp. 104-205.] L35 proprjttlML When we rubbed glass, we produced positive electricity on its surface. Was not that a creation of electricity '! So ; for an exactly equal amount of negative electricity was produced on the rubber, as 1 can show you. (The rubber, on being laid on the elec- troscope, caused a strong divergence of the leaves.) To show that this negative is equal to the jx)sitive, a very simple experiment will suffice. I rub this sealing-wax till, by the cracking, you can hear that it is highly electrified, but I do not remove the rubber from it. You see that there is no effect on the electroscope." — Gordon. § 323. When we wish, not merely to defect electrifica- tion bnt to measure it, our electroscope will not answer ; we need an electrometer. For a good but simple explana- tion of Sir William Thomson's quadrant electrometer, see Gordon's " Electric Induction," p. 35. (b. See Hand-Book note on Review Question 26, p. 411 of text-book. § 332. See Hand-Book note on § 653 of text-book. " Every electrified body from which no electrification is allowed to escape has a particular action on all neighboring bodies and this action is called induction." — Gordon. \ o induction can take place through a metal screen that is connected to the earth but the induction may act in curved lines around the edges of the screen, if the screen be small and the inducing charge intense. A body surrounded by a wire cage connected with the earth is thoroughly protected against injury by lightning. See (i onion's " Electric Induction," p. -41. § 334. The polarized conductor of § 332 showed — elec- tricity at the near end and + at the far end. In this par- agraph we are concerned only with the near end. 11 We will lengthen our cylinder so as to get the far end out of our way. How are we to do this? This is a large room (in the Royal Institution of Great Britain) and no doubt we might, at some ( <>nsi(ler;ible trouble and expense, so lengthen the cylinder that we could remove its other end to a distance of some twenty <>r thirty feet But we can do better than that. We will make the whole 13 G [Elements of Natural Philosophy, pp. 205-215.] world part of our conductor. The earth, owing to the water in it, is a good conductor (for frictional electricity). We will connect this wire from the cylinder to the water-pipes, and now we have one end of our conductor on the table and the other safely tfut of our way somewhere in Australia." — Gordon. , § 337. It will be better if teacher and pupils studiously avoid the use of the expression "electrical fluid'' and use, instead, the less misleading word " electricity." If the teacher wish to refresh his memory concerning the old "one-fluid" and "two-fluid" theories of Franklin and Dufaye, he may refer to DeschaneFs " Natural Philosophy," § 411, A. § 341. See DeschaneFs "Natural Philosophy," § 421, B. §342. See DeschaneFs "Natural Philosophy," §§ 421, D; 416; 422; 424; 425. § 343. Cottrell's Rubber is a very simple electric machine. It is thus described by Dr. Tyndall : " A strip of sheet brass or copper is sewn on to the edge of the silk pad employed as a rubber. Through apertures in the strip, about twenty pin points are introduced and soldered to the metal. When the tube is clasped by the rubber, the metal strip and points quite encircle the (glass) tube. When a fine wire connects the strip of metal with the knob of a Leyden jar, by every downward stroke of the rubber, the glass tube is powerfully excited, and hotly fol- lowing the exciting rubber is the circle of points. From these, against the rod, negative electricity is discharged, the free positive electricity escaping along the wire to the jar, which is thus rapidly charged." For a description of Armstrong's hydro-electric machine (for the developing of electricity by the friction of steam against the sides of orifices through which it is allowed to escape under high pressure), see DeschaneFs " Natural Philosophy," § 431. Many other forms of electric ma- chines are described in the same chapter. Of the late forms of electric machines, the Wimshurst machine is spoken of as being very simple and very efficient. [Element* of Natural Philosophy, pp. 215-222] 137 Full particulars, as to cost, etc, may be had by addressing Jas. \Y. Queen & Co.. Philadelphia. If the teacher or pupil has skill in the use of tools, he may easily make one. Full directions, including illustrations and working plans, are given in the " English Mechanic " for Oct. 1G, 1885 (No. 1073). Any bookseller can get the paper for you for a dime or two. An explanatory article on the same machine may be found in the "English Mechanic " for January 12, 1883, or " The Electrical World," June 12, 1886. See note in text-book following § 349. Always keep school (especially electrical) apparatus in a dry, well venti- lated room. Protect the electric machine, when not in use, with a cover of woolen cloth. In placing the machine by a stove to warm it, turn the edge (not the side) of the plate toward the fire. The plate maybe cleaned with a woolen cloth moistened with turpentine and then thoroughly rubbed with a clean, dry, warm cloth. If con- venient, connect the negative conductor to a gas or water- pipe when the machine is to be used. Keep the class back a little ways from the machine that the instrument may not be moistened by their breath. § 347. If you have a dielectric machine (Fig. 143), set it in action and, while a steady stream of sparks is passing between the prime conductor and the discharging knob, press the finger gently against the lower part of the upper plate (near the lower comb). It has no effect upon the series of sparks. Press the finger upon the plate near the upper comb. Notice that the sparks cease. Press the finger upon the upper part of the lower plate. The sparks cease. The first contact did not affect the series of sparks, because it made no difference whether the repelled — electricity of the plate A. e* aped by the lower comb or through the human body. The second contact canted a cessation of sparks, because (he free -f electricity of the plate, A. at that point was thus neutralized by the — I ■!■ ■< - tricity from the finger. Being neutralized, it could not 138 [Elements of Natural Philosophy, p. 222.] polarize the upper comb and prime conductor. The third contact had a similar effect, because the — electricity of the plate, B, being thus neutralized, could exert no in- ductive effect upon the plate, A. Exercises, Page 222. 1. See Exp. 22, p. 194. 2. See § 322. 4. Because they produce opposite effects when presented to a third charged body. See § 322 and Exp. 22. 5. That it may not condense moisture from the atmos- phere. See § 324. 6. (b.) Induction, (c.) Opposite. 7. (a.) Because the violent repulsion of the similarly charged leaves might tear them, the charge being too strong, in such a case. (Z>.) The gold leaves, the brass wire and the knob or plate of the electroscope form one continuous conductor, insulated from other objects by the glass jar. For the purpose of this explanation, we may assume that the elec- trified body held in the hand is charged positively. The -f electricity of such a body acts inductively on this insu- lated conductor, developing — electricity at the near end or on the knob and + electricity at the far end or on the leaves, which then diverge. Of these two separated elec- tricities (§ 332), the — on the knob is "bound" while the -j- on the leaves is "free" (§351). When the knob of this polarized, insulated conductor is touched by an unin- sulated body, the "free" -f electricity of the leaves escapes to the ground and the leaves fall together. The — elec- tricity is still "bound" at the knob, by the attraction of the inducing body and can not affect the leaves. But when the inducing body is removed from the immediate neighborhood of the electroscope, the — electricity, hith- erto "bound," becomes "free" and diffuses itself over the insulated conductor of which we have spoken. Part of [Elements of Natural Philosophy, p. 223.] 130 the charge passes to the leaves which now diverge again, but this time as the result of a — electrification. (c.) It is — , as explained above. 10. Refer to Figure 133. Let C represent the prime conductor and AB, the insulated globe. Ah is polarized by the iDductive influence of C\ the repulsion of the + electricity at B partly counterbalances the attraction of the nearer — electricity at A, and the resultant action across the intervening insulating air is, consequently, feeble. When the globe is held in the hand, the repelled 4- electricity at B escapes and no longer acts in opposition to the attraction of the — at A. The mutual attraction between the opposite electricities, being now unopposed, more easily overcomes the resistance offered by the inter- vening air. 11. Electroscope. 12 See §319 (1). 13. Since the charges are of opposite signs, the force will be attractive and not repel Ian t. See § 319 (2). 8xg _ 24x8 _ Our units are all C. G. 8. units. By recognizing the algebraic signs, we have ±^=^ = - n, which also indicates an attractive force. See § 321 (a), 14* The — 8 units will neutralize an equal number of the -f units, leaving -f 1<; units to be equally divided between the two balls (which are assumed to be of equal capacity). f - ns, the red lead along the lines formed by the negative jar and the sulphur along the lines formed by the positive jar." — Gage. § 354. If the person charging the jar hold it by the knob and present the outer coat to the charging body, the jar [Elements of Natural Phil>mphy. pp. 228-232.] 141 will be discharged tli rough his person when he ■ down on an ordinary table. The jar, thus charged, should iirst be placed on an insulated support and tken taken by the outer coat in the usual way. The "cascade" method of charging jars, in which a number (») <>f similar, uncharged jars are joined in settee, the outer coating of the first being in metallic connection with the knob of the second, and so on, and the ! then charged as if it were a single jar, was devised by Benjamin Franklin. In this case, the difference of po- tential ( V) between the outer coating of the last jar and the knob of the first will be the same as that of one of the same jars charged by itself while that of one jar of the y series will be — . This arrangement is, therefore, not as N good as a single jar fully charged by the same machine. See Hand-Book note on Ex. 10, p. 252, of the text-book. § 355. The outer coat being charged with u bound " electricity by the inductive influence of the inner coat, when it is touched by the discharger, the discharger is also charged in the same way without loss of intensity. If me discharger be iir.st brought into contact with the knob, the — electricity of the discharger will be attracted by the -f of the inner coat, which will thus be partly neutral- ized. The intensity of the charge would thus be weakened. On the effect of electricity upon the volume of bodies, see Il'ir/xr's M the knob of the jar and the tin strip, gradually discharging the jar. See Exp. 96, First Prin. Nat. PhV. In Exp. 43. one of the knobs is in place of the upper plate of Exp. 39. The swinging image takes the place of the dancing image. The " electric see-saw," represented in the ac- companying figure, is a pretty modification of the "swing" and. like it, is easily made by an interested teacher or pupil. The three pillars are insulators (glass tubing or sealing-wax), the two outer ones being connected respectively with the prime conductor and' the earth, or with the two coats of a charged Leyden jar. In Exp. 44, the inner coat of the jar is charged by conduction and then polarizes the outer coat and the pupil. In Exp. 5, the pupil was charged by conduction. The phenomena of successive polarization, attraction and repul sion are illustrated by the following interesting experiments : Float a small metal swan upon water in a glass or other insulating vessel. Connect the water with the prime conductor of an electric ma- chine in action, as shown in the figure. The swan thus becomes charged. Bring an extended finger near the swan. The finger becomes oppositely charged by the inductive action of the swan. On account of the attraction between these opposite electricities, the bird will follow the finger in any direction, as far as it can float From cork or pitch, carve the body of a large spider and attach to it eight linen threads (each about an inch and a half long) for legs. By a silk thread, suspend the spider between the knobs of two Leyden jars opjKisitely charged. It will vibrate between the two knobs, clasping them in succession with its legs as if for support. See First Prin. Nat. Phil., Exp. 97. 144 [Elements of Natural Philosophy, pp. 241, 242.] In Exp. 45, the thread is a good conductor for electricity of high potential. The kite and prime conductor, being similarly charged, repel each other. In the bottom of a small tin pail, pierce a few holes, so fine that water from the pail will escape from them only drop by drop. Sus- pend the pail from the prime conductor ; work the machine ; the water escapes in small streams ; electric repulsion. In Exp. 46, the divergence of the strips is due to the mutual re- pulsion between bodies similarly charged. Concerning the phenom- enon next mentioned, see § 336. The blowing away of the strips depends upon the principle stated in § 342. The air- particles at the point of the needle receive a charge from the point and are repelled, thus producing a wind. When held below the divergent strips, the — electricity of the air-particles neutralizes the + of the strips. If you have time, make a similar tassel of cotton or linen thread and repeat the experiment. The tassel is easily made by winding the thread around a cylinder (as a fruit-can), cutting across the threads and tying them together in the middle with another piece of thread. Instead of such a tassel, the hair of a doll's head may be easily pre- pared for the experiment ; or the doll (like all of these pieces of apparatus) may be bought of Jas. W. Queen & Co. See page v. of text-book. Place the doll upon the prime conductor, and work the machine. See Exp. 100, First Prin. Nat. Phil. In Exp. 47, the leaves were, at first, polarized by induction. After the needle-point was uncovered, they were charged by convection. See Exp. 36 and § 363. In Exps 48 and 49, the principle is the same. It is to be noticed that the motion here produced is not fully explained by the third law of motion. (§§ 72, 264 ) The air- particles, when repelled, exert direct action (repulsion) as well as reaction. The adjoining figure represents the " Phosphorus cups." The two insu- lated cups contain bits of phosphorus. Between them is a lighted candle. One cup communicates with the earth ; the other with the prime conductor. When the machine is worked, the flame of the candle is blown from one cup toward the other. The phos- phorus in the second cup will be ignited, while that in the first is not. Notice the direction of the flame, whether it is deflected by the + or — current. Reverse the connections and repeat the experiment. [Elements of Natural Philosophy, pp. 24s, 243.] Ub The "electric inclined plane," represented in the figure, is another modification of the " electric whirl." The' four pillars are insulators. The wheel, axle, and inclined bars are of metal. When either of the bars is connected with the prime conductor and the machine is worked, the wheel rolls up hill. If a Leyden jar be supported nppo a pane of glass or other insulator, it can receive only a feeble charge. (§ 354, a.) If, while thus insu lated, its outer coat be provided with a circle of points, as shown in the figure, the jar may be more fully charged. Hero again we see illustrated the important influenee exerted by pointed conductors. The jar may be pre- pared by thrusting sharp pointed tacks through a narrow strip of leather and binding the strip around the jar so thiit the heads of the tacks shall press against the outer coat. In Exps. 50 and 51, we have simply the principle of the Leyden jar. The water in the beaker and the insulated pupil, respectively represent the inner coat of the Leyden jar. The glass beaker and the India-rubber cloth respectively represent the glass jar. The water in the outer vessel and the uninsulated pupil, being in « -lee- Irical communication with the earth, respectively represent the outer coat of the jar. When the two coatsof any of these modified forms of the Leyden jar are connected by a person, a shock is felt. (§ 409.) After i>erforining Experiment 53, try the following : Charge the M hand -jar," as described in Experiment 51. Let the insulated pupil bring a metal ball suspended from his hand by a wet string, over some gunpowder on a metal plate having a good con- n. ction with the earth. The spark will ignite the powder. " Kinnersley's Thermometer," represented in the figure, -ts of two communicating glass tubes of unequal diameters. The smaller one is open at the top; the larger one is closed at both ends. Rex Is terminating in knobs pass through the ends of the larger tube. Both tubes are filled with alcohol to a level a little below the lower knob. When a spark is made to pass between the two kaobfl r; '« liquid is thrown with great violence from the open end of the smaller tube. The name of the ap- paratus is due to the fact that Kinnersley attributed the in . venu ut of the liquid to the high temperature produced by the spark- 146 [Memento of Natural Philosophy, pp. 248, 249.] In Experiment 67, tlie sparks seem to be simultaneous, because of the great velocity of electricity. They are, of necessity. successive, but our knowledge of their being successive is a result of the action of reason and not of the senses. The " diamond jar," represented in the figure, is a modification of the Leyden jar. The two coats are made of diamond-shaped or square pieces ot tin-foil, each having a round hole in its middle. These bits are placed so that their corners do not quite touch, the corners of the pieces of the inner fcoat being visible through the round holes in the pieces of the outer coat. When, in a dark room, the jar is charged in the usual manner, the sparks passing from corner to corner of the pieces of both coats, present a beautiful appearance. Experiment 69. — The appearance of the spark is greatly changed by reducing the tension of the ur in which it is produced. The accompanying figure represents aii oval glass vessel, which may be exhausted by an air-pump. The cap at the upper end carries a sliding rod terminating in a knob, which may be placed at a varying distance from another knob con- necting with the cap at the lower end. The upper knob is to be connected with the positive conductor of an electric machine ; the lower knob with the nega- tive conductor or with the ground. As a series of sparks is passing between the knobs, exhaust the air. At first, the sparks will have the ordinary appear- ance, but as the tension of the confined air is dimin- ished, they change their aspect. When the tension is reduced to about 6 em. of mercury, a sheaf of rays of violet light with a reddish tinge seems to proceed from the positive to the negative knob. The light at the positive knob is reddish purple ; that at the negative is violet. When the exhaustion is nearly complete, the rays become less dis- tinct and blend into an egg-shaped cloud cf pale violet, reaching from knob to knob. The tube used for bodies falling in a vacuum (Fig. 26), is often adapted for a similar experiment In this case, the upper rod terminates in a point instead of a knob v [Element* of Natural Philosophy, pp. 249-?:,:.] 147 The accompanying figure represents " Gassiot's Cascade," which consists of a glass vase, with the lower part of the inner surface coated with tiu-foil, and a capped bell -glass provided with asliding- rod. The vase and the bell-glass are placed upon the plate of an air- pump, the receiver exhausted, and the inner surface connected by means of the sliding rod with the prime conductor. A beautiful light seems to fill the vase and overflow upon the plate of the air-pump. The effect is very brilliant in a dark room. h\r/ l( 'ii/tnit ?o. — See Deschanel's "Natural Philosophy," §618 and Plate II (colored) in the same bouk. For the method of producing LicMenberg's Figures, see Deschanel's " Natural Philosophy," § 462. Eacercises, Bage 252. 1. Nothing. § 341. See Faraday's lath cage experi- ment, § 341 (b). 2. (a.) See § 351. (b.) The outer coat is polarized, not charged. The -f electricity of the outer coat can not escape. The + electricity of the outer coat repels the -f of the inner coat about as much as the — electricity o! the outer coat attracts it. Thus there is but little u con- densation." 3. (a.) See §§ 341, 342. An unpolished surface presents a multitude of little protuberances that act as pointed con- ductors, (b.) See the Leyden jar with circle of points, p. 145 of Hand-Book. 5. (a.) See § 356. 6. (a.) See Fig. 134. Place the dozen globes, M 9 iV, etc., in actual contact They will be polarized as a single body, and may all be charged as described in § 334. (b.) Charge one negatively by induction ; with it, charge another posi- tively by induction. 7. Connect the knob of the first and the prime-conductor; the outer coats of the first and second ; the knobs of the second and third ; the outer coats of the third and fourth ; the knob of the fourth and the ground. Figure such an arrangement, indicating by the signs + and — , the elec- trical condition of each coat of each jar. 148 [Elements of Natural Philosophy, p. 252.~\ 8. See Exp. 29, p. 212. 9. See § 319 (2). ; _ 28 x 56 Whence, d» = -^ = 49. 10. In passing from the outer coating of the last jar, at zero potential, to the knob of the first jar, the difference of potential will be n times the difference of potential be- tween the two coats of any one jar, n representing the number of jars. Compare § 399 (a). Where great elec- tromotive force is desired, this arrangement has great advantages over the same number of jars placed " abreast," as shown in Fig. 152. For instance, the striking distance (see next Exercise) is much greater. 11. See the preceding note. 12. By bringing the charged conductor into simultaneous contact with two similar conductors. - ^ - >• 14. See §360. [Elements of Natural Philosophy, pp. 255-260.] 149 §373. See Frick's "Physical Technics," p. 315 (§§ 277-279). § 382. To show that the R M. F. of a cell does not depend upon the size of the plates, connect two similar cells in opposition (i. e., connect the two -f plates to each other and the two — plates to each other), with a galva- nometer in the circuit, and notice the deflection (= 0). Lift one of the zincs nearly out of the liquid. The deflec- tion is still zero. Neither cell has an excess of E. M. F. We increased the internal resistance in the cell operated upon, but this affected the resistance of the whole circuit ill which both cells are. They are equally affected by the increased resistance. If two cells of different kinds be thus joined, the galvanometer needle will, in all proba- bility, show a deflection, owing to a difference in the E. M. F. of the opposing cells. § 383. Using a copper and amalgamated zinc battery (see Fig. 179 of text-book) or the bichromate battery (see Fig. 183), place a galva- nometer (§ 418) in the circuit and notice the deflection. Slowly raise one or both of the plates out of the liquid, noticing the decreas- ing deflections of the needle. The diminution of current is due to the increased internal resistance, for we have reduced the transverse section of our liquid prism. Next, place the strips in the liquid (Fig. 179) and notice the de* flection as before. Moving the strips further from each other, the deflection again falls. We have now weakened the current by in- creasing the internal resistance by lengthening our liquid prism. See §883. None of these changes affects the E. M. F. of the cell used. 150 [Elements of Natural Philosophy] Exercises, Page 264. 12 2. See § 386. ^t-t = 1. Ans., 1 ampere, 3 - 2oho = ° X 4. Its diameter is 4 times as great ; its sectional area (and, hence, its conductivity per linear unit) is 16 times as great ; its resistance per linear unit is only -^ as great ; it may, therefore, be made 16 times as long, 12 yd. x 16 = 192 yd. o 5. See § 386. = 0.2. Ans., 0.2 amperes. 6 - loh = °- 133 - Ans., 0.133 amperes or 133 milliamperes. 7. 1 ohm x ^) X w = 0.34. J? TP 8. G = -o-; 2 = — ; ^ = 18. -4ws., 18 volts. 9. C = -5- ; 1 = » ; R = 10. The total resistance is 10 ohms. This, less the external resistance (5 ohms), gives the internal resistance. Ans., 5 ohms. 10. fl r=f;l*=J;* = ^ 5 = 8«. § 388. For methods of cleaning mercury, see Pickering's " Physical Manipulation," p. 35. [Elements of Natural Philosophy, pp. 266-270.] 151 § 389. Connect, in opposition, two cells — one that bus been working for ten minutes and one that is fresh. The deflection of a galvanometer in the circuit will show that the fresh cell has the greater E. M. F. § 390. Concerning the construction and maintenance of very many forms of battery, see M Scientific American Supplements," Nos. 157, 158 and 159. Price, 10 cents each. § 392. This is often called the Grenet battery or cell. A teaspoonful or two of mercury disulphate placed in the solution will aid in keeping the zinc well amalgamated. Trouve's solution is said to be more nearly free from the troublesome formation of crystals. The recipe is as follows : 3 ounces of potassium dichromate. 9 " sulphuric acid. 1 pint of water. § 393. These cells are now sold in great numbers. At the beginning of 188G, the cells, complete with sal-ammo- niac, were sold at 85 cents each. Directions accompany each cell. There is little danger of its freezing. The in- ternal resistance of a cell is said to be about 1 ohm. §394. The internal resistance of this battery (of con- stant E. M. F.) is very variable, ranging, it is said, from 3 to 5 ohms. Never use a cracked porous cup in this or any other battery. The plates and cups require cleaning after about two months' use. § 395. This is not well adapted for school laboratory use, as the liquids are likely to become mixed when the cell is moved. The wire leading up through the liquid from the copper plate should be kept carefully insulated. A break in the insulation may be repaired with asphalium paint or shellac varnish. The internal resistance is from 2 to 4 ohms. Th« parts above the liquid should be dipped 152 [Elements of Natural Philosophy, pp. 210-272.] in melted paraffine wax. A few drops of oil on the liquid will check evaporation, § 397. The potassium di-chromate solution mentioned in § 392 may be used instead of the nitric acid. The offen- sive fumes are not so abundant. The porous cups of Bunsen or Grove cells should be kept in water when not in use to prevent their being cracked by the crystallization of zinc sulphate within their pores. After the battery has been used, it is well to rinse the zincs and carbons, first in water and then in dilute hydrochloric acid and then to soak the carbons in water for a day or two. Carefully avoid spilling any of the contents of the porous cup into the outer vessel. § 398. See Frick's "Physical Technics," p. 319 (§ 280). To show the importance of good connections, put a galvanometer into the circuit. Use, for some of the connections, one or more wires that have become rusty or corroded by exposure to acid fumes. Notice the deflection. Then clean all of the rusty connections by scraping them with a knife (no practical electrician can keep his knife well sharpened) and again send the current through the galva- nometer, noticing the increased deflection. Vary the experiment by twisting connecting wires together loosely and then tightly, noticing the deflection in each case. Be careful not to join cells in opposition, i. e., so that the current from one or more shall flow in a direction opposite to that of the others. Sometimes a battery seems unaccountably weak. The fault may be in a single cell. To test this and to locate the faulty cell if there be one, join the cells in series with a galvanometer in the circuit. Then throw cell after cell, in succession, out of the circuit (by re- moving or short circuiting it), noticing the deflection of the galva- nometer as the current is shunted by each successive cell. At each trial, after the first, all of the cells but one are in the circuit. If the sucessive deflections do not vary much, the cells are, probably, in equally good condition. If, however, the dropping of any cell pro- duces a marked variation in the deflection, that cell is faulty. The several cells of the battery should not touch each other, and their supports should be kept dry. Each cell may well stand on three small porcelain knobs. They should be connected by stout copper wires, well insulated. Paraffine insulation is desirable as it well resists the action of the acids and acid fumes. [Elements of Natural Philosophy, p. e?4.] 153 § 402. This does not mean that the external or the in- ternal resistance is to be increased for the sake of pro- ducing an equality, but that t he cells shall be grouped so as to make the internal resistance as nearly equal as possi- ble to the necessary external resistance, which will be determined by the circumstances of the case. Ohm's law shows that the internal resistance is a positive disadvantage, but it is an unavoidable accompaniment of high E. M. F. Representing the internal resistance of a single cell by r and the total external resistance by R, and the number of cells in the battery by n, the maximum current strength will be secured when the number of cells joined abreast equals y -^ . For example, if we have 40 cells, each with an internal resistance of 3 ohms, to be worked with an. external resistance of 8 ohms, we see, by this formula, /40 x 3 that the number joined abreast should be y - — = 4 o (nearly). Each group of 4 cells should be joined in mul- tiple arc and the ten groups joined in series. Gordon's rule is as follows : To obtain a maximum current, the ratio of the number of cells in series to the number of cells joined abreast should equal the ratio of the external resistance to the resistance of a single cell. Representing the number of cells joined tandem by JV and the number of cells joined abreast by n, this gives *l - a n ' ' r In the case given above, the number of cells, 40, must be divided into two such integral factors that one divided R 8 by the other shall, as nearly as possible, equal — or ■=. The best that can be done is to divide the cells into 10 groups of 4 each. N R 10 8 . — = — or -r- as 5 nearly. n r 4 3 J 154 [Elements of Natural Philosophy. .] Exercises, Page 275, 1 -° = § = m>i = 1 - 9996 +- 2. Internal resistance ( ) is 0.5 ohm. 1 (fj«- 0.501 3 - «j£i>I = - 199 " + 4- tt^f = 0.00099502. 1005 5 - IO0V5 * a000 " 95 - 0.00952. = 1.996 + , 1050 7. Because the line and the instruments offer a high resistance and, under such circumstances, this arrange- ment results in the greatest current strength. 9. The resistance of No. 6 wire is found (from the table) to be 0.411 ohms per 1000 feet, or 2.17 ohms per mile. The total line resistance is, therefore, 21.7 ohms. This is 4.8 times the resistance of a single lamp. As the fractional part of a lamp can not be cut out, it is neces- sary to remove or short circuit 5 lamps. 10. See Fig. 190 or Fig. 206, omitting the galvanometer from the latter or considering it one of very small re- sistance. 12. In App. K (2), the specific resistance of pure water is more than 50 times that of dilute sulphuric acid 7 18 (•| water and £ acid). ^-— > = 57. Then the conductivity of the dilute acid is more than 50 times that of water. 7 18 13. See App. K (2). ^— °- = 22, nearly. [Elements of Natural Philosophy, pp. 278-383.] 155 § 404 (c). For example, suppose that the three wires placed abreast haVe separate resistances of a, b and c ohms respectively. Then their several conductivities will be represented by -, ^ and - and their joint conductivity by 1 1 1 ab + ac + be ... . . . . , ... - + T + - = ■ — r— - — , and the joint resistance will a be abc * be -r — j- . Now, suppose a particular case in which a, b and c represent 3, 4 and 5 ohms respectively. We easily write out the result at once : 12 + 15 + 20 = 47 = 1H ' thG immber ° f 0hm8 * § 406. See Frick's "Physical Technics," p. 336 (§§ 292, 293). . § 408. See Frick's " Physical Technics," p. 311 (§ 275) and p. 334 (§§ 290, 291). Experiment 76. — The acompanying fig- ure better shows the arrangement of the apparatus. §410. Solder a pla- tinum strip 2 cm. by 5 cm. to each of two stout copper wires 20 \ cm. long. Pass the ^^^HBB wires through the neck of a glass funnel. Thrust a cork into the lower end ( f tin' funnel neck, seeing that the wires are on opposite sides of the cork. Warm the funnel carefully hut considerably, place it upright and poor into it melted sealing-wax until the wax covers the lower ends of the platinum Btripa When the wax is cool, it constitutes a [rood floor for the Support of the inverted test-tubes as shown in Fig. 194. 156 [Elements of Natural Philosophy, pp. 283-286.] A retort stand (see Fig. 301) furnishes a convenient sup- port for the funnel. Of course, the binding posts shown in Fig. 194 are in no wise important. The funnel may be provided with a tin or paste- board cover through which the test-tubes pass and by which they may be held upright. See " Nature/' Vol. 35, p. 131. See Frick's "Physical Technics," p. 340 (§§295-29?) and Deschanel's " Natural Philosophy," § 600. To a solution of salt, add a few drops of a solution of potassium ferro-cyanide, better known as yellow prussiate of potash. With this, wet a sheet of white paper and lay the paper on a sheet of tin. Connect the tin with the wire from the negative pole of a gal- vanic battery. See that the wire from the other pole terminates in an iron wire or stylus and, with it, write upon the paper. The current passes through the moistened paper, leaving a blue trace thereon. Vary the above experiment by using a solution of potassium iodide and starch with which to moisten the paper. Prepare the solution by boiling 30 cu. cm. of water and stirring into it 0.5 g. of starch previously reduced to the consistency of cream by thoroughly mixing it with a few drops of water. In this, dissolve a piece of potassium iodide, half the size of a pea. See Elem. Chemistry, Exp. 100. • " We have reason to believe that water is not an electrolyte and that it is not a conductor of the electric current. It is exceedingly difficult to obtain water free from foreign matter. Kohlrausch, however, has obtained water so pure that its resistance was enor- mous compared with ordinary distilled water. When exposed to the air for 4.3 hours, its conductivity rose 70 per cent, and in 1060 hours it was increased nearly forty fold. The oxygen and hydrogen which are given off at the electrodes in so many experiments en water containing foreign ingredients are, therefore, not the ions of water separated by strict electrolysis, but secondary products of the electrolysis of the matter in solution." — Maxwell. % 412. A silver salt solution may be prepared as follows : Place a silver coin in a large test tube and add a little of nitric acid (HN0 3 ). Warm the tube and contents to hasten the chemical action. The coin will dissolve with the evolution of reddish fumes due to the presence of the copper alloy of the coin. The liquid now contains [Elements of Natural Philosophy, p. ?S>;.] 157 solutions of silver nitrate (AgNO,) and copper nitrate, the green color being due to the latter. The copper nitrate is not of any use to us in this experiment ; we have it because it is more difficult to get pure silver, than it is to get rid of the copper nitrate. Nearly fill the tube with pure, soft water. Add hydrochloric (muriatic) acid (HCI), or a strong aqueous solution of common salt (NaCI) drop by drop. The chlorine (CI) of the acid or of the salt will combine with the silver (Ag) of the silver nitrate and form silver chloride (AgCI). The silver chloride thus formed will fall to the bottom of the test-tube as a solid, white precipitate. When so much of the acid or brine has been added that silver chloride is no longer precipitated, care- fully pour the colored liquid from the test-tube ; add pure, soft water, shake thoroughly, let the precipitate settle and pour off the liquid as before. In this way, wash the silver chloride several times. Dissolve a little of potassium cyanide in warm water (N.B. — Potassium cyanide is intensely poisonous, not only when taken internally, but even when brought into contact with an abrasion of the skin, a cut or scratch.) Pour this solution in small quantities into the test-tube until the silver chloride is nearly dissolved. It is well to add the solution of potassium cyanide drop by drop, so that there be no excess of it. The solution is now ready for the bath. It will interest the pupils to have each of them construct a battery and perform the work of electrotyping. Fasten a wire to a coin (or other small conductor of electricity), coat the wire with wax or varnish, place the coin in a bowl and half fill the bowl with a saturated solution of copper sulphate (blue vitriol). Tie a piece of bladder over the larger end of a lamp chimney and place the porous cup thus made in the bowl, support- ing it so that the bladder will be a little ways above the coin. In the porou cup, place some very dilute sulphuric acid. In the acid, sii-j.cikI by ■ wire a roll of sheet zinc previously amalgamated ) Join the wires from the zinc and the coin. (See § 394, a.) When th. mins copper coat has become thick enough, it may be •tripped off as a reversed copy. This reversed copy may now be sub- set ut.' trlcphone are perhaps a thousand million times less than those which would cause an ordi- nary electromagnet to attract a piece of soft iron close to its pole vith a force equal to a few grains." — Jenkin. Exercises, Page 349. L ° = f = 4.56 xT 6 + 10 :55 " 10 -° 4 - The P roWem ignores the resistance of the line, i. e., assumes that the circuit is short and of inconsiderable resistance. 2. See § 458. 3. C : c = tan m : tan n .\ 9.925 : c — tan 60° : tan 74°. .-. 9.925 : c = 1.73 : 3.49. .-. c = 20 + - 4. C = f - . .-. 1 = ^. .-. R = 30. Ans., 30 ohms. K K 5. The first wire has a weight of 2.4 grains and a resist- ance of 0.1 ohm per ft. The second wire has a weight of 1 grain and a resist- ance of x ohms per ft. Resistances are inversely as weights of equal lengths. 1 grain : 2.4 grains = 0.1 ohm : x ohms. .-. x = .24. 6. 1st wire, pure, 1 foot long, weighs 1 grain and has R = .2106 ohm. 2d wire, if pure, 1 foot long, weighing 8.2 grains would have R = .02568 ohm. 3d wire, commercial, 1 foot long, weighing 8.2 grains would have R = .02735 ohm. •-g|g = . 939 or 93.9*. 7. The resistance of the series of lamps will be 250 ohms. That of the wire may, then, be 5 ohms. This is at the rate of 25 ohms per 1,000 ft. No. 24 i< the nearest to the size desired, but as the line resistance " must not 172 [Elements of Natural Philosophy, p. 350.~\ be more " than 5 ohms, we must use the next larger size of wire or No. 23. 8. The resistance of the lamp circuit will be 2.5 ohms and that of the 200 ft. of wire, .05 ohms. This is at the rate of .25 ohms per 1,000 ft. The difference between this desired resistance and 200 ft. of No. 4 wire (B. & S.) is inconsiderable and may safely be ignored. In practice, the difference would probably have been ignored in a case like that of the last Exercise, and No. 24 wire used. 9. 1 ohm -^-.051 ohm = 19.60784. 1000 ft. x 19.60784 = 19,607.84 ft. 10. 206 -f- (1.6 + 25.4) = 7.63, the number of amperes. §386. 11. (2.8 + 1.1 + 9.36) x 14.8 = 196.248. § 386. 12. It is not running fast enough. With the given re- sistances, a 25 ampere current will require an E. M. F. of 212.5 volts. The dynamo must be " speeded up " so as to give the additional 12.5 volts. 13. 81.58 -r- 29.67 = 2.75, the total number of ohm 2.75 ohms — 1.14 ohms = 1.61 ohms. 14. -7.5)157.5(9 1575 4.58 4.42.— Ans. 15. See App. K (3). As the carbon filaments are hot when the lamp is in use, the hot resistance of an incan- descence lamp is of more importance than its cold resist- ance. (39.3 x 3 + 11.2) x 1.2 = 154.92. 16. (39.3 H- 3 + H.2) X 1.2 = 29.16. 17. The current is the same in both lamps. § 385. (97 x 2 -f 12) = 206, the number of ohms. See § 386. 206 x 1 (the number of amperes) = 206, the number of volts. 18. 3.8 x 10 = 38. [Elements of Xat'iml P/tilo.wphy, p. 351.] 173 19. The resistance of the arc 4- the resistance of the helices, etc., of the lamp = 4.42 ohms. 4.42 x 10 = 44.2. 20. The line wire is 3,300 ft. long. Its resistance is that of (3,300 x W =) 3,437.5 ft of pure copper wire of the same size. The greatest resistance admissable is S% of 24 ohms = 1.92 ohms. Let x = the required diameter in mils. 3,437.5 ft. of wire, x mils in diameter has R= 1.92 ohms. 3,437.5 ft. u 1 " " " 72=34,068.75 ohms. — = 17,744, the ratio between the resistances and, 1.92 therefore, the ratio between the sectional areas of the two wires. But the sectional areas are proportional to the squares of the diameters. Vl 7,744 = 133, the ratio be- tween the two diameters. 1 mil x 133 = 133 mils. 21. Ignore the resistance of the line wire. E = Cx R = .112 x (70 + 15 x 25) = 49.84 Consequently, each of the 25 cells of this battery ha<\ an E. M. F. of about 2 volts. Now consider the battery of 30 such cells and the two lamps in series: 0-*l: ?*W A -on« " R " 15x*0 + *0x2 ~ 17 ~ 22. Doubling the area of the plates, halves the internal resistance of each cell but has no other effect. §§ 400, 379 (2). E _ 2x30 2 °- R ~ 7.5x*0 4-*0x~2 = ^5 = °- 2105 - 23. The length of the actual line is 18,480 ft. The length of a similar wire of pure copper, having the same resistance, is (18,480 f t. x W = ) 20,533 J ft. The problem shows that 0.1 of the resistance of the external circuit is in the wire, the other 0.9 being in the lamps (§ 470). But 174 [Elements of Natural Philosophy, pp. 851-353.] the total resistance of the lamps is 225 ohms. Therefore, the resistance of the line is 25 ohms, the total external resistance being 250 ohms. 20,533^ ft. of pure copper wire, diameter required, has R = 25 ohms.. 20,533£ ft. of pure copper wire, diameter of 1 mil., has R = 204,101 ohms. — ~z — = 8,164, the ratio of resistances and, therefore, of sectional areas. \/8,164 = 90.3, the ratio of diameters. 1 mil x 90.3 ss 90.3 mils. § 470. A wire conveying a current of electricity (or a magnet) is capable of producing mechanical action in an- other wire bearing an electric current. Figure A represents a frame devised by Ampere for the purpose of rendering such a conductor movable without an interruption of Fig. A. Fig. B. the current carried by it. The rectangular wire frame is supported by the two pointed ends of the wire which rest in small metallic cups placed one above the other in the vertical axis of the frame. The upper point rests on the bottom of its cup, and carries the weight of the frame. Both cups contain mercury to render perfect the elec- tric communication between them and the ends of the wire frame. The cups are carried by horizontal metal arms, insulated from each other and supported by metal posts in communication with the bind- [Elements of Natural Philosophy, p. 353.] 175 ing poets as shown in the figure. If the wire frame be placed in circuit, and a magnet placed beneath as shown in Fig. 2?, the wire frame will assume such a position that its plane will be perpendicular to the length of the magnet. The experiment is the converse of that described in § 417 of the text- book. If no magnet be used other than the earth (§ 437) the frame will be placed so that its plane is perpendicular to the magnetic meridian, and in such a manner that the current in its lower side is from east to west. The current will then be upward in the western side and downward in the eastern sid«\ For the purpose of showing the effect of one current upon another, it is desirable that the two metal posts be at opposite ends of the base of the frame, and the frames suspend- ed between them, as shown in Fig. C. In this apparatus, as in that described above, the posts are con. nected with wires from a battery, con- nection between the posts being made by the movable frame. When the current is passed through this apparatus, the frame is placed so that its plane coincides with that of the two pillars, and so that the parallel currents in either side of the frame and its adjoining post are flowing in the same direction. If, instead of the frame just considered, we use one the wire of which does not cross itself at a, (Fig. JD), it will be seen that the current in either post flows in a direction opposite to that of the current in the adjoin- Ing side of the movable frame. In this case, the frame will be turned away until stopped by the collision of tin* win s in the upper part of the apparatus. In using the first frame, there is an attraction manif. st. d between the post v and the side fte, and between the post t and the side de ; in using the second frame there Fig. D. 176 \ Elements of Natural Philosophy, p. 353.] is a corresponding manifestation of repulsion instead of attraction. These several phenomena may be summed up as follows : Parallel currents flowing in the same direction attract each other; parallel currents flowing in opposite directions repel each other. The plates of a Voltaic Element (See p. 315) may be floated upon the diluted acid by means of a cork, the connecting wire passing above the cork. If the wire from another circuit be parallel to the conducting wire of this floating element (called De la Rive's battery), the law above given may be verified. A spiral coil of insulated wire (a helix) may be placed on the cork, in the circuit of the floating battery. The heiix will possess the properties of a magnet. The floating helix may replace the magnet of Fig. 209. The attraction of parallel currents flowing in the same direction may be shown by the " contracting helix " shown in Fig. E. A spiral of fine copper wire, supported as shown, is connected at its upper end with the positive pole of a battery, and just dips into a cup of mercury connected with the negative pole of the battery. When the current passes, each turn of the spiral attracts each of its neighbors. The spiral is thus lifted and the circuit broken with a spark at the surface of the mercury, (§ 407). The current being interrupted, gravity draws the spiral down again, and closes the circuit, with another spark. This circuit is thus automatically made and broken by the up and down vibratory motion of the helix. A solenoid is an elongated helix with the ends of its wire carried back until they nearly meet at the middle. The returning wires are sometimes on the outside of the helix, but more commonly in its axis. A solenoid may be suspended from Amperes' stand as shown in Fig. F. As each loop corresponds to the frame represented in Figs. A and B, the passage of a cur- rent will cause each loop to be placed perpendicular to the magnetic meridian. This means that the axis of the solenoid will be placed in a north and south line. (Exp. 102.) It may Fig. F. [Elements of Natural Philosophy, pp. 363-357.] 17? accordingly be said to have + and — poles. If it could be sup- ported so as to move freely about its centre of gravity, it would place its axis parallel to that of a dipping needle at the same place. (See Deschanel's " Natural Philosophy," p. 692.) Repeat Experi- ment 83, at first, with a bar magnet, and a solenoid suspended from Ampere's stand ; and 'secondly, with two solenoids as shown in Fig. F. In the latter case, the reason for the attraction or repulsion may be made more clear by placing the solenoids end to end and noticing that when unlike poles are placed opposite, we have parallel currents flowing in the same direction and, hence, attraction ; that when like poles are placed opposite we have parallel currents flowing in opposite directions and, hence, repulsion. A pole changer for Ampere's stand or other uses is described in Frick's "Physical Technics," p. 376 (§§ 317, 318). Also see the following paragraph. g 319. § 471. A joule measures the work done- by a coulomb falling through a difference of potential of a volt ; it is a volt-coulomb. We copy the following for reference : (0.101937 kilogrammeters. 0.737324 foot-pounds. 0.24067 lesser calories. 10 7 ergs. 1 kilogrammeter = 9.81 joules ; 1 foot-pound = 1 .35626 joules. §473. See Frick's "Physical Tech nics," p. 373 (§315) and p. 382 (§ 321). § 475. We copy the following for reference : 0.00134059 horse-power. 0.101937 kilogrammeters per second. 6.11622 kilogrammeters per minute. 0.00024067 calories per second. 0.24067 lesser calories per second. 0.144402 calories per minute. 10 7 ergs per second. 1 horse-power = 745.941 watts. 1 kilogrammeter \* r second = 9.81 watts. 1 foot-pound per second = 1.35626 watts. 1 watt (or volt-ampere) 178 [Elements of Natural Philosophy.] Exercises, Page 359. 1. A watt. 2. W = C*R = 100 x 44.76 = 4,476. 4,476 -T- 746 = 6. 3. § 471. Joule = C*Rt = 100 x 442 x 60 = 26,520 4. H = &Rt X 0.24 = 1.44 x 40 x 60 x 0.24 = 829.44, the number of lesser calories. But it takes 1,000 lesser calories to make 1 calorie. Hence, the answer is 0.82944 calories. If a pupil says that he does not kuow what a calorie or a lesser calorie is, remind him that the index will refer him, in either case, to § 579, and that the index was made for just such ends. 5. F. P.= C 2 Rt x 0.737335=25 x 100 x 60 x 0.737335 = 110,600.25. o rrr n n n W 30 > 000 6. W=CxE ., C =- =J ^- = 10. 7. W = C x E = 10 x 45.2 = 452, the number of Watts or about f H. P. 8. 25 x 37.7 = 942.5. 942.5 -T- 746 = 1J. 9 - w ° = i = m = °- 88 - (b.) H= C*Rt x 0.24 = (0.88) 2 x 125 x 1 X 0.24= 23.232. 10. (a.) 1.9 -r- 3.4 = 0.559. 1.9 -r- 30.4 = 0.0625. (b.) J = C*Rt = (.559)2 x o.4 x 1 = 0.12499. (.0625)2 x 0.4 x 1 = 0.00625, [Elements of Natural ffjUfctqpAgf ] K'J Review Questions, Page 301. 4. (b.) By mechanical action (§ 372) ; by chemical action (§ 373) and by induction (§ 456). m . . 1014 x 40002 W4 x ^000 6 - <"•> ' "T200*— = - IT " = 60 °- *** J^., 600 1b. (J.) See § 254(c)/ ^4 ns., 72.18 ft (c.) 4 = .714 + .— ^w». 7. See § 128. S = \gP\ 3,600 = 16.08/ 2 ; t = 14.96 + . v = gt = 32.16 x 14.96 + = 481.2 — , the velocity in feet. Before finishing the solution, it may be well to pro- duce a new formula for getting the velocity, in such a case as this, by a more direct method. v v* v = qt\ t = -; t? =— . Substitute this value of fl y 9 f av 1 v 2 m the formula: S = igf 2 ; S = jgj = 5-; v* = 2gS; v as y/2g&. (See § 254 c.) Using this formula, v = VfyS = a/64.32 x 3,600 = V23 1,552 = 481.19 + as previously obtained by the other method. K. E = 2? (§ 157) or K. E. = w ^ j* (See Note on page 130 of this Hand-Book.) Using this last formula, /481 2\ 2 K. E. as 25 ljj£) = 25x602 = 25x3,600 = 90,000, the number of foot-pounds. — Ans. N. B. — Some of your pupils will probably solve this problem in some such way as that given above. Possibly, none of them will do it more directly. In even such a case, the young teacher need not feel discouraged; the experienced teacher will not. Give the class the new formula, and have them use it in solving the problem. 180 {Elements of Natural Philosophy, pp. 361-366.] Then show tliem what they lost by failing to apply general prin- ciples. Have them re-read § 159 and lead them to see that the hall's kinetic energy at the end of its fall was due to the potential energy with which it began its fall and was equal to it, and that it would lift the weight to exactly the height from which it fell. But the energy necessary to lift this 25 lb. ball 3,600 ft. high is (25 x 3,600=) 90,000 foot-pounds (§ 153, a). 9. 27 in. x 13.6 = 367.2 in. or 30f tL—An*. 10. (c.) See§ 238. 11. (a.) See §§ 254, 256. 8.02y77 = 40.1, the velocity per sec. expressed in feet. 40.1 ft. = 481.2 in. 2 cu. in. x 481.2x3,600 = 3,464,640 cu. in. 3,464,640 -i- 231 = 14,998.44, the number of gallons. — Ans. 14. (c.) Either coat may be -f, the other coat being — 15. (a.) The chemical changes (§ 373) involved in the growth of vegetation has been claimed as one of the causes of atmospheric electricity. It is well known that thunder- storms are much more frequent in summer than in winter. 16. See §§ 430, 454. 18. See note in this Hand-Book on Ex. 7, p. 328 of text-book. 25. See note on p. L83 of text-book ; § 324 (b) and Exp. 20. 27. (a.) The 62 grains of air measures 200 cu. in. (§272.) £ of 200 cu. in. = 160 cu. in. (b.) \ of 200 cu. in. = 40 cu. in. (c.) 49.6 gr. x U) = 16.2529+ grains. See 4\5 § 289. (d.) 15 lb. x ( g) = 4.9152 lb. (e.) 1 Kg. (f\ 5 = .32768 Kg. or 327.68 g. (/.) 30 in. x 9.8304 in. 28. (a.) No. (b.) The charge of each inner coat wil be " bound " by the charge of the outer coat. [Elements of Natural Philosophy, p. 363.] 181 .61 2 29. For pressure on the bottom : 62.5 lb. xl.tt x * = 76.25 lb. For pressure on either side: The imaginary (2 1 \ 2 3 X 3 / 9 CU * ft * 62 ' 5 lb# X .61 1M X | = 25.42- lb. 3 30. 25 lb. x 6 x 100 = 15,000 lb.— Arts. * 31. H04 (*).!=! +A+B- •••^ = 4 - 1 ^ the number of ohms. 32. (c.) In a straight line. 33. (c.) 15 lb. x U = 12 lb. ^w*., 12 lb. per sq. in. 1 Kg. xtt = -8 A£. or 800 g. Arts., 800 #. per sq. cm- 34. («.) The room contains 6,000 cu. ft. or 10,368,000 cu. in. (See § 272.) .31 grains x 10,368,000 = 3,214,080 grains or 459.15 lb. Av. — A?is. 35. The 1,000 cu. cm. flask contains 700 cu. cm. of water. The 300 cu. cm. of mineral weighs 750 grams. An equal bulk of water weighs 300 g. 750 g. ■+■ 300 g = 2.5 — Am. 36. The tank contains 1 cu. m. or 1,000 I. of water. Each liter of water weighs 1 Kg. The 1,000 liters weigh 1,000 Kg., the pressure on the bottom. The pressure on any side will be one-half as much; the imaginary column (§§ 226, 231) has the same base but only half the altitude that it has in the case of downward pressure. OQ , , .031 x 242 .022 x 18* " , ., 38. (a.) — -— + — — = 1.27 +, the num- ber of kilogrammeter8. (b.) The first has a momentum of U x 31 =) 744; the second has a momentum of (18 x 22 =) 396. The momentum after impact is (744 — 396 =) 348. The weight being now 53 grams, the velocity will be 348 -7- 53 = 6.566+ m. the kinetic energy expressed in kilogram meters. 182 [Elements of Natural Philosophy, pp. 361-366.'] 39. (a.) The same as 38 (a). See problem above, (b.) 7444.366 = 1,140, the momentum after impact. 1,140 -~ 53 = 21.5, the velocity after impact. w* _ .053 x 21.5» _ * E - ~ W TSF^ ? - L25 ' the kinetic energy expressed in kilogram meters. 40. (a.) See Fig. 102. (c) (|) 4 = fff or .4096, the part of the air originally in the receiver that now remains, {d.) It will be Iff times as great. 41. Sin 9° : sin 70° = j : x. .156 : .940 = %:x .: x = 1. 42. A Leyden jar. The charged ball represents the inner coat. ; the dry air is the dielectric ; the walls of the room represent the outer coat. 44. 1 ft. of the first wire, pure, weighs 1 grain and has R ss 0.2106 ohm. 1 ft. of the second wire, if pure, would weigh 7.5 grains and have R = 0.02808 ohm. 1 ft. of the second wire, commercial, weighs 7.5 grains and has R = 0.03065 ohm. 0.02808 -r- 0.03065 = 0.916 or 91.6^. 45. Let the pupils wrestle with this for a fortnight before you help them with the following. If no one gets it, you must not be disappointed. [Elements of Natural Philosophy, pp. 361-366.] 183 In the accompanying diagram, the two ends of the lin-* win- ar«- connected with " three point switches," one of which consists of th • metal bit, it in, pivoted to the binding post, a, and the two binding posts, c and e. The push button, P, and the ball, A, may be n-spect- ively replaced by telegraphic key and sounder. The connections with line, battery, earth, etc., are sufficiently shown in the diagram. When the line is at rest, m is turned into contact with and it into contact with r. If the operator at the left wishes to send a signal or a message, he turns his switch from c to e and operates the button or key at P. The current passes from B, via P, e, a, line, i, r, A' (giving signal), and earth back to B, while B' is open circuited atP' and s. When he has finished, he turns m back to r. Then the other operator may turn n to s and signal at P', the current passing from ' *, i, a, c, A (giving signal) and earth, B being open circuited at P and e. The switch is not essential, of course, but it affords an easy means of changing the connections at the ends of the line. 46. H= C*Rt x 0.24 = (0.14) 2 x 4 x GOO x 0.24= 11.2896, the number of lesser calories. 48. The internal resistance should be as near 12 ohms (the external resistance) as possible. The 48 cells may be placed in series, in which case the internal resistance of tbe battery will be 96 ohms. Or they may be in a series of 24 groups each of 2 cells abreast, with an internal resist- ance of 24 ohms ; in a series of 16 groups of 3 abreast with a resistance of lOf ohms ; in a series of 12 groups of 4 abreast with a resistance of 6 ohms, and so on with series of 8, 6, 4, 3 and 2 groups or in a battery of 48 cells abreast, the resistance continually getting further and further away from the desired 12 ohms after we pass the third arrangement, namely, of 16 groups, each of 3 cells abreast E 49. R = p = 83.568, the total resistance in ohms. From this, deduct in g the external resistance (4.51 x 16 4-0.8), we have left 10.608 ohms. 50. See § 356. 184 [Elements of Natural Philosophy, pp. 361-366.'] 51. Sound, light and heat. 52. H= Cmt x 0.24=100 x 50 x 900 x 0.24=1,080,000, the numher of lesser calories. This equals 1,080 calories. 53. A watt is a volt-ampere and equals y^g- H. P. § 475. 140 x 9 -=-746 = 1.69. 54. Each series of 3 cells has an internal resistance of 12 ohms. The battery of two such series placed abreast has an internal resistance of 6 ohms. See § 402. 55. The increase in the length of the wire increases the external resistance 36 fold and thus decreases the current strength. This must be provided for by increasing the E. M. F., or by decreasing the internal resistance so as to keep the current up to its original strength. In either case, a greater number of cells is needed. 56. (a.) 2.628 ohms x 16.743 = 44 ohms. 5.5 E 11 57. C = -= = .— . The current will be greatest when it Z.Z the external resistance is so small that it may be ignored. Hence, with a single cell, the maximum current strength will be j ^ = J 0.5 amperes. Now, increase the battery to any number of cells in series. Eepresent this number by n. Then the current strength will be ~— = 0.5. ii . 4/ X 'Yl q. e. d. It may be clearer to some pupil if he be required actually to assign definite values to n, such as 5, 200, 1,000,000, etc., in succession, and cancel from numerator and denominator, the equal factors thus introduced. 58. W — C x E = 10.04 x 838.44 = 8,417.9376. 8,417.94 -h 746 = 11.28. § 475. 60. (a.) There being 1,000 lamps of equal resistance placed abreast, each will take y^q of the total current [Elements of Natural Philosophy, pp. 365, 366.] 185 See § 404. If each lamp gets 1 ampere, the total current must be 1,000 amperes. (b.) 50 ohms -r- 1,000 = 0.05 ohms. (c.) The electromotive force must be enough to send a 1 ampere current through the 50 ohms resistance of each lamp. E = C x R = 1 x 50 = 50, the number of volts. (d.) The external resistance is 0.05 ohms and the total resistance is 0.055 ohms. The total current is 1,000 amperes. E = C x R = 1,000 x 0.055 = 55. (e.) W = E x C a 50 x 1 = 50. (/.) This will leave 500 of the 50 ohm lamps abreast 50 -j- 500 = 0.1. (g.) The total E. M. F. is 55 volts, as above ascer- tained (d). The total resistance is now 0.1 + 0.005 = 0.105. C =l = oS>5 = 523 - 81 - (h.) 523.81 amperes -r- 500 = 1.0476 amperes. 61. The resistance of the lamp circuit is 48.9 ohms, which, added to the 20 ohms resistance of the battery, gives 68.9 ohms as the total R of the circuit. E = Cx R = 1.16 x 68.9 = 799.24, the total E. M. H (in volts) of the 40 cells. 799.24 volts -5- 40 = 1.998 volts, the E. M. F. of each cell. A series of 60 such cells would give an E. M. F. of 1.998 volts x 60 = 119.88 volts and have an internal resistance of 30 ohms (} ohm per cell). The total resistance of the circuit now is (16.9 + 32 + 20 + 16 + 30 =) 114.9 ohms. C _E_ 119,88 ° - R - 114.9 - 1M3 ' 62. This would have halved the internal resistance of the battery. C = !L - U9 ' SS - 1 2 " R " 16.9 + 32 + 20 + 16 + 15 "~ 186 [Elements of Natural Philosophy, p. 366.] 63. W = C l R = 10 2 x 83.5 = 8,350, the number of Vatts. § 475. 8,350 -J- 746 = 11.19, the number of electrical H. P, 11.19 +■ 15.3 = 0.73 or 73^. 73 64. 11.19 H. P. x snr = 9.77 H. P. Od. 9.77 -7- 15.3 = 0.64 or CHAPTER VII. § 477. Do not fail to get Mayer's little book on "Sound." See Experiment 58, therein. See p. 23 herein. § 478. See Frick's " Physical Technics," p. 163 (§ 133). § 481. See Dolbear's "The Telephone," p. G4. §483. See First Prin. Nat. Phil, Exps. 139, 140; Pickering's "Physical Manipulation," p. 125 and Desch- anel's "Natural Philosophy," § 629. § 484. See First Prin. Nat. Phil, Exps. 141-144 and Daniell's " Principles of Physics," p. 429. § 485. " It is marvellous how slight an impulse throws a vast amount of air into motion. We can easily hear the song of a bird 500 ft. above us. For its melody to reach us, it must have filled with wave pulsations a sphere of air 1000 ft. in diameter, or set in motion 18 tons of the atmosphere." — Youmans. § 487. Experiments made at the U. S. Arsenal at Watertown, Mass., go to show that the velocity of sound depends to some extent on the intensity and that ordinary determinations of the velocity of sound (cannon being used to produce the sound) contain an error, due, perhaps, to the bodily motion of the air near the cannon. § 488. In 182G, at Lake Geneva, two boats were moored at a distance of 13,500 in. (between 8 and 9 miles) from each other. From one boat, a bell was hung in the lake. By a simple contrivance, a quantity of gunpowder was ignited in the air at the instant when the hammer struck the bell in the water. The other boat had a trumpet lhaped tube with its lower opening covered with a mem- brane and facing, under water, toward the first boat and the bell. An observer, with his ear at the upper end of the 188 [Elements of Natural Philosophy, pp. 373,374.] hearing trumpet, noted the interval between seeing the flash and hearing the sound. He found the velocity of the sound in water to be 1,435 m. per second or more than four times its velocity in air. See § 653, c. If a pressure of x dynes per sg. cm. applied to a fluid produces a compression, y {i.e., reduces unit volume of the fluid to volume x 1 — y), then is - called the coefficient of elasticity of that fluid. In if the formula, given in the text- book, this is represented by i? and the density of the fluid by D. § 488 (a). It may be well to give the following problems to the class, one daily: Chlorine gas is about 36 times as heavy as hydrogen. (a.) In which gas, under the same atmospheric pressure, will sound travel the faster? (b.) How many times as fast? Ans. (a. ) In hydrogen, the lighter gas. (b.) The tension or elas- ticity, being the same in both cases, need not be considered. ^36 = 6. If a body of gas be subjected to a pressure of two atmospheres instead of one, its volume will be halved ; its density and its tension or elasticity will be doubled. Will sound travel through air thus compressed with greater or with less velocity than it does through the ordinary atmosphere, the temperature being the same ? Ans. There will be no change of elasticity arising from the change of temperature. The act of compression would, as a matter of fact, heat the air, but the conditions of the problem require that time be given for it to cool down to the original temperature. The loss of velocity due to doubling the density will just balance the gain due to doubling the tension. If an unconfined body of gas be heated, its elasticity is unchanged but its density is lessened. How will such heating affect the velocity of sound transmitted by the gas ? Ans. It will increase it. If a confined body of gas be heated, its elasticity is increased but its density is unchanged. How will such heating affect the velocity of sound transmitted by the gas ? Ans. It will increase it. Given two gases. The elasticity and density of the first are to be \/\~,A [Elements of Natural Philosophy, pp. $74, 376.] 189 considered as standards (or unity). The second has a density of 27 ; it is confined and heated until its elasticity is 3. Sound moves through the first with a velocity (c) of 1,200 ft. per second. I want to find the velocity ( V) of sound in the other gas. I proceed as follows : r : F= y\ : |/§ ; or, 1,200 ft. : V = f/j : f/~ . or 1,200 ft. : V = 1 : i- Therefore, V = 400 ft. State the principle that underlies my solution. Ans. See the second sentence in § 488. In some classes, it may be well to give the problem and withhold the solution. Each teacher can tell which plan will be the better for his class. It is not well to assign any problem when you know that no member of the class can solve it. This applies to any problem in the text-book as well as here. § 491. " Practically, musical and unmusical sounds often shade insensibly into one another. The tones of every musical instrument are accompanied by more or less of unmusical noise. The sounds of bells and drums have a sort of intermediate character ; and the confused assemblage of sounds which is heard in the streets of a city blends at a distance into an agreeable hum." — Deschanel. § 493. A valued correspondent writes to the author as follows: " None of the Philosophies make any distinction between loudness and intensity of sound. * * * * Now it is true that intensity depends on amplitude and. otlver thingsbeing equal, loudness depends on intensity and, of course, on amplitude. But a viol string at- tached to a block of lead of the size of the viol may have the same amplitude as when attached to the violin, but the loudness is far inferior. (§ 510.) There exists the same distinction between quan- tity and intensity as in electricity. Attached to the violin, the whole of the wood vibrates, though with no greater amplitude than the string, or even with less, but the quantity of tone is far greater. So Tyndall's deal rod, reaching down to the sounding-board five stories below, had as much amplitude of vibration and as much intensity of sound as when a violin was laid on its upper end. but the quantity (and loudness) was, in the former case, small and in the latter large. So a battery of large cells is related to a battery of small cells. An intensity battery (§ 400, b) of ten cells gives more power to an electro-magnet than a single cell does, notwithstanding magnetic 190 [Elements of Natural Philosophy, pp. 375 > ^ 76 -] power is said to depend on quantity. In fact, it depends on both quantity and intensity. So, loudness is the result of both intensity and quantity in the vibrations of the air or other medium of sound. I have a glass bell which yields, to the viol bow, a painfully intense sound which is yet not at all loud. Some bass viols yield a great quantity of sound (like some human voices) which, after all, pene- trates but a short distance and sounds ■ hollow '." J. D. Everett says : " The loudness or intensity of a sound is measured, physically, by the amount of energy which it communicates to the ear in a given time and this energy, in comparing two simple sounds, is propor- tional to the square of the amplitude of the particles of air in the neighborhood of the ear. But from the point of view of sensation, this rule of comparison can be admitted only when the two simple sounds compared are of the same pitch, for the ear is unequally sensitive to simple sounds of different pitches. Sounds may be so high in pitch as not to be heard at all by the human ear. (See note in this Hand-Book, on § 496.) And, within the limits of audibility there is considerable difference in sensibility. Within the range of pitch employed in music, the ear is more sensitive to sounds of high than of low pitch, that is to say, the same amount of energy of aerial vibration produces a more intense sensation when the pitch is high than when it is low. Of two compound tones of equal energy, that which is strongest in high harmonics (§ 527) will generally affect the ear the most." We quote from another author : "The sensible loudness of sounds does not coincide very closely with their physical intensity. This arises partly from modification in the form of the vibration induced by so complicated a transmis- sion through the auditory apparatus and partly from causes purely physiological." § 494. Suppose a bell to be struck. Aerial waves are started in every direction, as spherical shells. At a certain instant one of these waves, say the first, has travelled 5 ft. It then forms the surface of a sphere whose radius is 5 ft. Subsequently the wave has travelled 10 ft., when it forms the surface of a sphere whose radius is 10 ft. At the second instant, the energy of the wave is spread over four [Element* of Natural Philosophy, pp. 376, 877.] 19 1 times as much surface as it was at the first instant. Hence the amount of energy represented by any given surface (e. g., the tympanum of the ear) will be only one-fourth as great, or the sound will be one-fourth as loud at the second instant as at the first. (It is a well-known geo- metrical truth that similar surfaces are to each other as the squares of their homologous parts.) This argument assumes that, in the propagation of sound, there is no loss of energy ; that the total energy of the larger and outer spherical shells is the same as that of the smaller and inner shells. This cannot be strictly true. The vibration implies friction and condensation. These imply the gene- ration of heat at the expense of the energy that produces the vibrations. (§ 626.) Consequently, sonorous energy diminishes with distance somewhat faster than according to the law of inverse squares. The loudness of a sound depends also upon the density of the air in which the sound is produced ; not upon the density of the air in which it is heard (§ 486 a. and b.). Aeronauts find that when their balloons have reached high elevations they have to speak with some effort to be heard. If two cannon be charged equally and one fired in the rarefied air at the top of a mountain, the other in the heavy air at the foot of the mountain, the first may be un- heard by the gunners in the valley while the second is plainly heard by the gunners upon the mountain. § 496. It is well known that the range of the human voice is different in different persons. Some sing bass, the rate of vibration being comparatively slow ; others sing the higher parts, the rate of vibration being quicker. It is equally true, though not equally well known, that the range of hearing sounds is different in different persons. Some persons are unable to hear low sounds which are not deficient in intensity and which are easily recognized by most persons. Others are unable to hear acute sounds which are audible to most persons. One person may com- 192 [Elements of Natural Philosophy, pp. 377-380.] plain of the shrillness of a sound while another insists that there is no sound at all. If the vibrations be fewer than about 16 per second, the sound will not be heard continu- ously, that number of vibrations being the fewest (or the corresponding wave length being the greatest) that can be detected by the human ear. Place the end of a thumb or finger in the ear ; press the ends of the fingers of the same hand forcibly and steadily against the palm ; a very deep rumbling tone will be heard. The highest tone that can be detected by the human ear consists of about 38,000 vibrations per second. See Mayer on " Sound," p. 115, and Dolbear's " The Telephone," pp. 67-71. § 502 («). See First Prin. Nat. Phil, § 333, a, and Beechanel's "Natural Philosophy," §§ 639-641. Note. — The teacher will find an interesting description of the iuman ear in Daniell's " Principles of Physics," pp. 431-436. [Elements of Natural Philosophy.] 193 Exercises, Page 3 SI. 1. 82 — 32 = 50, the number of degrees above freez- ing point. 1.12 ft. x 50 = 56 ft. (§ 489.) 1,090 ft. + b6 ft. = 1,146 ft., the velocity (§ 487). 1,146 ft x 18 = 20,628 ft, the distance.— A ns. 2. 1,090 ft. + (2 ft x 15) = 1,120 ft, the velocity. See § 4'.'<.<. 3. In a transverse wave, the particles move across the line of propagation of the wave ; in a longitudinal wave, the particles move backward and forward in the line of propagation (§ 485). 4. 1,150 ft - 1,090 ft. = 60 ft. 60 ft. -j- 2 f t = 30, t he number of centigrade degrees above the freezing point (§ 489.)— A ns. 50 2 25 5. (8 494.) — : = — . It sounds about half as loud 7 70 8 49 to B as it does to A. 6. The velocity is 1,120 ft. The sound required 3 sec. to reach the cliff. 1,120 ft x 3 = 3,360 ft— Ans. 7. The velocity must be 1,100 ft. per sec. (§482.) This rekxaty implies a temperature of 5° C. 8. (§ 482.) 1,120 -~ 4 = 280, the number of vibra- tions ; 15° C. 9. 332 m. = 33,200 cm. 33,200 cm. ~- 830= 40 cm.— Ans. 10. 1,128 ft i 8 ft as 141 ; 1,128 ft. +• 12 ft. = 94. I mm 141 to 94 vibrations per sec. — Ans. 11. It took the sound ^ sec. to reach the cliff. The velocity of sound at the ordinary temperature of the air (15° C.) is 1,120 ft. ^ of 1,120 ft = 210 ft.— Ans. 194 [Elements of Natural Philosophy, p. 384.] § 505. See " Nature/' Vol. XVIII, p. 631, on the " Car- bon Telephone/' The " Scientific American Supplement," No. 142, tells "How to Make a Working Telephone." For further information concerning the various forms of tele- phones and historical accounts, see " The Speaking Tele- phone," by Prescott, the "Electrical World" (N. Y.) for April 10, 1886, and "Scientific American Supplements," Nos. 120, 128, 162, 163. Toy "telephones," in which sound waves are mechanically transmitted from one station to the other maybe bought for a dime. They may be made easily. See First Prin. Nat. Phil., Exp. 148. See Mayer on " Sound," Exp. 40. Also see the " Scientific American," Vol. XL, p. 282, and Dolbear's "The Tele- phone," pp. 80-82, and 103 et seq. The microphone is an instrument for detecting sounds otherwise inaudible. It is such an aid to hearing as the microscope is to seeing. Its action depends upon the principle involved in the carbon tele- phone, mentioned above, that the resistance of certain electric con- ductors is diminished by an increase of pressure. The microphone is placed, with a telephone, in the circuit of a galvanic battery, as shown in the figure. One of the simpler forms consists of a thin sounding-board, a b, set upright on a wooden base, cd. At one side of the sounding -boa; i, two horizontal metal arms, m n, carry two blocks of gas carbon, e i ; a rod of gas carbon, o, with pointed ends, is supported in cavities in the opposite faces of e and f. The arms, [Elements of Natural Philosophy, pp. SSj-JM.] 1""> m n, are fastened to a 6, by metal screws, communicating with the binding posts, d f, by means of wires on the other side of the sound- ing-board. By means of these screws, tin- arms may he hold in various positions on a 6 and held either firmly or loosely. The ire between e and t and the ends of o may thus be adjusted with considerable variety and delicacy. Sound waves falling upon n t, ntfW-t the pressure upon the ends of o and thus vary tin* resist- ance of the carbim portion of the circuit , that is, they produce rapid ions in the current passing through the microphone. These variations in the current cause corresj)onding vibrations in the dia- phragm of the telephone, T. In fact, the microphone and battery replace the transmitting telephone of the already familiar telephonic circuit. As long as the voice is the sole motive power of the apparatus, as is the case with the telephones, it is evident that what is heard at the receiving telephone must be fainter than what is sjokeu at the trans- mitting telephone (§ 165). But when, as in the case of the micro- phone, the energy of the voice is used merely as the means of regu- lating the strength of a current from a galvanic battery, there is no such necessary limitation to the intensity of the resulting sound. A small boy could hardly be expected to lift a son pile-driver twenty feel in aminute, but he may work the throttle- valve of an engine that will do it. The sensitiveness of the instrument is remarkable. The circuit being closed, the drawing of a fine i)encil-brash or a single hair over the surface of a b produces a sound that is very plainly audible. The one who draws the brush or hair hears nothing ; the listener at the telephone, in another room, may be startled by the sound he hears. It is said that three nails, placed in a circuit so that the ends of one, representing o, shall rest upon the ends of two representing vi e and n i, constitute a microphone. The microphone has been made so as to reproduce articulate sounds. See " Scientific American Supplements," Nos. 137, 163. '• T«» show the production of induced currents in a telephone and tln-ir physiological effect, attach the ends of the wires from a Bell nl.phone to the leg muscles of a frog (£ 408) and speak in the tele- phone. The pronouncing of the word 'sucker' causes the leg to move or ' jump ' while ' lie still ' has scarcely a perceptible effect." I & On tlie phonograph, see " Scientific American Sup- plements," Nos. 11$, 134, ami Miwr-m •• Sound," p. 170. I Bftfc See DolbeaPs " The Telephone," pp. 72-75. Many sounds may be transmitted by the same air, at the 196 [Elements of Natural Philosophy, p. 390, 391.] same time, without destroying or affecting each other. An orchestra of fifty pieces would probably send to the ear fifty series of sound waves, each different from the other in rate and amplitude of vibration, etc. Any attempt to imagine the resultant motion of any particular air particle due to these fifty separate forces would be bewildering. Yet, from this " aerial entanglement " the ear extracts order, and is able to detect and follow the sounds of any one instrument. Still we must remember that the ear may be stunned by a loud sound, so as to be unable to perceive a feeble one. It is sometimes impossible to hear the sound of a human voice amid a heavy storm ; but the sound of that voice exists. At the same time it is equally true that feeble sounds, no one of which has sufficient energy to awaken sensation, may accumulate upon each other, unite their forces, so to speak, and thus produce a confused sound, which commands the action of the auditory nerve ; e. g., the rustling of leaves, or " the hum of a whispering school." Tuning-forks (or diapasons) like those men- tioned in Exp. 5 require great care, as a little rust or a slight change in the elasticity of either one will change its rate of vibration. In such case, they must be tuned to unison again by an expert. After using the forks, wipe them with a woollen cloth moistened slightly with vaseline, wrap in woollen and lay away carefully. See Hand-Book note on § 722. § 510. The following beautiful experiment is due to Wheatstone : Stand a long wooden rod, an inch square, upon a music-box or the sounding-board of a piano. Let it pass freely through two ceilings above. In the second room above, on the end of the rod, place a violin. When the piano is played, the tremors are transmitted through the length of the rod to the violin and there become plainly audible throughout the room, although in the room below, between the piano and the violin, no sound is audible. See Daniell's " Principles of Physics," p. 379. [Element* of Natural Philosophy, pp. 393^397.] 197 Exp. S. — For a rope •.'•• !t. lung, a thickness of \ inch is enough. If an old rope can not be liad, the new one should be rolled up and beaten with a wooden mallet until it is quite x't't. Exp. 10. — The length of the air-column must be one- fourth the wave-length because the pulse started by the outward swing of the prong of the fork travels twice the length of the air-column in half a wave-period (§ 482). We know this from the reinforcement of sound that we hear. When the pulse has travelled the length of the air- column twice, it coincides with the effect of the prong as it swings in the opposite direction. If the pulse travels twice the length of the air-column in half a wave-period, ft travels once that length in a fourth of a wave-period. This is the Baying that the length of the air-column is one-fourth the wave-length. On the resonance of flames, see Harper's Magazine for March, is: it. p. 633. Also sec Dolbear's •• The Telephone," pp. 75-77. J 515. The accompanying figure represents a tube, i, dividing into two branches at c, and reuniting at c. and thenoe prolonged to o. The right-hand branch is so made that the part b n may slide over a b. When b is pushed up to a, the two branches, cm e and c n e, are of equal 108 [Elements of Natural Philosophy, pp. 395-405.] length. If a sounding tuning-fork be then held at i and the ear at o, the sound of the fork is distinctly heard, the waves that pass around by //?, and those that pass around by n, meeting at e in like phases. But when b n is drawn out (as shown in the figure) to a certain length, determined by trial, the sound of the fork is wholly destroyed. This length of a b will be one-fourth the wave-length of the particular fork used, for then the path of the waves pass- ing by n is half a wave-length greater than the path of the waves passing by m. The waves meet at e, in opposite phases, and a total interference is the result. The parts of the tube from c to i and from e to o should be so long that the sound transmitted directly by the air external to the tube is inaudible. If you cannot get such a tube, draw the figure on the black-board and explain to the pupils what it means. Ask them what they should expect when the distance, a b, equals a half wave-length and in what way this apparatus may be used to determine the wave- length of a tuning-fork. § 519 (b). See Frick's "Physical Technics," p. 172 (§ 146). Concerning longitudinal vibrations, see the next paragraph in Frick. § 523. See Dolbear's " The Telephone," p. 66. Multi- plying by 11 the numbers in the last line of § 521, gives the numbers of vibration for the octave when C has 264 vibrations. See DanielPs " Principles of Physics," p. 387. For description of methods of counting vibrations, see Deschanel's "Natural Philosophy," §§ 651, 652. § 524. Concerning the vibration of plates and nodal lines, see Deschanel's "Natural Philosophy," Fig. 565 and Mayer on " Sound," Exps. 27-31. § 525. See Frick's "Physical Technics," p. 165 (§ 136). § 529. The vibrations of the strings of musical instru- ments are usually compounded of several of these modes of vibration. To see how the string can thus vibrate is not easy ; it may help to think of ripples upon the waves [Fl> phi/, p. JOS.] 109 of the ocean. The Lower tones of the piano contain fptu or live harmonics blended with the fundamental, while in the violin there are still more. The tuning-fork is probaU v as free from harmonies as any known sonorous body. Any sound may be resolved into a combination of ele- mentary musical tones occurring simultaneously and in >ueces8ion. Hence, the study of musical sounds must necessarily form the basis of acoustics. See DanielFs • Principles of Physics," pp. 381, 382, 395-397. For a description of Lissajous' Experiment and Black- burn's pendulum, see DcschaneFs "Natural Philosophy," 76, f577, A. Also see Mayer on "Sound," chapters 1 V and XVII. Concerning manometric flames, see Desch- aitel'fl " Natural Philosophy," § 674. J5 530. " A wooden rod, when held in the middle, and rubbed half way between the middle and one end with chamois leather covered with powdered rosin, emits a musical note due to longitudinal vibra- tion of the rod. The rod, in fact, alternately stretches and contracts, the middle remaining stationary, while the two ends recede from it together and approach it together. The cross section at the middle is, therefore, a node and the ends are autinodes. " The time of a complete vibration is, just as in the case of u string or an open organ pipe, the time that a pulse would occupy in traveling over twice tin* length of tin- rod. Hence, from observing the pitch of the note emitted, the velocity with which longitudinal pulses travel along the rod can be inferred. For example, if the npte be Cof 512 vibrations persecondandthe length of the rod be 10 feet, a length of 20 feet is travelled over 512 times in a second and the velocity is 10,240 feet per second. This is one of the most con- \. ii. nt practical methods of determining the velocity of sound in solid bodies. ' The existence of nodes in a vibrating body is beautifully shown by firmly fixing a square plate of metal in the middle and bowing the with a well rosined double bass or violoncello bow. By varying the bowing, the plate can be made to give several distinct no:, if sand be sifted over the plate, it quickly settles on the nodal lines in each case. For the deepest tone, the nodal lines divide the plate into four equal squares. For the next tone, they divide it into four equal triangles. For some of the higher tones, they form very elabo- rate figures. To obtain any particular figure known to be among 200 [Elements of Natural Philosophy, pp. 405, 406.] those which the plate is capable of giving, the finger should be applied to one of the nodal lines of that figure and the bow should be applied about midway between two nodal lines." — Everett. If very light powder (e. g., lycopodium) be mixed with the sand, it will not move with the sand to the nodal lines but will form little heaps in the centres of the vibrating segments. These heaps will be in a state of violent agita~ tion with more or less of gyratory movement as long as the plate is vibrating. These motions are due to currents of air caused by the vibrations of the plate. In a vacuum, the powder will go, with the sand, to the nodal lines. The writing sand and sifting boxes sold by stationers are desirable for the above experiment with Chladni's plate. § 533. Let one side of an open organ pipe be made of glass. Stretch a membrane on a frame small enough to enter the pipe. Sprinkle some sand on the membrane and lower it into the pipe. The sand grains will exe- cute a lively dance with enough noise to be easily heard. When a tube, open at both ends, is held so as to surround a small hydrogen flame (see Ele- ments of Chemistry, § 21) a musi- cal tone is heard, which varies with the dimensions of the tube and often attains considerable [EUments of Katural Philosophy, pp. 4O6-4W.] 201 power. The sound is due to the vibration of the air and products of combustion within the open pipe. The vibra- tion is caused l»v alternate rising and falling of the flame. See Elements of Chemistry, Exp. 29. § 535, a. See Daniell's " Principles of Physics," p. 440. Note. — Concerning harmony and dissonance, see Darnell's "Prin- ciples of Physics," p. 437. Exercises, Page 408, 1. 144 x { = 180, the number of vibrations for its third. (§ 521.) 144 x f = 216, the number of vibrations for its fifth. 144 x 2 = 288, '• " " " " " octave. 2. Wave length =(1,120 ft. -h 512=) 2.1875 ft. (§ 482.) 2.1875 ft. -^ 2 = 1.09375 ft. (§ 533.)— Am. 3. See § 519, (1.). (a.) 50 vibrations, (b.) 200 vibra- tions. 4. i of i of 100 = 25.— Ans. 5. Ignore the number of vibrations and see § 519. G. (a.) 17£ft. (b.) ljin. (See second problem above.) 7. (a.) 2 ft. (b.) 1 ft. 8. (a.) 5 ft. (b.) 1,120 ft, ^ 5 ft. = 224, the number of waves started each second. The period of each wave is ¥ £j of a second. 9. Three beats per second. 10. (b.) 398 or 402 per second. 11. 320; 384; 512. li. 264 x 2 x i = 792. L'rciric fjtfcstions, Page 410, 5. (d.) See § 523. If the instrument be tuned to the pitch adopted by the English we shall have 204 x 2 x j = 880.— .! 202 [Elements of Natural Philosophy, pp. 4 10, 411.) 8. (a.) v = 144.72 ft.; 2 x 144.72 % 289.44.— ^«& 4000 2 (&) 20 lb. x ^* = 20 lb. x « = 20 lb. x | = 8| lb.— ^rcs. 10. (a.) See Fig. 116. The atmospheric pressure at B would equal that at A or at C. Gravity would draw the water in the long arm down to C,_ and that in the short arm down to A. The action of the siphon would be de- stroyed, (b.) The height to which the water could be raised (a b in Fig. 116) would be lessened because of the diminu- tion in atmospheric pressure, (c.) The liquid would rise through the atmosphere except what could be retained in the siphon above the level of the lower end of the shorter arm. 15. Strike a key of a piano ; strike it again with more i>rce. The tones differ in intensity. Strike a key of a piano; strike another key with equal force. The tones differ in pitch. Strike a key of a piano ; sound the same tone with equal loudness upon a flute. The tones differ in timbre. 18. v = 8.02 Vh. The velocity of the jet is 56.14 ft. or 673.68 in. The quantity of water discharged per second is 1347.36 cu. in. The quantity of water discharged in 3600 seconds is 4850496 cu. in., or 20997 gal. 189 cu. in — Ans. 23. (a.) During the 6 seconds it falls 578.88 ft. " " first 4 seconds it falls 257.28 ft. erature of boiling water or any higher temperature, an abrupt subpermanent enlargement of the bulb is produced and the freezing point is found to be lowered. Then again, for weeks And months and years, there is a gradual shrinkage as shown by a gradml rising of the freezing point (? 543). A very delicate mer- : ury thermometer that has been kept for years at ordinary atmos- pheric pressures when out of use and never, when in experimental \ posed to any temperature higher than 30° C or much lower than C. becomes very constant and may not show any change of as much as 0.1° C. within the rang' from — 20' C. to 40° C. But the abrupt and irregular changes produced by exposing the ther- mometer to temperatures much above or much below some such limited range as that, constitute a very serious difficulty in the way urate thermometry by the mercury-in-glass thermometer. cJee M Encyclopaedia Britannica," § 19 of Article " Heat." I-'..r HiiijM raimvs below the freezing point of mercury (— 89.4° C), alcohol thermometers are generally need. Per v. tv high temperatures, pyrometers and other instru- ments are used. One form of pyrometer ia described on the ii' Thermometers used to register the hL or the lowest temperature within a given period are called registering thermometers. They are of two classes. If the tube of amerury thermometer be sufficiently eouirarted just the bulb and the tube pined In i horizontal position, mercury 208 {Elements of Natural Philosophy, pp. J/.13, 417.] will be pushed through the neck when the temperature rises and fails to return when the temperature subsequently falls. The mercury thus left in the tube serves as an index to show the highest tempera- ture reached during the time of exposure. Such an instrument is -palled a maximum tliermometer. It is readjusted for a subsequent observation by bringing it into a vertical position. Alcohol is used in the minimum thermometer. The horizontal tube contains an index of glass which is of less diameter than the bore of the tube. The instrument is adjusted for use by bringing the index into contact with the end of the alcohol column in the tube. When the alcohol expands, part of it flows by the index without moving it. When the temperature falls, the index adheres to the end of the receding alcohol column and is drawn after it into a posi- tion that indicates the minimum temperature reached during the period of exposure. See Deschanel's "Natural Philosophy," §§ 178-193. § 548. The increase in length of a linear unit of a solid body when it is heated from 0° C. to 1° C, is called the co- efficient of linear expansion for that substance. For homo- geneous solids, the coefficient of voluminal expansion is three times the coefficient of linear expansion. The expansion of a liquid may be absolute (i. e. , its real increase in volume) or apparent (i. e., its increase in volume relative to the increase in the capacity of the containing vessel). For example, the absolute expansion of mercury in a thermometer is greater than its apparent expansion. The determination of the coefficient of expan- sion of mercury is of great importance because this liquid is used for so many purposes in scientific investigation, bee Deschanel's " Natural Philosophy," §§ 177 (2) ; 194-201. § 549. Linear expansion may be shown by the pyrometer, an instrument represented in the figure. One end of the metallic rod, A, is fastened at B, while the other end passes freely through the post, C, and presses against the short arm of the lever, P. The long arm of the lever forms a pointer which, by moving over the graduated arc, renders visible any change in the length of A. The rate of expansion for the rod being known, the pyrometer may be used (as its name indicate*) to measure temperatures. [Elements of Natural Philosophy, pp. 417, 41$.'] 209 See First Prin. Nat. Phil., Exp. 173; "Nature," Vol. 35, p. 89; Deschancl's "Natural Philosophy," §§ 202-205. § 550. The experiment with the brass and iron bar may be represented by placing a thin card of gelatine on tbe palm of the hand. The gelatine being a poor conductor; the under surface becomes the warmer and expands the more, thus bending the edges upward. When thick glass- ware is strongly heated, it tends to bend in a similar way, but as it has little flexibility, the tendency often results in breakage. (a.) The now common incandescence electric lamps may be used for the illustration of this fact. § 552. See Frick's " Physical Technics," p. 413 (§ 347) and Deschanel's "Natural Philosophy," §§ 206-216. * When heat is applied to a body, it increases the kinetic energy of the molecules (raises the temperature), and increases the potential energy by forcing the molecules further apart against their mutual attractions and any external forces that may resist expansion. Since the internal work to be done when a solid or liquid expands varies greatly for different substances, it would be expected that the amount Of »*xpansion for a given rise of temperature would vary greatly."— Anthony and Brackett. 210 [Elements of Natural Philosophy, pp. 420, 421.] § 555. See First Prin. Nat. Phil, Exps. 174, 176 ; also Deschanel's "Natural Philosophy," §§ 177 (3) ; 217-224. § 557. " If air be substituted for mercury in the thermometer and means provided for maintaining its volume constant and measuring- its pressure, the instrument becomes an air thermometer. The air thermometer is taken as the standard instrument for scientific pur- poses. Its use, however, involves several careful observations and tedious computations. It is, therefore, mainly employed as an in- strument with which to compare other instruments. By making such a comparison and constructing a table of corrections, the read* mgs of any thermometer may be reduced to the corresponding read- ings of the air thermometer." — Anthony and Brackett. § 558. When we double the kinetic molecular energy of a body we double its absolute temperature. [Elements of Natural Philosophy.] 211 Eocercise*, Page 423. 1. 273 : 273 + 30 = 900 : x ; .-. x = 998.9. 2. 273 + 10 : 273 = 170 : x ; .\ x = 164—. 3. 273 : 373 = 1,000 : x ; .\ x = 1,366.3. 4. 288 : 323 = x : 15,000 ; .-. x — 13,374.6. 5. 185° F. = 85° C. (§546.) 358 : 283 = 98 : x ; .-. x = 77.4 + . 6. (§ 557.) 490 : 500 = 1,000 : x ; .: x = 980. 7. 283:291.7) __ , .. _ , 590:530 [ = lo5 : * ; •'****«■•»** 8. 273 : 333 = 231 : z; .-. a: = 281.7 + . °. The 20 cu. ft. or 34,560 cu. in. of air weighs 10,713.6 grams. (§272.) _ + _=_ = -. The balloon full of heated air will weigh |f °f 10,713.6 gr.; the weight thus supported will be Jf of 10,713.6 gr. = 1,847-1- gr. 10. f of 36 = 20. Ans., 20° C. 11. | of 35 = 63. Aiut., 63° F. 12. (a.) 20° C. (b.) 68° F. 273 + 30 1,109,890 13. 273 ~~ 1,000,000 1 . 373 x 1,013,600 1,385 14 ^73-x-Tooo^oo = i^oo • the number of llters - 212 [Elements of Natural Philosophy, p. 4££.] § 560. The effects of an increase of heat in a body are partly internal work and partly external work. The internal ivork may be to increase the kinetic energy of the molecules, i. e., to raise the temperature ; to work a change of volume, cohesion, elasticity, etc., such work being dono by or against the molecular forces ; to produce vibrations within the several molecules ; and to work chemical changes. The external work is done by or on a body as it expands or shrinks. Suppose an iron bar to be heated in a vacuum. The work done by the heat is two-fold ; an increase of tempera- ture and expansion. The expansion represents work done against the molecular forces. When the same bar is heated in the air, the work done is three-fold. The two kinds oi internal work done in the former case are repeated and external work is added, for the surrounding atmosphere is pushed back by the expanding iron. In this case, the external work is relatively very small. Suppose a given quantity of a gas to be heated. Very little work is done against the molecular forces in expand- ing the gas (§§ 57, 62), the work done being chiefly two- fold, namely, the internal work of raising the temperature and the external work of. overcoming the atmospheric (or other) pressure. Suppose water above the temperature of 4° C. to be heated. It expands (§ 553). The work done by the heat is three-fold, namely, the internal work of raising the tem- perature and separating the molecules to a greater dis- tance from each other (expansion) and the small amount of external work involved in pushing back the atmosphere. Now suppose that water at 0° 0. is heated to 3° C. It contracts. The heat works an elevation of temperature ; internal work is done by the molecular forces in crowding the molecules nearer together. External work is also done by the atmospheric pressure. In the process of liquefaction, nearly all of the work is [Elements of Natural Philosophy, pp. 424-426.] 213 internal and ia spent in producing ■ new arrangement of the molecules. If expansion accompanies the liqoeiaction (as is usually the case), externa] wmk i> done and addi- tional heat is needed. If contraction is the accompaniment (as in the case of melting ice), external work is done by the atmospheric pressure and less heat energy is needed. This indicates that the freezing point of water is low by pressure. § 5C2. Some substances, when heated, decompose 1»< melting. Under certain conditions, a liquid may be cooled below the melting point without solidifying (§ 588). Some alloys melt at a lower temperature than any of their con- stituents ; e.g., an alloy of tin. had. bismuth and cadmium melts at 62° C. M. " There are many reasons for believing that the molecules of solids and liquids are in a state of continual motion. It can easily be supposed, that, at the "exposed surface of the substance, the motion of a molecule may at times be so violent as to project it be- yond the reach of the mutual attractions. If this occur in the air or in a space filled with any gas, the molecule may bo turned back and made to rejoin the molecules in the liquid mass ; but many will find their way to such a distance that they will not return. They then constitute a vapor of the substance. As the number of free molecules in the space above tin- liquid increases, it is plain that then may come ■ time when as many will rejoin the liquid asescape from it. The space is then saturated with the vapor. The more violent the motion in the Liquid, i. 6., the higher its temperature, the more rapidly will the molecules escape, and the greater must be the Dumber la the space above the liquid before the returning will equal the outgoing molecules. In other words, the higher the tem|>craturp, the mon- dene • the vapor that saturates ■ given space. If the space above a liquid be a vacuum, the escaping molecules will at first meet with no obstruction and, as a consequence, the space will lx- very quickly saturated with the vapor." — Anthony erature to rise above the ordinary boiling point. Experiments upon liquids in spaces but little larger than their own volumes show that, at a certain temperature, the liquid suddenly disappears ; thai is, it is converted into vaj>or in a space but little larpr th;m it- own volume. It is supposed, that above the temperature at winch this occurs, which is called the critical temperature, the substance cannot exist in the liquid state." — Anthony and Brackett. § 570. The same principle may be illustrated by the ap- paratus represented in the accompanying figure. The receiver, R, having been exhausted with an air-pump, is closed by the stop- cock, ft. The flask, F 9 is half full of water and heated by a lamp placed beneath. As the water boils, tin- steam escapes through the open stop-cocks, a and c. When the steam has i \pelled the air from /■'. (lose a and c, removing the lamp at the same time. The water gradually cools and ceases to boil. Water may be dashed over Fmd the water made to boil as in the last experiment. When this has been done a few times, the water may be allowed to come to rest. It will be several degrees below the boiling point. Opening a and ft, the \apor of F escapes into R and the water begins to boil vigorously. By keeping R cool, the water in ^Fmay be made to boil for a considerable time. § 573. " If a liquid be introduced into a highly heated capsule, of poured upon a very hot plate, it does not wet the heated surface, but forms a flattened spheroid, which presents no appearance of boiling hut i-vaporates very slowly. The temperature of the spheroid is below the boiling point of the liquid. The spheroid does not touch 216 [Elements of Natural Philosophy, p. 432.] the heated plate but is separated from it by a non-conducting layer of vapor. This accounts for the slowness of the evaporation. To maintain the spheroid, the temperature of the capsule must be much above the boiling point of the liquid ; for water, it must be at least 200° C. If the capsule be allowed to cool, the temperature will soon fall below the limit necessary to maintain the spheroid, the liquid will moisten it and there will be a rapid ebullition, with disengage- ment of a large amount of vapor." Hence many disastrous steam boiler explosions. Water in the condition now described is said to be in the sphe- roidal state. " If a surface be heated, a molecule of gas striking against it is "heated ; it leaves the hot surface with a velocity greater than that with which it had approached it. If the surface be fixed, the gas in front of it is driven away from it by the bombardment of the mole- cules which have touched the hot surface and, on their return, strike their fellow molecules ; in front of the hot surface, the gas is, there- fore, under a greater pressure than it would have been had the sur- face been cold. * * * A layer of particles in such a condition is called a Crookes's layer. * * * The layer of aqueous vapor be- tween water in the spheroidal state and the heated surface is a Crookes's layer ' ; particles strike the heated surface, rebound and rtrike the liquid, thus maintaining a clear space between the metal and the drop! Ether and small drops of bromine float in the same way on the surface of hot water. A lump of carbonate of ammonia thrown into a red-hot platinum crucible assumes the spheroidal state superficially but does not melt. The hand can be safely immersed in melted metal if it be not too dry and if the immersion be effected with a certain degree of prompt deliberation ; a Crookes's layer of water vapor intervenes between the hand and the metal. " When liquid sulphurous acid is dropped into a white-hot plati- num crucible, it sinks greatly in temperature on account of its rapid evaporation and its slow reception of heat across the Crookes's layer ; if a little water be added to it, the water freezes. Ice can thus be produced in a white hot platinum crucible. A similar Crookes's layer is formed if a quantity of solid carbonic dioxide be lightly placed on the tongue ; the extreme cold (— 80° C.) is not felt. When the hot solid body cools down, the Crookes's layer disappears, the liquid suddenly comes in contact with the solid, still relatively hot, and the liquid explodes in vapor. This occurs, in the case of water and iron, at about 180° C." — Daniell. [Elements of Natural Philosophy, pp. J&S-ML] 217 § 576. See First Prin. Nat. Phil, Exp. 181. § 579. A lesser calorie is sometimes called a millecalorio or a water-gram-centigrade unit. Another heat unit has been proposed, viz., the Electro- magnetic Unit. This is the amount of heat developed in one second in an electrical circuit of one ohm's resi.st;m< m by a one ampere current. It is called & joule and is e< called regolatint and depends u|H>n the lowering of the Pn 1> >int by pressure. If heavy weights be hung at each end of a wim hanging over a block of ice, the wire will slowly cut it* way tin 218 [Elements of Natural Philosophy, pp. 441, 442^ the ice, regelation closing the cut behind the slowly advancing wire so that at the end of the experiment, the ice is still one solid block as at first. The pressure brought the freezing point of the particles beneath the wire below the temperature of the ice. Consequently, they melted. The liquid particles passed above the wire, where (there being no pressure from the wire) the freezing point was higher than the temperature of the liquid particles which are even colder than the block of ice from which they were liquefied. They, there- fore, froze again, firmly uniting the two parts of the block. See Deschanel's " Natural Philosophy," §§ 238, 239. § 591. If a liquid be heated, under pressure, to a tem- perature above its ordinary boiling point (§ 569), there is a rapid production of vapor and remarkable lowering of the temperature, when part or all of the pressure is removed. Liquid nitrous oxide (N 2 0) at 0° C. is still far above its boiling point and its vapor exerts a pressure of about 30 atmospheres (§ 277). If this liquid be drawn off into an open vessel, it boils with extreme violence but is soon cooled to its boiling point for the atmospheric pressure (— 88° C.) and then boils away slowly while its tempera- ture remains at that low point. See Elements of Chem- istry, § 80. In any case, the formation of vapor is work and, there- fore, requires the expenditure of energy. Whenever a molecule is shot off from the exposed surface of a liquid and thus passes beyond the attraction of the molecules left behind (see Hand-Book note on § 564), it obtains its motion from the energy of the liquid mass and keeps it at its expense. Thus, as the vaporization goes on, the departure of each succeeding molecule robs the still liquid mass of part of its molecular energy, lessens its heat and lowers its temperature. See First Prin. Nat. Phil, Exps. 187, 189, 190. § 592. " Only a certain amount of vapor can exist in a given space at a given temperature (see note on § 564). If a space saturated with vapor be cooled, some of the vapor must condense into the liquid state. Any diminution of the space occupied by a saturated vapor will cause some of the vapor to become liquid for, if it do not [Elements of Natural Philosophy, pp. U?-446.] 219 condense, its density and pressure must increase ; but a saturated vapor is already at its maximum density and pressure " If the vapor in a given space be not at its maximum density, its ue will increase when its volume is diminished until the max- imum pressure is reached; when, if the temperature remain con- stant, further reduction of volume causes condensation into the liquid state without further increase of density or pressure. This i nt is true of several of the gases at ordinary temperatures. Cblodne, sulphurous acid (SO.), ammonia, nitrous oxide (N g 0), car- bonic acid (C0 2 ) and several other gases become liquid under suffi- «i tot pressure. At a temperature of 30.92 C, pressure ceases to liquefy carbonic acid. This is the critical temptrature for that sub- stance. The critical temperatures of oxygen, hydrogen and tin; other so called 'permanent gases' are so low that it is only by methods capable of yielding an extremely low temperature, com- bined with great pressure, that they can be liquefied. By the use of such methods, any of the gases may be made to assume the liquid state." — Anthony and Brack) tt. See Daniell's "Principles of Physics," p. 217. § 593. Liquefaction is work and requires the expendi- ture of energy. The quantity of thermal euergy required to melt a unit mass of a substance is the heat equivalent of fusion of that substance. See Friers " Physical Technics," p. 416. § 594. See Frick's " Physical Technics," p. 437, and Deschanel's "Natural Philosophy," § 349. § 597. " The specific heat of substances is not perfectly constant at all temperatures. Therefore, there is a necessity of the qualifica- tion, ' from 0° C. to 1° C This want of constancy is, among gases, most remarkable in those which are most condensible ; but among solids and liquids the variations of specific heat are still more re- markable and indicate differences in the amount of internal work associated with changes of temperature at different temperature, this internal work being done in effecting changes in the density, the intermolecular stresses, the allotropic form, and so on." — DanieU. The specific heat of a body may, where both the increments are small, be found by dividing the number of calories supplied to unit- by the increment of temperature produced. § 598. See Deschanel's "Natural Philosophy," §§ 343, :*44 aud Daniell's "Principles of Physics," p. 372. 220 [Elements of Natural Philosophy, pp. 446-448.] § 600. The following is known as Dulong and Petit's Law of Atomic Heat : The product of the specific heat by the atomic weight of any elementary substance is a constant quantity, or To raise the temperature of an atom of any element one degree requires an amount of heat which is the same for all elements. This law may be extended to compound bodies. For all compounds of similar chemical composition, the product of the total chemical equivalent by the specific heat is the same. (a.) The variations in the last column of the following table are within the limits of experimental error. ± .„„„„ SPECIFIC ATOMIC WEIGHT. -^ -_ elements. HEAT (See Chemistry.) PR °DUCT. Iron 0.114 55.9 6.372 Copper .. 0.095 63.17 6.001 Mercury 0.0314 (solid) 199.71 6. 128 Silver 0.057 107.067 6.137 Gold 0.0329 196.15 6.453 Tin 0.056 117.7 6.591 Lead 0.0314 206.47 6.483 Zinc 0.0955 64.9 6.198 (b.) " This product (the atomic heat of elements ; the molecular heat of compounds) has this physical meaning : Of any substance, whose atomic or molecular weight we know, we may take a number of grams numerically equal to the atomic or molecular weight ; e. g., 35.5 grams of chlorine or 16 grams of marsh gas; we may call such a quantity the gram-atom or the gram-molecule of the substance. The atomic heat or the molecular heat of a substance is the number of lesser calories of heat necessary to raise the temperature of a gram-atom or a gram-molecule of the substance through 1° C. * * * The specific heat of a substance determines the temperature which it will assume when a definite quantity of heat is supplied to it or liberated in it." — DanieU. Exercises, Page 448, 1. Find the number of calories (§ 579) that may be furnished by the several quantities of water in cooling to any given temperature, as 0° C. [Elements of JRtfml Philosophy, p. U9-] 221 1 Kg. at 40° gives 40 heat units. 2 " " 30° * GO " " 3 " " 20° 4< 60 " " 4 « " 10° " 40 " " 10 " " 200 " " These 200 heat units would warm the 10 Kg. of water 20° above the given temperature or to 20° C. It Qwkefl no difference what tempera lure be chosen for the reduc- tion. If, e. g., we try a temperature of 10° C, we shall have (30 + 40 + 30 + =) 100 heat units. This quan- tity of heat will warm 10 Kg. of water 10° above the chosen temperature or to 20° C. If a still higher temperature be chosen for the reduction and care being given to the algebraic signs, the result will still be the same. 2. (See § 598.) 19.366 x = 0.634; x = .0327 + . Ans. 3. (See § 595 [2.]) 85 x = 80 x 15; x = 14.117+. Aiis. 4. The specific heat of ice being 0.5 (§ 600 [2.]), it will require 50 heat units to warm the ice to the melting point It will require 800 more to melt it. 95 x = 850 ; x = $.M.—A7is. 5. The specific heat of steam is 0.48. Each pound of steam, in cooling to 100° C, would yield 12 heat units. These, with the heat from condensation and cooling to 25° C. would yield (12 + 537 + 75 =) 624 heat units. The required quantity of steam must furnish 624 x heat units. To warm the ice to 0° C, will require 20 heat units. This, with the heat required for fusion and warm- ing the melted ice to 25° 01, amounts to 545 heat units. 624 x = 545 ; x = .87 + .— An*. 6. There will be (48 + 537 + 80 =) 665 heat units furnished by the steam. Each Kg. of mercury will require (10 x .0333 =) .333 heat units. 0.333 x = 665; x = 1997.— Ans. 222 [Elements of Natural Philosophy, pp. 448, 449.] 7. (See § 593.) 80° C.—Ans. 8. Let x = the temperature. Then, 80 + x = 10 (20 — a?)j x — 10.9 + .— Ans. 9. The water can furnish 60 heat units for melting ice. This will melt £ of a pound of ice. The result will be \ lb. ice and of lb. of ice cold water. 10. The steam can furnish 6370 heat units in cooling to 0° 0. This heat must warm 1010 g. of water and can raise it to (6370 -j- 1010 ==) 6.3°+ C.— Ans. Or, we may let x represent the temperature. Then 10(637 — x) = 1000 a;; x = 6.3° + . 12. (See § 598.) Iron. Water. Specific Heat, 0.1138 Weights, 200. Change of temperature, 300 — x 1. 1000. x 6828 - 22.76 x = 1000 x x= 6.67 + . Ans., 6.67°+ C. 13. Ans., 0.31 + . 14. .0952 x 300(100 — x) = .505 x 700 x ; x = 7.47 + . Ans,, 7.47° 0. 15. To melt the snow will require 400 heat units (ounce- centigrade). The water can furnish 460 such heat units for melting snow. Hence, the snow will be melted and the water warmed. 5(80 + x) = 23(20 — x) ; x = 2.14 + . Ans., 2.14° C. 1 6. The warm water gave up 50 heat units. As the snow was wet, its temperature must have been 0° C. (§ 543.) Let x represent the weight of the snow, and 1 — x the weight of the water that made the snow wet. To melt the snow and warm it to 10° C, required 90 x heat units. To warm the water, required 10(1 — x) heat units. Then, 90 x + 10(1 — x) = 50 ; x = J, The "wet snow" was half snow and half water. — Ans. Proof. — The half pound of snow would require 40 heat [Elements of Natural PJUUmphy, p. 449.] 223 Tinits to melt it The pound of water would then require 10 heat units to warm it to 10° C. The total of heat energy required is (40 -f 10 =) 50 units. This is exactly the amount furnished by 5 lb. of water in cooling from 20° C. to 10° C. 17. 150 x 299 x .0314 = .0333a;; x = 42,291 +, the number of grams of mercury. — Ans, 18. The water can furnish 350 heat units for melting the snow. This will melt (350 -v- 80 =) 4.375 lb. of snow. The result will be 1J lb. of snow in 11 J lb. of ice cold water. 22 4 [Elements of Natural Philosophy, pp. 450-452.'] § 603. See Daniell's "Principles of Physics," p. 373. § 604. Conductometers are instruments for illustrating differences in thermal conductivity. The conductometer of Ingenhaus, represented in the figure, consists of a hot water vessel with handle and pro- jecting rods of different metals. These rods are coated with wax. The distances to which the wax melts on the several rods indicate their relative conductivity. An- other form of conduct6meter con- sists of a metal ring from which radiate rods of various metals and other substances, as glass, slate, etc. The extremities of these rods have little cavities in which bits of phosphorus are placed. The ring is placed around the flame of a lamp, heat is conducted along the rods and ignites the phos- phorus in the good conductors and fails to do so in the poor conductors. See " Science Lectures at South Ken- sington," Vol. II, Lecture 2 ; DeschaneFs "Natural Phi- losophy," §§ 328-338 and Daniell's " Principles of Physics," p. 375. § 605. The low conductivity of liquids may be illustrated with the apparatus shown in Fig. 291. See First Prin. Nat. Phil., § 394. Mercury is a good liquid conductor of heat. It is a metal. Hydrogen is the best known gaseous conductor. Many chemists think that hydrogen is a metal. § 606. For the purpose of exhibiting convection currents, the apparatus shown in Fig. 291 may be used, the jacket, C, being carefully filled with hot water. Fill a half liter (or a pint) Florence flask with hot water colored with ink or indigo. Provide a perforated cork carrying a short tube about half a centimeter in diameter. Covering this tube with a finger, hold the flask at the bot- [Elements of Natural Philosophy, pp. 452-454.] 225 torn of a deep pail of water. When the finger is removed from the tube, convection currents may be seen. They will continue for some considerable time. If the flask be held mouth downward, there will be no convection currents. § 608. The theory of a luminiferous ether is generally accepted by physicists. J. D. Everett, Professor of Nat- ural Philosophy at Queen's College, Belfast, says that the existence of this ether "is now universally accepted by physicists." See DauielPs "Principles of Physics," pp. 218, 219 and "Encyclopaedia Britannica," article Ether. On the other side of the question, see Judge Stallo's u Con- cepts and Theories of Modern Physics," pp. 112 et seq. § G10. See First Prin. Nat. Phil, Exp. 202 and § 397 a. When the iron poker is very hot, its energetic molecular vibrations produce ether waves of varying lengths and frequencies of vibration. Some of these waves are of such a length that they constitute obscure heat rays (§§ 617, 718), by means of which the poker's warmth may be felt at a distance ; others are of such a length that they constitute luminous rays (§ 717), by means of which the poker is visible ; still others are so short and quick that they con- stitute actinic or ultra-violet rays (§ 719) and by the aid of these, the iron may be photographed. If the iron be intensely hot, it may emit so great a proportion of violet and blue light (short waves) that the poker may be called Ci blue-hot." As the poker cools, the more rapid vibrations of the iron molecules cease and the ultra-violet ether waves are no longer produced ; the poker thus becomes less easy to photograph by its own radiations. Gradually, the violet avfl eease to be emitted and the colorchanges (§ 717), the change of color continuing as rays of increasing wave li are successively dropped from the train of waves sent out until finally, about the time when the temperature sink- below 525° C, it ceases to radiate light and disap- pears from sight into the darkness. But the longer and 226 [Elements of Natural Philosophy, pp. 454-4S9.] less rapid waves that constitute obscure heat are still emitted and may be felt for some time by the cooler hand held near it. In fact, it never ceases to radiate heat and can not do so until its temperature falls to the absolute zero (§ 558). § 617. See First Prin. Nat Phil., Exp. 203 ; also Desch- anel's "Natural Philosophy," §§ 322-324. § 618. See § 625 and Deschanel's "Natural Philosophy," § 326. At the April (1886) meeting of the National Academy of Sciences, held at Washington, Prof. Alfred M. Mayer stated that he had obtained foci of dark rays with a combination of thin lenses of ebonite, but the heat of such foci was not sufficient to inflame substances. From this, it appears that ebonite is diathermanous for obscure heat. § 619. See First Prin. Nat. Phil, Exp. 205. §620. See Deschanel's "Natural Philosophy," §§310, 311. § 621. See First Prin. Nat. Phil, Exp. 204. § 622. When two bodies are placed opposite each other with the intervening ether (of which we cannot get rid whether air be present or not) one of two cases may present itself : (1.) Both may be of the same temperature, in which case one loses by radiation to the other just as much energy as it gains from the radiation of that other. As the two bodies exchange radiant energy to the same extent, there is no change in their relative temperatures. (2.) One may be hotter than the other. Then one radiates a more energetic system of ether waves than the cooler one can and thus loses more energy to the other than it gains from that source. Consequently, their tem- peratures finally become equal, after which the exchange of energy continues on equal terms for both, neither [Elements of Natural Philosophy, pp. 469, 4';o.] 22? profiting by the exchange and the temperatures of both remaining relatively the same. Not only does the fire warm the room ; the room also warms the fire. The sun warms the earth and the earth, to a less extent, warms the sun. The warming of a colder body by a hotter one depends upon the difference of two similar but unequally opposed actions. This law, that bodies are always radiating and receiving energy ; that the amount of radiation depends upon the temperature of the radiating body and that when the temperature of a body is constant, it is receiving as much energy as it is radiating, is known as Prevost's Law of Exchanges. § 623. SeeDeschanel's "Natural Philosophy," §§313-321. § 624. See First Prin. Nat. Phil, Exp. 206 and Hand- Book note on § 7tZ. § 625. On the subject of the note following this para- graph, see Deschaners "Natural Philosophy," §325 and Tait's " Light," Chap. XVI. 228 [Elements of Natural Philosophy.'] Questions, Page 401. 1. Because our bodily sensations of warmth and cold depend largely on the rapidity with which heat is conveyed to the body or from it. See § 540. 2. Because the watery vapor in the atmosphere, being diathermanous to luminous heat (§ 618), allows the sun's rays to pass freely. These rays heat the surface of the earth, which then radiates obscure heat. The same watery vapor is athermanous to these rays and prevents their out- ward passage. The vapor thus acts as a trap in which the heat is caught. 3. The clouds act as a blanket to shut in the earth's obscure rays and thus keep it warm. 4. See § 624. 5. The glass acts as did the watery vapor mentioned in Question 2 above. 6. Step on them with bare feet in a cold room and you will soon see that the oil-cloth and linen are the better conductors. 7. Sawdust, with its air-filled spaces, is a good non- conductor of heat. So are plaster-of-Paris and alum. 8. The woollen being a poor conductor, tends to keep the intense heat from the bodies of the workmen. The double windows inclose a layer of non-conducting air. 9. The surface of the earth is heated chiefly by radia- tion ; the atmosphere, by convection. See § 605, a. [Elements of Natural Philosophy, p. 4G2.] 229 § 627. Crookes's Radiometer is an instrument for con- verting the energy of heat (generally derived from lumin- ous rays) into the energy of mechanical work. It consists of a glass globe, containing a high vacuum and carrying a vertical needle axis " on the summit of which is poised a rotating vane consisting of light rods to the extremities of which discs are fixed, each similarly blackened on one side." Such an instrument, placed in light, has the black- ened sides of its discs more heated than the unblackened sides (§ 623) ; if the radiant energy be sufficient, the vane rotates. Read the quotation from Daniell in the Hand- Book note on § 573. In that case, the heated surface was supposed fixed. Here the heated surface (the blackened discs) is not fixed and, reaction being equal to action and in the opposite direction, the tendency is to drive tin- heated surface or discs backward, thus producing rotation. ■ If the hot surface be the front aspect of a disc, the back of which is, by some means, kept cooler than the front, and if this disc be suspended in a gas, the heat of the front surface increases the pressure toward the front and the gas flows round to the back of the disc. Thereafter, the disc is struck on the hotter surface by fewer molecules with greater velocities; on the colder surface by a greater number of molecules with lesser velocities ; thus there is compensa- tion ; the result is that the disc is equally pressed upon in front and on the back ; it does not move. " Let us now suppose that the particles recoiling from the heated surface do not meet other (gaseous) molecules but impinge on the walls of the vessel. A layer of such particles is a Crookes's layer. This will occur when the gas is so rarified that the mean, free path of the molecules (§ 62) exceeds the distance between the hot surface and the walls of the vessel In such a case there is no flow of gas from the hotter surface toward the colder one : each molecule which strikes the hotter surface and rebounds with a greater speed adds independently to the recoil which the hotter surface suffers and, if the hotter surface be movable, it is driven backwards. * * When the distance between the discs and the opposite wall is excessively small, the exhaustion need not be very good; indeed, the effect <>f repulsion may be made manifest even in the open air. * * Too complete a rarefaction is not an advantage, for it leaves an insufficient supply of working molecules." — Daniell. 230 {Elements of Natural Philosophy, pp. 463-466.] § 629. See Deschanel's " Natural Philosophy," § 356. § 630. See Deschanel's "Natural Philosophy," § 357 A. The second law of thermodynamics is as follows : When heat is converted into work, under the conditions that exist on the earth's surface, only a small part of the heat drawn from the source can be transformed. The rest is given to a refrigerator which, in some form, must be an adjunct of every heat engine. This still exists as heat and is wasted as far as any useful effect is concerned. § 631. The experiments of Count Rumford (see page 206) showed that heat is transformed mechanical energy, but it was important to show that the heat evolved is always proportional to the mechanical energy expended. Joule worked to this end from 1842 to 1849. By means of weights, he revolved paddle-wheels in a vessel of water. Stationary wings prevented the water from taking a rotary motion with the paddle-wheels. In this way, the water was warmed. The heat evolved was determined from the rise of temperature ; the energy expended, by the fall of the weights. The experiment was varied by using mercury instead of water and by revolving an iron plate upon a fixed iron plate under water. The results are remarkably concordant and indicate 424 kilogrammeters per calorie. See Deschanel's "Natural Philosophy," § 357. A kilogrammeter equals 98,000,000 ergs. See Hand- Book note on § 154. Then, the dynamical equivalent of a calorie (424 kilogrammeters) is 424 times 98,000,000 ergs or 41,552,000,000 ergs as stated in the text-book. § 633. See Firrt Prin. Nat Phil, § 410. §634. See Deschanel's "Natural Philosophy," §§ 351, 359, 360 and Tait's "Heat," §§ 45-48. At very high temperatures, compound substances are separated into their elements. To effect this separation, the powerful forces of chemical affinity must be overcome and a considerable amount of energy must be consumed* [FJtuunt* $f Natural PkiJ M dpky, j>]>. \B6-f71.'] 231 The principle <>f toe oo mw t valU n) oi eneigy naturally leads us tosupppSfl that this separation (called dissociation) requires an expenditure of energy equal to that evolved in their chemical union, I. e., that the dissociation of one kilogram of water, for example, into its elements, oxygen and hydrogen (see Elem. of Chem., § 40) would require the expenditure of 34,462 calo- ries or an equivalent <>f about 14,611,888 kilogram meters. § 636. The accompanying figure represents a piece of apparatus illustrative of the single acting engine. It consists of a metal globe, with cylinder, piston and rod, and handle. The globe is to be partly filled with water and held over a lamp. The pressure of the steam thus generated will raise the piston. Remove the globe from the lamp and throw upon it some cold water. The steam is quickly condensed and atmospheric pressure forces the piston back with vigor. Candle bombs, which may be had of J. W. Queen & Co., at a pmall price, afford the means of illustrating, in a peculiarly striking manner, the convertibility of heat energy into mechanical energy. § 637. See Frick's " Physical Technics," p. 439 (§ 367). § 639. A model of the centrifugal governor may be used with the whirling table (Fig. 7). See Frick's " Physical Technics," p. 142. § 642. The water, air and other contents of the con- denser are removed by an " air pump." Thus, part of the energy saved is expended in maintaining the vacuum. § 643. The combustion of 100 lb. of coal yields 808,000 heat unite, equivalent fco L, 123,436; 000 foot-pounds. An engine at the Buffalo Water Works, which is considered very economical, developed a power of 80 t 48&,638 foot- pounds, per 100 lb. of 00ft] burned. For full information upon the steam-engine, see Thurston's " The Growth of 232 [Elements of Natural Philosophy, p. ^7i.] the Steam-Engine. " With any safe boiler pressure, it is impossible, even with a perfect engine, to convert into work more than about 15 per cent, of the heat used. Concerning the "perfect engine," see Deschanel's "Natu- ral Philosophy," §§ 358, A; 362-393. Within the last few years, gas and petroleum engines have become common. Gas engines derive their power from the combustion, in the cylinder, of an explosive mixture of air and coal gas. In the petroleum engine, air is forced into the cylinder through a passage containing crude petroleum. The air forms, with the vapor of the petroleum, an explosive mixture which is burned in the cylinder. While there are practical difficulties connected with the satisfactory lubrication of the sliding parts under the high temperatures to which they are necessarily sub- jected, they offer certain advantages as " ready motors " and, under some circumstances, are preferable to smal[ steam engines. All of these engines are devices for converting the po- tential energy of chemical separation (oxygen and fuel) into mechanical energy through the intermediate form of heat. But the chemical separation was wrought, at some period of the world's history, by the energy of the sun- beam (vegetable growth). Thus, we see that the energy of the engine is transformed solar radiation. See Daniell's "Principles of Physics," p. 367. Exercises, Page 471* 1. See § 631. 2. (§ 634, a.) 2,220 -f- 15 = 148. Ans., 148 oz. 3. 5,747 g. or 5.747 Kg.— Ans. 4. 34.462° C— Ans. 5. 80 x 1,390 = 111,200, the number of feet (in vacuo) that the ice must fall. 6. (80 + 100 + 537) x 1,390 = 996,630, the number of feet. — Ans. [Elements of Natural Philosophy, p. 472.] 233 7. 8080 x 1390 x 5 + 2000 = 28078, the number of feet. — Ans. 8. 88.42$ of 5 lb. = 4.421 lb., the quantity of carbon. 5.61$ of 5 lb. = .2805 lb., the quantity of hydrogen, 8080 x 1390 x 4.421 = 49653135.2 34462 x 1390 x .2805 = 13436561.49 Total number of foot-pounds, 63089696.69 63089696.69 -r- 2000 = 31544.8 + , the number of feet — Ans. n /c B 1K *\ 15 ° X 1920 X 1920 . OO OVK* 9. (See § 157.) j———^ + 32 = 37.o6 + . Ans., 37J° F. 10. (a.) If the water were boiling hot, -^ = 1203.72 + , the number of pounds. — Ans. If the water were ice cold, - — ^,r- = 1014.75, bo 7 the number of pounds. — Ans. See § 634 (b). 8080xW_x_80 = lhm _ AM V ' 2000 x .1138 T 11. 1390 x 48 x (80 + 100 + 537) = 47838240, the mechanical equivalent of the heat expressed in foot-pounds. «* = 47838240; ^~ = 47838240 ; » = 392.234. Zg D4.0/4 Ans., 392.2 ft. per second. -.o ra Cl oo\ 8x2000x2000 _„, 12. (See § 132.) ^^ g^— m - 3.57 + . Ans., 3.57 lb. 13. (a.) Ans., 1390 ft. or 424 meters. (§ 631.) (b.) 424 m. x .0333 = 14.1192 m.— A ?is. 14. The weight makes no difference, as an increase in the weight would increase the working power and the work 234 [Elements of Natural Philosophy, p. 472.] to be done at the same rate. It may be called 1 gram (oi anything else). That weight of water heated 100° would require 100 heat units. That weight of lead heated 100° would re- quire (.0314 x 100 =) 3.14 heat units, equivalent to 133136 gram-centimeters. (See § 600.) o- = tt^tt = 133136; v* = 260946560 ; v = 16153.8. 2g 1960 — Ans. 15. 772000 -h 1390 = 555.4—, the number of pound- centigrade heat units. 772000 -^ 772 = 1000, the num- ber of pound-Fahrenheit heat units. (§ 579, a, 3 and 4.) tja 64 x 1400 x 1400 OQO ■ ., , . - 16 ' 6iMlTiMo-^o = ^ — Ans. 1W 7 x 1000 x 1000 .- t 17 ' 64.32 x 772^70^1138 = 1? ' 7 + ' the number of degrees Fahrenheit. 7 x 1000 x 1000 9.8 + , the number of 64.32 x 1390 x 70 x .1138 degrees centigrade. 18. (442 — 374) x 6 x .056 = 22.848, the number of heat units for heating. 25.6 x 6 = 153.6 the number of heat units for melting. 772 x 176.448 = 136217.856, the number of foot-pounds. 19. The weight of the ball makes no difference. (See the 14th problem above.) Call it, for convenience, 1 lb. 1 ^4.3^x13^ = 16 + ' the nUmber ° f heat UllitS ieveloped. Suppose the ball to be even ice cold. Its temperature would have to be raised 326° C. This would require [Elements of Natural Philosophy.] 235 Review Questions and BM irises, Page 473. 1. (326 x 1.8) + 32 = 618.8.— A ru. 5.37 x 1.8 == 9.666.— Ans. (See § 546.) 2. There is no difference. (See § 546.) 3. 760 : 750 ) . nnA k A _ *_■ 373:473[ =4 ' 500:a; - •*• * = 5 > 631 + ' Atis., 5,631 -f cu. cm. 4. 27 inches x 13.6 = 367.2 inches or 30.6 ft.— Ans. {§§ 300, 253.) 10. (a.) - 3° F. = — 19*° C; 77° F. = 25° C. (b.) 18° C. = 64.4 F.; 20° C. = 68° F. 11. 273° C. See §§ 557, 559. 13. Ans., 1, t, -&. 15. (a.) The 424 kilogrammeters of energy would gen- erate one calorie. (§ 631.) 16. (a.) 4,000 -r- 62.42 = 64.08-f, the number of cubic feet.— Ans. (See § 226, note.) (b.) 64.08 -r- 1.09 = 58.78 + , the number of cubic feet. — Ans. 17. 30 inches x 13.6 x -^ = 510 in. or 42J ft.— Ans. 22. (a.) 273 : 283 = 546 : 566. 566 cu. cm. — 546 cu. cm. = 20 cu. cm., the expansion. ,. 64.32 x 50 x 50 (*•) aJ"qo = 2,500, the number of foot- pounds. (§ 157, a.) 23. 100 x .1138 = 11.38, the number of heat units re- quired. (§ 579, a, 3.) 1390 x 11.38 = 15,818.2, the number of foot-pounds RMjuind. (§ 631.) To lift 7 T. of iron 1 ft. would require only 14,000 foot- pounds. CHAPTER IX. § 644. The idea of a luminiferous ether (§ 608) exist- ing and acting as a carrier of motion must be clearly formed and constantly maintained. Our physical sensa- tions result from motion acting upon the nerves. One kind of motion is competent to excite one nerve ; another kind, another nerve, etc. The peculiar kind of motion im- posed upon the ether by the vibrating molecules of a lumi- nous body and transmitted by the ether to the retina of the eye awakens the sensation of sight. The difference between a longitudinal and a transversal wave may be made more clear by imagining two rays, one of sound and one of light, to come from directly over- head, i. e. f vertically downward. In the former case, the vibrations will all be vertical, while in the second case they will all be horizontal. Concerning the corpuscular or emission and the undulatory theories of light, see Tait's "Light," §§ 31-34 and 205-220 and Stokes's " Nature of Light," Lecture I. " While I have endeavored to place before you, with the utmost possible clearness, the basis of the undulatory theory, do I therefore wish to close your eyes against any evidence that may arise of its incorrectness ? Far from it. Yon may say, and justly say, that a hundred years ago another theory was held by the most eminent men, and that, as the theory then held had to yield, the undulatory theory may have to yield also This is perfectly logical. Just in the same way, a person in the time of Newton, or even in our own time, might reason thus : ' The great Ptolemy, and numbers of great men sifter him, believed that the earth was the centre of the solar system. Ptolemy's theory had to give way and the theory of gravitation may, in its turn, have to give way also.' This is just as logical as the former argument. The strength of the theory of gravitation rests on its competence to account for all the phenomena of the solar system. On a precisely similar basis rests the undulatory theory of [Elements of Natural Philosophy, pp. 475, 4:0.] .'!. lijrht ; only that the phenomena which it explains are far more varied and complex than the phenomena of gravitation." — Tymhiil. " That light is not itself a substance may be proved from the phenomenon of interference. A beam of light from a single pMUPM is divided by certain optical methods into two parts, and th»\s<\ after travelling by different paths, are made to reunite and fall u|>on a screen. If either half of the beam is stopped, the other falls upon the screen and illuminates it, but if both are allowed to p;i screen in certain places becomes dark and thus shows that the two portions of light have destroyed each other (see § 713). Now we cannot suppose that two bodies when put together can annihilate each other ; therefore, light cannot be a substance. What we have proved is that one portion of light can be the exact opposite of an- other portion, just as + a is the exact opposite of — «, whatever a may be. Among physical quantities we find some which are capable of having their signs reversed and others which are not. Thus a displacement in one direction is the exact opposite of an equal dis- placement in the opposite direction. Such quantities are the meas- ures, not of substances, but always of processes taking place in a substance. We therefore conclude that light is not a substance but a process going on in a substance, the process going on in the first portion of light being always the exact opposite of the process going on in the other at the same instant, so that when the two portions are combined, no process goes on at all." — Encyclopaedia Britannica, Vol. 8, p. 569 (ninth edition). The difficulties that encumber the undulatory theory of light are set forth at the bottom of p. 571 of the volume from which the above quotation was made, under the heading Electromagnetic theory of light, which see. § 645. Concerning sources of light, see Tait's " Light," SS M-30. § 646. When ether waves fall upon a body and pass through it, they are still propagated by the ether that lies between the molecules. With respect to the transmission of obscure heat rays (§§ 617, 718), bodies are diatherma- nous or athermanous ; with respect to luminous rays (§ 717), they are transparent or opaque; with respect to actinic rays (§ 719), no special terms are yet in use. A perfectly transparent body, like colorless, thin glass with 238 [Elements of Natural Philosophy, p. 476.] a polished, clean surface, is invisible by the light that passes through it though the presence of the glass may be manifested by reflected light. For example, the sunlight reflected by the windows of a distant house may make the glass magnificently visible. If glass be roughened or ground, the numerous facets thus produced reflect light and make the glass visible from all directions. Transmitted light is irregularly turned from its path so that while light passes through the glass, objects can not be clearly seen through it. Such glass is translucent. When the glass is powdered, it presents so many facets and reflects the light so often that the energy of the ether waves becomes entangled, as it were, in the molecules of ordinary matter and fails to find a passage through. Glass powder is, therefore, opaque. In such cases, the ether loses energy, ordinary matter gains it and the body is heated. " When a succession of waves impinges on a mass of ordinary matter, the effect varies according to the nature and the condition of the body which receives their shock; if it be an ordinary opaque mass, that mass may be warmed, the energy of wave motion being transformed into heat ; and the waves which have impinged upon the opaque mass are ex post f ado called a beam of radiant heat ; if they fall upon the eye, they may produce a sensation of light and the wave system is then called a beam of light ; falling upon a sensitized photographic plate or a living green leaf, it may operate chemical decomposition and it is then called a beam of actinic rays. Hence we speak of heat rays, of light rays and of chemical or actinic rays (§§ 717-719), these names being given to one and the same train of waves according to the effect which it is found competent to produce. But while ether waves are in course of traversing the ether, there is no heat, light or chemical decomposition ; merely wave motion and transference of energy by wave motion." — Daniell. § 649. " It is very remarkable to find how slowly the human race have reached some even of the simplest facts of optics. We can readily understand how constant experience must have forced on men the conviction that light usually moves in straight lines — i. e., that we see an object in the direction in which it really lies. But how they could have believed for ages that objects are rendered visible by something projected from the eye itsel f — so that the organ [Elements of Natural Philosophy, pp. 476-4SO.] 239 of sight was supposed by the most enlightened of them to be analo- gous to the tcntacula of insects, and sight itself a mere species of touch — is most puzzling. They seem not till about 350 B. C. to have even raised the question, - If this is how we see, why cannot we see in the dark? or, more simply, — What is darkness? The former of these questions appears to have been first put by Aristotle." — Tait. § 650. See Friek's "Physical Technics," p. 209 (§ 181) and Deschanel's "Natural Philosophy," § 748. " Another beautiful illustration is easily obtained by cutting with a sharp knife a very small T aperture in a piece of note pa; N t. Place this close to the eye, and an inch or so behind it place another piece of paper with a fine needle hole in it. The light of the sky passing through the needle hole forms a bright picture of the T on the retina. The eye perceives this picture, and in consequence re- ceives the impression of the T much magnified, but turned upside down."— Tail. § 653. See Deschanel's " Natural Philosophy," §§ 685- G88 A and Tait's * Light," chap. VI, for good descriptions of the various methods for determining the velocity oi light. Foucault's experiment, therein described, was per- formed in 1850 and showed a velocity of 298,000,000 m., as stated in the text. In 1879, Prof. Miohelson, slightly modifying the Foucault method, made at Annapolis a new determination which exceeded in accuracy anything ever done before. Michelson's Annapolis result is 299,910 Km. (or 299,910,000 m.). In the meantime, Prof. Newcomb had secured a government appropriation of $5,000. He secured the co-operation of Michelson and in the years 1881, 1882 and 1883, two independent series of observations Avere undertaken, one at Washington by Prof. Newcomb and one at the Case School of Applied Sciences at Cleveland, 0., by Prof. Michelson. XcwcomVs result is 299,860 Km. ; Michel- son's is 299,853 Km. "The accordance is surprisingly close, far less than the probable error which, according to Prof. Newcomb, may easily be 25 or 30 Km." He thinks that, with the help of past experience and without auy 240 [Elements of Natural Philosophy, p. 480, 4SI.] radical change in the apparatus, a precision of 5 or 10 Km. can be attained. J. E. H. Gordon, on p. 120 of his " Electric Induction, " • In air and vacuum the velocities of light and electromagnetic in- duction are sensibly equal." " In both cases, a disturbance is propa- gated through the ether." He considers this "a very strong argu- ment for considering that the electric and the optic ethers are identical, for the velocity with which a wave is propagated in a medium is a measure of the density and elasticity of that medium." It will be well for the teacher to study these " Four Lectures on Electrostatic Induction," carefully. § 654. This law is strictly true only when the source of light is a luminous point. If the rays be parallel, there will be no variation in intensity, excepting so far as may be due to the absorption of light by the medium that it is traversing. If the rays be converging, the intensity will increase toward the focus. A bright spot that may practically represent a luminous point may be provided by making a small hole in a metal screen and placing a drop of glycerin in the hole. The glycerin will form a double convex lens of short focus. When a sunbeam, concentrated by a lens, is thrown upon the glycerin, an intensely bright spot of light appears on the other (the dark) side of the screen. This focus of the glycerin lens may be used as a source of light for many experiments. Similarly, the rays of an electric lamp may be converged by an achromatic lens of very short focus, as the high power objective of a microscope. The intensity of light illumi- nating a surface is proportional to the area of the cross-section which the surface presents to the direction of radiation. In the figure, let the horizontal lines represent rays of light from a source (e. g., the sun) so distant [Wnnent* of Natiini" PkBrtuphy, p. f*/.] 241 that the rays may be considered parallel. Some of these rays fall u|k»:i a screen, A B, which l>cing placed perpendicular to the rays, reeetaet the greatest possible amount of light. If the screen be placed in the position represented by A B" , it will evidently receive fewer r th<»se previously received by A C, which represents the cross- BectloD which the screen now presents to the direction of the rays. But if the light which illuminated .1 be diffused over the gn-at. i surfac .1 />' . the intensity must be correspondingly diminished. This explains, in great part, why the heat of the sun is less intense (§ 644) at morning and evening than at noon ; in winter than in summer ; at the poles than at the equator. A photometer is an instrument for measuring the inten- sity of light. The simplest is Bunsen's, which consists of a sheet of white porous paper, with a grease spot in the middle. If the paper be placed between the eye and a lamp, the spot will appear lighter than the rest of the paper. If the Jamp be placed between the eye and the paper, the spot will appear darker than the rest of the paper. Illumina- tion from the rear makes the spot appear lighter; illumina- tion from the front makes it look darker. The spot may he placed between two lamps, so that the illumination from the rear will just equal the illumination from the front ; the spot will then disappear. The lights then falling upon the two surfaces are equal in intensity. Suppose that a candle be placed at a distance of one foot from the paper, and that a lamp on the other side be moved back and forth until a place be found at which it causes the spot to dis- appear. Suppose the lamp now to be three feet from the paper. Then will the intensity of the lamp light be nine that of the candle light If the spot disappear when the lamp is at a distance of four feet, the intensities of the lights will be as l 2 to 4 2 or as 1 to 16, varying inversely uares of the distances. See Flick's "Pin Technics," p. lsi. and DeschaneVs "Natural Philosophy." at. Phil, § 428 (a) and (b). 242 {Elements of Natural Philosophy. ,] Exercises, Page 482. 1. The diameter of the shadow will be 5 times that of the coin. The area of the shadow will be 25 times that of the coin. 3. (c.) See § 608. 4. (p.) See § 649. 5. 2 2 : 6 2 = 1 : 9.—Ans., 9 candle power. § 655. See Frick's " Physical Technics," pp. 183-189 ; Mayer and Barnard's little book on " Light," pp. 16-26. § 656. See First Prin. Nat Phil, Exp. 212. § 658. See Tyndall's " Fragments of Science," p. 280. § 659. " We are liable to deception by trusting to the direct or uncontrolled evidence of our senses. Some of the most perfect illu- sions which have ever been contrived depend solely upon the obvious fact that the eye (or any other organ of sense) can inform us only as to what reaches and affects it ; not, in any way whatever, of whence or how that which affects it managed to reach it." — Tait. § 660. In other words, the image of any point (in a plane mirror) may be found by drawing a line from the point perpendicular to the mirror and producing it to twice its length. § 663. Two mirrors attached to each other so as to form an angle that is a submultiple of 360°, are often used by designers for obtaining symmetrical patterns. The optical toy, called the kaleidoscope, is constructed on the same principle. See Deschanel's " Natural Philosophy," §§ 700- 705. § 672 (a). For a description of the pretty experiment of the phantom bouquet, see Deschanel's " Natural Philos- ophy," § 712. [Element* of Natural Philosophy.] ■iv.\ Exercises, Faye 498. 1. Forty- five degrees. -.'. Make an accurate diagram. The conjugate focus will he on the principal axis, 36 inches from the mirror. n. (a.) See § 660. (b.) See § 665. 7. See §674. 8. He cannot in either case. Whatever his position, the image will appear as far back of the mirror as the man is in front of it, and the part of the mirror used to give a complete image will be half the length of the man. If the mirror is not half the length of the man, it can not give a full length image of him, no matter what his dis- tance from it. Let M X represent the mirror, A B the c a 6 A fl J ^ ^^ ^=^ - ■ ^^ > -**-^ ( V I 5T J J L> man, and a b his image. The triangles, A e i and A a b, are similar and A e = \ A a; therefore e i = { A B. But e i is the part of the mirror used in forming the image. Suppose now the man to move either way, as to C D. The image appears at c d and C e = | C c. Hence, n'= \cd or \ C D. Wherever he stands, he can not see his com- plete image unless the length of the mirror is half his own length ; if it is too short in one case, it will be too short in every such case. 9. Sixty degrees. 244 [Elements of Natural Philosophy, p. 499.] 10. Let M N represent the mirror; E E' the two eyes and e e ' the two images of the eyes. Of course, E E' are in the same horizontal line. When E' is closed, E sees the image of E' at e'. Placing the wafer at W, hides e'. When E is closed, E' would see the image of E at e, were it not for the wafer which hides it. See § 662. By drawing the parallelogram, E E' e' e, and remembering that M N is midway between E E' and e e', it may be proved, geometrically, that Ee' and E' e will inter- sect at W as represented in the figure. 11. Construct the figure. See Fig. 340. [Elements of Natural Philosophy, pp. 500, 501.] % I B §676. See Ma\er and Itaniard's "light/ 1 pp. 59-91; Frick's "Physical Technics." pp. 189-201 Hid Desehanel's "Natural Philosophy," § Wk § 678. The ratio that is called the index of refraction is constant^ for any two given media, whatever the angle of incidence. The relative positions of the incident and the refracted rays may be represented by the apoaratus represented in the accom- panying figure, which may be used either as a moving diagram or as a means of experimentally verify- ing the law. B' is a slider travelling up and down a vertical stem. A C and B C are two rods pivoted on a fixed point, B, of the ver- tical stem. C B' and C B' are two other rods jointed to the former at C and C, and pivoted at their lower ends on the centre of the slider. B C is equal to B' C\ and B C to B' C. Hence the two triangles, BOB' and B C B y are equal to one another in all positions of the slider, their common side, B B', being variable, while the other two sides of each remain unchanged in length though altered in position. The ratio BC B C or is made equal to the CB' ~ C B index of refraction of the liquid in which the observation is to be made. For water and air, the index is | (or 1.336). If the apparatus be immersed in water to the level of B, ABC will represent the path of a ray and C will appear to be in a straight line with A and B. 246 [Elements of Natural Philosophy, pp. 501, 502.] The difference between the angle of incidence and the angle of refraction measures the amount of bending of the ray and is called the deviation. These two angles and the deviation increase or de- crease together. The path of the refracted ray may be constructed as follows : Suppose the ray to pass from air into water. Let B A represent the surface of the water and C the direction of the inci- dent ray. Measure A and B, as 4 and 3 equal parts, e. g., centi- meters or inches. The ratio between A and B slumld represent the index of refraction for the given media. In this case, it is f or 1.33. At A, erect a perpendicular cutting the line, C, at H. At B, let fall the perpendicular, B K. From as a centre, with a radius equal to O H, describe an arc cutting B K at D. Draw D which will represent the path of the ray in the water. From the above, it will be easily seen how to construct the path when the wave passes from the water instead of into it. The same result may be obtained as follows : Given the ray in air ; lay off upon it 4 equal parts starting at 0, the point of incidence. Through H, 3 units distant from 0, draw A E, perpendicular to N, the refracting surface. From as a centre, with a radius of 4 units, draw an arc cutting this perpendicular at E. Draw the straight line, E D. D will represent the position of the ray iia the water. § 679. The figure on the next page represents a piece of apparatus very convenient for showing many of the phe- nomena of refraction as well as of total reflection (§ 681). It consists of a circular tank about 18 inches in diameter, with a glass side. It is graduated at its circumference and furnished with a mirror adjustable at any point on the circumference. This mirror reflects a beam of light to the [Element* of Natural Philosophy, p. 50*.] 2 17 centre of the tank which is filled with water to its hori- zontal d iame ter. See Frick's * ' Physical Technics," pp. 1 90- 192. In the application of the second and third laws, it is sometimes necessary to distinguish between specific gravity and optical density. The nature of the transparent body has a retarding effect on the velocity of the transmitted light (§ 683). More than this, each transparent substance has its own rate of transmission for ether vibrations of each particular wave length and this is found, in each case, only by experiment. Some substances transmit ether waves more rapidly than do some other substances that are less dense. For example, light travels more rapidly throng)] water than it does through alcohol or turpentine, although both alcohol and turpentine are lighter than water. On account of this greater retardation of ether waves, these lighter substances have a greater index of refraction than water has ; they are said to be optically denser. 248 [Elements of Natural Philosophy, pp. 602-507.] § 680. See First Prin. Nat. Phil, Exp. 223. In the first century of the Christian era, Cleomedes performed this coin and cup experiment and showed that, in a similar way, the air may render the sun visible to us while it is still below the horizon. § 681. See First Prin. Nat. Phil, Exp. 227. § 682. The optical illusion known as mirage is explained in Deschanel's "Natural Philosophy," § 726. It is a result of total reflection by the atmosphere and is often seen in hot countries, especially the Sahara in Africa. See Deschanel's "Natural Philosophy," § 819. § 683. The text refers to the First Prin. Nat. Phil, § 443, a. In addition to the illustration of marching soldiers there given, the following may be used to show that a change of wave-front necessitates a change in the line of propagation : " Suppose two persons are pushing a two-wheeled cart along by turning the wheels. If one turns his wheel faster than the other does, the direction in which the cart travels will be changed." Concerning a method of proving that light moves more slowly in glass than it does in air, see Tait's " Light," § 233. § 686. The angle formed by the meeting of the two refracting sides of a prism (or of their planes produced) is called the refracting angle of the prism or, simply, the angle of the prism. The \ construction for a ray re- fracted by a prism may be done as follows : Assume the index of refrac- tion to be § (=1.5. See § 678/0. Let E F H represent a section of the prism with the refract- ing angle at E. Assume b c to be the path through the prism. We are required to find the di- rection of the ray on either side of the prism. Draw E B par- allel to 6 c and make it 3 [Elements of Natural Philosophy, p. 507.] 24$ units long (e. g., 3 centimeters or inches). Produce H E in- definitely. From B, draw B M perpendicular to H E produced and draw B N perpendicular to EF. From E&s a centre, with a radius of two units, describe an arc cutting B M and B N at C and A re sjjectively as shown in the figure. From b, draw 6 a parallel to A /.', to represent the incident ray, and from c draw c d, to represent the emergent ray. Then will abc d- represent the refracted ray. In case the construction proves impossible, it may be understood that the position assumed for b c is more divergent from F H than is possible. Try the construction with an equilateral triangle as the section of the prism and with b e making a right angle with E H. You will find that you can not locate the points A and C. To show that this is an impossible position for b c, we have only to imagine the ray moving in the other direction, i. e., from e toward b and thence into the air. Under such circumstances, the angle of inci- dence at b would be 60°, which largely exceeds the critical angle for glass and air (?j 682). The ray could not, under such circumstances, emerge from the glass at b but would be reflected back into the glass from the face E F. Conversely, if a ray moving in the direction assumed for c b can not pass from glass to air, it is impossible for a ray entering the glass from the air to take the direction indicated by be. See Hand-Book note on Ex. 9, page 515 of text-book. Next, given a b, the direction of the incident ray, to find the di- rection of the two refracted rays. From E, draw E A, parallel to a 6, and make it 2 units long, or draw the arc from A' as a centre with a radius of 2 units as shown in the figure on the page last preceding. Through A, draw A If perpendicular to 2?i^and of indefinite length. From Ebbb. centre, with a radius of 3 units, describe an arc cutting the prolongation of N A at B. Draw B E. From B, draw B M,& l:n<* '^rpendicular to the prolongation of HE at M, cutting the arc first drawn at C, 2 units distant from E. Draw C E. Draw b c par- allel to B E to represent the ray passing through the prism. Draw e d parallel to C E to represent the emergent ray. In either of these cases, the ratio between A /?and B E is taken equal to the index of refraction for the given media. The angles, B E A and B E C, measure the deviations at the first and second refractions res|>ectively, while the angle, A E C, measures the total deviation. One of these constructions may well be giv«>n to the class as op- tional or honorary work, as follows : Given E F If, tfafl s.rtion of a prism and c d, thfl path of a ray through tin* prisni, to find a method 250 [Elements of Natural Philosophy, pp. 507-514.] of determining the direction of the incident and emergent rays. Give the class a week for the solution. If at the end of that time any member of the class has succeeded, have him give his solution to the class and see that he is commended for his skill. If no pupil succeeds, the teacher may give the solution and then assign the problem with the position of the incident ray given, the position of the two refracted rays to be determined. After the first solution is given, this will be more easy and, during the ensuing week, some of the pupils will probably accomplish it. See that the constructions are carefully made, i. e., that straight lines are straight ; that par- allel lines are parallel ; that equal lines are equal, etc. Also, insist upon neatness. See Frick's "Physical Technics/' p. 192. (b.) A vessel for the purposes mentioned in the text may easily be made by boring a hole through a wooden prism and cementing pieces of window glass over the ends of the hole. The cavity thus made is to be filled with water or other transparent liquid before cementing the second plate in place. § 687. See First Prin. Nat Phil, § 450, b and Picker- ing's " Physical Manipulation," p. 155. § 689. The focal distance of a lens may be approximately found by holding the lens facing the window and near a wall on the opposite side of the room. Move the lens forward and backward until the image on the wall is clear. Measure the distance from the lens to the wall or screen. § 695. Measure the distances (D and d) of the image and object from the lens and the corresponding linear dimensions (L and I) of the image and object. Verify this formula: -=- = -=-. I a § 698. See Frick's "Physical Technics," p. 199. [Element* of Natural Philoaoiriy.] 251 Exercises, Page 515. 4. (a.) See § 695. (b.) The image formed by a concave lens can not conform to any of the given conditions. See §697. 5. (a.) See Fig. 352. (b.) 12 inches. (§689,*.) (c.) 9 inches. 6. (a.) See the lower part of Fig. 356. (b.) See § 689 (a.) and corresponding note in this Hand-Book. 7. They will be equal. Construct the image. § 693. 8. Eight inches. 9. (a.) 5 feet from the flame. (§ 690.) Notice the principle of reversibility that prevails in optics. If the direction of an ether wave be reversed (the light having been reflected or refracted or not), the wave will retraverse its original path (§ 647). (b.) One will be five times as long as the other. See Fig. 358, and compare the similar triangles, ABO, and a b 0. The sides, a b and A B, are proportional to their distances from 0, 252 [Elements of Natural Philosophy, pp. 516-520.] § 700. See Deschanel's "Natural Philosophy/' § 777 and Tait's" Light," §§ 612, 613. " That which we call white light is, in the state in which we receive it from such a body as a white-hot bar of iron or, perhaps in its purest form, from the crater of the positive pole of the electric light (see Fig. 247), a mixture of long and short waves ; waves of all periods are either continuously present or, if absent for a time, are absent in such feeble proportions or for such short intervals that they are not appreciably missed by the eye. White light of this kind is comparable to an utterly discordant chaos of sound of every audible pitch ; such a noise would produce no distinct impression of pitch of any kind ; and so white light is uncolored." — Daniell. §701. See Daniell's "Principles of Physics," p. 451. Concerning abnormal dispersion, see Tait's " Light/' §§ 196-198. § 702. See Deschanel's "Natural Philosophy," § 778. § 703. See Frick's "Physical Technics," p. 196; Desch- anel's " Natural Philosophy," § 779, with colored plate (frontispiece) and §§ 783-790; Daniell's "Principles of Physics," pp. 449 and 456-460 ; Tait's " Light," chap. XVI, and Hand-Book note on § 722. The figure above rep- resents one form of the spectroscope. § 704. A simple form of whirling table for use with [Elements < : t Philosophy, p. 520. \ 253 Newton's Disc (see Exp. 2 on preceding page of text-book) is shown in the accompanying figure. SceTait's "Light," §§ 19-21. " The expression ' white light ' standing alone is wholly vague ; physiologically it means light which produces the sensation of white ; physically it may mean : — "1. A mixture of all possihle light-waves, long and short, in certain proportions. " 2. A mixture of two complementary single colors (§ 705, 6). " 3. A simple color blended with a comple mentary compound one of any degree of com- plexity. " The white light of sun-light at sea-level is made up by a mixture of colored lights in the following proportions : — Red, 54; orange-red. 140; orange, 80; orange-yellow, 114; yellow, 54; greenish -yellow 206; yellowish-green, 121; green and blue-green, 134; cyan-blue 32; blue, 40; ultramarine and blue-violet, 20; violet, 5." — Daniell. § 705. Most of the colors seen in nature may be imi- tated by mixing some prismatic color with white of feeble intensity. Each red constituent of the spectrum is com- plementary to a constituent lying somewhere in the green. Each orange or yellow is complementary to one of the blues or violets. The yellowish-greens are not com- plementary to any single constituent of the spectrum, but their complements may be made by mixing red and violet Lights (W pigments). Lights may be mixed by causing two si>ectra to overlap so that at any given point there will be a mixture of two colors, one from each spectrum. Also see Exp. 2, p. 519 of text-book. Any two colors may thus be mixed. Another method is by setting a plate of glass, O, upright on a table with two pieces of dif- ferently colored papers on the table at equal distances from A o the glass, as at A B and a b. ZZ ~L_ ' ■ -■- j^, When the observer stands on G Cx B 254 [Elements of Natural Philosophy, p. 520!\ the same side as A B, he will see a 6 by light transmitted through O and an image of A B formed by reflection by the glass. The image of A B will coincide with a b (§ 660) and the observer will see a mixture of the two colors. When the eye is near the plane of the glass, as at E, the image of A B will have the greater brightness ; when it is at e, the color of a & will predominate. It is easy thus to vary the ratio in which the colors are mixed. When sunlight passes through a plate of colored glass (or similar body), some of its rays are absorbed, becoming entangled, as it were, in the glass and thus heating it. Other rays find easy passage through the glass. The char- acter of the absorption may be determined best by exam- ining the transmitted light with a spectroscope, dark bands appearing in the spectrum in the positions belonging to the rays filched from the sunbeam by the glass plate. Common red glass absorbs nearly all except the red rays ; cobalt- blue glass absorbs the yellow, orange and scarlet, and yields a spectrum in which the extreme red is separated by a broad dark space from the green, blue and violet. V | R G R (See § 700, a.) If two glass plates, one of which thus absorbs rays such as the other transmits, be superposed 4 the double plate will be opaque. Thus, red glass and green glass are very transparent separately viewed, but appear black when they overlap. On the contrary, red light and (bluish) green light are complementary to each other, forming white light when mixed. A blue glass and a yellow glass overlapping, appear green, although violet blue and yellow are com- plementary colors and such colored rays would form a more or less perfect white. The color of a mixture of pigments depends, like the color of superposed plates, on the composition of the colors cf each transparent particle as revealed by the spectroscope and not on the apparent colors as seen by the naked eye. See Tait's "Light," §§ 184-189 and Deschanel's "Natural Philosophy," chap. 63. "Within the limits of visibility (see Hand-Boob, note on §716) there is an indefinite variety of integral and fractional numbers, each of which represents the frequency of a particular kind of radia* tion, a particular kind of light. Physically, there are as many kindg [MmeMi "/ Not oral Philosophy, p. 620.] 255 of light as there are possible frequencies b c U m o n the limits men- tioned. These kinds of light, each physically characterized by the number of waves which strike the eye during a second, are recog- nized by the eye as being distinct, not as the result of any conscious process of counting the number or impulses suffered by the eye dur ing a second, which would be absolutely impossible, but in conse- quence of the distinct and peculiar sensation attending the reception, in the eye, of wave-motion of each particular frequency, a sensation known in each case as that of a particular color. Thus when we look at a Bunsen burner, the flame of which is caused to emit a dingy-yellow light by contact with common salt, we recognize the sensation as one of yellow light. Color is a sensation ; it is not a material existence ; but the physical basis and cause of the special sensation of yellow light is in this case the joint, simultaneous im- pact on the eye of two kinds of ether- waves, which have the respect- ive frequencies of 508,905,810,000,000 and 510,604,000,000,000 per second. Either of these trains of waves impinging singly on the eye would produce the sensation of yellow, the slower one giving a yel- low very slightly more orange in its tint than the other does. " The term * yellow light,' which means primarily a certain sen- sation, means secondarily the physical cause of this sensation — that is, a train of ether-waves of a particular frequency. Any particular tolor is best specified by a statement of the frequency of the single (rave-motion which can produce that color when it enters the eye; the analogy between light of any given color and a sound of any given pitch being obvious. " Even beyond the ordinary range of visibility, some eyes are affected by ultra-violet ether-waves (§717); a sensation of lavender gray color results. A spectrum is often seen, especially if the dispersion be small, to contain three bright bands of lavender-gray in the ultra-violet region. " The color of a colored object, as seen by transmitted light, is produced by subtraction of the light absorbed from the light Inci- dent upon the object. The kind of light transmitted may vary with the thickness of the absorbing medium. A solution of chloride of chromium in a thin layer, absorbs much yellow, orange and yel- lowish-green light ; in a thicker layer, it absorbs all but the red and some green and blue; in a still thicker layer, the only <« »1« r - transmitted is red. Thus a wedgc-shajH-d layer of this solution ap pears to vary in color, according to tin* thickness, from a greenish- blue, through purple, to red. Iodine vai>or transmits a blue group and a red group, as also ultra-violet rays; together these produce an impression of purple ; in thicker layers, the blue rays alone are 256 [Elements of Natural Philosophy, p. 520 .] transmitted and the vapor appears blue. When a strong solution of blood is interposed in the path of a beam of light, no light but red is transmitted ; dilute the solution gradually and successively, the solution appears more and more yellowish and of increasingly paler hue. " The special absorptions of absorbent bodies are most thoroughly studied, not by means of their visible colors, but by the prismatic analysis of the light which passes through them. It is then found that some substances absorb several distinct kinds of light, belong- ing to different regions of the spectrum. Transparent colored objects, through which light is filtered, give dark bands across the spectrum— the so-called Absorption bands which indicate what kind of light has been stopped and extinguished by the absorbent object — these bands varying in breadth with the degree of concentration of the absorbent solution employed and varying in position with its nature. (See § 625 and note.) " The color of a colored object seen by reflected light is also gen- erally due to absorption. An object seen by reflected sunlight does not seem to be colored in any degree unless there have been abscrp tion of some of the components of the incident white light ; th? color of a colored object is complementary to the color that would have been produced by these absorbed components had they jointly impinged on the eye. " Some of the light incident on a piece of colored glass is reflected at its surface ; there is no absorption ; if the incident light be white, the light reflected is also white. If a piece of green glass be laid upon black paper, and if it be looked at in such a direction that day- light is not directly reflected from it into the eye, it will be nearly invisible and will be devoid of color ; it will appear black. If col- ored glass be ground to powder, the powder is white ; white light is reflected at every facet while the light reflected from the lower sur- faces of the fragments and again issuing into the air has nowhere traversed a layer of sufficient thickness to cause the extinction of all the absorbable components of the incident sunlight. The finer the powder, the whiter it is ; the coarser it is the more marked is its color. If the upper surface of a sheet of green glass be ground, it will appear almost white ; if the ground surface be looked at through the glass, it will appear green, for the light issuing from the glass is white light which has undergone a certain amount of absorption. If the green powder be immersed in water or oil, there is less reflec- tion at the several facets ; there is deeper penetration of the light into the mass and, consequently, more absorption ; the color appears to deepen. Hence the value of oil as a medium in painting. [Elements of Natural Philosophy, p. 520.] 257 " A solution of chloride of copper placed in a deep black-walled vessel will not appear to have any color ; it will seem black ; it re- flects no light except from its surface. If powdered chalk be mixed with it, light is reflected from the white particles of chalk and passes out in every direction, through every part of the surface ; so much of the reflected light is absorbed that it appears green when it reaches the eya — the milky mats appears green. In a similar way, a piece of malachite is penetrated by light to a very small depth ; internal reflection occurs ; absorption of all the outpassing light takes place with the exception of certain kinds which jointly ap|iear green ; the malachite is green. A piece of polished gold reflects white light at its surface ; it also reflects interiorly and from within the substance of the gold at a very small depth there is re- flected in all directions a quantity of light which, by absorption before leaving the surface, has become of an orange color. If the layer of gold be very thin, that part of the light which would be absorbed by a thicker layer may, in part, pass through and issue into transparent media before its energy is wholly converted into heat. A thin piece of goldleaf thus appears transparent and allows a greenish-blue kind of light to pass through it, which, if the leaf be rendered very thin by the action upon it of a solution of cyanide of potassium, may become violet, for both green and violet light then find their way through. ■ Greenish-blue glass prevents, in whole or in part, the transmis- sion of violet light, of red, of orange and of other kinds of light that are present in white sunlight. The complex of undulations thus denied transmission would, if collectively allowed to impinge on the eye, have produced a single impression of red light. If this compound red-light had not been obstructed by the colored glass, the transmitted beam would have been white ; this compound red-light thus obstructed by the greenish glass, and the compound greenish- light transmitted by it, will pass together through a piece of char glass and will together produce the sensation of white light. To the eye it is a matter of indifference whether the red or the greenish light lie monochromatic or compound ; monochromatic red-light and monochromatic greenish blue-light, allowed to fall upon the same spot in the eye will mingle and, if they be of the proper tint, will produce the compound sensation of white light. These colors, red and greenish -blue, each of the proper tint, are thus complementary to one another ; together, they make up white light. 'The following pairs of colors are, among others, thus comple- mentary to ope another : red and a very greenish-blue ; orange and cyan-blue (a rather greenish-blue) ; yellow and ultramarine blue ; 258 {Elements of Natural Philosophy, pp. 620-525.] greenisli-yellow and violet ; green and ' purple,' the latter being a color not in the spectrum but formed by the superposition of blue and red." — Daniell. § 706. See Tait's "Light," chap. x. and Frick's "Phys- ical Technics," p. 197 (§ 168). " Fill a glass bulb about 1£ inches in diameter (those furnished for air-thermometers answer the purpose) with a filtered solution of common salt in water. Cover the aperture of the porte-lumiere (heliostat) with a black cardboard so as completely to exclude the light from a darkened room. Cut a hole in the centre of the card- board of the same diameter as the bulb and allow a circular beam of light to pass through it and also through a hole of about 4 in. diameter in the centre of a white cardboard about 2 ft. square and strike the bulb placed at a distance of about 2 ft. in front of the white cardboard. A miniature rainbow will be reflected back from the bulb upon the screen around its aperture. Any spot on the screen where red appears means that an eye situated at that point would see red in the glass bulb. Every other color, unless the eye was moved, would require another bulb in the proper relative position." — Gage. § 711. See Frick's "Physical Technics," p. 198 (§ 169). § 712. " The imperfection of the achromatism of the eye is readily proved by looking through a plate of cobalt glass at a small hole in the shutter of a dark room. The hole at first appears red with a blue space around it ; but, by an effort of the muscles of the eye, we can see the hole blue, and then there is a red space surrounding it. Rays of so widely different refractive index cannot be seen in focus simultaneously."— Tait. § 713. See Tait's "Light," chap, xiv.; Pickering's "Phys- ical Manipulation," p. 199; Stokes's "Nature of Light," Lecture II; Frick's "Physical Technics," p. 219 (§ 189) and Daniell's " Principles of Physics," p. 501. If rays of red light fall perpendicularly upon the flat surface of a plano-convex lens of several feet focal length, the convex surface being pressed against the plane surface beneath at a, a black spot will appear at a and black rings at w, x, y and z. The centre is black because the waves reflected from the two sur- faces in contact at a meet in opposite phases. They meet in opposite phases because the wave reflected from the rarer medium changes {Elements of Natural Philosophy, pp. 6*6-698.] 25$ C V \ \ V \ \ Z m \z l^>^^w -J2^^" a h C d e (It phase or logos a lialf wave length while the wave reflected from the denser medium does not. The fintf dark ring shows that tin- waves reflected from b interfere with those reflected Cram ». Tin 1 waves reflected from 6 inns' travel one red wave length furtln-rtlianthr wav. s dfrom w. That is, // m equals half a red wave length! 1m similar manner, we see that c x equals a wave length ; d y, a wave length and a half ; e z, two wave lengths. The diameter of the fourth dark ring, z z' or 2 in 2 may be found by nnas urement. The radius of curvature, C z, may also be measured. C m z is a right-angled triangle with the two sides, Cz and tti z, found by direct measure - ment. Hence, we can easily determine the value of C m. Ca = Cz. Then Ca — Cm = am — ez = 2 wave lengths of red light. The twinkling of stars is an effect of interference. See haniell's '* Principles of Physics," p. 508. § 714. See Frick's u Physical Technics," p. 222 (§§ 191- 193); Tait's " Light," §§ 235-242; Pickering's " Physical Manipulation," p. 202; Deschanel's " Natural Philosophy," p. 1024 et seq. y and Danicll's " Principles of Physics," p. 50C. § 716. All known ether waves vary from about 107 > to about 4 x 10 16 vibrations per second. There may. of course, be ether-waves t hat have a frequency of vibration lian tlic first of these numbers and others that haves frequency greater than the number last given, but we are not provided with senses that can recognize them if they do exist and, at present, have no experimental means of investigating them even if they are awaiting investigation. (See Hand-Book note on Jj 496.) But the limits above indicated cover what we may tall a range of about eight 260 [Mements of Natural Philosophy, pp. 528, 529] and a half octaves. But the human eye has a range of only about a single octave, being sensitive to vibrations ranging from about 392 x 10 12 , per second, a frequency that gives rise to the sensation of the extreme red of the spectrum, to about 75? x 10 12 , a frequency that occasions the sensatioL of violet at the other end of the spectrum. These wave- lengths are sometimes measured in "tenth-meters," which name is given to 1 meter -f- 10 10 = 0.0000000001 m. = 0.00000001 cm. See Tait's " Light," § 231. § 717. The length of luminous waves is most accurately measured by diffraction spectra. See Deschanel's " Natural Philosophy," §§ 821, 822. The use of Newton's Rings for this purpose was explained on p. 259 of this Hand-Book. " Ether waves do Dot traverse all substances with equal speed hence their wave-lengths in different substances vary. If any par ticular kind of radiation have to be spoken of, it may be denned by specifying its wave-length in some specified medium, but it is better to state its numerical frequency." — Daniell. § 718. All of the various rays that constitute a sunbeam, i.e., ether-waves of all known lengths, are thermal rays, for their energy is convertible into heat when they fall upon a thick layer of lamp-black which absorbs most of them. If the frequency of the waves is less than 392,000,000,000,000 (=r 392 x 10 12 ) per second, the wave is too long and too slow to cause vision or, as a general thing, to agitate the molecules upon which they strike, with a motion brisk enough to shake them to pieces and thus to work chemical decomposition. The energy of such waves is convertible only into sensible heat; they are dark-heat waves. "If they fall upon an ordinary photographic plate they do not produce chemical decomposition ; but if the molecules upon which they impinge be specially heavy and complex, even these slow heat-waves may be found to toss and shake them with briskness sufficient to break them up." § 719. See Frick's "Physical Technics," p. 200. Ether waves with a frequency greater than 757 x 10" [Elements of Natural Philosophy, p. 5 :•. ] 861 per second are s? rapid that the human eye is unable to ! , >.] 2W tioned in the note on £ 679 (page 24, of this Band-Book). By means of the movable mirror, the incident beam may be thrown in any desired direction. By rendering the water slightly turbid with milk and throwing a little smoke into the space above the water, the paths of the incident, reflected and refracted beams will all be made visible. By adjusting the mirror so that the reflected beam makes an angle of 90° with the refracted beam, both the reflected and the refracted light will be polarized, the plane of vibration in one beam being perpendicular to the plane of vibration in the other, as may be shown by examination with a tourmaline analyzer or with a Nicol's prism. (See § 744.) If such an analyzer be placed in the path of the incident beam (the incident beam being thus polarized), and then turned about its axis, the intensity of the re- flected and the refracted beams will alternate between maximum and minimum. By such means, the polarizing angle of any liquid is easily ascertained. The law may be expressed as follows : The tangent of the polarizing an- gle is equal to the refractive index (§ 678) of the reflecting substance, — or mien the reflected ray is com- pletely polarized, it is perpendicular to the refracted ray. §743. See Frick's "Physical Tech- nics," p. 233 (§§ 200-212) and Daniells " Principles of Physics," p. 509. § 744. The accompanying cut shows the position of the bisecting plane rela- tive to the ends of the prism. It is evident that two Nicols, placed in proper position, constitute a complete polari- scope. When placed so that the analyzer 268 [Elements of Natural Philosophy, p. 54$.] quenches the light transmitted by the polarizer, the prisms are said to be " crossed." See "■Nature," Vol. 35, p. 184. " By far the most perfect polarizer for a broad beam of light is a crystal of Iceland spar sufficiently thick to allow of the complete separation of the two rays. But such specimens are rare and costly, so that the polarizer in practical use is now what is called NicolCs prism, invented in 1828." — Tait. If on a clear, bright day, we examine the blue sky with a Nicol, we shall find traces of polarization in many direc- tions, but the effect will be most noticeable in directions at right angles to a line from the sun through the eye of the observer, i. e., when we are looking across the direction of the solar rays. When the sun is in the horizon (rising or setting), the best effect is produced by looking through the Nicol at some point of the sky that lies in a circle drawn through the zenith, the north and the south points. When the sun is in the zenith, the best results will be found by looking toward the horizon. Mr. Tyndall says: " The sun was near setting and a few scattered neutral-tint clouds, which failed to catch the dying light, were floating in the air. When these were looked at across the track of the solar beams, it was possible, by turning the Nicol round, to see them either as white clouds on a dark ground, or as dark clouds on a bright ground. In certain positions of the prisms, the sky -light was in great part quenched, and then the clouds, projected against the darkness of space, appeared white. Turning the Nicol 90° round its axis, the brightness of the sky was restored, the clouds becoming dark through contrast with this brightness. Experiments of this kind prove that the blue light sent to us by the firmament is polarized, and that the direction of most perfect polarization is perpendicular to the solar rays. Were the heavenly azure like the light scattered from a thick cloud, the turning of the prism would have no effect upon it ; it would be transmitted equally during the entire rotation of the prism. The light of the sky is in great part quenched, because it is in great part polarized." This quotation forms part of a very interesting dis- course on the Structure and Light of Vie Sky. See " Fragments of Science," Chapter X. When a plate of quartz, or a solution of sugar enclosed in a tube with glass ends, is placed between two crossed Nicols, there is a partial restoration of light. '* The action thus exerted by quartz or [Element* of Natural Philosophy, p. 549.] 269 vugar is called rotation of the plane of polarization, a name which precisely expresses the observed phenomena." A solution of l«mf- eugar turns the plane of i>olarization in one direction called right, handed; hence the chemical name of such sugar, destrote. A soln- tion of grape-sugar produces a left handed rotation of the plane of }M)larization ; hence its chemical name, levulose. (See Dcsehanei's Nat. Philoe., §§ 838, 839.) Among the latest studies in this field is ihat described in the following extract from Nature, No. 4!»2 : " rt is known that Faraday did not succeed in proving electro magnetic rotation of the plane of polarization of light in gases, nor have others succeeded. Considering the interest attaching to this question, Herr Kundt and Herr Rontgen lately thought to repeat the attempt with very strong currents and under the most favorable conditions. The result is that they have been able to prove the rota- tion, at least in the case of sulphide of carbon vapor. " Sulphide of carbon was chosen, on the one hand, because it shows a strong electro-magnetic rotation in the liquid state, and on the other, its vapor has a considerable tension, even at low temperatures. An iron tube was used for enclosure and heating of the substancu; it was closed at the two ends with glass plates 1 cut. thick, and itself enclosed in a tin-plate tube ; so that steam could be led between the tubes to heat the inner tube throughout to 100° C. The outer tube was surrounded by six large wire coils, each having 400 windings of wire 3 mm. thick, through which was passed the current from 64 large Bunsen elements. A little sulphide of carbon was introduced into the inner tul>e, and the air having been driven out by vapor forming at the ordinary temperature, the tube was closed and fixed in position, and steam was sent through the space round it. "When the whole tube had taken the temperature of l>oiling water, the glass plates and the sulphide of carbon vapor within became quite transparent. A beam of light rectilinearly polarized Ly a Nicol was now sent through, and a Nicol at the other end extin- guished it. The current of the 64 elements being now allowed to flow, a distinct brightening of the field was observed. The brighten ing became still greater when, after closing the circuit, the foremost Nicol was turned to darkness and the current then reversed with a commutator. The rotation of the plane of polarization occurred, as was to be expected, in the direction in which the positive current passed through the wire coils. " To test whether the rotation might not be due wholly or in part to the glass plates closing the inner tube, the experiment was ma til the number of ergs. 17. (b.) 16.08 ft. x GJ- x 6£ = 679.38 tt—Ans. (c.) 16.08 ft. x 17 = 273.36 ft.— An*. (d.) v as gt\ 448 = 32.16tf; / = 13.9 + Arts., 13.9-+- seconds. 22. I-) ?= jT£=, the part that the remaining air is of that originally in Hie receiver. The tension is fff of one atmosphere. See § 289 and Ex. 7. p. 180. 83. 02.42 lb. x 150 x 20 x 10 = 1,872,600 lb r ^-4fw. (§23.1.) 272 [Elements of Natural Philosophy, pp. 557, 558.] 25. (a.) Because the atmospheric pressure is not great enough to support such a column of water. (b.) The piston should be lowered to within 28 feet of the surface of the water. 28. | of surface weight = 120 lb.; surface weight = 320 lb * 320 = 4' l! = I) 4000 mi - x 2 = 8000 mi -> the distance from the earth's centre. Ans., 4000 mi. 39. (a.) (1.12 x 50) + 1090 = 1146; 1146 ft. x 18 = 20,628 ft. or 4 miles nearly. — Ans. (b.) 180; 216; 288. 40. (a.) It contains \ cubic meter of water, or 500 liters, which weigh 500 Kg. — Ans. (b.) 100 cu. cm. x 50 x 25 = 125000 cu. cm. = 125 l of water which weigh 125 Kg. 4L (*•> ^W^~^T = U ' thenumber of horse -P<™*- 4 42. On p. 147 of the text-book, we find the formula, v = V%g$ ; v 2 = 2gS. Substituting this value, vn? _ ZgSw ==wS=26 528Q _ 132 ooo, the number of foot-pounds. — Ans. See solution of 7th, page 361. 43 ' 302 ! 20^ } " 441 •• 576 .-. x = 73H Ans., 73ff lb. 44. Its diameter is 9 times that of the earth. Since solids are proportioned to the cubes of their like dimen- sions, Saturn in (9 x 9 x 9 =) 729 times as large as the earth. But it is only .12 as dense; hence, its mass is (729 x .12 =) 87.48 times that of the earth. 1 V^'v | = 16 ' 08 :x; •'* X = 17 * 3664 - Ans., 17.36+ ft. [humerus of Natural Philosophy, pp. oo'j,50u.] 273 „ . fc 150x1,920 x 1,'J.*" 6L <*> 64.32 x 772 ^2,000 = 5 '° + ' 32 + 5.5 ^ 3T.5.— A us., 37±° F. 52. (a.) 50 — 32 = 18. 18 x # = 10.— Arts., 10° C. (c.) Potential energy of chemical separation in fuel and atmospheric oxygen ; heat; mechanical kinetic energy of moving train ; heat developed by friction. 63. 1,390 x 30.48 = 42,367.2, the number of grain- centimeters. See § 1*54. 980 x 42,367.2 = 41,519,856, the number of ergs. 55. (a.) With less difficulty. See §§ 622-0 M. 56. (a.) See § 658 (a). 59. (a. ) It transmits only red light, (b.) It reflects only red light. 62. (b.) See § 35; 440 lb. = 200 Kg. A liter of air weighs 0.0896 #. x 14.42' s= 1.292032 g. The difference between the weight of a liter of hydrogen and that of the air it displaces (1.292032 #. — .0896 #. = 1.202432 #.) is the lifting power of a liter of hydrogen. The lifting power required is 200,000 #. 200,000 g.-r- 1.202432 #.=166,329.5+, the number of liters. See Appendix G. Ans., 166.3295 A7. 63. (a.) 15 lb. x (jtf = 2.54 lb.— Ans. See § 289. (b.) 8 = yP = 16.08 ft. x 6± x 6i = 679.38. ft. — Ans. 64. (a.) The boat displaced equal quantities of fresh and of salt water. Let x = the weight of fresh water dis- placed = weight of the river cargo. 1.028 x = the weight of stilt water displaced = weight of the ocean cargo. .028 x = 44,800 lb. x = 1,600,000 lb.— Ans. (b.) The water is 5 times as heavy ; an equal bulk of water weighs 60 lb.; 60 lb. — 12 lb. = 48 lb.— Am. 274 [Elements of Natural Philosophy, pp. 560-569.] 65. (a.) See § 475. 9 x 140 = 1,260, the number of watts. 1260 -j- 746 = 1.69 nearly, the number of H. P. (b.) See § 228. 24 x 170 x 12 = 48,960, the num- ber of cu. in. in "the imaginary column." This is 28 J cu. ft. See Note, p. 124. 62.42 lb. x 28£ = 1,768.57 lb. This is the total load supported by water pressure including the piston and its head. 66. 424 grammeters = 42,400 gram-centimeters. See § 154. 980 ergs x 42,400 = 41,552,000 ergs. Appendix D. The accompanying figure illustrates the method of performing this pretty experiment. It is well to place the bottle on a plate be- fore breaking off the tip of the " drop." Appendix L. See Frick's "Physical Technics," p. 360 (§§307,308). Appendix M. See Frick's "Physical Technics," p. 365 (§§ 310-312). Concerning the polarization of resistance coils, see "Science," Vol. 9, p. 12. Appendix K (4). An illustrated description of the ex- periment on the varying electrical resistance of selenium will be found on p. 139 of Gordon's " Electric Induction." T »*S BOOK is B P^flMril ^^ =========: =====^ == __ ENT H DAY ^f^ssai^i L *> 21-j YB 05199 UNIVERSITY OF CAUFORNIA UBRARY