HANDBOOKSfor Students andGcneml Readers 
 
 UC-NRLF 
 
 Ifi? 200 
 
 PRACTICAL PHYSICS 
 
 GUTHR1E 
 
LIBRARY OF THE UNIVERSITY OF CALIFORNIA. 
 
 Miss ROSE WHITING. 
 
 September, 1896. 
 Accession No. fa 3 & 7 &~ Oa*s No. 
 
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 Zoology of the Invertebrate Animals. By ALEX. MACALISTER, 
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HANDBOOKS for Students and General Readers 
 
 PRACTICAL PHYSICS 
 
 MOLECULAR PHYSICS 6* SOUND 
 
 BY 
 
 FREDERICK GUTHRIE, PH.D. F.R.SS. L. & E. 
 
 PROFESSOR OF PHYSICS 
 IN THE ROYAL SCHOOL OF MINES, LONDON. 
 
 NEW YORK 
 
 HENRY HOLT & COMPANY 
 1879 
 

EXPLANATORY. 
 
 THIS Series is intended to meet the requirement of 
 brief text-books both for schools and for adult readers 
 who wish to review or expand their knowledge. 
 
 The grade of the books is intermediate between the 
 so-called "primers" and the larger works professing 
 to present quite detailed views of the respective sub- 
 jects. 
 
 Such a notion as a person beyond childhood re. 
 quires of some subjects, it is difficult and perhaps 
 impossible to convey in one such volume. Therefore, 
 occasionally a volume is given to each of the main 
 departments into which a subject naturally falls for 
 instance, a volume to the Zoology of the vertebrates, 
 and one to that of the invertebrates. While this ar- 
 rangement supplies a compendious treatment for those 
 who wish, it will also sometimes enable the reader 
 interested in only a portion of the field covered by a 
 science, to study the part he is interested in, without 
 getting a book covering the whole. 
 
 Care is taken to bring out whatever educational 
 value may be extracted from each subject without im- 
 
vi Explanatory. 
 
 peding the exposition of it. In the books on the 
 sciences, not only are acquired results stated, but as 
 full explanation as possible is given of the methods of 
 inquiry and reasoning by which these results have 
 been obtained. Consequently, although the treatment 
 of each subject is strictly elementary, the fundamental 
 facts are stated and discussed with the fulness needed 
 to place their scientific significance in a clear light, 
 and to show the relation in which they stand to the 
 general conclusions of science. 
 
 Care is also taken that each book admitted to the 
 series shall either be the work of a recognized author- 
 ity, or bear the unqualified approval of such. As far 
 as practicable, authors are selected who combine 
 knowledge of their subjects with experience in teach- 
 ing them. 
 
AUTHOR'S PREFACE. 
 
 I HOPE that the following outlines of Practical Physics, 
 including Molecular Physics, Waves, Sound, Light and 
 Heat, may be of use to those Teachers and Students 
 who wish to give or to get more than a mere word- 
 knowledge of the matter. Such knowledge alone no 
 more gives its owner a right to be reckoned a Physicist 
 than does a knowledge of sound and harmony entitle 
 him to be called a Musician, or a knowledge of per- 
 spective and colour to the name of Artist. 
 
 It has been the strong wish and effort of some few 
 Physicists of late years to bring practical work into 
 their teaching, and thus to do for Physics what has 
 been for so long done for Chemistry with great gain. 
 For it seems that knowledge got by the head alone 
 is often very fleeting : whereas when head and hand 
 learn together, the power of keeping is strengthened. 
 And we look upon such practical teaching as good, 
 not only because it is the only way to forge the link 
 by which man is bound to nature, but also because 
 it forms the one discipline of truth in the ways of 
 
 matter. 
 
 FREDERICK GUTHRIE. 
 LONDON, 1878. 
 
CONTENTS. 
 
 COHESION OF SOLIDS. 
 
 SUCTION PAOB 
 
 1-7. Hardness. Form-Elasticity. Tenacity. 
 
 Torsion .1-8 
 
 COHESION OF LIQUIDS AND GASES. 
 
 8-19. Jets. Rupture. Drop size. Bubble size. 
 
 Viscosity 8-19 
 
 VOLUME-ELASTICITY OF SOLIDS, LIQUIDS, 
 AND GASES. 
 
 20-23. Elasticity of Liquids. Elasticity of Gases. 
 
 Relation between volume and pressure. 19-23 
 
 COHESION OF LIQUIDS AFFECTED BY 
 ADHESION TO SOLIDS. 
 
 24-29. Capillarity 23-28 
 
 COHESION OF SOLIDS AFFECTED BY ADHESION 
 TO LIQUIDS. ABSORPTION OF GASES. DIF- 
 FUSION. 
 
 30-59. Solution. Diffusion of liquids into liquids. 
 Diffusion of gases into liquids. Absorption. 
 
Contents. 
 
 PACK 
 
 Occlusion. Breath pictures. Diffusion of 
 gases into gases. Effusion. Diffusion of 
 liquids into gases. Vapour tension. Dif- 
 fusion of liquids into solids. Osmose. 
 Dialysis. Transpiration . . . 29 54 
 
 DENSITY. SPECIFIC GRA VITY. 
 
 60-73. Of Solids. Liquids. Solids lighter than water. 
 
 Solids soluble in water. . . . 55-63 
 
 VORTEX MOTION. 
 74. Vortex motion in gases and liquids. . 63-65 
 
 WA VES. 
 
 75-83. Water waves. Reflexion of water waves. 
 Stationary water waves. Waves governed 
 by elasticity. Notes. Detection of sound. 
 Sensitive flame. Reflexion of sound. Ab- 
 sorption of sound. Refraction of sound. 
 Dispersion of sound 65-82 
 
 ORIGINS OF SOUND WAVES. 
 
 84-95. Transverse vibrations of rods. Composition of 
 vibrations. Transverse waves in strings. 
 Nodes, Stationary waves. Vibrating strings 
 as sources of sound. Musical scale. Nodes 
 in rods. The bell. Thunder. Nodes and 
 segments of vibrating plates. . . 83-104 
 
 THE GAS WAVE. 
 
 96-99. Vibrations in gases Closed and open tubes. 
 
 Nodes in open tubes. Resonance . 104-112 
 
Contents. xi 
 
 LONGITUDINAL VIBRATIONS IN LIQUIDS 
 AND SOLIDS. 
 
 SECTION PAGB 
 
 loo-iio. Transmission of sound. The string telephone. 
 Interference. Beats. Singing flames. Si- 
 nuosities. Effect of motion of source of sound. 
 Sympathy. Approach caused by vibra- 
 tion. The phonograph. . . .112-124 
 
 APPENDIX. 
 
 111-115. The vernier. Parchment paper. Hints on 
 glass working. To etch a scale on glass. 
 The siphon barometer. . . . 125-133 
 
 ELEMENTARY EXPERIMENTS RELATING TO 
 
 SOUND AND WAVES .... 134-150 
 
 APPARATUS AND MATERIAL FOR EXPERI- 
 MENTS IN SOUND AND WAVES . . 151-154 
 
 INDEX 
 

 PRACTICAL PHYSICS. 
 
 PART I. 
 
 MOLECULAR PHYSICS AND SOUND. 
 
 COHESION OF SOLIDS. 
 
 i. Hardness. Form-elasticity. The pressure 
 required to alter the relative positions of two contiguous 
 parts of a body measures its hardness. As this pressure 
 is greater with greater surfaces of contact, some unit of 
 surface must be fixed upon. The term hardness is 
 generally applied loosely to difficulty of fracture. The 
 following remarks may show that our speech and ideas 
 in regard to hardness are deficient in precision. Glass 
 is said to be harder than lead, yet a glass cup is more 
 easily broken than a leaden one more easily broken, 
 though not so easily bent. Hard bodies are always 
 elastic ; elastic bodies are not necessarily hard, nor are 
 they necessarily brittle, nor are soft bodies necessarily 
 plastic. Toughness seems to imply a resistance to 
 change of form, which resistance increases more rapidly 
 than the displacement; thus, while a band of vulcanised 
 caoutchouc will be extended to a degree proportional 
 to the weight hung at one end, a leathern strap will 
 
2 Practical Physics. 
 
 not be extended twice as far if the weight on it is 
 doubled. Toughness is generally associated with 
 texture, and stretching causes partial fibration in the 
 line of pull. 
 
 The hardness of minerals, stones, and similar 
 bodies, is usually referred to the terms of the follow- 
 ing series : 
 
 (1) Talc . . . Silicate of magnesium 
 
 (2) Gypsum (selenite) . Sulphate of calcium 
 ($) Rock salt . . . Chloride of sodium 
 
 (4) Calc-spar . . . Carbonate of calcium 
 
 (5) Apatite . . . Phosphate of calcium 
 
 (6) Felspar . . . Silicate of potassium 
 
 and aluminum 
 
 (7) Quartz . . . Silica 
 
 (8) Topaz . . . Fluosilicate of aluminum 
 
 (9) Corundum (sapphire, 
 
 ruby) . . . Alumina 
 (ro) Diamond . . . Crystallised carbon 
 
 Each of these scratches all of those above it, and is 
 scratched by those below. Thus, if a body under exa- 
 mination is found to scratch felspar, but to be scratched 
 by quartz, its hardness is said to be between 6 and 7. 
 This method of comparison is somewhat vague ; it is 
 usually applied by rubbing an edge or point of one 
 body on a surface of the other, and although of course 
 the common surface of the two is identical, the sur- 
 faces are not equally supported by surrounding matter. 
 On rubbing together two equal spheres of iron and 
 lead, the latter metal is rubbed off ; on pressing them 
 together, the lead is indented, showing that its cohesion 
 
Hardness. Tenacity. 3 
 
 or hardness is less than that of the iron. Nevertheless, 
 a leaden bullet will pierce an iron plate, and a rapidly 
 revolving disc of iron will cut the hardest steel. Also 
 if a glass tube be broken in the middle, the jagged 
 edge can be broken off by the smooth tube, and the 
 smooth tube can be scratched by the ragged edge. 
 
 2. The cohesion of metals is usually measured 
 as tenacity, that is, by finding the maximum weight 
 which wires of a given thickness will carry. The 
 drawing of a wire through a stock tends, however, to 
 render the metal fibrous, and to give it a skin which 
 is more tenacious even than the interior. Since the 
 surface varies with the diameter, and the sectional 
 area with the square of the diameter, two wires, each 
 of sectional area 0, will support more than one of 
 sectional area 2 a, because the sum of the circum- 
 ferences or skin-rings of the two is greater than the 
 skin-ring of the larger wire. Thus, a drawn steel rod 
 of i meter in length will not support so much as the 
 same steel drawn into a wire 1,000 meters long, cut 
 up into 1,000 lengths of i meter each, and forming a 
 bundle. The tenacity of the skin can be reduced by 
 annealing (heating and slow cooling), but it is here, 
 as always, impossible to get the solid body perfectly 
 homogeneous. Some experimental measure may be 
 got of the tenacity, by fastening one end of the wire 
 to a spring balance rigidly fixed and the other to a 
 pianoforte peg, and turning the peg till the wire 
 breaks. After one wire has been broken, a second is 
 taken, and the index is more narrowly watched, or 
 made self-registering. 
 
 3. Wires which are pulled by forces insufficient 
 
4 Practical Physics. 
 
 to break them are elongated, and return after the 
 withdrawal of the stretching force more or less com- 
 pletely and rapidly (from a second to several days) to 
 their original lengths. To prove that within the limits 
 of such elasticity the extension is proportional to the 
 stretching force, two points or lines are marked on 
 the wire, which should for this purpose be two or three 
 yards long, the marks being an inch or two from each 
 end. The wire is hung vertically, is gently weighted, 
 and while so strained it is annealed by passing along 
 fc the flame of an air-gas burner. If the metal will 
 bear it, each part is made red-hot in succession. 
 This removes kinks, and makes the wire absolutely 
 straight. The distance of the marks apart is then 
 measured by a cathetometer, and the distance is again 
 measured when the stretching weight is changed. It 
 may be assumed that all parts of the wire are stretched 
 equally ; it may also be assumed that the volume of 
 the metal remains approximately unchanged, so that 
 if the elongation is such that the length m becomes /z, 
 
 the original diameter d becomes d\/. Besides 
 
 V n 
 
 this true elasticity, whereby wires recover their length, 
 they, when stretched nearly to breaking, become per- 
 manently elongated. A thin copper wire may be cau- 
 tiously stretched between the hands a quarter of its 
 length longer, and every wire will bear more if loaded 
 gradually than if loaded quickly, even though the latter 
 operation be quite continuous. 
 
 4. Elasticity. Bodies differ from one another in 
 regard to elasticity (i) as to the pressure required to 
 produce a given deformation, and (2) as to the reco- 
 
Form-elasticity. Torsion. 5 
 
 very of their original form after deformation. Hard 
 steel and glass, for example, recover their form very 
 perfectly even after great deformation ; while in lead 
 the recovery is complete only when the deformation 
 has been very small. The pressure necessary to cause 
 and maintain a given deformation may be called degree 
 of elasticity. Vulcanised caoutchouc is nearly perfectly 
 elastic for small displacements, but its elasticity is not 
 so strong as that of glass, steel, or ivory. The elas- 
 ticities of wires and rods can of course be directly, but 
 only roughly, measured by the elongation method. If 
 a rectangular rod be bent from the straight to an arc, the 
 outer face is elongated and the inner crushed together, 
 and accordingly there is a certain surface which is 
 neither stretched nor crushed. When a rod or wire, 
 which may be supposed to be vertical and fastened 
 above, is twisted, every series of particles which to 
 begin with lay in a horizontal plane still do so, but 
 the plane itself is raised. Particles which lay in a 
 vertical line now lie in a spiral, and contiguous ver- 
 tical lines of particles must slide over one another. 
 The rod or wire shortens, and there is on the whole 
 an intermolecular motion proportional to the pressure 
 maintaining the twist or torsion. And this fact fur- 
 nishes the best method of proving that with the same 
 substance the elasticity, or effort to regain original 
 shape, varies with the angle of torsion or deformation. 
 5. A horseshoe magnet, M, is set up under a 
 bell-jar in a vertical plane (fig. i). Two pieces of 
 cardboard or mica are stuck on the poles on alternate 
 sides. Two little equal soft-iron bullets are soldered 
 to the ends of a stiff brass wire, w 3 which is then bent 
 
6 
 
 Practical Physics. 
 
 twice at right angles in a plane, so that when the 
 centre of the wire is in the axis of the jar the bullets 
 may rest on the cardboard. One end of the wire 
 which is being experimented on is soldered to the 
 middle of the brass wire, the other passes through a 
 FlG . x- narrow glass tube, /, at the upper end of 
 which it is fastened by a drop of sealing- 
 wax . The tube passes stiffly through a 
 cork in the mouth of the bell-jar and 
 carries an index, which passes over a 
 scale of angles on the cork. A horse- 
 shoe keeper is placed on the magnet, and 
 the tube is turned till the balls are in 
 contact with the cardboard. The keeper 
 is then removed, and the balls are at- 
 tracted to the poles. Gradually turn the 
 tube in the cork till separation ensues ; read off the 
 angle of torsion, o l5 measure the length, /,, of the 
 wire from the glass tube to the brass wire. Soften 
 now the wax which holds the wire in the tube and 
 alter the length of the free wire to / 2 , pushing the 
 tube through the cork till the balls rest exactly where 
 they did before. Turn as before till separation ensues. 
 The new angle being a 2 , it is found that 
 
 l\ __ 
 
 "2 
 
 Or if the wire be twice as long, the upper end must 
 be twisted through twice the angle in order to give a 
 given thrust at the lower end. One may derive the 
 same fact by reasoning only, in the following way. 
 Suppose a pair of tangentially acting forces, //, 
 
Torsion. Torsion Pendulum. 7 
 
 applied at given arms, a a, to the middle of a wire 
 of length /, fixed at the top but hanging free below, to 
 cause an angular twist of a there, and therefore also at 
 the bottom of the wire. Clamp the wire in the middle, 
 and the frictional resistance of the clamp will perform 
 the same office as the pressures fi and /. Twist now 
 the bottom end also with pressures/ and/, also acting 
 at arms a and a. They will turn the end round through 
 an angle , and if the clamp be now loosened, the wire 
 will be found to be in equilibrium. So that, applied 
 at the end, a pair of twisting forces (a couple) will 
 give a torsion angle 2 a if they give an angle a when 
 applied in the middle 
 
 FfG. 2. 
 
 o 
 
 6. To show that, with the same length of wire, 
 the pressure is proportional to the angular displace- 
 ment, the wire can be fastened as in fig. 2. Its cross- 
 arm at the bottom rests against the two vertical arms 
 of two balanced levers provided with scale-pans. If 
 the upper end of the wire receives a given twist, the 
 lower end is kept in its place by altering the weights 
 in the scale-pans. With double the twist the weights 
 must be doubled, and so on. 
 
 7. By far the best proof of this relationship, 
 
8 Practical PJiysics. 
 
 although an indirect one, is the isochronism of a tor- 
 sion pendulum. A cannon-ball is bored through the 
 middle ; a steel wire is fastened to it with lead, the 
 other end being supported on a strong stand ; the ball 
 is twisted round three or four times, and let go. It may 
 keep its motion forwards and backwards for forty-eight 
 hours. Whatever may be its angular amplitude of 
 swing, its period is very nearly identical. This can 
 only be the case if the angle of displacement is pro- 
 portional to the pressure of displacement a condition 
 approximately fulfilled by the common pendulum only 
 when the arc traversed is so small as to be sensibly 
 equal to the corresponding chord. 
 
 COHESION OF LIQUIDS. 
 
 8. That liquids have cohesion is shown in a 
 variety of ways. A drop of water on a board strewn 
 with powdered resin is nearly spherical. The .smaller 
 the drop the more nearly spherical. So is a drop of 
 water on a sheet of paraffin, or a drop of mercury upon 
 almost every substance. The spherical is the form in 
 which the mean distance of all parts from the centre of 
 mass is the least. It is the most compact form for a 
 given mass. This shows that cohesion moulds the drop 
 to the spherical form. This result is very elegantly 
 shown by making such a mixture of alcohol and water 
 as has the same specific gravity as olive oil. Alcohol 
 being lighter and water heavier than oil, alcohol is 
 added to water in which there are a few drops of oil 
 
Liquid Cohesion. Jets. Rupture. 9 
 
 until the latter just float when the mixture has cooled to 
 the ordinary temperature. Fresh oil is then, by means 
 of a pipette, poured into the middle of the mixture. 
 Spherical globes several inches in diameter can thus 
 be formed. 
 
 9. One of the best, as it is one of the simplest, 
 methods of measuring the cohesion of liquids is to sus- 
 pend a flat, round plate of glass, thoroughly cleaned, 
 from one pan of a balance, and to counterpoise it ; 
 the surface of the glass being adjusted so as to be 
 exactly level, bring under it a dish of water, and lift and 
 support the dish till the bottom of the plate is in con- 
 tact, without air bubbles, with the water, taking care not 
 to wee the top ; load gradually the other pan till the 
 plate is torn away. It does not matter what the plate is 
 made of, provided it is wet by water ; the same force is 
 required, and this is the force required to tear asunder 
 a given surface of water from the neighbouring lower 
 surface. It is not the separation of water from glass, 
 because the lower surface of the glass remains com- 
 pletely wetted. A good way of hanging the glass is to 
 heat it and fasten by wax three threads to its upper 
 surface. These are tied together a few inches above 
 the plate, and fastened to a single thread which is 
 fastened to the pan of a balance. On wiping the glass 
 dry and replacing the water by alcohol, a less force is 
 found to be necessary. 
 
 10. A beautiful way of showing that water has 
 cohesion is to let a smooth vertical column of water, 
 not flowing too fast, fall fair upon a small round cup 
 or horizontal disc. The water is thrown off horizon- 
 tally, but is not scattered as spray; it draws itself 
 
IO Practical Physics. 
 
 together, forming a sort of film water-bottle of grace- 
 ful form. Mercury acts in a similar manner. 
 
 11. Another method of showing liquid cohesion 
 is to close one end of a wide glass tube, bend it in the 
 middle, draw out the other end, and tie over it a piece 
 of black caoutchouc tubing. The tube (fig. 3) is 
 nearly filled with water, which is then boiled uniformly 
 till about a quarter has been boiled off. The caout- 
 chouc is then pinched between the fingers near the 
 glass, and the flame is withdrawn. In a few seconds 
 the fingers may be taken away, and the narrow part of 
 the neck may be sealed off over the flame. The 
 pressure of the air closes- the caoutchouc, and assists 
 the closing of the glass. On cautiously turning the 
 FIG. 3 . tube over, the liquid stands as 
 
 in the figure. Accordingly, as 
 the water-column does not 
 break, it must have cohesion. A 
 smart rap on the table breaks 
 the column, and the water then stands at the same 
 height in both limbs. 
 
 12. The cohesion of liquids can be most ac- 
 curately measured and compared by determining the 
 degree to which such cohesion has affected the size of 
 afaikn drop. What is here meant by a drop is a 
 FIG. 4 . mass f liquid (fig. 4) which has 
 
 J~~~ | wetted a solid and which has ac- 
 
 ^- ^ AT *Y\ cumulated on the solid until its 
 ^ cohesion has been overcome by 
 its own weight. It then falls, its size depending 
 very little upon the nature of the solid from which it 
 falls, but very much upon the rate at which it drops, 
 
Drop-size. 
 
 il 
 
 upon the shape of the surface from which it drops, 
 upon the density of the liquid, and upon its cohesion. 
 To show how much depends upon rate, other things 
 being the same, let water flow from a siphon provided 
 with a stop-cock upon a glass sphere (a round glass 
 flask) so that the drops succeed one another at the rate 
 of 2 per second. Catch 100 in a weighed flask and 
 weigh. Let now the drops succeed one another at the 
 rate of i in 10", or twenty times as slow as before ; 
 catch 100 and weigh. The first hundred will weigh far 
 more than the last : about one-third as much again. 
 And of course every drop of the quick delivery bears 
 this proportion to every drop of the slow. 
 
 13. Again, other things being the same, the 
 flatter the surface the larger the drop. Fasten (fig. 5) 
 three round glass flasks one above the othrr in order 
 of magnitude, and put a little muslin 
 cap on each. Let water flow ircm 
 a tube upon the upper one. Droj s 
 will fall from this to the next lower, 
 from this to the third, and from the 
 third into a basin. The same quan- 
 tity of water drops in the same time 
 from each sphere, or if anything a 
 little less from the lower spheres on 
 account of evaporation. And ytt 
 the drops succeed one another far faster from the 
 lower than from the uppei spheres. The largest 
 drops are those which fall from a flat surface. The 
 effects of density and cohesion are opposed to each 
 other, but experiment shows that increase in specific 
 gravity, which by itself always tends to diminish drop 
 
 FIG. 5. 
 
12 Practical Physics. 
 
 size, may be more than counterbalanced by increased 
 cohesion. Thus if the radius of a sphere of platinum 
 be i *i 4 centimeters, and various liquids be made to 
 drop from it at the rate of one drop in every 2", at a 
 temperature of 26 C., the actual volumes in cubic 
 centimeters of i drop of each liquid are as follows : 
 
 Water . . . . .< 0-148 
 
 Glycerine . . . . 0*103 
 
 Mercury . . . . 0-058 
 
 Benzol '55 
 
 Oil of Turpentine . . . 0*050 
 
 Alcohol .... 0*049 
 
 (glacial) Acetic acid . . . . 0*043 
 
 The mercury is made to touch the platinum by rubbing 
 the surface of the platinum with a little mercury in 
 which a minute fragment of sodium has been dissolved. 
 The sodium is rubbed into the mercury in a dry por- 
 celain mortar, whereupon the two unite with liberation 
 of heat. The platinum is then washed in fresh clean 
 mercury. 
 
 Constancy in delivery is got by using a siphon and 
 inverting into the basin which feeds the siphon a flask 
 containing the same liquid (fig. 6). The level of the 
 FIG. 6. liquid never falls sensibly below 
 
 the neck of the flask if the latter 
 is notched. If the liquid can be 
 had, like water, in any quantity, a 
 more exactly constant level is got 
 by allowing the basin to continu- 
 ally overflow by receiving a succession of drops con- 
 
Bubble-size. 13 
 
 taining a greater supply of liquid than the siphon has 
 to deliver, and by regulating the overflow by laying a 
 square piece of linen with one corner hanging over the 
 edge of the basin. This acts as a siphon of variable 
 capacity. In the case of mercury the linen is replaced 
 by a piece of amalgamed platinum foil. 
 
 1 4. Bubbles, The cohesion of liquids also de- 
 termines the shapes and sizes of bubbles properly so 
 called ; that is, masses of gas liberated in the midst of 
 a liquid and finally separated from their sources by 
 the buoyancy of the surrounding liquid. Films en- 
 closing air or gas are also called bubbles. The bubble- 
 size of a gas issuing through an orifice in the middle of 
 a liquid is influenced (i) by the rate at which the 
 bubbles succeed one another (this is of very small 
 effect) ; (2) nature of the solid from which the gas is 
 delivered ; (3) size of orifice and distribution of solid 
 about it; (4) temperature of gas and liquid; (5) ten- 
 sion of gas ; (6) nature of liquid. 
 
 1 5. The apparatus employed is shown in fig. 7. 
 The quart bottle A is filled a little above the mark a 
 with water, which in some experiments is covered with 
 a film of oil. Through its cork three tubes, c E F, pass 
 absolutely air-tight. The tube c is a simple funnel 
 tube open near to the bottom of A. The tube D also 
 reaches to the bottom of A and acts as a siphon. Its 
 longer limb is narrowed at the end, and delivers its 
 water into the little flask M whose neck bears a mark. 
 The shorter limb of D bears a cock E to regulate 
 its discharge. The third tube F, which opens imme- 
 diately under the cork of A, is fastened by a caout- 
 chouc joint to the tube B. In this joint, and pressing 
 
14 Practical Physics. 
 
 the ends of both tubes, is a compact mass of cotton 
 wool. B passes through the cork of the little test-tube 
 G, which is divided into millimeters and contains the 
 liquid through which the bubbles are to pass. 
 
 Through the cork of G another tube H is passed, 
 which is bent round near the lower end h so as to open 
 upwards, and is beneath the surface of the liquid in G. 
 
 FIG. 7. 
 
 H is connected by a caoutchouc joint with i, which 
 passes nearly to the bottom of a second little test-tube 
 j. The tube j contains a few drops of the liquid which 
 is in G, and the space between I and the sides of j is 
 filled with cotton wool moistened with the same liquid. 
 The last tube K, which opens immediately under the 
 cork of j, is either open to the air or connected with a 
 gas bag containing the gas under examination, or 
 
Bubble-size. 1 5 
 
 fastened to a chloride of calcium tube according to 
 the requirements of the experiment. In some experi- 
 ments the little tubes G and j are surrounded with 
 water contained in the vessel N. A thermometer T is 
 placed in the water of N. 
 
 The apparatus is used as follows. B and F being 
 disconnected, the bottle A is nearly filled through c. 
 The end of F is closed by the finger, and, the stop- 
 cock E being opened, the siphon D is filled once for 
 all by applying the mouth to its longer end. E being 
 then closed, the tube G is filled up to the required 
 mark with the liquid which is to serve as a bubble 
 medium. The cotton wool in j is moistened with the 
 same liquid. All the joints are made fast, and the 
 tube K is connected with the gas bag L. On turning 
 the stop-cock E, water flows through the siphon D into 
 the flask M. To supply its place, gas must enter by 
 
 F, that is, gas must bubble through the liquid in G. 
 Before entering G it becomes saturated with the vapour 
 of the same liquid in j. If all the joints are tight, it 
 follows that the volume of water entering M is equal to 
 the volume of gas which bubbles through the liquid in 
 
 G. It is a sufficient test of the tightness of all the joints 
 (as far as H) to run off a little water by D so as to bring 
 a bubble or two of the gas through h and to allow the 
 apparatus to rest. If the tube H remains full of air to 
 its extremity for a quarter of an hour, the apparatus 
 may be considered as air-tight. A metronome is ad- 
 justed to beat to the required time. M is removed and 
 emptied. E is turned till the bubbles passing through 
 the liquid in G keep time with the beats of the metro- 
 nome. This rate is maintained till the liquid in A sinks 
 
1 6 Practical Physio*. 
 
 to a. The flask M is then put in its place, and from 
 that instant the bubbles passing through G are counted. 
 When M is filled exactly up to the mark the experiment 
 is finished. The proximity between M and G enables the 
 eye to count the bubbles and to watch without diffi- 
 culty, at the same time, the rise of the liquid in M. The 
 contents of M, divided by the number of bubbles, gives 
 the mean volume of a single bubble. The use of the 
 cotton wool in the joint between B and F is to check 
 the flow of gas through the apparatus. When this 
 plug is absent, the considerable volume of gas in the 
 upper part of A, being in direct communication with 
 G, causes by its elasticity an irregular delivery of 
 bubbles through G. Of course as M is filled, the level 
 of the liquid in A falls. The difference between the 
 limbs of the siphon D is diminished ; the flow through 
 D is retarded, and the bubbles follow one another 
 more slowly ; this, however, makes exceedingly little 
 or no difference in the size of the bubbles. 
 
 1 6. The radii of the tubes being shown in column 
 (i), the volumes of the air bubbles delivered from the 
 tubes at the rate of i bubble in 2" are shown in 
 column (2). The liquid medium is water. 
 
 (i) (*) 
 
 0-1428 0-035 
 
 0*4595 0<I 49 
 
 0-6035 0-152 
 
 1-4099 0-178 
 
 17607 0-244 
 
 2*0998 o'3 I 9 
 
 17. The combined effect of the cohesion and 
 
Bubble-size. *%j 
 
 specific gravity of the liquid in determining the bubble- 
 size, is measured by altering the liquid while other 
 circumstances .are maintained the same. In the fol- 
 lowing table are given in cubic centimetres the bubble- 
 sizes of air passing through various liquids. 
 
 Mercury . . . . .0-4120 
 
 Glycerine 0-1145 
 
 Water 0-0860 
 
 Butyric acid 0-0582 
 
 Acetic acid 0*0572 
 
 Alcohol 0*0480 
 
 Benzol ...... 0*0480 
 
 Oil of Turpentine .... 0*0453 
 
 Acetic ether ..... 0*0372 
 
 In determinations of this last kind the gas bag L is 
 replaced by a chloride of calcium tube. The cotton 
 wool of j is saturated with the liquid under examina- 
 tion in G, so that the bubbling gas is dry air already 
 saturated with the vapour of the liquid through which 
 it has subsequently to bubble. It is clear that if the 
 air so charged were to come into contact with the 
 water in A, the vapour would dissolve in the water, 
 while the air would become moist. A difference in 
 volume would be thereby occasioned, according to the 
 difference of the tension of the vapour of the liquid in 
 G and j on the one hand, and that of water on the 
 other. To avoid this source of error, the vessel A is 
 filled with mercury ; and after each experiment the 
 vessel A is completely refilled with mercury, so as to 
 expel the vapour of the liquid used in the previous 
 experiment. The mercury is then run. off at D until 
 c 
 
i8 Practical Physics. 
 
 it falls in A, nearly to the mark a. The liquid under 
 examination in G should have a height above h in- 
 versely as its specific gravity. This is easily effected 
 by means of the graduation of the tube G. By this 
 means the pressure on the gas as it issues from h is 
 the same in all the experiments. The vessels A, G, 
 and j are all sunk in the same trough of water, so 
 'hat the volume of the air undergoes no alteration 
 from temperature, either during or after its passage 
 through G. When the growth- time of the bubbles has 
 "been brought exactly to the pre-determined value 
 (say 2"), and the mercury in A has sunk to a, a 
 graduated burette is brought under the siphon D, and 
 kept there while 100 bubbles pass through G. 
 
 1 8. The size of an air bubble iormed under 
 given conditions in a mixture of two liquids, A and B, 
 is a mean between its size through A and through B. 
 And a very accurate estimate of the relative quantities 
 of the two constituents of a mixture can be got if we 
 know the bubble size in each constituent. 
 
 19. Cohesion of Gases Viscosity. Although a 
 gaseous mass will preserve neither its shape nor its 
 volume unless enclosed by Folid or liquid walls, and is, 
 'herefore, destitute of that cohesion which is repre- 
 sented by hardness and form-elasticity, it offers, accord- 
 ing to its nature, a variable resistance to bodies passing 
 through it. Now, as such resistance in the case of 
 solids and liquids is obviously and directly associated 
 with their hardness, we may here mention the chief 
 direct experiments on the viscosity of gases. This 
 has been most accurately determined in a direct man- 
 ner by pendulum experiments. A pendulum is made 
 
Volume-elasticity. 19 
 
 to swing, beginning with a given arc, in a chamber 
 which can be filled with any gas. By raising or 
 lowering a mercury valve, a constant tension of the 
 gas in the chamber can be obtained. The time 
 occupied by the pendulum in performing a given 
 number of oscillations is noted. A more exact method 
 is to place timed chronometers under bell-jars con- 
 taining various gases, and also in vacuo. 
 
 VOLUME-ELASTICITY OF SOLIDS, LIQUIDS, 
 AND GASES. 
 
 20. No direct and exact measurements have 
 been made of the compressibility of solids. For sen- 
 sible compression such enormous pressures are re- 
 quired, that at present exact measurements are wanting. 
 And even with most liquids the compressibility is so 
 small, even by great pressures, that special ' piezome- 
 ters ' are used. One form of piezometer, which can be 
 made without much difficulty, is shown 
 in fig. 8. A very stout glass tube, T, 
 is closed at the bottom, and about 
 half-way up in its side two platinum 
 wires, p l p 2 , are fused through the glass. 
 Some mercury is poured in, and then 
 two tubes, one containing air and the 
 other the liquid under examination, 
 both being closed at the top and open below, are 
 introduced, so as to stand in the mercury. Finally, a 
 little dilute sulphuric acid is introduced, so as to cover 
 c 2 
 
2O Practical Physics. 
 
 the platinum wires, and the tube is then hermetically 
 sealed. On connecting p and / 2 with the poles of 
 a two-cell piatino-zinc battery, the water is decom- 
 posed into its two elements, which, not being able to 
 escape, exert a greater and greater pressure on the 
 sulphuric acid, and thence on the mercury surface, 
 and so compress the air in the one tube and the 
 liquid in the other. As we shall see in 22, the 
 volume of a given mass of air is inversely proportional 
 to the pressure upon it. Hence, if the volume of air 
 is halved by the pressure thus generated, we know 
 that the pressure is doubled, that is, instead of being 
 exposed to one atmosphere, it is exposed now to two, 
 and so on. It is not safe to generate a pressure of 
 more than four or five atmospheres ; and it is dan- 
 gerous to allow the platinum to be exposed above the 
 liquid, for the clean platinum may determine the recom- 
 bination of the elements of water with great violence. 
 21. Elasticity of Gases : Relation between 
 Volume and Pressure. It appears that gases, vapours, 
 and liquids are continuous in their elastic properties. 
 The gases most difficult to condense are hydrogen, 
 nitrogen, and oxygen, and a few compound gases. The 
 three gases named follow very nearly the generalisation 
 that their volume varies inversely with the pressure 
 to which they are subjected. Substances which are 
 gaseous under ordinary conditions of temperature and 
 pressure, may, when the pressure is increased or the 
 temperature diminished, become liquids. Such hque- 
 fiable gases are often called vapours; and ihe gene- 
 ralisation which connects vapours and gases is that 
 the nearer a vapour is to liquefaction, either by in- 
 
Volume and Pressure of Gases. 21 
 
 then 
 
 thickly 
 FIG. 9. 
 
 and 
 
 860 
 
 creased pressure or by diminished temperature, the 
 more does it depart from the generalisation that its 
 volume varies inversely as the pressure upon it. 
 
 22. A tube of about in. internal bore, and 4 ft. 
 long, is thoroughly cleaned, and one end is closed 
 and flattened by pressing on it when red hot a piece 
 of flat charcoal ; or the edge may be turned so as to 
 form a lip, and a well-fitting cork being driven in, is 
 tied down by thin copper wire, which passes also 
 beneath the lip. The cork is 
 smoothly covered with sealing- 
 wax (fig. 9). The tube is then 
 bent so as to form two parallel 
 limbs, of which the shorter, 
 which is the closed end, is about 
 6 in. long. It is now fastened to 
 an upright support, and a drop 
 or two of mercury is poured 
 into the open end, so as just 
 to cover the bend and shut off 
 the air in the closed limb. 
 Adjust a millimeter scale to 
 both limbs so that the o is on a 
 level with the mercury. Sup- 
 pose the barometer stands at 
 760 millimeters of mercury at the time of the expe- 
 riment ; and suppose that the top of the closed tube 
 is opposite the 200 millimeter mark : pour mercury 
 into the long limb until the mercury in the short limb 
 stands at 100; the mercury in the longer limb will 
 then be seen to stand at 860, that is, 760 millimeters 
 above the mercury in the shorter limb. The two 
 
22 Practical Physics. 
 
 columns, each 100 mm. long, in the two limbs balance 
 one another. Therefore, in order to halve the volume 
 of the air in the shorter limb, it has had to be pressed 
 by an additional atmosphere. A similar relationship 
 is observed for all pressures. On compressing a gas, 
 it is heated ; and a gas, when heated, tries to expand. 
 If, therefore, mercury is poured suddenly into the 
 longer limb, the air compressed in the shorter limb 
 becomes warm, and by its increased tension balances 
 a longer column than it would when cold. Before 
 finally measuring, the apparatus should be allowed to 
 stand for a few minutes to cool say thirty minutes. 
 
 23. When the observations of gas-volumes extend 
 over several hours during which the barometric pres- 
 sure may have altered and has perhaps never been 
 the mean (760 mm.), it is convenient to reduce all 
 observed volumes to this mean pressure in order to 
 compare them fairly with one another. Thus the ob- 
 served volume of a gas to-day when the barometer 
 is 754*2 mm. is 69*22 c.c. The gas would measure 
 at 760 mm. 
 
 7*? 4" 2 
 69*22 c.c. x -^-that is, 68*69 c.c. 
 
 In general terms if HJ, H 2 be the two barometric 
 heights, and z/,, v z be the corresponding volumes 
 of the same mass of gas 
 
 HI 
 
 " = Z ''il 
 
 Every mass of matter at rest is of course exercising 
 as much pressure as it supports. The compressed 
 gas is accordingly exercising a pressure, tension or 
 elasticity, equal to the compressing force. There 
 
Capillarity. 
 
 23 
 
 being the same mass (weight) of air before and after 
 the compression, doubling the pressure, in halving the 
 volume, of course doubles the density. 
 
 COHESION OF LIQUIDS AFFECTED BY ADHESION 
 TO SOLIDS. 
 
 24. Capillarity. It is found experimentally that 
 the height to which a liquid rises in a cylindrical tube 
 of a solid which it wets, is inversely proportional to 
 the diameter of the tube. More generally expressed, 
 when a tube is partly plunged into a liquid, the differ- 
 ence in height between the inner and the outer liquid 
 is inversely proportional to the diameter of the tube. 
 That this is approximately true is seen at once by 
 binding together two square plates of glass in such a 
 way that they form an angle of about 2 opening. 
 The plates are wedged slightly apart 
 along one edge by two thin bits of 
 cork, and the opposite edges being 
 brought together, a vulcanised caout- 
 chouc band is passed round. On 
 allowing the base of the hollow 
 prism formed by the plates to dip 
 into coloured water, the latter forms 
 between the plates an open curve, 
 called a rectangular hyperbola, such that the vertical 
 height of any point of the curve above the level surface 
 of the water is inversely proportional to the distance 
 of this point from the edge along which the plates 
 
 FIG. 10. 
 
24 Practical Physics. 
 
 touch each other. For exact measurements and veri- 
 fication of the generalisation above given, some forn 
 of cathetometer should be used for the height mea- 
 surement, while the diameter should be measured 
 indirectly by ascertaining the length of a certain 
 length of a known liquid filling the cavity of the 
 capillary tube. 
 
 25. Although round and often uniform in bore, 
 the ordinary capillary thermometer tubes are unsuit- 
 able for such experiments on account of the great 
 thickness of the glass. A piece of glass tube is 
 softened and drawn out to about 6 ft. as uniformly 
 as possible. The central part of this is taken as 
 being the most uniform in bore. A little mercury is 
 drawn in, and the thread tube being laid upon a scale, 
 the length of the mercury column at different parts ot 
 the tube is measured. That part of the tube where 
 its length is nearly constant may be employed. Its 
 diameter is determined by weighing one or two feet 
 of it when empty, and again when full of distilled 
 water. Let its weight when empty be 14632 gram. 
 Let this length measure 563-2 millimeters, and sup- 
 pose it weighs 1-4740 when full of distilled water. 
 The cylinder of water 563-2 mm. long weighs 0-0108 
 gram. Then 
 
 TT r 2 x 563-2 mm. weighs 0*0108 gram. 
 measures 0*0108 c. c. 
 
 io'S c. mm. 
 r = 0*0248 mm. 
 
 If the tube be wide, say 5 or 10 mm. in radius, 
 mercury may with advantage be substituted for water. 
 
FIG, it. 
 
 Capillarity. 2$ 
 
 The result will then have to be divided by the specific 
 gravity of mercury (13*5). But with narrow tubes, the 
 film of air between the mercury and the glass intro- 
 duces a sensible error. 
 
 The diameters of two tubes having been thus 
 determined, they may be laid side by side on to a 
 freshly varnished paper millimeter scale in such a 
 way that their ends project below. The scale is cut 
 away to a point between the tubes at the o line. The 
 heights are then at once read off. Very exact com- 
 parative measurements can be got in this way of the 
 capillary heights in different tubes of the same liquid. 
 For absolute measurements the tubes must be per- 
 fectly vertical, as the downward 
 pressure of the liquid column de- 
 pends upon the height of the top 
 of the capillary column above the 
 level in the reservoir, and not upon 
 the absolute length of the column. 
 
 26. If many capillary heights 
 have to be determined, a steel mil- 
 limeter scale may (fig. n) be filed 
 to a sharp point at the o line, tak- 
 ing care that nothing is filed off. 
 Longitudinal scratches are made 
 along the scale for the tubes to 
 rest on, and they are fastened to 
 the scale by a little soft wax or 
 varnish. The scale is then clamped 
 vertically. This is effected by comparing one of its 
 edges with two plumb lines which, as seen from that 
 edge, appear under an angle of about 90. The vessel 
 
26 Practical Physics. 
 
 containing the liquid is then placed on a table which 
 can be raised very gradually and steadily by a screw. 
 After the scale point touches the liquid the latter is 
 further raised about \ inch, so that the capillary tubes 
 may be wetted inside above their proper level. The 
 liquid is then lowered and the point of the scale 
 wiped. Finally the liquid is raised very slowly and 
 with extreme caution till the point touches the liquid. 
 The capillary readings may be at once taken either 
 by the naked eye or with a pocket lens, or through a 
 horizontal telescope moving on a vertical stand. With 
 narrow tubes the latter plan has no sensible advan- 
 tage. 
 
 27. That kind of capillarity which may be called 
 negative requires in general for its measurement a 
 somewhat different form of apparatus. Mercury and 
 glass may be taken to represent this relationship. 
 The bore of the capillary tube having been measured 
 as before, it is connected by a caoutchouc tube 
 (fig. 12) with a wide trans- 
 
 FlG. 12. ' 
 
 parent reservoir of mercury, 
 such as a wide glass tube 
 drawn out at the bottom and 
 turned up. The two are partly 
 filled with mercury, and the 
 levels are read off by a distant 
 telescope or by a cathetometer. 
 It is best to take the larger 
 
 tube so wide that its capillarity can be neglected. 
 
 The depression of the level in the narrow tube is 
 
 found to be inversely proportional to its diameter or 
 
 radius. 
 
Capillarity. 
 
 All phenomena of capillarity seem to show that 
 the raising or lowering of the liquid level is brought 
 about by the shape of the free liquid surface. The 
 shape itself is determined by the relation between the 
 cohesion of the liquid and the adhesion between the 
 liquid and solid. 
 
 28. If we immerse fig. 13, a capillary U~ s ^ a P e d 
 tube, in water so that its shorter limb a is covered, the 
 liquid stands at b in the longer limb B. On with- 
 drawing the reservoir, the liquid FIG. 13. 
 surface at a becomes convex, and 
 there is a certain difference in 
 height between a' and b '. On 
 touching the convex surface at a' 
 with blotting paper, some of the 
 water is removed and the surface becomes flatter. 
 When it is quite flat there is the same difference if 
 level between a' and b' as there was between b and 
 the liquid in the reservoir. Again (fig. 14), let a wide 
 
 FIG. 14. 
 
 tube A be connected with a capillary tube B. Pour 
 water into the two, and you get a definite capillary 
 elevation, which difference is maintained until the 
 liquid reaches the top of the narrow tube; the surface 
 of the liquid in this tube then begins to flatten, and 
 when it is quite flat the level in both tubes is the 
 
28 Practical Physics. 
 
 same ; on adding more water to the wider tube, the 
 level in it may be raised considerably above that in 
 the narrow tube, the surface in which becomes then 
 convex. 
 
 29. The connection between the curvature and 
 the cohesion and adhesion is generally attributed to an 
 alteration in the density of the liquid at and near the 
 solid. Without discussing this question, the relative 
 capillarities of different liquids in regard to the same 
 solid can be at once measured by replacing the water 
 of 26 by other liquids. With regard to the variation 
 effected in capillary height by variation in the solid, 
 it is difficult, if not impossible, to obtain tubes of 
 exactly the same diameter and of different material. 
 And although, assuming that the law of capillarity 
 holds good with all solids and all liquids, we might 
 make use of tubes of different diameters, it is far 
 easier to apply drop-size, 12, 13, for this purpose, 
 for, like height, drop-size is affected positively by the 
 increased cohesion of the liquid and negatively by its 
 density. In most cases it has to be borne in mind 
 that the surfaces of solid bodies are coated with films 
 of air, and it is the relationship of this film towards 
 the liquid which mainly, at all events at the first 
 moment, determines the capillarity. In the vacuum 
 of the most perfect barometers the surface of the 
 mercury is perfectly level, and allowance for capil- 
 larity in the tube rather introduces than eliminates 
 error. 
 
COHESION OF SOLIDS AFFECTED BY THEIR 
 ADHESION TO LIQUIDS. SOLUTION. 
 
 30. The degree of solubility of solids in liquids 
 is so much affected by temperature that it will have 
 to be mainly considered in connection with HEAT. 
 Also the rate of solution in so far as it is affected by 
 convection currents of course depends upon tempe- 
 rature. With regard to the comparative solubility of 
 salts at the same temperature, a few hints may be 
 here given. As solutions of sdt in water are always 
 heavier than water, the salt in order to saturate the 
 water must be frequently stirred with it, or far better, 
 it is hung in a muslin bag at the surface of the water. 
 If, as is almost invariably the case, it is more soluble 
 in hot than in cold water, it is heated with water till 
 the water is so far saturated FIG. 15. 
 
 that a portion ot the salt 
 separates out on cooling to 
 the required temperature. If 
 the first plan is adopted, the 
 solution should be allowed 
 to evaporate till salt begins 
 to separate. 
 
 31. To determine the 
 quantity of salt in a solu- 
 tion, a long-necked flask 
 of hard glass is dried and 
 weighed, and a few grams 
 of the solution being introduced by a pipette without 
 soiling the neck, the flask and solution are weighed 
 
3O Practical Physics. 
 
 together. The flask is tilted on one side, and the 
 water is evaporated off without boiling. Such evapo- 
 ration may be advantageously assisted by a current of 
 air, which may be caused to flow over the surface of 
 the liquid by inserting a glass tube, /, open at both 
 ends, and heating the projecting part, which there- 
 upon acts as a chimney. Or the neck of the flask 
 may be connected with an exhauster such as a water 
 air-pump. 
 
 32. How far a salt may be heated to get it 
 anhydrous without decomposing it depends upon its 
 chemical nature, and for this and for the determination 
 of the quantity of the salt or its constituents by pre- 
 cipitation, the reader is referred to chemical treatises. 
 It may be useful, however, to know for physical 
 experiments that the following amongst the more 
 common salts become perfectly anhydrous at no C. 
 without undergoing the slightest decomposition : the 
 chlorides, bromides, and iodides of potassium and 
 sodium ; the chloride of ammonium ; the nitrates of 
 sodium, potassium, ammonium, lead, barium, and 
 silver ; sulphate of potassium, chromate of potassium, 
 chlorate of potassium, bichromate of potassium, etc. 
 
 33. Diffusion of Liquids into Liquids. The 
 solution of a salt in a liquid only presents the simple 
 condition of contact between pure salt and pure water 
 at the first instant of contact. Immediately after- 
 wards the salt is surrounded by a salt solution, and 
 this again by water. Further mixture is then brought 
 about by the passage of salt from the salt solution 
 into the water> for it is this passage which enables 
 fresh portions of the salt to leave the mass. The 
 
Diffusion of Liquids. 31 
 
 mixture of a salt with water by diffusion appears to be 
 due to the motion of the salt itself, and not to the 
 solution of it. 
 
 34. The diffusion of salts through water may be 
 measured by the arrangement represented in fig. 16. 
 
 A cylindrical vessel about i in. diam. 
 
 , J , ,. , , , 
 
 and 4 in. high is placed on a glass sup- 
 port in a beaker; the cylinder is filled 
 up to the brim with a solution of a salt 
 of known strength, say 6 per cent. Water 
 is then poured into the beaker so as to 
 be about J in. above the edge of the 
 cylinder. Diffusion at once begins, the 
 salt solution pours over the edge of the cylinder, and 
 is replaced by nearly pure water at the mouth of the 
 cylinder. After the lapse of a given time, the con- 
 tents of the beaker are run off by a siphon into a 
 basin, into which the outside of the cylinder, the 
 stand and the beaker are all washed. The amount of 
 dry salt is determined by evaporation and, weighing 
 the residue, as in 31. A 6 per cent, solution of 
 some other salt being experimented on under like 
 conditions, the ratio between the two residues is the 
 relative diffusion. It is obvious that this kind of 
 experiment is so far defective as after a time the 
 diffusion of the salt takes place into a salt solution 
 instead of into water. And this occurs soonest with 
 those solutions whose diffusion is the greatest. 
 
 35. Chloride of potassium and sulphate of potas- 
 sium are convenient salts to compare, for they differ 
 considerably in diffusibility (in the ratio of i to 0*6987) 
 and are both readily estimated by evaporation. On 
 
32 Practical Physics. 
 
 comparing in this way solutions of various strengths 
 of the same salts, the generalisation is established 
 that the rate at which a soluble salt diffuses from a 
 stronger to a weaker solution is approximately pro- 
 portional to the difference of strength between two 
 contiguous strata. 
 
 36. Diffusion of Gases into Liquids. Absorp- 
 tion. A simple, and for most purposes sufficiently 
 
 FIG. 17. 
 
 d) (2) (3) (4) 
 
 exact absorptiometer, is constructed and used as fol- 
 lows. A tube (fig. 17) a, about the diameter of a 
 burette, is drawn to a neck in the middle, and a very 
 well-fitting glass stop-cock, , is then inserted. Both 
 above and below the cock a millimeter scale is 
 etched on the glass, and the tube is calibrated. By 
 a cork fitting the top, and a piece of tubing through 
 the cork, mercury is drawn up out of a trough past 
 
Absorption of Gases by Liquids. 33 
 
 the stop-cock, which is then turned off. The gas to 
 be examined is introduced below, and the liquid (say 
 thoroughly boiled water) is put into the upper tube. 
 The cock is now turned till the whole of the mercury, 
 but none of the water, has passed into the lower tube. 
 It is then turned off, and the level of the liquid read 
 off in the upper tube, and that of the mercury in the 
 lower one (2). Next the cock is turned, and some 
 of the water is run in. The quantity is known from 
 the sinking of the water in the upper tube, and the 
 applied calibration of that part. After standing a few 
 minutes, the thumb well smeared with burnt caout- 
 chouc is pressed upon the opening of the lower tube, 
 and the whole is taken out of the mercury trough and 
 well shaken. This is done several times at intervals, 
 the tube always being opened under the mercury. 
 Finally, the whole, mercury trough and all, is placed 
 in a capacious beaker, and surrounded with water of 
 the temperature of the air, and the height of the mer- 
 cury read off (3). The pressure to which the gas is 
 subjected, and under which absorption has taken 
 place, is measured by the barometric pressure at the 
 time diminished by the difference between the heights 
 of the mercury inside and outside the tube. The 
 inside column is assisted by the column of water 
 above the mercury. If we wish to experiment with 
 pressures above the atmospheric, a bent tube, c (4), 
 the shorter limb of which passes through a caoutchouc 
 stopper, is fixed into the lower end of the absorption 
 tube, and any required quantity of mercury is forced 
 into c till a given pressure is reached. 
 
 37. It seems that the quantity (mass, weight) 
 D 
 
34 Practical Physics. 
 
 of a given gas which a given liquid absorbs, is almost 
 exactly directly proportional to the pressure. Since 
 the density varies directly as the pressure, it follows 
 that a liquid absorbs the same constant volume of a 
 given gas, whatever the pressure may be. The * co- 
 efficient of absorption ' is the volume in cubic centi- 
 meters (reduced to 76 cm. pressure and o C.) of 
 the gas which i cubic centimeter of the liquid absorbs 
 at atmospheric pressure (76 cm.). This coefficient 
 varies greatly with the temperature, the quantity ab- 
 sorbed being always less at higher than at lower tem- 
 peratures. The coefficient of absorption should 
 therefore be referred to some fixed temperature, say 
 oC. 
 
 38. Condensation of Gases by Solids. Occlusion. 
 Porosity seems to be always comparative, so that 
 condensation of gases into the pores of solid bodies 
 is continuous with the penetration of a gas into the 
 densest metals. To measure exactly the volume of a 
 gas which a solid will absorb, the gas may generally 
 be collected over mercury in a graduated and cali- 
 brated tube. The solid which has to effect the absorp- 
 tion must be first deprived of any gas which may be in 
 it. For a mere qualitative experiment, that is, to show 
 the fact of absorption, the solid should be heated as hot 
 as it will bear in an air-gas flame, and be plunged under 
 the surface of mercury. This process answers well with 
 charcoal. A barometer tube is filled with dry gaseous 
 ammonia, so that the mercury is at the same height 
 inside as outside the tube, and the gas is therefore at 
 atmospheric pressure. Now pass up a pellet of hard 
 charcoal, which has been heated and quenched as 
 
Condensation. Occlusion. 35 
 
 described, into the gas : absorption at once begins, 
 and the charcoal absorbs nearly a hundred times its 
 own volume. To measure the absorp- FlG 
 tion exactly, a pellet of hard charcoal, 
 such as cocoanut charcoal, is placed in a 
 tube, one end of which is closed ; the 
 other end is fastened to the mercury air- 
 pump, and the glass is heated as hot as 
 it can be without softening while the 
 pump is in action. The caoutchouc joint 
 connecting with the pump is drawn out 
 and pinched off, so as to preserve the vacuum, and 
 the glass tube, pellet of charcoal, and caoutchouc, are 
 weighed together. Then the caoutchouc is pulled 
 off, the pellet rolled out on to the mercury, imme- 
 diately plunged beneath its surface, and introduced 
 into the gas. It is better even to heat it again in 
 forceps as high as possible without burning it. The 
 tube and caoutchouc are again weighed by themselves. 
 After absorption appears complete, the eudiometer 
 should be removed to a deep mercury well and lowered 
 into it, till there is the same level inside as out. The 
 temperature is measured by enclosing the whole in a 
 glass cylinder full of water of observable temperature. 
 Diminished by increased temperature, the gas-absorb- 
 ing power of a solid appears to depend both upon the 
 extent of the porous surface, and on the density of 
 the solid. It also appears that the more easily a 
 vapour is condensible, the greater is its faculty for 
 being absorbed. While some metals act, like silver, 
 which absorbs oxygen while melted and gives it up as 
 it cools, most metals condense gases on their surfaces 
 D 2 
 
36 Practical Physics. 
 
 and absorb them into themselves to the greatest degree 
 when they are cold. 
 
 39. If chloride of ammonium be added to chlo- 
 ride of platinum, an almost insoluble double chloride 
 is formed, which, after slight washing, may be strongly 
 heated. Everything excepting metallic platinum is 
 driven off, and this metal then presents the appearance 
 of a spongy grey mass. Held on a platinum wire, a 
 pellet of this will ignite a jet of hydrogen. Brought 
 into oxygen over mercury, it condenses and absorbs 
 that gas. 
 
 The gases which have been absorbed by solids 
 can be generally detected and prepared for examina- 
 tion by heating the solid in a hard glass tube in con- 
 nection with the mercury air-pump. The gases 
 expelled are carried down the moving column of 
 mercury, and are delivered below. 
 
 40. It is probable that occlusion is similar in 
 kind to absorption, but as it takes place in compact 
 solids, a different name has been given to it. Metal- 
 lic iron, when heated and cooled in a current of hydro- 
 gen, absorbs and retains about 2^5 times its volume of 
 hydrogen. If iron be deposited electrolytically in a 
 continuous film, which is done by electrolysing a 
 solution of the ammonio- sulphate of iron, a still larger 
 proportion of hydrogen is occluded. When hydro- 
 gen is evolved electrolytically at the surface of metal- 
 lic palladium, the metal absorbs nearly 1,000 times 
 its own volume of hydrogen without losing its lustre. 
 The volume of the palladium is increased during the 
 absorption, and this causes it to curl and twist in a 
 remarkable manner. 
 
Breath Pictures. 37. 
 
 41. So great is the attraction between some 
 solids and the vapours of some volatile liquids, that 
 it affords the means of producing extremely perfect 
 vacua. A piece of cocoanut charcoal is placed in a 
 hard glass tube, which is then drawn out at both 
 ends, and contracted to narrow necks. To one end 
 is sealed by fusion a small retort containing liquid 
 bromine. This is heated till it boils, while the 
 carbon is heated as hot as the glass will bear. The 
 further end is then fused off, and the retort is also 
 fused off. As the tube cools the bromine vapour 
 disappears, being absorbed by the carbon, and this 
 absorption is so complete, that if two platinum wires 
 have been previously fused into the tube at a very 
 small interval apart, it is found, as long as the char- 
 coal is cold, that the interval between them is so 
 perfect a non-conductor for electricity that no dis- 
 charge takes place between them when they are con- 
 nected with the terminals of an induction coil of such 
 strength that, in air of the ordinary tension, a spark 
 of several inches in length is produced. This implies 
 the existence of as perfect a vacuum as can be got by 
 the most perfect arrangement of the mercury air- 
 pump. 
 
 42. Breath Pictures. The film of air which 
 covers most surfaces has a different power of con- 
 densing vapours from that possessed by the bare 
 surface of the solid. Hence, if we rub a clean sheet 
 of glass with a point of hard wood or brass, the air- 
 film is rubbed off at the lines of contact, and on 
 breathing upon the glass the invisible lines become 
 visible, for the vapour in the breath is not condensed 
 
,38 Practical Physics. 
 
 upon them. Exposed to the vapour of mercury, the 
 invisible writing on a glass plate may be made per- 
 manent. Such breath pictures are best examined by 
 means of daguerreotype plates, that is, plates of copper 
 covered with silver. These are so sensitive that they 
 will furnish a print of a medal or other body which is 
 not even in contact with them. Such a plate will 
 condense the water of the breath as a brownish dew 
 where there is a film of air or gas, but as a bluish dew 
 where there is none. To cover the plate with gas- 
 film it is covered with charcoal which has been satu- 
 rated with that gas, while to get it quite free it is 
 covered with charcoal which has been freshly ignited, 
 and kept covered while cooling. Jf, now, the plate 
 has been saturated wiih a gas, say carbonic acid, by 
 the first plan, and a medallion is placed on it which 
 has been deprived of all gas .by the second, the 
 medallion surface will lay hold of a portion of the 
 carbonic acid of the plate, and abstract more the 
 nearer it is to the plate. On afterwards breathing on 
 the plate, the parts of the plate which were nearest to 
 the medallion will be covered with a bluish dew, the 
 other parts with a brownish dew. This shows that 
 the metallic surfaces can exert actions upon each 
 other at perceptible distances ; possibly every metal- 
 lic surface is in a similar condition to that of a free 
 surface of mercury, which is found to be clothed with 
 an atmosphere of mercury vapour, so closely bound 
 to the liquid, that at ordinary temperatures and atmo- 
 spheric pressures its presence cannot be detected at 
 i millimeter above the surface, and which, in still air, 
 protects the mercury from further vaporisation. 
 
Diffusion of Gases. 39 
 
 43. Diffusion of Gases into Gases. The unham- 
 pered diffusion of gases into gases has been but little 
 studied. The essential conditions for experiment are 
 of course that the heavier gas should be below, that 
 the two should, at a given time, be brought into con- 
 tact without disturbance, and that the condition of the 
 mixture at the end of a given time should be ascer- 
 tainable without disturbance. 
 
 44. That gases mix with one another rapidly 
 and perfectly by diffusion is seen by filling two wide- 
 mouthed bottles over water with any two gases, cover- 
 ing their mouths with glass plates, turning that one 
 over which contains the lighter gas and placing it on 
 t e other one so that the two plates are in contact. 
 On sliding the plates out and replacing them after 
 only a few seconds the contents of the two are found 
 to be identical : namely half and half, if the vessels are 
 of equal capacity. This beinsj so it follows that half 
 the number of atoms of the lower gas have passed up 
 and half those of the upper have passed down through 
 the original common surface at the vessels' mouths. 
 But it by no means follows from this that the diffusive 
 energy of A into B is equal to the diffusive energy of 
 B into A, because under the condition, the sum of the 
 volumes being constant, the diffusion of A into B may 
 be both a cause and a consequence of the diffusion 
 of B into A. 
 
 And this being true also when one of the gases is 
 unlimited in volume, makes the apparently simple 
 phenomenon really a complex one, even when the 
 vessel has the simplest (cylindrical) form. A glass 
 cylinder A (fig. 19), about 6 in. long and i in. internal 
 
1 
 
 4O Practical Physics. 
 
 diameter, is closed at one end, the other end has 
 ground into it a glass stopper carrying a tube an inch 
 FIG. 19. long and J in. internal diameter ground flat 
 on the top. The stopper being greased, the 
 cylinder and tube are filled with mercury and 
 then by displacement nearly filled with the 
 gas. A glass plate is pressed on to the end 
 of the narrow tube and the whole is carried 
 to a room of uniform temperature where it is 
 supported in a clamp. If the gas be lighter 
 than air (nitrogen, hydrogen, coal gas) the 
 narrow tube is directed downwards other- 
 wise upwards. The glass plate is removed for a given 
 interval of time. It is then replaced and the mercury 
 shaken up in the two tubes. A sample of the gas is then 
 taken out for analysis. The actual quantity of the gas 
 which has diffused out is proportional with the same 
 gas to the sectional area of the exposed surface. The 
 generalisation which has been established experimen- 
 tally is that with different gases under the same con- 
 ditions the quantities vary inversely as the square 
 roots of the specific gravities. This generalisation is 
 more closely reached if instead of one large surface 
 FIG. 20. of contact a number of small 
 
 ones are used, such as exist 
 in a thin plate of plaster of 
 Paris, or artificial graphite. 
 And the adoption of such a 
 ^ device enables us to measure 
 "^^ the ratio of exchange between 
 two gases in the following 
 manner. A glass tube A (fig. 20) is fitted with a solid 
 
Diffusion of Gases. 41 
 
 cylindrical plug which is pushed in to about J in. from 
 the end. Fine plaster of Paris paste is poured upon 
 the top of the plug. After a time the latter is with- 
 drawn and the plaster is allowed to dry for a day or 
 two. A piece of sheet caoutchouc is stretched over it 
 and tied tightly round the tqp. The tube is filled with 
 a gas over mercury. The caoutchouc is taken off, and 
 diffusion through the plaster at once begins. In the 
 case of gases lighter than air the mercury is seen to 
 rise in the tube. With gases heavier than air it falls. 
 Since difference of pressure affects the rate, it is ne- 
 cessary to keep the pressure constant. This is done 
 either by dropping mercury into the trough from a 
 pipette or letting it run out through a siphon. By 
 constant watchfulness the mercury is kept at the same 
 level inside as out. After a time the caoutchouc cover- 
 ing is tied on again and a sample of the gas analysed. 
 Or another way of performing the experiment is to 
 maintain the level as long as any tendency to change 
 manifests itself. The volume of the air (nearly pure 
 atmospheric) which is now in the tube is compared 
 with the volume of gas originally in the tube, and 
 the second divided by the first is the specific diffusion 
 of the gas in regard to air. As however air itself is a 
 mixture, the constituents of which have slightly diffe- 
 rent diffusion rates, the gas which has replaced the 
 escaped gas is not quite pure air: it is rather richer in 
 nitrogen. The absolute error introduced on this 
 account is very small, and the error affecting the com- 
 parison between two gases in the tube is only a small 
 fraction of the absolute error. The whole apparatus 
 may be enclosed in a bell-jar of continually renewed 
 
42 Practical Physics. 
 
 carbonic acid, while the adjustment of the level of 
 the mercury may be effected by tubes passing through 
 the supporting table. 
 
 45. The same relation is found to exist (when 
 the porous plate is thin) between the diffusive powers 
 through plates as that which exists with free intercourse, 
 namely that the volume passing varies inversely with 
 the square root of the specific gravity of the gas. So 
 that if the tube A were filled with hydrogen (density = i) 
 and surrounded by oxygen (density =i 6), four vols. of 
 hydrogen (\/i6) would pass out for every i vol. of 
 oxygen (N/I) which entered. When all the hydrogen 
 had escaped therefore the distance between the mer- 
 cury and the plaster would be one-fourth of what it 
 was when the tube was full of hydrogen, supposing 
 the pressure to have remained the same throughout 
 on both sides of the plaster. 
 
 46. To merely exhibit this differential diffusion, two 
 round porous earthenware battery cells a, b, are fastened 
 FIG. ax. by caoutchouc connectors to 
 
 a glass tube c from which a 
 G horizontal tube d bent at right 
 angles enters a safety flask e, 
 through whose cork passes a 
 second tube /"which dips into 
 coloured water ; on placing a 
 bell-jar G containing hydrogen 
 or coal gas over a, air is driven 
 out of/; on filling the jar G with carbonic acid and 
 surrounding b with it, the liquid in/ rises. 
 
 47. Effusion. A distinction is generally made 
 between the passage of one gas into another by 
 
Effusion of Gases. 43 
 
 diffusion through porous solid, which is always a reci- 
 procal motion, and the passage of a gas through one 
 or more holes in a solid into a more or less complete 
 vacuum. The first kind of motion is in the strictest 
 sense molecular, for on mixing gases the molecules of 
 each are separate. The gas in the second case moves 
 in currents. 
 
 48. A hole not larger than a pin-hole is bored 
 through a thin circular plate of brass or platinum. 
 The sides of the hole are hammered and the hole re- 
 bored until under a hand lens the edges appear flat 
 and smooth (fig. 22) The edge of the plate is then 
 coated with a rim of shel- 
 
 - IT I FlG - 22 ' 
 
 lac and dropped into a 
 glass tube having a waist 
 narrower than the metal 
 
 disc. The whole is held nearly vertically and warmed 
 to melt the shellac, so that a perfectly air-tight con- 
 nection is made. One end of the tube is drawn out 
 and bent down so as to serve as a delivery tube ; the 
 other is connected with an apparatus to be described 
 m 59, whereby a constant pressure is maintained. 
 The quantity of gas which passes through the per- 
 foration in a given time is measured. The motion is 
 here caused of course by the difference of pressure on 
 the two sides of the hole, the pressure at one side 
 being that of the atmosphere. To measure what is 
 generally understood by effusion the end a is left open 
 and the end b is connected with a mercury air-pump. 
 The gas which is drawn out of b is collected and 
 measured. For gases other than air the gas is placed 
 in a loose bag connected with a. A convenient form 
 
44 
 
 Practical Physics. 
 
 of orifice for effusion experiments is shown in fig. 23, 
 where the glass tube a is heated 
 at its end and allowed nearly 
 
 FJG 
 
 another tube with shellac. For openings which are so 
 large that the mercury air-pump cannot be depended 
 on for maintaining a constant vacuum, an ordinary 
 air-pump with a barometer gauge will answer, but 
 there should be interposed between the pump and 
 the tube a reservoir vacuum. The gas may in this 
 case be contained in a gasometer, which must be 
 maintained so as to give a constant pressure. 
 
 49. Diffusion of Liquids into Gases. In 44- 
 46 it appeared that when one gas diffused into an- 
 other, the second diffused into the first. It appears 
 also that whenever a gas is soluble in a liquid the 
 liquid is aerifiable into the gas. The cohesion of 
 liquids, whereby their aerification is restrained, de- 
 pends so much upon their temperature that we shall 
 have to reconsider the question under HEAT. The 
 
 apparatus used for mea- 
 suring the rate of eva- 
 poration which liquids 
 exhibit under like con- 
 ditions is as follows. 
 The gas which is to 
 effect the evaporation 
 enters at a from a limp 
 bag ; and it is drawn 
 over the liquid by 
 means of the flow of 
 The liquid to be 
 
 FIG. 24. 
 
 e t 
 
 water from the gas-holder, G. 
 
Evaporation. Vapottr Tension. 45 
 
 evaporated is in the cylindrical vessel. At the bottom 
 of v is a considerable quantity of mercury, above which 
 is the liquid. The tube for the entrance of the gas is 
 widened into a funnel-shape, and the throat of the 
 funnel is partly choked with cotton-wool. The cork is 
 made tight with a large quantity of shellac, having a 
 smooth surface. The gas exit and entrance tubes pass 
 water-tight through the sides of a vessel containing 
 water. The water maintains the temperature constant. 
 The mercury prevents v from floating. The funnel- 
 shaped opening containing cotton-wool prevents the 
 liquid from presenting an irregular surface through 
 disturbance. Dry air is first passed through the ap- 
 paratus, so as to dry up any of the liquid which is 
 sticking to the glass. The whole is wiped dry and 
 weighed. Having been put together and the joints 
 made tight, a known quantity of water is allowed to 
 flow out of G. and that this flow should be uniform it 
 should be delivered into litre flasks of which one may 
 fill every five minutes. After a known quantity of air 
 or gas has been drawn over, the vessel v is removed, 
 dried, and re-weighed. 
 
 50. Experiments show that the more a gas is 
 soluble in a liquid the more is the liquid volatile in 
 the gas. Thus water is more volatile in oxygen than 
 in hydrogen, or nitrogen, or olefiant gas, while alcohol 
 is more volatile in the latter gas than in any of the 
 others. Water at its maximum density, that is 4 C., 
 is less volatile than at higher or lower temperatures. 
 Such differences only refer to the rate and not to the 
 final amount of the liquid volatilised. For if a liquid 
 be introduced into a gas in a barometer tube standing 
 
46 Practical Physics. 
 
 over mercury, the depression of the mercury will be 
 the same whatever be the nature of the gas, showing 
 that the same quantity or volume of vapour has been 
 formed. 
 
 51. Vapour Tension. Looking upon a liquid 
 evaporating in the air, we find the evaporation pro- 
 ceed against and overcome the air pressure. In 
 order to find with what pressure the vapour separates 
 itself from the parent liquid, that is the vapour tension 
 of the liquid, the atmospheric pressure must be re- 
 moved. It is clear that a body in the barometric 
 vacuum is not subject to any pressure at all, and 
 accordingly if a liquid be introduced into the vacuum 
 the depression it causes in the mercury measures its 
 spring or vapour tension. 
 
 52. For most purposes the simple * eudiometer' 
 tube serves for such measurement. A millimeter 
 scale is either etched on the tube or supported 
 closely behind it, the readings being taken through a 
 vertically sliding telescope. In comparing different 
 liquids at the same temperature, if that tempera- 
 ture be the atmospheric, the barometer tube after 
 being filled with mercury is inverted into a trough 
 having plate-glass sides. The height is measured 
 inside and outside the tube, and the difference is the 
 barometric height. A sufficient quantity of the liquid 
 is introduced by a small bent pipette for there to be 
 a little of the liquid remaining as such above the mer- 
 cury. The difference of the new heights of the mercury 
 inside and outside now represents the atmospheric 
 pressure minus the vapour tension. So that the vapour 
 tension is the difference between the first pair of dif- 
 
Vapour Tension. 47 
 
 ferences and the second. This would be exact if the 
 liquid were only just but completely evaporated. As, 
 however, to ensure saturation of the vacuum it is best 
 to allow a little liquid to remain, the weight of this 
 has to be added to the weight of the internal column of 
 mercury. The height of the bottom of the liquid column 
 may be taken as that of the top of the mercury column. 
 The top of the liquid column is taken as the lowest 
 point of its upper surface. To translate the liquid 
 column pressure into mercury pressure, that is, to find 
 what length of mercury would have the same p 1Gt 
 downward pull as the observed length of 
 liquid, the length of liquid must be divided 
 by the ratio between the density of mercury 
 and the density of the liquid, or what comes 
 to the same thing, the ratio between the 
 specific gravity of the mercury and that of 
 the liquid. 
 
 53. Let, for example, a barometer tube be filled 
 with mercury and inverted. 
 
 mm. 
 
 Let the reading of the mercury inside the 
 tube be ...... 780^2 
 
 Let the reading of the mercury outside the 
 tube be 30-5 
 
 Then the barometric height (atmospheric 
 pressure) . . . -=7497 
 
 Let a liquid be now introduced which has the specific 
 gravity of 0*872, and let the upper surface of the liquid 
 stand at 540-4 mm., the lower surface of the liquid 
 stand at 535 - o mm., the inner surface of the mercury 
 
48 Practical Physics. 
 
 stand at 535*0 mm., the outer surface of the mercury 
 stand at 40*6 mm. Then inside the tube there are 535 
 mm. of mercury and 5*4 mm. of liquid. The "5*4 
 
 mm. of liquid are equivalent to 5*4x ^ mm., or 
 
 0*3 mm. of mercury. So that inside there are 535*3 
 mm., and outside 40*6 ; so that the mercurial pressure, 
 that is, the difference between the atmospheric pres- 
 sure and the vapour tension, is 4947 mm. The 
 atmospheric pressure being 749*7, the vapour tension 
 is 255*0 mm. 
 
 How vapour tension varies with temperature will 
 be described in the treatise on HEAT. It may be 
 here mentioned that the additional elements to be 
 taken into account are (i) the variation in density 
 of the mercury according to temperature, and (2) 
 the elongation of the scale if it be etched on the 
 glass. 
 
 54. The vapour tensions of solids are measured 
 in a similar manner. In order to avoid the irregularity 
 of the mercury surface when a solid rests upon it, the 
 barometer tube may be made double, and one limb 
 FIG. 26. being graduated, the solid is introduced into 
 the other. This form of barometer is indeed 
 or liquids also advantageous, because the 
 liquid being introduced into one limb, the 
 height of the mercury in the other has not to 
 be corrected for the liquid column. By this 
 means, or by a series of barometer tubes ar- 
 ranged side by side, it is easy to show that the vapour 
 tensions of saline solutions are less than those of 
 water, and are less according as the solutions are 
 
Osmose. 49 
 
 stronger. Also that the solid water in crystalline salts 
 containing water of crystallisation has various vapour 
 tensions, while the water in solutions however strong 
 of gums, glues, or other colloidal substances, exerts 
 the same vapour tension as pure water, and indeed 
 that the water in gelatinised colloid solids (jellies) has 
 precisely the same vapour-tension as water itself. 
 
 55. That colloid bodies have little or no hold 
 on water and other crystalloid bodies (the terms will 
 be more fully explained in 57, 58) is shown very 
 simply on placing some strong solution of gum arabic 
 in a basin under the receiver of a good air-pump. On 
 rapid and nearly complete exhaustion being effected, 
 the gum boils violently. If a 50 per cent, solution of 
 glue be placed in a test tube, and surrounded with 
 water in a larger tube, the glue solution boils before 
 the water if the latter be heated very gradually. The 
 glue solution boils in fact at 97 '5 C. 
 
 56. Diffusion of Liquids into Solids. Osmose. It 
 seems that no liquid can penetrate through a crystalline 
 solid without dissolving it. By enormous pressure 
 water can be forced through masses of iron as in the 
 cylinders of hydraulic presses, but it seems from 
 analogy probable that the water passes between the 
 crystals of iron and not through them. Bodies which 
 as solids show no traces of crystalline form are called 
 amorphous, their fracture is conchoidal. Such bodies 
 are glass, resin, glue, gum, some varieties of quartz, 
 caoutchouc. Such of these as are soluble in liquids, as 
 gum and glue in water, or resin in alcohol, may or may 
 not form jellies with the liquid. Thus gum arabic does 
 not, but gelatine on being heated with water does, 
 E 
 
5O Practical Physics. 
 
 on cooling, form a jelly. So does caoutchouc with 
 benzol. A jelly appears to be the result of the partial 
 reaggregation of the particles of the colloid. 
 
 Perhaps melted caoutchouc and fused glass may be 
 considered to be colloid liquids. A colloid solid, even 
 when insoluble in a liquid, may and often does allow 
 that liquid to penetrate it, but it does not allow col- 
 loids to pass through with anything like the same 
 facility. The passage of crystalline solids in solution 
 and liquids through colloid septa is properly called 
 osmose. * Vegetable parchment' or ' parchment paper' 
 is convenient for studying osmose (see Appendix). A 
 glass tube about i in. wide and 2 in. long has a 
 piece of parchment paper tied tightly over one end. 
 The tube is then weighed, partly filled with a salt solu- 
 tion of known strength, and again weighed. It is then 
 immersed to such a depth in distilled water, in a wide 
 basin, that the upward and downward pressures at the 
 parchment surface are as nearly as possible equal. 
 The inner vessel gains in weight, but loses in salt. 
 The quantity of water which has passed inwards 
 minus the quantity of salt which has passed outwards 
 is the difference of the first and second weighings. 
 The absolute quantity of sa T t which has passed out- 
 wards is got directly by evaporating the contents of 
 the outer vessel, or indirectly by evaporating those of 
 the inner vessel, and subtracting from the amount 
 known to have been there to begin with. In such 
 rases it is difficult to say whether there is an exchange 
 between salt and water or between salt solution and 
 water. But the balance of motion is in favour of 
 the water. Thus, if a bladder be used about 4-5 
 
Dialysis. 5 1 
 
 times as much by weight of water passes to the salt 
 solution as of salt to the water, if the salt be chloride 
 of sodium. The osmic equivalents of other salts are 
 determined in the same way. But the osmic equiva- 
 lents depend also upon the nature of the membranes. 
 Bladder gives different values from vegetable parch- 
 ment. 
 
 57. Dialysis. The difference referred to above 
 seems to depend upon the power which the membrane 
 has of absorbing one or other liquid. A piece of bladder 
 softens and swells in water, but hardens and shrivels 
 in alcohol. Placed between water and alcohol, the 
 former penetrates it and diffuses from the other side 
 into the alcohol, while little alcohol can pass the other 
 way. Take now caoutchouc instead of bladder ; this 
 softens and swells in alcohol, but is almost imper- 
 meable to water. If accordingly a caoutchouc mem- 
 brane separates alcohol from water, the alcohol will 
 pass through and little or no water will return. It is 
 thus that wine strengthens in skins and bladders, but 
 weakens in caoutchouc bags. Water, however, passes 
 in some quantity through caoutchouc. A toy air-ball, 
 for instance, if completely filled with water and per- 
 fectly closed will go on losing water with great regu- 
 larity for weeks. And if dry air be passed along two 
 tubes joined together by a piece of caoutchouc tubing 
 which is immersed in boiling water, the air will be 
 found to be no longer dry. The facility with which 
 crystalloid bodies in solution pass through many col- 
 loid membranes, and the hindrance almost amounting 
 to obstruction which the same membranes present to 
 colloids, render the separation of colloids from crys- 
 E 2 
 
52 Practical Physics. 
 
 talloids easy in cases where it would be difficult to 
 effect the separation by other means. The dialyser 
 consists of a sheet of parchment paper stretched be- 
 tween two concentric hoops of gutta-percha. This tabor 
 which may be rilled with a mixture of gum and salt 
 in solution is floated on pure water. After some 
 days, the outer water being removed, scarcely a trace 
 of salt is found in the tabor, while scarcely a trace of 
 gum has passed out of it. It is thus that the metallic 
 and alkaloid poisons may be separated from the col- 
 loidal mucilage of the contents of the stomach, while 
 of course the most effective nitration accompanies the 
 dialysis. 
 
 It appears that the oxides of iron, tin, aluminum, 
 and silicon, are or may be colloidal, and may be then 
 either soluble or insoluble in water. 
 
 58. To obtain soluble oxide of iron, hydro- 
 chloric acid is digested with freshly-precipitated hy- 
 drated sesquioxide of iron until no more is dissolved. 
 Placed in the dialyser, hydrochloric acid alone passes 
 through, leaving the oxide of iron in solution in water ; 
 after some days the separation is complete. The 
 solution is very apt to gelatinise, and will not again 
 dissolve by adding more water or heating. Solu- 
 ble alumina may be got in a similar way. Soluble 
 silica is prepared by adding basic silicate of soda 
 (soluble glass) to an excess of hydrochloric acid and 
 dialysing as above. 
 
 59. Transpiration of Gases through Capillary 
 Tubes. The amount (volume) of gas which passes in 
 a given time through a tube depends upon the width 
 and length of the tube, upon the difference of pres- 
 
Transpiration. 
 
 53 
 
 sure between the two ends of the tube, upon the tem- 
 perature of the gas and upon its density. For mea- 
 surement, each of these factors must in turn vary, all 
 the rest being constant. The apparatus of most general 
 use is shown in fig. 27. 
 
 Water dropping from A is made to continually over- 
 flow the funnel tube B : the overflow being carried away 
 
 FIG. 27. 
 
 by c. B passes air-tight through a cork in the mouth 
 of a vessel v, and dips beneath the surface of the water 
 in the little tube D. 
 
 The gas in v escapes by the tube E, and after 
 being dried in the two tubes F and o, passes into the 
 tube H, the lower part of which is capillary, and 
 which is surrounded by a vessel to hold ice, or hot 
 
54 Practical Physics, 
 
 water, or paraffin, &c. Thence the gas escapes 
 through i, and is collected in the tube j, which is con- 
 stricted and marked at j, and stands in an overflowing 
 vessel K. The effective pressure on the gas, that is 
 the difference between the pressures at the two ends, 
 is independent of the barometric pressure, and is 
 measured by the length of the column from the sur- 
 face of the water in B to the surface in D. And this 
 length remains the same. The rate is measured by 
 the time required to fill the vessel j. The following 
 facts appear from experiment : (i) The time required 
 for the passage of a given volume of air through a 
 capillary tube is equal to the sum of the times required 
 for the passage of the same volume of air through 
 each part of the tube taken separately. (2) The open- 
 ing up of the tube into spaces where the resistance is 
 zero and its je-entrance into the capillary does not 
 affect the rate, provided that the entire length of 
 capillary tube remains the same. (3) Under like 
 conditions the same passage of air takes place down 
 a conical capillary tube, whether it passes from the 
 broad to the narrow end, or the reverse. (4) The 
 time (resistance) varies approximately as the square 
 of the absolute temperature, that is the temperature 
 measured from 273 C. (5) The time varies nearly 
 exactly inversely as the pressure, but rather more 
 rapidly than that reciprocal. 
 
Specific Gravity. 55 
 
 DENSITY, COMPARATIVE WEIGHTS OF EQUAL 
 VOLUMES, ABSOLUTE WEIGHTS OF UNIT VO- 
 LUME, SPECIFIC GRAVITY. 
 
 60. The exact methods adopted for finding the 
 specific gravities of bodies vary according to the nature 
 of the bodies. We will consider separately the fol- 
 lowing cases : 
 
 Solids. 
 
 1 i ) A solid in lumps not less than a hazel nut, in- 
 soluble in water, (a) heavier than water, (b) lighter 
 than water. 
 
 (2) A solid in lumps not less than a hazel nut, 
 soluble in water, (a) heavier than water, (b) lighter 
 than water. 
 
 (3) A powder insoluble in water, (a) heavier, (/;) 
 lighter than water. 
 
 (4) A powder soluble in water, (a) heavier, (b) 
 lighter than water. 
 
 Liquids. 
 
 (5) A liquid to be had in considerable quantities. 
 
 (6) Very small quantities of liquids. 
 
 6 1. A balance suitable for taking specific gravi- 
 ties should, when loaded with 50 grams on each pan, 
 show the effect of 0*0002 gram. Most balances are 
 provided with a short-slung brass pan having a hook 
 at its bottom. This brass pan is sometimes lighter 
 and sometimes heavier than the pan on the other 
 side. If lighter it is best to add a chip of glass or 
 a watch-glass to make it heavier. It is not advisable 
 to attempt to make or use a counterpoise. Weights 
 
56 Practical Physics. 
 
 are added to the weight pan till there is equilibrium, 
 and the weight so added has to be deducted from all 
 subsequent weighings. This is not necessary when as 
 in (3), (4), (5), (7) and (8) an apparatus is weighed 
 along with the substance : for then the error of the 
 balance counts as weight of apparatus. 
 
 The most usual way of performing the determina- 
 tion of (i) depends upon the fact that a body totally 
 immersed in water is buoyed up by a force equal to 
 the weight of water it displaces, that is by a force equal 
 to the weight of water having a volume equal to the 
 volume of the body. In other words, the weight which 
 a body loses in water is the weight of water whose 
 volume is equal to its own. And the specific gravity 
 of a substance, being the ratio between the weight of 
 any volume of the substance and the weight of an, 
 equal volume of water, is* got by dividing the weight of 
 the body by the weight which it loses in water. We 
 may here neglect the buoying effect of the air upon, 
 the body and the weights. 
 
 62. As an example of (10) we may take quartz. 
 A watch-glass placed on the substance pan is counter- 
 poised by 4-3256 grams. A lump of quartz is placed 
 on the watch-glass and the two require 57237. 
 Accordingly, weight of quartz (in air) = 1-3981. 
 
 The quartz is tied to a fibre of cocoon silk having 
 a loop at the othei end, so that when hanging by 
 the loop from the hook of the substance pan the 
 quartz is about two inches from the bottom of the 
 balance (or pan support). Being so hung it is again 
 weighed (the watch-glass remains). The new weight 
 is 57244. The silk fibre weighs therefore 0-0007. 
 
Specific Gravity of Solids. 57 
 
 Breathe on the surface of the quartz and hang it in a 
 vessel of distilled water of such a width that the quartz 
 may swing freely, and of such a height that about half 
 the silk is immersed. Any air bubbles which adhere 
 to the quartz are teased off with the feather of a pen. 
 Let the weight in the water be 5*1270. Since the silk 
 fibre has very nearly the same density as water, the 
 part immersed does not affect the weight. The part 
 outside may be taken as 0*0003, so that 5*1267 is the 
 weight of the watch-glass and immersed quartz. And 
 therefore 57237 5'i267 or 0*5970 is the weight lost 
 by the quartz, that is the weight of an equal volume 
 of water, and therefore 
 
 1^81 or 
 5970 
 
 is the specific gravity of this specimen of quartz. 
 
 63 (i). To find the specific gravity of a solid 
 insoluble in water and lighter than water, the device is 
 employed of fastening to it a body of sufficient weight 
 to sink it. Example : 
 
 64. Let it be required to find the specific gravity 
 of paraffin. Let the weight of the paraffin in air be 
 4*2730. A piece of lead, weighing in water say 7*5964, 
 is stuck to the paraffin. The two together weigh in 
 water 6*4236. Accordingly the weight lost by the 
 paraffin is equal to the weight of the paraffin in air-f 
 weight of lead in water diminished by the weight oi 
 both together in water, or 
 
 =4*2730 + 7*5964-6-4236=5*4458. 
 Therefore the specific gravity of the paraffin is 
 
58 Practical Physics. 
 
 4^130 or 07846. 
 5*4458 
 
 65. Solids soluble in Water. (20). We wish to 
 find the specific gravity of a salt which can be obtained 
 in pretty large crystals like rock-salt, washing soda or 
 alum. A piece of the salt is found to weigh 5 -2 103 
 grams in air. Next it is weighed in some liquid of 
 known specific gravity in which it is insoluble, say oil 
 of turpentine of specific gravity 0*8742. Let its weight 
 in turpentine be 37020. The loss in weight in tur- 
 pentine, that is the weight of an equal volume of tur- 
 pentine, is 1*5083. What is the weight of this same 
 volume of water ? Since 
 
 sp. gr. of turpentine = ^_ 
 
 wt. of equal vol. of water 
 
 wtofanyvol. of turpentine = wt of ^ yo , 
 sp. gr. ot turpentine 
 
 or I ^ _ W k of equal voL of water 
 
 0*8742 
 
 = 17254 
 And therefore the specific gravity of sal 
 
 = 5^3 3. 
 
 17254 
 
 66. (2^). A solid lighter than water and soluble 
 in it. Such substances are rare ; some kinds of 
 shaving soap are of this nature. The methods of 
 ib and 20 are combined. That is, a known weight 
 of the substance is weighted with a sinker whose 
 weight in a suitable liquid of known specific gravity 
 has been ascertained. 
 
Specific Gravity of Liquids. 59 
 
 Thus, weight of soap =5-7321 grams. 
 
 ,, sinker in turpentine =2 '4050 
 Let weight of both in turpentine =2 '4011 
 .*. wt. of turpentine having vol. equal to soap 
 
 = 5736o. 
 
 /. wt. of water having vol. equal to soap 
 5736o 
 0-8742 
 
 /. sp. gr. of soap = -5 ^ 2I _. 0-8736. 
 ' 
 
 67. Before considering 30, 3^, 40, 4^, it will be con- 
 venient to consider liquids. There is great choice in 
 the methods which can be here adopted. The most 
 convenient, and one of the most exact, is that in which 
 the specific gravity bottle is employed. 
 
 (50.) A little flask capable of holding about 30 
 to 50 grains of water has a rather conical stopper 
 perfectly ground into its neck. Through the stopper 
 is a very fine hole ; the stopper may be made of a 
 piece of thermometer tubing. The F 
 
 flask is weighed empty. Suppose 
 its weight is 57230. As we do not 
 require to know the absolute weight 
 of the flask apart from inequality of 
 the balance, we may here dispense 
 with the preliminary weighing of 
 6 1. The stopper being removed, 
 the flask is filled by a pipette with 
 distilled water until the water is about on a level with 
 the edge. With the exception of the neck it is 
 wrapped lightly in a soft cloth, and being held by the 
 
60 Practical Physics. 
 
 finger and thumb by the neck, and held a little 
 obliquely, the bottom of the stopper is placed in con- 
 tact with the water, and the stopper is pressed home 
 uniformly, not too quickly and without a grinding 
 motion. The excess of water is so squeezed out, 
 and any drop remaining on the top and about the 
 crack between the neck and the stopper is wiped off, 
 care being taken not to warm the flask and especially 
 not to press in its elastic bottom. It is then re- 
 weighed. Suppose it now weighs 36*4723 grams. 
 The water in it weighs 36*4723 57230 or 30-7493 
 grams. Let the water be emptied out and the flask 
 thoroughly dried, first by shaking and then by warm- 
 ing with rapid twirling over an air-gas burner and 
 drawing air out of the flask by the mouth with a piece 
 of glass tube. When thoroughly cooled it is to be 
 filled with the liquid as before. Its weight is now 
 found to be say 38-4820. The liquid in it accordingly 
 weighs 38-4820 57230 or 32-7590, and the specific 
 
 gravity of the liquid is _ _ !' C 653. This 
 
 307493 
 
 method, it is clear, is equally applicable whether the 
 liquid be heavier or lighter than water. The flask 
 maybe more rapidly dried if it be rinsed out with 
 alcohol and then with ether. 
 
 68. Another method, and one of greater rapidity 
 and almost equal accuracy, is to weigh a conveniently 
 shaped lump of glass suspended from the short scale 
 pan by a silk fibre, as described in 62, and then to 
 weigh it in succession in air, in water, and in the liquid. 
 Its loss of weight in the liquid divided by its loss 
 of weight in water is the specific gravity of the liquid. 
 
Specific Gravity of Powders. 61 
 
 69. Sometimes only very small quantities of the 
 liquid can be ob- FlG . 29 . 
 
 tained. A piece of 
 light tubing (fig. 29) 
 may then be drawn 
 out at both ends as a capillary P. The tube P is then 
 used exactly like the specific gravity flask of 67, 
 being weighed empty, full of water, and full of the 
 liquid. Liquids which cannot be drawn into the 
 mouth with impunity are drawn into the tube P by 
 means of the enveloping tube Q ; the end R is placed 
 in the mouth, P is subsequently removed, and the two 
 capillary ends wiped. 
 
 70. Occasionally still smaller quantities of liquids 
 are at our disposal. If the liquid be somewhat heavier 
 than water and insoluble in it, the following device 
 may be sometimes used with advantage. A drop of 
 the liquid is placed beneath the surface of a small 
 quantity of water, and a saturated solution of some salt 
 which is without action on the liquid, is added with 
 gentle stirring, till the drop is in indifferent equili- 
 brium. The specific gravity of the salt solution being 
 taken in one of the ways described above, is, of course, 
 identical with that of the liquid drop. 
 
 71. (30.) A powder insoluble in and heavier than 
 water. The specific gravity flask is weighed empty, 
 and again full of water ; it is then emptied, dried, 
 nearly filled with the powder, and weighed. The 
 powder is covered with distilled water, and put 
 into the air-pump vacuum to remove adhering air; 
 the flask is then filled up with water and again 
 weighed. 
 
62 Practical Physics. 
 
 Let 
 
 Empty flask weigh = 57230 . . w\ 
 Flask full of water =36-4723 . . w z 
 Flask + powder =20-2356 . . w s 
 
 Flask + powder + water =40 -403 8 . . w 4 
 Then- 
 
 Water completely filling flask =307493= w 2 Wi 
 The powder weighs = 14-5126=^3^ 
 
 Difference between weight of 
 powder and weight of equal 
 vol. of water = 
 
 /. Weight of water having same vol. as powder 
 
 = 10-5811= w z w l (w 4 w z ) 
 /. Specific gravity 
 
 10-5811 
 
 72. (3&) If tjie powder be lighter than water and 
 insoluble in it, the flask is first weighed empty, then 
 full of water, it is then inverted into a little basin of 
 water, and a quantity of the powder is floated up into 
 the flask, it is re-inverted, dried, and weighed. The 
 water being evaporated off, the flask and powder are 
 weighed together. The data are as in 30. 
 
 73. (40.) Let the powder be heavier than water, 
 but soluble in it. Proceed as in 30, but employ some 
 liquid, say turpentine, of known specific gravity 
 (0*8742) in which the powder is insoluble. 
 Let 
 
 Empty flask weigh . . 5*7230 . . w\ 
 Flask full of turpentine . 30-4723 . . iv 2 
 
Vortex Rings. 63 
 
 Flask + powder . . . 18-9379 . . w 3 
 Flask + powder + turpentine 32-4040 . . w 4 
 
 Then w 3 w\ (w^w^ is the weight of turpentine 
 having vol. equal to that of powder, and therefore 
 
 3-2149-1-9317 
 
 
 sp. gr. of turpentine 0-8742 
 
 is the weight of water whose vol. is that of the powder, 
 and therefore the specific gravity of the powder is 
 
 5^' ot '3'49 or 9 - oo8 . 
 1-467 1-467 
 
 VORTEX MOTION. 
 
 74. As a connecting link between ordinary motion 
 of translation of fluids air and water currents on the 
 one hand, and the motion, which gives rise to waves, 
 on the other, stands the beautiful phenomenon of vor 
 tex motion, which combines both kinds, and enables a 
 mass of fluid to travel through a mass of fluid with- 
 out much disturbance to the latter. Smoke rings, gun- 
 ners' rings, rings following FIG. 3 o. 
 the spontaneous ignition in 
 the air of impure hydride of -* g 
 phosphorus, and occasion- 
 ally steam rings from loco- 
 motives, are familiar ex- 
 amples of these. They can be conveniently shown on 
 a large scale by replacing the back of a box, fig. 30, by 
 canvas or ' duck,' cutting in the front a circular hole, 
 
64 Practical Physics. 
 
 which should have a sharp edge and be provided with 
 a sliding cover. Two flasks, containing respectively 
 ammonia-water and hydrochloric acid-water, are con- 
 nected by tubes with the inside of the box, and on 
 being heated, fill the inside with clouds of chloride of 
 ammonium. On removing the cover from the hole, and 
 hitting the canvas back, ring after ring of cloud-charged 
 air passes out, and may be made to blow out a candle at 
 ten or fifteen yards. On sending them at a gentle rate, 
 and examining their structure, they are found to have 
 an internal motion, indicated in fig. 3 1 by the arrows, 
 FIG. 31. as though they were rings of 
 
 elastic material, rolling in tubes 
 touching and exercising friction 
 on their circumferences. A 
 character of these rings is that 
 when they are in rapid move- 
 ment, general and internal, they 
 show great elasticity one towards the other, in fact, it 
 is impossible to get two to break one another. 
 
 Similar, but imperfect, liquid vortex rings are seen 
 when ink is dropped gently into water. They are 
 formed in great beauty as fol ows : a round side- 
 chamber is fastened to the end 
 of a long trough having glass 
 sides. The side-chamber com- 
 municates with the trough by a 
 circular opening rather less than 
 the chamber. The other end of the chamber is 
 covered by a stout piece of vulcanised caoutchouc. 
 The trough and chamber are filled with clear water, a 
 little colouring matter is put into the water in the 
 
Waves. 65 
 
 chamber by means of a pipette. The caoutchouc is 
 struck by a round-headed mallet, or thrust in by a 
 lever attached to the trough, resembling a 'lemon 
 squeezer.' If sulphate of indigo is used as a colouring 
 agent, the water soon clears itself if it holds some 
 hypochlorite of lime in solution, and so the trouble of 
 refilling is avoided 
 
 WAVES. 
 
 75. The wave in general. Conceive a 
 number, n, of particles, exactly alike one another, 
 and arranged in a straight line at equal distances, 
 say one inch apart. Let the particles be called 
 a, t>, c, d, e, &c. Let the particle a move in any 
 way, but come back to its original place in the time 
 10 seconds. Suppose that b starts i second after 
 a, and performs a path just like a's path. Let c start 
 i second after b, let d start i second after c, and so 
 on ; each particle completing its course in the same 
 time, 10 seconds, and these courses being identical in 
 size and shape, but differing in position, because the 
 starting points are i inch apart. Suppose, now, that 
 when a has come back to its original position, that is, 
 after 10 seconds, the particle, , which is 10 inches 
 from a, just begins to stir. The particle, #, has been 
 moving for 10 seconds, and has completed \% of its 
 course, the particle b has been moving for 9 seconds, 
 and has completed T % of its course, and so on ; the 
 
 F 
 
66 Practical Physics. 
 
 particle j has been moving i second, and has com- 
 pleted ^ of its course, the particle k is just about to 
 move or just moving, and has completed nothing, or 
 an infinitely small fraction of its course. Let now (at 
 the end of 10 seconds) a start afresh as before, and 
 next , and then <:, and so on, each starting always 
 afresh as soon as it gets home. It is clear that during 
 the next 10 seconds, and ever afterwards, a and k 
 will be moving alike, and be in similar positions, so 
 will b and /, c and ?;z, d and ;/, and so on. 
 
 The distance from a to k, or from b to /, or from 
 c to m, &c., always in our case 10 inches, is the 
 wave's length. Wave-length is the distance between 
 any one particle and the next particle which has 
 completed the same fraction of its course as the first 
 one has completed : this is called being in the same 
 phase. 
 
 The greatest difference in the positions of one 
 and the same particle is called the wave's amplitude. 
 
 A wave is accordingly a travelling condition of 
 matter in regard to the position of its particles. 
 
 It follows from the example that the travelling 
 condition has passed from a to k in the same time as 
 sufficed to bring a back to its original position ; and 
 universally, a wave travels its own length in the same 
 time as that in which any particle completes an entire 
 course. 
 
 76. Waves governed by gravity. Liquid waves. 
 These are familiar as water waves. The actual 
 motions of the individual particles, which motions 
 produce the water wave, can be seen if we employ a 
 long trough of water with glass sides, and float a wax 
 
Water Waves. 67 
 
 pellet slightly loaded with sand, so that it only just 
 floats in the water, near to the glass side. A paddle, 
 nearly fitting the trough, is placed about 6 in. from 
 one end, and advanced about J in. towards the wax, 
 and immediately afterwards back again. This gives 
 rise to a travelling elevation, followed by a travelling 
 depression; these dandle the wax pellet, and it is seen 
 to describe a circle. If the wave's motion is said to 
 be one of advance, the pellet rises advancing, then 
 sinks advancing, then sinks retreating, then rises re- 
 treating. The first two parts of the motion are 
 due to the wave's elevation, the latter to its valley. 
 In such a wave each particle describes a nearly 
 circular orbit in a vertical plane which lies in 
 the direction of the wave's motion. The wave- 
 length is from top of crest to next top of crest, 
 a to b, or from bottom of valley to next bottom of 
 valley, c to d, FlG - 33- 
 
 or from any /^T**? -V^Nf / 
 
 particle, e, in ,/^ i >. -/- ^~ -^ 
 
 any phase, to c r d 
 
 the next particle, f, in the same phase. It is clear 
 that particles at the same height are not necessarily 
 in the same phase. The particles e and g, for in- 
 stance, are at the same height, but one is going down 
 while the other is going up. The amplitude is the 
 length of the line a ^, or the vertical distance between 
 the top of a crest and the bottom of a valley. 
 
 77. Reflexion of water waves. Stationary 
 
 waves. If the wave generated in the trough of 76 
 
 be watched as it strikes the end of the trough, it is 
 
 seen that the elevation is reflected as an elevation, 
 
 F 2 
 
68 Practical Physics. 
 
 and the depression as a depression, also that the height 
 to which the wave rises and the depth to which the 
 valley sinks on reflexion are about double the original 
 wave height. If we use a shorter trough, we can start 
 a fresh wave of such a length and at such a moment 
 that the beginning of the advancing valley of the 
 second wave meets the beginning of the reflected 
 elevation of the first wav'e in the middle of the trough. 
 FlG 34 The line of particles across the mid- 
 
 dle of the water surface will . then 
 always be urged upwards and down- 
 wards by the same pressure, and 
 will not vary in height, and the 
 water will rise at a and fall at b, and vice versa simul- 
 taneously. The particles at a and b are always in 
 opposite phases, and therefore a and b are half a wave- 
 length apart, or the wave-length is double the trough's 
 length. The systems of swayings to and fro in this 
 and similar cases, are called 'stationary' waves. The 
 line through n is a nodal line. With regard to the 
 actual motion of the water particles in such cases, 
 suspended wax pellets show that the actual motion at 
 the reflecting faces is vertical, and that there the motion 
 is greatest. At the node, particles sweep through it in 
 arcs, without altering its height. All the other parti- 
 cles also move in arcs of lesser amplitude as they lie 
 deeper, until at a depth of about a wave-length the 
 movement is inappreciable. If the trough be of a 
 lesser depth, the friction on the bottom retards the 
 wave's motion. The water in a trough can be set 
 in motion in a variety of ways ; thus, if the centre 
 be depressed and released, two nodal lines will be 
 
Stationary Liquid Waves. 69 
 
 formed, each at \ the trough's length from the ends. 
 The wave here is half as long as in the FlG> 35 . 
 
 former case, or the wave-length is 
 equal to the trough's length. If we 
 count the number of times an eleva- 
 tion appears in the middle in, say, 
 
 five minutes with the binodal system, and also with 
 the mononodal, we find that with the same trough 
 
 number with binodal _ \/2 
 number with mononodal "~ i 
 
 rate of progression 
 length of path 
 
 calling rate of progression of binodal r z 
 
 mononodal r* 
 
 length of path of binodal 7 2 
 
 mononodal /, (=2/ 2 ) 
 
 2/2 
 
 or r = v/7. 
 
 r z 
 
 Or if the length of one wave is twice as great as that 
 of a second, the first will move faster than the second, 
 in the ratio of \/2 : i. 
 
 78. Such waves, in rectangular troughs, are how- 
 ever restrained, and do not move so swiftly as when 
 in open water, or when reflected from the sides of 
 circular troughs. The connection between wave-length 
 and rate of wave progression is practically exhibited 
 
70 Practical Physics. 
 
 as follows : two cylindrical troughs, which should be 
 at least as deep as they are wide, are nearly filled 
 with water ; the bottom of an empty beaker glass is 
 alternately pressed down and raised in the centre of the 
 water of one of them. With a little practice the hand 
 and water help one another. The beaker is with- 
 drawn, and the surface allowed to free itself from 
 ripples. The water is then found to be in the follow- 
 ing kind of motion. It sinks in the middle zs it rises 
 at the circumference, and vice versd, and the central 
 motion is about twice as much as the circumferential. 
 At almost exactly ^ of the radius from the circum- 
 FIG. 3 6. ference there is a nodal ring. Such motion 
 will continue for ten or fifteen minutes in 
 troughs of about 2 ft. diameter. The 
 position of the nodal ring, and the ampli- 
 tude of the motion, can be measured by 
 dipping a sheet of sized paper into the water in a 
 vertical plane along a diameter. 
 
 If we count how many times the elevation appears 
 in the middle in a given time, we find (i) that whether 
 the undulation is vigorous or nearly expired, the same 
 number of reappearances occur in exactly the same 
 time, and secondly, if the diameter of the trough A is 
 d M and that of B is */ b , then if N a be the number of 
 reappearances in a given time with A, and N b those 
 with B, we find experimentally 
 
 Now, as before, the number of reappearances of the 
 crest in the middle varies directly with the rate of 
 
Rate of Progression of Waves. ?l 
 
 progression of the wave and inversely with its length 
 of path. The path is in both cases twice the respec- 
 tive radius, that is, it is the respective diameter. 
 Calling r a the rate of progression in A, and v b that 
 in B, we have therefore 
 
 !> 
 
 Nq ffq _ 'V4 
 
 or the rates of progression are directly proportional to 
 the trough diameters, that is to the wave-lengths. It 
 appears from experiments of this nature that a wave 
 i meter in length will travel in open water almost 
 exactly 83 meters in a minute, or about 3 miles in an 
 hour. Of course in open water the moving water has 
 to set a larger and larger ring of water in motion as 
 the circle increases. The wave loses in amplitude as 
 it spreads. It also appears to gain a little in length, 
 The latter point requires examination. 
 
 The rate of recurrence of the same phase in the 
 same place, which may be called the rate of pulsation, 
 depends of course on, and is the same as, the rate of 
 swing to and fro of each particle. Each particle is 
 virtually a pendulum, but only those symmetrically 
 situated move in equal or indeed similar arcs. Still 
 the same relationship exists with the wave as with the 
 pendulum ; for the rate of swing of the latter also 4 that 
 
72 Practical Physics. 
 
 is, the number of times of its reappearance in the same 
 phase in the same place, is inversely as the square root 
 of its length. The relationship is still more close. If 
 a pendulum be taken whose vibrating length is exactly 
 the radius of the circular trough, the pulsating water 
 and the swinging pendulum will keep exact time with 
 one another if the swing of the pendulum be small. 
 Further, all liquids give rise under like conditions (of 
 wave-length) to waves which travel at the same rate 
 whatever be the densities of the liquids : just as all 
 pendulums swing at the same rate whatever be their 
 weight, if they are of the same length. 
 
 79. Waves governed by elasticity. In all other 
 wave systems the elasticity of the matter in which the 
 wave travels takes effect, for in all other systems 
 change of volume accompanies the wave in its motion. 
 This is true as well when a wave of transverse dis- 
 placement travels along an elastic rod or cord as it 
 obviously is when the particles move in succession to 
 and fro longitudinally, that is, in the same direction as 
 the wave itself moves, either in solids, liquids, or gases. 
 
 In the latter case indeed the wave may well be 
 called a wave of change of density; and as elasticity 
 varies with density, it may also be called a wave of 
 elasticity. Such waves travel so fast that their rate of 
 motion can only be got at either directly by taking great 
 lengths of them, or indirectly by finding the ^number 
 of recurrences of the same phase in a given time. And 
 this is again generally measured by the varying physio- 
 logical effect on the perception when the drum of the 
 ear receives various numbers of pushes and pulls in 
 
Waves of Elasticity. 73 
 
 a given time, and so communicates sensations of 
 notes of different///^, that is, shriller or graver notes. 
 Perhaps the simplest conception of the formation 
 of an air wave system from a solid is to imagine 
 a sphere surrounded by air, and to suppose the 
 sphere to swell and shrink alternately, alternating 
 spherical concentric shells of condensation and rare- 
 faction would be thrown off. All particles at the 
 same distance from the sphere would be in the same 
 phase at the same time. As a result of experiment it 
 is found that at the end of the first second the first 
 shell would be at 1,100 feet from the sphere, and there 
 would be as many shells of compression as the num- 
 ber of times the sphere had swollen during the second. 
 Alternating with these would be as many spherical 
 shells of rarefaction. Each air particle moves fro and 
 to as it takes part in the wave motion, in a straight line 
 radial to the shells. A particle begins to move when 
 the front of the shell of compression touches it, and 
 it completes its motion when the back of the next 
 shell of rarefaction leaves it. Accordingly, an air 
 wave, like a water wave, travels its own length in the 
 time that a particle occupies in going through all its 
 changes of position, so as to be ready to start again in 
 the same direction. The length of an air wave is the 
 distance between any two particles in the same phase : 
 from one place where there is maximum density to 
 the next, or from one place of minimum density to the 
 next, or from any other place of given density to the 
 next but one. There is thus a very great analogy be- 
 tween an air or sound wave and a water wave, as fig. 37 
 
74 
 
 Practical Physics. 
 
 shows, where in (i) the closeness of the lines repre- 
 sents the closeness of the particles of air which are 
 made to correspond with the elevations and depres- 
 sions in (2) which represents wave system of elevation 
 and depression. It is clear that if all air waves travel 
 at the rate of 1,100 feet a second, and there are n waves 
 started in a second, the whole air space within a 
 radius of i, TOO feet will at the end of a second consist of 
 n shells of condensation alternating with n shells of rare- 
 faction all at equal distances apart. In other words, 
 
 FIG. 37. 
 
 NX N^ 
 
 there will be n waves in a radius of 1,100 feet. Each 
 
 i TOO 
 
 wave will be therefore feet long and universally 
 
 wave-length in feet= 
 
 no. of feet wave travels in i second 
 no. of waves generated in i second. 
 
 The amplitude of an air wave is the greatest dis- 
 tance between two positions of one and the same 
 particle. The vis viva of the air wave has to be 
 exerted on a greater and greater mass as the wave 
 spreads, and accordingly the amplitude diminishes. 
 Air waves are audible when the amplitude cannot be 
 
 more than 
 
 10,000,000 
 
 of an inch. A system of scund 
 
Notes. 75 
 
 waves slightly increases in wave-length as the wave 
 radiates. 
 
 80. Conversion of sounds into Notes. Without 
 entering upon the anatomy and physiology of the 
 ear, we may assume that an elementary sound is pro- 
 duced by a single air wave thrusting in and pulling out 
 the drum of the ear. The duration in time of this 
 excursion is the same as that of the excursion of any 
 air particle. The extent of the drum's excursion de- 
 pends upon the vigour (vis viva) of the blow it receives 
 (\ mv*}. And the loudness of the sound is not ne- 
 cessarily proportional to the vigour of the blow, nor 
 to the extent of the drum's excursion. Sounds are 
 seldom simple in their origin, and even when they are 
 so, echo and the reverberation of surrounding bodies 
 generally prolong the sound and alter its character. 
 But even a single air wave produces a sensory effect 
 which endures after mechanical action has ceased for 
 a time of about -^ of a second. If a second similar 
 sound is produced within this time interval, the sen- 
 sations of the old and new sounds are continuous. If 
 other similar waves succeed at the same small intervals, 
 a continuous sound is produced, called a note. The 
 quicker the sequence, the shriller the note, the higher 
 its pitch : the slower the sequence, the graver the note, 
 the lower its pitch. A large humming-top has a round- 
 headed nail driven into its peg. The lower part of 
 the upper stem is cut into a triangular prism, the upper 
 part being thinned. Three circular discs of tin-plate 
 have triangular holes in their centres, so as to fit on 
 to the stem. One of these has two rings of holes, the 
 
?6 Practical Physics. 
 
 outer being twice as numerous as the inner. The 
 FlG 38 two other discs are toothed, 
 
 the larger having twice as 
 many teeth as the smaller. 
 The two can be placed to- 
 gether on the stem, the larger 
 being below and the two 
 being separated by a triangu- 
 lar washer. The top is filled 
 with wet sand, and the hole 
 stopped. The single perforated disc being slipped 
 on the top is spun in the usual way on the bottom of 
 a tumbler. Air is blown upon the two rings of holes 
 in succession through a glass tube, the bent-down end 
 of the tube being held as near as possible to the disc 
 without touching it. A puff of air passes through each 
 hole as it comes beneath the tube, and this momen- 
 tary air-puff reaches the ear as a sound-wave. The 
 puffs succeeding one another with greater rapidity than 
 1 6 in a second, a continuous note is heard which for 
 the same ring of holes becomes graver as the top 
 languishes, but is always for the outer ring an octave 
 higher than for the inner ring. So when the two 
 toothed rings are put on and the top spun, a card held 
 in contact with the twice as numerously toothed disc 
 gives always the note which is the higher octave of 
 that given by the other disc. Both become graver as 
 the rate fades. Hence it follows not only that a 
 higher pitched note is the result of more frequent 
 sound waves in the same time (and therefore shorter 
 waves), but that what is known in music and re- 
 cognised by most ears as the relation between a note 
 
Sensitive Flame. 77 
 
 and its higher octave is the relationship between the 
 impressions which n and zn sound waves in the same 
 space of time make upon the perception, or the re- 
 lationship between the impression which a series of 
 
 sound waves of length / and a series of length - make 
 
 upon the perception. Whether the feeling called 
 pitch depends upon the appreciation of the rapidity 
 of sequence or upon the duration of each distortion 
 of the ear-drum is not easy to decide, for the one is 
 the inverse of the other. Perhaps the fact that a 
 single long wave produces a different impression from 
 that produced by a single short wave, and that this 
 difference reminds one of the differences between grave 
 and shrill notes, may be regarded as evidence that 
 duration of individual impression rather than rate of 
 sequence is to be considered as the origin of pitch. 
 
 8 1. Detection of sound. Sensitive flame. In 
 order to render visible facts connected with the re- 
 flexion, refraction, absorption, and dispersion of 
 sound, use is made of the effect of the sound wave on 
 fluid jets. Three kinds of jets are used. A liquid 
 pouring in a smooth vertical jet from a cistern at such 
 a slow rate that it is ready to break up into drops, 
 will so break up if subjected to sonorous vibrations. 
 A jet of air rendered visible by being charged with 
 smoke becomes stunted under the same conditions. 
 Perhaps the most striking and convenient is the 
 sensitive flame. Coal gas is collected in a mackintosh 
 bag provided with a stop-cock. The bag is placed 
 between boards, which are so loaded that the elasticity 
 is increased by about ^th part. The gas is led to a 
 
78 Practical Physics. 
 
 long straight burner, having an orifice of about ^Vth 
 of an inch. This will give a flame about a foot high 
 and \ in. diameter. The stop-cock is turned on 
 till the jet is on the point of ' flaring.' Most sounds 
 and notes will, when not too far from the flame, cause 
 it to duck down and flare. This is especially the 
 case with sibilant sounds hissing, crumpling, rustling, 
 clinking, scraping, &c., all of which sounds consist of 
 or contain high notes. Notes which are so high as 
 to be inaudible to the ear affect the flame. For the 
 flame to be affected it is necessary that if the jet be 
 of rigid material, the orifice of it should be exposed 
 to the beat of the waves. 
 
 . 82. Reflexion of sound. Let a sensitive flame 
 be placed at one end of a metal tube 1 2 feet long and 
 a few inches in diameter. Remove the pea from a 
 dog-whistle, and sound the whistle at a distance of 
 1 2 feet. If the flame respond, diminish the supply of 
 gas till it ceases to do so. Then bring the sounding 
 whistle towards the other end of the metal tube. As 
 it gets near the end, it will cause the flame to duck 
 and flare, and when it is on the axis of the tube it 
 may be some feet from it without ceasing to cause 
 the same effect. Diminish the sensitiveness of the 
 flame, so that when the whistle is sounded at the other 
 end of the tube the flame remains tranquil. Place be- 
 hind the whistle a parabolic or spherical mirror, so that 
 the whistle is in the principal focus and the axes of the 
 tube and mirror coincide. The flame again flares. 
 Place a cloth between the whistle and the mirror, the 
 flame is restored. To exhibit the law of reflexion of 
 sound, namely, that the angles of incidence and re- 
 
Reflexion and Absorption of Sound. 79 
 
 flexion are equal, and that the incident beam, the 
 reflected beam, and normal to the surface at the place 
 of incidence, are all in one plane, arrange two metal 
 tubes, each about 4 feet long, horizontally (fig. 39), 
 and at right angles to one FlG 39< 
 
 another. Sound the whistle, 
 w, and regulate the gas so that 
 the flame, sf, is not affected. 
 Then introduce at a a sheet of 
 cardboard inclined at 45 to ~ 
 
 each tube ; the flame flares. The hand placed at a 
 also reflects the sound waves to sf. The flame of a flat 
 fishtail burner produces the same effect, and so does 
 even the sheet of heated gas from such a flame when 
 the burner is placed somewhat lower down. 
 
 The absorption of sound is exhibited in a similar 
 manner. The tubes are now placed in the same 
 straight line, with their ends about an inch apart. 
 The whistle is sounded uni- 
 formly, and the flame is so 
 adjusted that it responds 
 freely. A sheet of cardboard 
 or paper, or a flat gas flame 
 
 at a, cuts off the sound by reflexion. A single fold of 
 a wet towel produces the same effect ; while several 
 folds of a dry towel fail to cut off the sound. The 
 films of water in the wet towel being of different sizes, 
 break up the waves they receive into waves of different 
 sizes, and urge them in different directions. Through 
 the dry towel the air is continuous, and part of the 
 wave proceeds unbroken. 
 
 Perhaps the most complete arrangement for 
 
8o Practical Physics. 
 
 showing most facts connected with reflexion and 
 FlG . 4I . absorption, disper- 
 
 sion, &c., is shown 
 in fig. 41, where two 
 spherical mirrors, 
 about 18 in. in dia- 
 meter, are placed 
 with their axes in one line, at a distance of about 
 4 feet. The whistle is supported in the principal focus 
 of the one, and -the sensitive flame in that of the 
 other (the distance of the principal focus from the 
 mirror is half the radius of the mirror, and it is 
 measured once for all by finding where the image of 
 the sun, or of a gas flame at a distance of 20 or 30 
 yards, is formed on a transparent paper screen). 
 The flame is so adjusted that without the mirrors no 
 effect is produced; also when only one mirror is in 
 position. When both mirrors are in position the flame 
 flares. This flaring is not prevented by placing a 
 2-inch square screen between w and sf, however 
 close it may be put to either ; but on placing it close 
 to w, between w and its mirror, or close to sf, between 
 sf and its mirror, the flame ceases to flare. The 
 actual tracing of the sound-wave before and after 
 FIG. 42. reflexion is shown by the 
 
 device in fig. 42. A per- 
 fectly flat and very smooth 
 elliptical board, japanned, 
 is surrounded by a smooth 
 wall 2 or 3 inches high, the axes of the ellipse being as 
 three to four. Two brass knobs are fastened above the 
 board about J in. apart, in such a way that the straight 
 
Refraction of Sound. 81 
 
 line joining them is bisected by one focus of the ellipse. 
 Dry lycopodium is scattered through muslin uniformly 
 over the wood, and the whole is covered by a glass 
 plate. One of the knobs is connected with the inner 
 coating of a Leyden jar, the other with the outer 
 coating and the earth. The inner coating of the jar 
 is also connected with the prime conductor of an 
 electrical machine. On turning the machine, sparks 
 pass from knob to knob, giving rise to sound waves. 
 These waves are reflected, and converge to the other 
 focus. The lycopodium is found to be arranged in 
 two families of concentric circles around the foci. 
 Strictly speaking, we do not get here a tracing of a 
 moving wave ; for a moving wave can leave no tracing 
 of accumulation, because each particle moves equally 
 in its turn. What we find is the tracing of a system 
 of stationary waves, due to the interference of the 
 echo waves with the original waves. 
 
 83. Refraction of sound. As a ray or beam of 
 light on passing from an optically rarer medium to an 
 optically denser one is bent towards the normal at 
 the point of impact, so a beam of sound in passing 
 from a lighter gas to a denser one is bent in the 
 same way. If it passes into a lighter gas, it is 
 bent away from the nor- FJG 
 
 mal. It is possible to con- 
 struct gas sound lenses 
 on this principle. Let a 
 whistle, w (fig. 43), be at 
 such a distance from the 
 singing flame, sf, as just 
 to affect it. Fill a toy caoutchouc balloon with 
 G 
 
82 Practical Physics. 
 
 air, and hold it close to the flame ; the flame still 
 flares. Fill a similar balloon with hydrogen, and 
 place it in the same position; the flame ceases to 
 flare, because the balloon acts then as a dispersing lens. 
 Remove the balloon, and reduce the gas so that the 
 flame ceases to flare, then introduce a similar balloon 
 in the same place filled with carbonic acid ; the flame 
 now flares, because the balloon acts as a condensing 
 lens. 
 
 It is well known that sound travels with less loss 
 through air of uniform density than through a hetero- 
 geneous atmosphere. This appears to be the reason 
 why sounds are heard distinctly in frosty weather, 
 where by contact with snow or ice-cold ground the air 
 is of a pretty uniform temperature, and contains the 
 same amount throughout of aqueous vapour. Also 
 when the air is throughout of the same temperature 
 and saturated with moisture, as after a shower of rain, 
 sounds are distinct. The obstruction of mist particles 
 to sound is not so hostile to its clearness as variation 
 Flf% 44 in density. This is shown 
 
 experimentally by placing 
 W the sensitive flame at one 
 end (fig. 44), and the 
 whistle at the other end 
 
 r 
 
 fllj11 "" "of a long box open at 
 both ends, and arranging the flame so as just to flare. 
 Then if carbonic acid, or steam, or coal gas be allowed 
 to enter through several jets in the bottom of the box, 
 the flame ceases to flare! If coal gas is employed, 
 the box should be tilted a little upwards towards the 
 whistle, to prevent an explosion. 
 
Transverse Vibrations of Rods. 83 
 
 ORIGINS OF SOUND WAVES. 
 
 84. Transverse vibrations of rods. If a 
 
 square rod is fastened rigidly at one end, and plucked 
 at the other end, it will swing backwards and forwards 
 at a certain rate, and if it be not plucked too far, its 
 rate of swinging is the same, whether its excursion be 
 great or small. The rate of swinging, that is, the 
 number of swings to and fro, depends upon the elas- 
 ticity of the rod, upon its density, and also upon its 
 length and thickness in the direction of swing. If 
 we are considering rods of the same material, and 
 examining them at the same time, density and elasti- 
 city are out of count, because they are constant. It 
 is found that if n be the number of vibrations to and 
 fro in a given time, / be the length of the rod, and / 
 its thickness in the plane of vibration, 
 
 To prove this, take a carefully planed deal rect- 
 angular rod, i in. wide, \ in. thick exactly, and about 
 12 ft. long. Clamp it firmly between cardboard in a 
 vice horizontally, and so that its \ in. faces are hori- 
 zontal, and so that 10 feet are free. Set it swinging 
 gently horizontally. It will hang down in a curve, 
 but this does not matter. Adjust a leaden bullet at 
 the end of a silk thread, so as to swing at the same 
 rate as the rod. Adjust another such pendulum to 
 swing twice as fast as the first. Now shorten the rod 
 till it swings at the same rate as the second pendulum : 
 on measuring the rod it is found to be about 7 ft. long. 
 G 2 
 
84 Practical Physics. 
 
 = 2 1 , ^2=2^2, -^2=2 2 nearly. 
 
 This shows that the number of oscillations varies in- 
 versely with the square of the length. Now return to 
 the 10 ft. length, but turn the rod, so that the i in. 
 faces are horizontal. It will now be found to swing 
 with the shorter pendulum, that is, twice as fast as it 
 did when, being of the same length, it was of double 
 thickness in the direction of swing. Accordingly, if 
 we take a nicely- worked square steel rod, and clamp 
 it at one end rigidly, and furnish the top with a bright 
 bead, so that, by the retention of images, the reflection 
 of a flame in the bead appears as a streak of light, we 
 FIG. 45. shall get a line of 
 
 light (i) if the rod 
 is plucked from a 
 to ft, also a line 
 I \ / f^\ r\ /; (2) if it is plucked 
 I \ / V_y \J C/ from c to d; it will 
 * 2 3 * 6 6 7 trace out the line 
 (3) if plucked simultaneously from a to b, and from 
 d to c ; the line (4) will be shown if it be plucked 
 simultaneously from b to a and d to c. If in case (2) 
 when the point has performed a quarter of its path, the 
 rod receives an equal blow from a to , it will travel in a 
 circle (5). If it receive such a blow when it has nearly 
 completed its (2) motion, it will trace out the ellipse 
 (6). If it receive the blow soon after starting, it will 
 describe the ellipse (7). In the cases (3), (4), (5), (6), 
 (7), where both motions are imparted, it is seen that a 
 point moving along the curve, or up and down the line, 
 moves as often up and down as to the right and left. 
 
Transverse Vibrations of Rods. 8$ 
 
 If (fig. 46) the rod be twice as thick one way as 
 the other, and it receive simultaneous impulses from 
 d to c and from b to 
 0, it will swing to the 
 left and back again 
 while it is moving up 
 (in the figure), and 
 to the left and back 
 while it is moving 
 down, and so trace *' * 3 & $ 
 
 out (i). If it receives simultaneously an impulse 
 from d to c and an impulse from a to b, it will, for 
 similar reasons, trace out the curve (2). If, when, by 
 reason of the impulse from d to c, it has got half up, 
 it receives an impulse from a to b, it will describe the 
 figure of 8, (3) : (4), and (5) show the curves traced 
 out, when the a b impulse is imparted at different 
 phases of the cd motion. In all cases, a point passing 
 along these curves travels twice as often to the right 
 and left as up and down. 
 
 If the width of the rod be to the breadth as 2 to 3, 
 figures must be formed of such a kind that a point 
 moving over them passes three times p IG . 47 . 
 
 from left to right and back while it 
 passes twice up and down. These 
 conditions will be seen to be ful- 
 filled by figures of which types are 
 shown in fig. 47. 
 
 Other ratios, such as 3 : 4, 3 : 5, 
 4:5, &c., give characteristic figures of more complex 
 shape. As the vibrations die out the point of the 
 rod makes shorter and shorter excursions in both 
 directions. So that, for instance, in the first case, with 
 
86 Practical Physics. 
 
 the square rod the lines (3) and (4) become shorter, 
 (5) becomes a circular spiral, and (6) and (7) become 
 elliptic spirals preserving their eccentricity and the 
 directions of their axes. But if a b be a little longer 
 than c d the point will, starting from case (3), have 
 come a little back to the right before it begins to move 
 down, and it will have got twice as much to the right 
 before it begins to move up, and so on. It will form 
 a curve which apart from its fading off is not a closed 
 curve, but which, as only a fraction of it is visible at 
 once, changes in aspect from (3) to (6), from (6) to 
 FIG. 4 8. (5), from (5) to (7), from (7) to (4), from 
 (4) to (7), to (5), to (6), to (3). So when 
 the dimensions are as 2 : i (fig. 46), if 
 there be a little defect in the ratio, the 
 figure will pass from (i) to (4), to (3), to 
 (5), to (2), to (5), to (3), to (4), to (i). 
 And so for other cases. If both defect 
 in ratio and fading off occurs, a spiral is 
 traced, out of which an idea is given in fig. 48. 
 
 85. These figures can be imitated artificially, and 
 the whole course of the point registered graphically, by 
 FIG. 49. pivoting two pendulums to 
 
 two adjacent sides of a square 
 table, and fastening with some 
 vulcanised caoutchouc joints 
 two arms to the upper parts 
 of the pendulums at right 
 angles to one another in a 
 horizontal plane. The ends 
 of the arms are also joined 
 together by a ball and socket joint or by a Hooke's 
 
Composition of Vibrations. 
 
 joint This joint carries a vertical glass tube pen 
 charged with aniline colour, or a style to scratch 
 lampblack off smoked glass. 
 
 Use is made of the constancy of these figures or 
 the reverse to test the consonance of tuning-forks, 
 and to make one fork either be in perfect unison with 
 another, or at a known interval from it. Thus to adjust 
 a fork to be in uni- FIG. 50. 
 
 son with the fork N, 
 a beam of light, L 
 (fig. 50), is thrown 
 upon the polished 
 face of one prong of 
 N which is vertical, 
 thence it is reflected 
 and strikes the po- 
 lished face of one 
 prong of A, thence 
 it is reflected and 
 falls upon a screen at /. If, however, the prongs of 
 N are bent in, as the dotted lines represent, the light 
 strikes with a greater incident angle at a', is reflected 
 higher on the prong of A, and reaches the screen at /'; 
 when the prong of N is bent outwards the light will 
 be reflected to / 15 so that as the prong moves in and 
 out the spot of light travels rapidly from /' to / x and 
 back, forming a vertical streak. If A be bowed at the 
 same time and its prongs are bent inwards at the 
 same time as those of A, the light reflected from a 
 will strike the fork A at b' with greater incidence than 
 before, and the ray will be reflected to /' . When the 
 prongs of both forks are bent outwards the light will 
 
88 Practical Physics. 
 
 appear at / 2 , so that when both forks are sounding, 
 a streak of light extends from /" to / 2 . Suppose now 
 the fork A to be a little out of tune, and to be a little 
 too high or swift in its vibration, the reflecting prong 
 of A will have come a little back when the prong of N 
 has reached the end of its excursion, so that the light 
 will fall a little lower than /'. When the N prong 
 is bent outwards, the A prong will be twice as 
 much in advance, and the spot will be twice as far 
 above / 2 as it was below I", and so on, until 
 the A prong is upright, when N is at its maximum 
 excursion, that is, J of a complete vibration to and/w, 
 in advance of N. The streak of light will then reach 
 from /' to /!. In double the time A will be half a 
 vibration in advance of N, that is, when the prong 
 of N is bent in to its utmost, the prong of A is benc 
 out, the last bends the ray down as much as the first 
 bends it up, so that there is only a spot of light at /. 
 This begins immediately to grow until A is a complete 
 vibration in advance of N. The forks are now again in 
 the same phase, and the maximum length of streak is 
 obtained. To bow a fork without stopping it or 
 altering its phase, the bow is made to touch the fork 
 with a sliding motion. The shortening and lengthen- 
 ing of the line of light (which is easily distinguished 
 from the shortening due to languishing, for the latter 
 is not followed by lengthening) takes place the more 
 quickly the greater the disagreement between the 
 forks. To see whether the fork A is too fast or too 
 slow, for the effect on the light line would be the 
 same, one prong of A is loaded with a little wax con- 
 taining a swan shot. If this makes the gaping of the 
 
Transverse Vibrations of Rods. 89 
 
 line more rapid of course the fork was already too 
 slow, for loading diminishes the rate. If loading 
 makes the gaping of the line less rapid, the fork A is 
 too quick ; in the former case metal is filed off the 
 upper part of the prongs, for this unloads them without 
 diminishing the elasticity. In the latter case metal is 
 filed off the root of the fork, for this diminishes the 
 elasticity without sensibly affecting the inertia. 
 
 For other ratios besides I : I, as when we wish to 
 adjust a fork so as to be the higher octave of the fork 
 N, one fork, say N, is clamped vertically as before, and 
 this alone would give a vertical streak. The fork to 
 be adjusted is clamped horizontally with its polished 
 face vertical. This alone would give a horizontal 
 streak. When the two forks are sounded together, if 
 their rates are nearly in the ratio of i : 2, a curve of 
 light resembling one of those in 84 will be formed, 
 and this will pass more or less rapidly through the 
 figures (i) (4) (3) (5) (2) according as the octave- 
 harmony is less or more perfect. As before, loading 
 the fork shows whether it is too fast or too slow, and 
 it has to be filed as before till one of these forms 
 remains constant for a long time. If it takes a minute 
 for the figures to pass through all shapes and return to 
 its original shape, this means of course that the fork A 
 in a minute gives one vibration more, or one vibration 
 less than twice the number made by N in a minute. 
 So that if N gives 520 complete vibrations in a second 
 or 31,200 in a minute, A gives 62,399 in a minute or 
 1039-983 in a second instead of 1040- which is the 
 higher octave of N. This to the ear would be perfect 
 harmony. 
 
92 Practical Physics. 
 
 reflected from the fixed end, returns reversed and 
 bursts into the empty tube with increased velocity and 
 amplitude. 
 
 If we take one of the above tubes and by a motion 
 of the hand send a series of complete waves down it 
 of such a length that, when the front of the reflected 
 first elevation (in the form of a depression) has 
 reached the middle, the front of the second elevation 
 FIG. 51. reaches the middle coming in the 
 
 " opposite direction, the middle point 
 will be pushed up and down at the 
 same time with the same pressure 
 and will remain at rest. When this 
 second elevation has reached the 
 end the reflected first elevation has 
 reached the beginning. It is seen 
 that each contour of the cord, i, 2, 3, is a complete 
 wave, so that the wave-length is equal to the length of 
 the cord. Now the point m being always at rest 
 because it is always subjected to equal and opposite 
 pressures may be considered rigid. That is, instead of 
 one cord vibrating in two segments with a node 
 between, one segment moving up as the other moves 
 down, we may consider each half by itself moving up 
 FIG. 52. and down between two fixed 
 
 ^ ^ points. It will keep the same 
 
 time as the two together. The 
 length of the cord is now only half the wave- 
 length. 
 
 Now (comp. 77) the 
 
 number of vibrations = ve C1 ^ . 
 wave-length. 
 
Stationary Waves. Nodes. 93 
 
 and since 
 
 it follows that if / be the length of the cord 
 
 m 
 
 Though thus derived from the advance and reflexion 
 of two elevations or depressions, we may pluck the 
 middles of the two halves, the one up and the other 
 down, simultaneously and observe the segmental 
 vibration with the central node. So when the cord 
 vibrates as a whole, being plucked in the middle, we 
 may, if we choose, regard its two halves as being re- 
 flected from the two fixed ends. Although above (p 90) 
 we neglected the automatic depression which accom- 
 panied the elevation, when the end is rigidly fastened 
 this depression or reflexion from the beginning is of 
 absolute importance. Thus when a wire is struck at 
 a quarter its length from one fixed 
 end, its successive conditions are 
 shown in fig. 53. That is, while part 
 of the stored energy of the displaced 
 segment determines the progression 
 of the depression to a', the other 
 part carries the segment back across 
 the normal line producing an ele- 
 vation. 
 
 87. With the elastic tube one can study the 
 growth and establishment of such segmental vibra- 
 tions or stationary waves. Taking one of the elastic 
 
94 Practical Physics. 
 
 tubes move the hand quickly to and fro and by and 
 bye the cord and the hand will fall into one another's 
 FIG. 54. humour and the cord will fall into 
 
 segments separated by nodes. 
 
 The rate of vibration of the 
 segments is inversely proportional 
 to their lengths, that is proportional 
 to their number. That such seg- 
 mentary vibration when once estab- 
 lished is automatic is shown by 
 rigidly fixing an elastic tube in a 
 vertical position and while gently 
 restraining (damping) the middle by letting it pass 
 between the fingers, plucking the middle of one-half. 
 The tube being released vibrates in two segments with 
 a central node. Damped at one-third and plucked at 
 one sixth from the bottom it vibrates in three seg- 
 ments and so on. In this experiment it should be 
 remembered that the upper part of the tube has a 
 little the greater tension, so that the upper segment to 
 be synchronous with the lower segment should be a 
 little the longer : and so for the other cases. 
 
 FIG. 55- 88. By the elastic cord it can 
 
 be shown that a string may vibrate 
 as a whole and in segments at the 
 same time provided there is always 
 either an odd or an even number 
 of automatic nodes : and in all 
 cases however it may be vibrating 
 in segments it can vibrate as a 
 whole. 
 The nodes on wires are well shown by stretching 
 
Sounds of Vibrating Strings. 95 
 
 a wire several feet long horizontally and dividing it 
 into eight equal parts by seven stirrups of paper 
 resting on the wire. The second stirrup from one 
 end is gently pinched around the wire and the wire is 
 gently plucked where the first stirrup rests. The $rd, 
 5th, and yth stirrups will be jerked off, for they are at 
 the centres of segments ; the 4th, 5th, and 6th will 
 retain their places, for they are at nodes. 
 
 89. Vibrating strings as sources of sound. The 
 conditions which determine the rate of vibration of a 
 stretched string or wire are, as we have seen, the 
 stretching pressure or weight hung at one end, the 
 length and the mass 
 
 or in an unloaded string since m a d* if d be the 
 diameter, for the same material 
 
 Steel wires (pianoforte wires) are the most convenient 
 for studying this 
 
 .... . r 10.56. 
 
 relationship. A 
 
 table (fig. 56) has 
 
 two iron pegs 
 
 driven obliquely 
 
 in at one end. 
 
 At the other end 
 
 are two pulleys let into the table so that their axes 
 
 are on the table. Two mahogany wedges nearly of 
 
 the same height as the pulleys, are permanently fixed 
 
 at the same distance from the pulleys, so that measured 
 
96 Practical Physics. 
 
 from the top of the wedge to the top of the pulley 
 there is a whole number of units of length, say 64 in. 
 Two other movable wedges or bridges a little higher 
 than the fixed ones are provided, and the table is 
 divided into inches numbered from the axes of the 
 pulleys. The wires being horizontal the vibrating 
 length is the distance from the top of the pulley to the 
 top of the bridge, or from the axis of the pulley to the 
 centre of the base of the bridge. Let wires of the 
 same metal and the same gauge be fastened to the 
 pegs and passed over the pulleys. Bring the movable 
 bridges to any the same distance from the pulleys, say 
 1 8 in., and hang a weight of say 10 Ibs. at the end of one 
 wire, and also 10 Ibs. at the end of the other. The two 
 wires are perfectly identical and under identical con- 
 ditions : plucked gently and in the middle they will give 
 identical notes. Weight now one of the wires, further. 
 Its note will rise in pitch till it is weighted with 40 Ibs., 
 whereupon it will give out the easily recognisable 
 higher octave of the other wire. And so, whatever be 
 the weight or stretching pressure on the first wire, and 
 whatever its length, the second will give the higher 
 octave of the first, provided its length is the same, 
 when the weight on the second is 4 times as great as 
 that on the first With short wires, say i foot long, this 
 can be repeated. For suppose both wires are stretched 
 with 5 Ibs., then one with 20, then the first being 
 stretched by 80 Ibs. will give the higher octave of the 
 second, or the second octave above its original note, 
 that is 4 times its original number of vibrations. 
 
 Birmingham steel wire of 14 gauge will easily bear 
 a strain of n 2 Ibs. if there are no kinks in it. Such 
 
Vibrating Strings. 97 
 
 experiments, and they can be multiplied without 
 limit, prove that n oc Vs. 
 
 Start with the wires of equal length, stretched with 
 10 and 40 Ibs. respectively, then move the bridge 
 of the first wire till the length of that wire is halved. 
 The notes will now be in unison, showing that halving 
 the length, other things jemaining unchanged, has' 
 doubled the number of vibrations. Or start with 
 two wires of the same length, stretched with 5 and 
 80 Ibs. respectively, so that the second gives four 
 times as many vibrations as the first and move the 
 bridge of the 5 Ib. wire till its length is only one 
 quarter of that of the 80 Ib. wire, unison is restored. 
 
 These experiments prove that n a j. Both these 
 
 relationships can be elegantly verified in the following 
 manner. Put the bridge of the one wire at any whole 
 number of inches, say 30, and fasten-to the wire a 
 known weight, say 56 Ibs. Hang from the other wire 
 an unknown weight in a bag. Move the bridge of the 
 second wire till there is unison. Suppose this distance 
 be found to be 24 inches. Then, since there is 
 unison, if x be the unknown weight 
 
 ^56"^ ^Z or -5! = _* _ or x = 35 . 86 lbs . 
 30 24 900 576 
 
 On actually weighing the bag of weights the result 
 agrees generally within one or two ounces. 
 
 To confirm the relationship n oc L, it is necessary 
 
 to determine d with great accuracy, or rather to 
 compare accurately the diameter of one wire with that 
 
 H 
 
98 Practical Physics. 
 
 of the other. This is best done by measuring exactly 
 equal lengths of the two wires and weighing them, the 
 
 weights being w^ and w 2 , then -L = ^_^i . Let two 
 
 ^2 V Wz 
 
 such wires be of equal length, vary the stretching 
 pressure on one till there is unison. It is then found 
 that the square roots of the stretching pressures are 
 directly as the diameters, or the stretching pressures 
 are directly as the weights of the wires 
 
 V ^ 
 
 Or, taking equal stretching pressures, vary the lengths 
 till there is unison, it is then found that the lengths 
 
 are inversely as the thicknesses -L = _ 2 , or the square 
 
 / 2 #! 
 
 / 2 w 
 of the lengths inversely as the weights ~ = 
 
 The relative diameters of dissimilar metals are ob- 
 tained by weighing equal lengths, taking the square 
 roots of the weights, and dividing by the specific 
 gravities. 
 
 90. Musical scale. The scale most generally 
 in use is formed as-fcllows. Let a note consist of n 
 vibrations a second. Then 
 
 Note Major Major Major 
 
 Tonic Second Third Fourth Fifth Sixth Seventh Octave 
 
 n | |# ^n |# f y/z 2n. 
 
 Sometimes the 'middle C' is taken as having 256 
 vibrations a second ; the eight complete notes from 
 this C to its higher octave are 
 
Musical Scale. 99 
 
 CDE'F G A B c 
 256 288 320 341-3 384 426-6 480 512. 
 
 Whole numbers are obtained throughout if, as is 
 sometimes done, 264 vibrations are given to C 
 
 CD EF GA B C 
 
 264 297 330 352 396 440 495 528. 
 
 Suppose therefore we have a wire stretched over a 
 board between two pegs, one of which is fixed and 
 the other has a hole in it through which the wire 
 passes, and suppose we have a bridge at a distance / 
 from the peg with the hole. The latter can be turned 
 round with a key if it has a square head until the 
 length / is in unison with a C luning-fork. Divide the 
 distance / into lengths, namely 
 
 CDEFGA B C 
 
 I V */ V- 
 
 Then the bridge being placed at one or other of these 
 places, the wire will give the corresponding note. Such 
 a wire with its scale is a monochord. 
 
 In the harp, pianoforte, and other stringed instru- 
 ments, the number of vibrations per second which 
 each string gives is determined partly by the string's 
 length, partly by its weight, and partly by its tension. 
 That is, the strings producing the higher notes are 
 not only the shortest ; they are the thinnest and are 
 stretched the most. The wires of the graver notes are 
 loaded with spirals of thin wire. To avoid ' thinness' 
 of sound, which accompanies thin, i>hort, highly 
 strung wires, several, two or three, similar wires are 
 placed side by side and struck by the same hammer. 
 
 H2 
 
ioo Practical Physics. 
 
 This enriches the note. The c tuning' is always 
 effected by varying the tension, that is, turning one of 
 the pegs to which the wire is fastened. The hammer 
 is not applied at the centre of the wire so as to sound 
 only the fundamental note, but at such a distance 
 from the end that besides the fundamental note har- 
 monics are sounded as well, which enrich the sound, 
 without, to most ears, impairing its purity. 
 
 91. Further development of nodes, Nodes in 
 rods. In 84 we considered the note of a rod 
 vibrating as a whole, and found that the rate of vibra- 
 
 on varied inversely with the square of the length. 
 FIG. 57. A longish rod or wand may be 
 
 , ^-----^^^^^ easily shaken at one end so as to 
 " divide itself into two parts, a seg- 
 
 ^z^^js*^*****" nient and half a segment, separated 
 ===:3 by a node rather less than one-third 
 from the free end. By a more rapid motion two 
 segments and a half may be got, there being then two 
 automatic nodes, one at nearly one-fifth and the other 
 at nearly three-fifths from the free end. As the seg- 
 ment and the free part vibrate at the same rate, the 
 rate of vibration of the whole may be very roughly 
 considered as the rate of the half segment at 
 the end, that is the rate of a rod of length ^/ 
 fastened at one end. Since the number of vibrations 
 varies inversely with the square of the length, the 
 number of vibrations of the Fundamental note beings, 
 the number now is 9 x //, and if there are two nodes it 
 is 25 xn and so on. These are the first and second 
 harmonics. The nodal line can be traced on a tuning- 
 fork when it is sounding its first harmonic by holding 
 
Nodes of Rods. Bells. 101 
 
 it horizontally with the broad face of the prongs hori- 
 zontal, scattering sand on both prongs and bowing 
 near the root of the fork. All the sand except that 
 which is over the nodal line is thrown off. 
 
 If we hold an elastic rod in the middle and move 
 the middle transversely to and fro, the rod will fall 
 into one whole and two half seg- FJG ^ 
 ments, separated by two automatic ^>c^~~^><^"" 
 nodes ; the rate of vibration in this 
 case must be 16 times as fast as that of the fundamen- 
 tal note. The nodes are at the length of the rod 
 from its ends. A strip of glass laid on two parallel 
 threads at the distance of the nodes apart and lightly 
 fastened to the threads gives off a highly clear note 
 when struck in the middle. It is the note of the 
 * musical glasses.' In order to get the gamut of the 
 musical glasses, if the lengthjpf the first glass is / 1? that 
 of the second must be /j >/|, that of the third / t V^ 9 
 and so on (comp. yo). Strips of glass of these lengths 
 being cut, they are supported at a quarter their lengths 
 from their ends on stringsand form a scale of whole notes 
 
 92. The Bell. If we hold a circular elastic 
 hoop on two opposite sides and bend it F 
 in and out rapidly, we find that at four 
 points there are nodes, and between them 
 segments (quadrants) which move in and 
 out, the points of maximum motion being 
 four in number and situated midway 
 between the nodes. Such is the motion of a bell 
 when sounding its fundamental note. This is shown 
 by employing an inverted bell or goblet and bowing 
 it. If while it is sounding a little pellet of wax hung 
 
IO2 Practical Physics. 
 
 from a thread is carried round the edge outside so as 
 always to lean upon the goblet, it is thrown off with 
 violence where the goblet was bowed, and also at 
 the opposite region, and also at quarter circumference 
 distance from these points. But at the intermediate 
 points, circumference distance from these, the pellet 
 remains comparatively at rest. If the goblet be filled 
 with water and then bowed as before, the water is 
 thrown into great commotion at the bowing place and 
 quadrant distances from it, but at the nodes it remains 
 more tranquil. 
 
 The note given out by a drum depending upon 
 the vibration of a membrane is seldom pure ; the 
 membrane breaks up into independently vibrating 
 pieces according to the place where it is struck. The 
 clash and clang of cymbals and the rattling boom of 
 a gong are characteristic of the variety of air waves 
 FIG. 60. to which they give rise. 
 
 -^ j> /The clap, rattle, roll and 
 
 ( \ ' > / boom of thunder denote 
 
 ci^ J&taei i&u> Zoom, the course of the light- 
 ning flash and its attitude towards us. 
 
 93. Nodes and segments in vibrating plates. 
 If a uniform circular brass plate about i foot in diameter 
 be clamped by a screw in the middle, it can be made 
 to break up into any even number of sectors greater 
 than two and maintain its own vibration, giving out 
 notes of higher pitch according as the number of 
 sectois is greater. These sectors so pulsate that 
 when one is moving in one direction the two neigh- 
 bouring ones are moving in the opposite. The sec- 
 tors are separated by radial nodal lines upon which 
 
Vibrations of Plates. 103 
 
 strewn sand accumulates when the plate is sounded, 
 thus tracing out the posi- 
 tion of the nodes. 
 
 The formation of these 
 lines is assisted by gently 
 pressing the plate with a 
 point where the node should meet the circumference. 
 Thus in (i) the plate is bowed at b and the finger/* 
 touches the plate at ^th of the circumference from b. 
 The plate gives out its lowest or fundamental note. 
 In (2) the finger is placed at T ^th the circumference 
 from l>, in (3) at y^th, in (4) at ^th, and so on. At 
 the beginning of the stroke the bow should be pressed 
 firmly and moved slowly across the edge at an angle 
 of about 80. As soon as the plate begins to speak 
 a lighter and more rapid stroke is given. 
 
 94. If a round glass plate be clamped at a dis- 
 tance of rd its radius from its edge, and a bundle of 
 well resined horsehairs be drawn with lateral pressure 
 through a small hole in the middle (fig. 62) FlG 
 the sand collects in a ring at one-third the 
 radius from the edge. The vibration of a 
 round plate and the vibration of a rectan- 
 gular plate in 91 are the counterparts of 
 the water mononodal undulation in a cylindrical 
 trough and the binodal undulation in a rectangular 
 trough ( 77, 78). 
 
 95. With a square plate clamped in the middle 
 an almost endless variety of segmental vibrations and 
 corresponding sand-marked nodal lines can be formed. 
 It will be noticed, and is indeed an essential condition 
 of all free vibration, that the number of vibrating 
 
104 
 
 Practical Physics. 
 
 elements is even, and that all symmetrically situated 
 elements are, at the same time, in the same phase of 
 motion. 
 
 FIG. 63. 
 
 / b 
 
 These figures can be rendered permanent by un- 
 screwing the nut which secures the plate in the 
 middle, and pressing upon the sand figure some 
 gummed cardboard. 
 
 96. The Gas-wave. That continuity of matter 
 is essential for the production of sound is shown by 
 setting a hammer to strike a bell under the exhausted 
 receiver of an air-pump. If the hammer and bell be 
 hung or supported by non-resonant matter, the 
 vibrations of the bell are almost inaudible. If, instead 
 of air, hydrogen be admitted into the vacuum, the 
 vibrations continue to be almost inaudible. For even 
 when the tension inside the receiver is restored, the 
 blow which the lighter gas (which is only ^ as dense 
 as air) gives to the glass of the receiver is unable to 
 communicate so much motion to it, as ; when commu- 
 nicated to the outer air, suffices to give rise to an 
 audible sound wave. (Compare empty and sand- 
 loaded tubes, 86.) 
 
 In the preceding we have examined the pro- 
 duction of sound, that is, air waves, by the vibration 
 of rods, strings, membranes, plates, &c., and it is rare 
 that a sound wave is neither started nor controlled by 
 solid matter. The singing of a kettle depends indeed 
 
Vibrations of Gases. 105 
 
 upon the collapse of strings of steam bubbles in water, 
 and a few other instances may be adduced : but it not 
 unfrequently happens that, although solid matter de- 
 termines the sound wave, it does not itself participate 
 in the motion its presence causes. Pure wind instru- 
 ments, as the flute, are examples of this. It must be 
 allowed that there is great ignorance concerning the 
 motion of the air at the mouth of a tube over which a 
 lateral current is passing. It appears that at the first 
 instance air is caught by the edge and sent down the 
 tube as a condensation. This returns after reflexion 
 from the bottom at an interval dependent upon the 
 length of the tube, reappears at the mouth as a con- 
 densation, and passes out of the mouth pushing away 
 the air current. The wave of condensation, however, 
 on leaving the tube's mouth, leaves a region of rare- 
 faction behind it into which the air current is pushed. 
 The latter again partly enters the tube, and sends down 
 it a wave of compression. There is accordingly a 
 kind of vibration of the air current towards and away 
 from the tube's mouth, which vibration is governed by 
 the time required for the wave to travel to and fro in 
 the tube. 
 
 Accordingly of two tubes closed at the bottom, 
 one of which is twice as long as the other, the longer 
 will give the lower octave of the shorter, that is, a 
 wave system of twice the length, of doiuVe the time 
 interval, of half the rate of recurrence (pitch). 
 
 97. Let us confirm this as follows. Take any 
 tuning-fork the number of whose vibrations per second 
 is known, say c, which makes suppose 256 complete 
 vibrations in a second. From 79 it appears that 
 
io6 
 
 Practical Physics. 
 
 wave length in feet = 
 
 no. of feet travelled in i second 
 
 FIG. 6 4 . 
 
 no. of waves generated in i sec. 
 In this case therefore = VV\ = 4 ft. 
 3*6 in. Take now a tube open at 
 both ends and about \ inch diameter, 
 plunge the lower end into water, and 
 holding the sounding fork above it 
 move the tube up and down till the 
 sound of the fork is greatly and sud- 
 denly increased. Measure the length 
 of the tube from the open end to 
 the level of the water, and it will be 
 found to be about i foot 0*9 in. Cut eight or ten tubes 
 of exactly this length, and grind their ends flat on a wet 
 sandstone or the side of a grindstone. Prepare some 
 glass, metal, wood, or cork discs the size of the 
 outside measurement of the tube, and some pieces of 
 vulcanised caoutchouc tubing about i in. long and 
 rather less in diameter than the tubes. When such a 
 disc is inserted into the caoutchouc and the latter is 
 drawn on to the glass tube, the tube is of course closed 
 at one end. Two tubes joined by a piece of caout- 
 chouc form an open tube of double length and so on. 
 It is clear that if we denote a region of maximum 
 motion by a bundle of horizontal lines, and node by a 
 vertical dotted line, we have in a tube open at one end 
 the following condition (fig. 65) when the tube is sound- 
 i fi i ts fundamental note. If we 
 attach another unit length to the tube, 
 it refuses to sound, because to do so 
 would necessitate a region of maxi- 
 mum motion at the bottom, an 
 
 FIG. 63. 
 
Closed and Open Tubes. 107 
 
 evident impossibility. But a tube of 3 units length will 
 sound, and so will all odd multiples of the unit (fig. 66) 
 tube. Further, if we examine what different forks will 
 resound to the same tube close at one end, we find that 
 
 FIG. 66. 
 
 a fork giving rise to three times the number of vibrations, 
 one giving rise to 5 times, FlG . 67> 
 
 7 times, and so on, will re- . 
 
 sound (fig. 67), while no ' ^ 
 
 even number multiple of j 1 
 
 the vibrations (submul- ' i ' ^ 
 
 tiplesofwavelengths)will i p j 1 1 
 
 do so, for they necessitate ' s ' ~ : ^ 
 
 maximum motion at the \ = i i i 
 
 = i = = ; = 
 
 bottom. The first over- 
 tone, sometimes called ' harmonic/ got by blowing 
 with violence across the open end of a tube closed at 
 the bottom, has therefore \ wave length of the fun- 
 damental, the second |, and so on. 
 
 Take now a second tube of the same length as the 
 first, also closed at the bottom, and FlG 68 
 
 fasten the closed ends together. The g r ^ 
 
 second tube will take up the vibra- ^ 
 tions of the same fork. The double diaphragm in the 
 middle may be withdrawn, for the pressure on it from 
 one side is always equal to that on the other ; so that 
 a tube open at both ends must be twice as long as a 
 
io8 Practical Physics. 
 
 tube closed at one end to sound the same note. In 
 the former case an automatic node is formed in the 
 FIG. 6 9 . middle. Three unit lengths of 
 
 H ff tube refuse to sound to the same 
 
 555 : ^ fork, because the wave length being 
 the same, there would be a node at an open end if 
 there were maximum motion at the other, whereas 
 there must obviously always be maximum motion at 
 an open end. A length of 4, 6, 8, &c. units will 
 resound, 
 
 Or, if (fig. 70) we take the first open tube which re- 
 
 FIG. 70. 
 
 sounds to the fork as the unit length, all open tubes which 
 
 FIG. 71. 
 
 are multiples of this length will resound. And in the 
 same manner as before, on examining what forks resound 
 
Nodes in Open Tubes. 109 
 
 to the same open 'tube (fig. 71), we find that they are all 
 the forks whose vibrating numbers are multiples (or 
 wave's-length submultiples) of the lowest. This series 
 includes, therefore, all the octaves of the lowest fork. 
 
 98. The node or nodes in an open FlG> 72> 
 tube, and the regions of maximum motion, 
 can be examined in an open organ pipe. 
 Such a pipe has one free open end, but 
 the end where the air current vibrates 
 is not so free. A little tambour, covered 
 loosely with tissue paper, will rustle at 
 the top and bottom of the tube, but 
 remain tranquil near the middle. 
 
 A node being a place where the change 
 of density is greatest, and half-way between 
 the nodes being where there is least 
 change of density though greatest motion, 
 the existence of one or other condition can be 
 shown by the effect on flames as follows. Let 
 an open organ pipe (fig. 73) have three holes cut 
 along one side, at ^, ^, f the pipe's length from the 
 end. These holes are covered with gold-beater's 
 skin, and the skin is covered by a little box in 
 each instance. Into all three of these side cham- 
 bers coal gas is led, and to each there is a small jet 
 at which the gas can be burnt. The jets are set 
 burning at all three places. When the fundamental 
 note is sounded the central jet alone is extinguished. 
 For the alternate compression and rarefaction of the 
 air at the node which is formed there moves the 
 membrane in and out, and so puts out the flame. 
 On sounding the next harmonic, that is, the higher 
 
no Practical Physics. 
 
 octave, nodes are formed at the first and third gas 
 
 FIG. 73. 
 
 I 1 
 
 jets, and these are extinguished while the central 
 one now continues burning. It is evident that the 
 first experiment only shows a differential effect, since 
 the positions of the jets are not the regions of greatest 
 motion, and therefore are not free from variation in 
 pressure. 
 
 99. Resonance. The acceptance by a tube of a 
 system of waves of a sonorous body is called resonance; 
 FIG and for narrow tubes the 
 
 relationship established 
 in 97, 98, holds good. 
 But with wider tubes, 
 even when cylindrical, but 
 more markedly if of irre- 
 gular shape, the relation- 
 ship between the sound 
 wave and the vessel measurements is not so obvious. 
 
 Thus a wider cylinder will present a possibly 
 longer path by dint of reflexion, so that such a tube 
 will also sound to a graver fork, and, indeed, may 
 sound more fully to a graver fork, for, by repeated 
 reflexion, it can furnish a great variety of paths of the 
 required greater length. 
 
 Let us next employ the resonant cavity to measure 
 
Resonance. 1 1 1 
 
 the relative rate's at which sound travels in different 
 gases, and so confirm the formula 
 
 z/oc 
 
 Fill a tube so far with water that it resounds to a 
 given fork. Lead a current of carbonic acid gently to 
 the surface of the water, so that the air may be ex- 
 pelled by displacement. The tube of carbonic acid 
 no longer resounds to the fork, but it does so if water 
 be poured in so as to shorten the resonant column. 
 This shows that for sound to reach from end to end 
 (and back again) in the same time in two columns, 
 one of air and the other of carbonic acid, the carbonic 
 acid column must be the shortest, or, in other words, 
 the sound travels fastest through air. If, on the other 
 hand, a tube be taken closed at one end, inverted, and 
 filled by displacement by hydrogen or coal gas, a fork 
 which resounds to this tube will do so, if the gas is 
 replaced by air, only when the column is shortened. A 
 copper tube which resounds to a fork when heated, 
 does not do so when cooled, unless virtually shortened. 
 All these experiments show that sound travels more 
 slowly through a gas of greater density, if the elasticity 
 remains unchanged, as is the case in all these experi- 
 ments, since the gas has the same elasticity as the air. 
 When a gas is compressed its density and elasticity 
 increase together, and accordingly no change in velo- 
 city occurs. This is the condition of change brought 
 about by variation in barometric pressure ; such a 
 variation accordingly is not accompanied by any 
 change in sound velocity. The acquirement, however, 
 
112 Practical Physics. 
 
 of aqueous vapour, which diminishes density without 
 affecting elasticity, increases velocity. 
 
 100. Longitudinal vibrations of liquids and 
 solids. Although the transverse vibrations of solids are 
 accompanied and caused by states of compression or 
 rarefaction, or both, these states do not pursue the same 
 course as the vibration itself does. Both solids and 
 liquids are, however, capable of such compression and 
 F f rarefaction, and so of convey- 
 
 ing sound waves in the same 
 sense that air does. This 
 is shown in the case of 
 liquids, by fastening a tube 
 containing water, mercury, 
 or other liquid, fig. 75, on 
 
 -i to a sounding-board, and 
 
 plunging into the top of the 
 
 liquid a cork cone fastened to the end of a tuning- 
 fork. The sound heard proves that the wave of 
 condensation travels through the water. The actual 
 velocity of sound through water is about four times 
 that through air. The actual comparison between 
 the rate of a wave through air and through a solid is 
 established as follows : a tuning-fork is held over a 
 narrow cylinder into which water is poured until 
 the maximum resonance is reached. A solid cylin- 
 drical rod, say of oak, is held in the middle between 
 finger and thumb, and one of the free ends is rubbed 
 longitudinally towards the middle with a piece of 
 leather covered with powdered resin ; a pretty clear 
 note is thus produced, the origin of which is the 
 breaking of the brittle resin powder at a certain 
 
- 
 
 Longitudinal Vibrations of Solids. 1 1 3 
 
 degree of strain, setting up of a wave of altered 
 density, which, after being reflected at the further end, 
 returns to the end being rubbed. It then beats and 
 pulls the air, giving rise to an audible air wave ; the 
 time required for the next solid wave to pass down 
 and up : that is, the time interval between two solid 
 waves (and therefore between the two air waves to 
 which they give rise), is directly proportional to the 
 length of path (twice length of rod) and inversely pro- 
 portional to rate of travelling. If the rod be so cut 
 down that it gives the same note as the tuning-fork 
 and its resonant column, it follows that the solid 
 wave takes the same time to travel from end to end 
 of the rod as the air wave takes to travel from the 
 mouth of the jar to the water surface and back again ; 
 for it must be borne in mind that a rod vibrating as 
 above described resembles a pipe open at both ends, 
 which (97) has been shown to have twice the length 
 of the closed pipe giving the same note. Thus it is 
 found that if the air column resounding to a given fork 
 be 6 in. long, an oaken rod must be cut down to about 
 10 feet to give the same note. The velocity of the oaken 
 wave is to the velocity of the air wave as 10 feet is to 
 twice 6 in., or as 10 to i. A deal or steel rod must be 
 32 times as long, or, reckoned from the middle, 16 
 times as long as the similarly vibrating air column. 
 
 1 01. The comparative rate of metal waves is 
 found in a similar way, but wires may be employed. 
 The actual wave lengths can be traced out by 
 the arrangement of lycopodium, if the waves be 
 reflected from the bottom of a tube, so that nodes 
 may be established. And this method enables us 
 i 
 
Practical Physics. 
 
 either to compare different solids, using the same gas 
 in the tubes, or different gases, using the same solid 
 FIG. 7 6. exciter. In fig. 76, sup- 
 
 pose there are two rods 
 of the same length, 
 one of brass and the 
 other of glass, each 
 supported in its middle by a cork fitting into the end 
 of a glass tube, the other end of which is closed. If 
 the tube be of the right length, measured from the 
 end of the rod to the bottom, that is, any multiple of 
 the half wave length of the note, stationary waves will 
 be formed, in whose nodes the lycopodium accumu- 
 lates. If both rods are of glass, and one tube be 
 filled with hydrogen, the waves in the latter are found 
 to be longer than those of the air. 
 
 102. The conveyance of sound through solids is 
 not only quicker, but more perfect, than through air. 
 A watch is heard to tick when placed at the end of a 
 deal rod several yards long, if the ear be placed at 
 the other end. A piano in one room gives its vibration 
 to wooden rods passing into a room several score 
 yards off, and will, if the rod be connected with a 
 sounding-board in the second room, appear to be 
 FIG. 77. played there. 
 
 If two round 
 tubes, about 
 3 in. in dia- 
 meter, have 
 a membrane 
 stretched 
 tightly over 
 one end of each, and a thiead be fastened to the 
 
Transmission of Sound. Interference. 1 1 5 
 
 membranes through the centre by means of knots 
 and a little wax, the voice speaking into one can 
 be heard in the other, though the thread be 20 or 30 
 yards long, provided it is kept moderately stretched. 
 It may even be carried round corners, if it be sup- 
 ported at the corners by short flexible threads. By 
 employing steel wire and metal membranes, conver- 
 sation can be heard from a quarter of a mile, 
 
 103. Interference Beats. If a mass of air is 
 acted on simultaneously by two systems of waves, it 
 will be affected (i) according to the relative phases of 
 the two systems, if they are of equal length, and (2) 
 according to their lengths. We need only look at a 
 few cases of each. Let us suppose that in all cases 
 the waves have equal amplitudes. First, let the wave 
 systems be of equal wave length, and start together. 
 Fig. 78, (i) the waves aug- FIG 7 s. 
 
 ment one another's ampli- ^ ^ ^, 
 tude throughout. If the / \ . / \ / \ A.) 
 one system is ^ of a wave Y/ v/ \s 
 
 length before the other, we a r ^"\_y' x ~\ ;^~\^>(*} 
 
 get (2), and so on. A dif- ^ ^^ ^^ ^^ 
 ference of J wave length * 
 
 gives perfect extinction. If I - '^ 
 the difference be still further I 
 
 3 ^ , ^- -~^/0> 
 
 increased, the joint wave "" 
 
 system increases in ampli- I" "'" 
 
 tude, and therefore in loud- r /"> ./~~\. /""Nirt 
 
 8 \.^/ \^/ \ / 
 
 ness, until f (9) is reached, ^. X-N r\ 
 
 which is the same as (i). | . / \ / \ / V} 
 To show this, a tube, shown * \J \J \J 
 in fig. 79, is used. A caout- 
 1 2 
 
Ii6 Practical Physics. 
 
 chouc tube containing a whistle is fastened to a. The 
 sound waves are divided at b, half each wave, that is, 
 FIG. 79. condensation of half am- 
 
 plitude, and rarefaction of 
 half amplitude, goes to the 
 right, and half to the left. 
 If their paths be equal, 
 they meet again as they parted, and augment one 
 another's amplitude, and so restore the full sound. 
 But if the movable loop, //, be drawn out, so that 
 the additional path of the left limb of the wave is 
 equal to half the wave length, the two wave systems 
 will encounter one another at <:, in opposite phases, 
 as in case (5), fig. 78, and the two wave systems pro- 
 duce silence. The gradual extinction of the sound, 
 and its gradual restoration, as the sliding piece is 
 pulled twice as far out, shows that all the cases of 
 fig 78 are passed through. 
 
 104. In the next place, considei the effect which 
 two wave systems have on one another, if they have 
 some very simple relation in their wave-lengths, say 
 i : 2, and suppose (i) that they start in the same 
 phase, (2) that the shorter wave is | a long wave in 
 advance, (3) when the short one is f in advance, and 
 so on. Fig. 80 shows the effect. 
 
 Next let there be some other but integral relation 
 between the wave-lengths of two wave systems which 
 are started simultaneously, fig. 81, where seven waves 
 of one system are as long as 6 of the other. If 
 they start together it follows that the first condensa- 
 tions will travel together and the amplitude will be 
 their sum. Condensation No. 3 of the 6 system will 
 
Interference. 117 
 
 be sent off at the time half-way between the 3 and the 4 
 of the 7 system, that is, at the time when a maximum 
 
 FIG. 80. 
 
 3, "// \^\/_\V// \V / \ sf/ \Y>y"" 
 
 f \J 
 f 
 
 fasf; f asl; f asf; J as f ; | as f. 
 
 rarefaction of that system is evolved. These will 
 annihilate one another. When the 6th of the 6 sys- 
 tem is sent off, the 7th of the 7 system will be sent 
 off also, and these will assist one another. 
 
 FIG. 81. 
 
 A burst of sound called a beat is heard when the 
 region of augmentation reaches the ear ; these are 
 alternated with periods of comparative silence. 
 
 105. Interference is shown experimentally by 
 the tuning-fork. If such a sounding fork be held over 
 its resonance tube horizontally and gradually revolved, 
 
n8 Practical Physics. 
 
 four positions are found in which the sound is almost 
 extinguished, and these positions are when the side 
 faces of the fork are at about 45 with the resonance 
 tube. In the corresponding lines the wave of rarefac- 
 tion from one prong cuts the wave of condensation 
 from the other, and mutual destruction ensues. If 
 FlG 82f when the fork is in this position 
 
 one of the prongs be surrounded 
 k v a paper tube, so as to absorb 
 its vibrations, the sound of the 
 other prong is restored. So 
 when the fundamental note of 
 the vibrating plate ( 95) is 
 sounding, it is weakened from the circumstance that 
 neighbouring segments are always in opposite phases. 
 If two pieces of cardboard cut to the shape of two 
 segments be held over two opposite segments, so as to 
 kill their sound, the other two segments sound louder. 
 On setting the plate in any other condition of vibraticn 
 and passing the palm of the hand close over its surface 
 without touching, its effect in lessening the interference 
 is made audible. 
 
 It follows from 104 that the beats, being condi- 
 tions of density, travel through the air at the same 
 rate as the waves whose interference causes them. The 
 more nearly notes are in unison, the longer the interval 
 in time and space between the beats. Practically, the 
 audibility of beats is of great importance in estimating 
 the difference between notes in near accord ; and the 
 elimination of beats is a guide in bringing notes to 
 strict accord. For the number of beats which two 
 notes sounding together give in a second is the diffe- 
 
Interference. 1 19 
 
 rence between the numbers of their individual vibra- 
 tions in a second. Thus in 89, where the bridge of 
 the monocord was moved till unison was obtained, 
 perfect unison is preceded by beats which get less 
 and less frequent till they cease to be distinguishable. 
 On continuing to move the bridge in the same direc- 
 tion they become audible again, and as the bridge is 
 moved the rapidity is increased they get too nume- 
 rous to count, until, when they reach about 32 in a 
 second, their existence is perceived as discord. 
 
 Beats are readily produced between forks in unison 
 by loading one prong of one with a piece of metal 
 stuck on with wax. The beats become more frequent 
 as the metal is fixed nearer to the end, and also as its 
 weight is increased. 
 
 1 06. Small flames burning inside open tubes 
 often, by establishing currents, blow them- FIG g 
 selves partially out, so that full combustion 
 ceases ; the current stops and the flame strikes 
 back ; this gives rise to an air wave, according 
 to the length of the tube, in such away that the 
 advent of the air wave at the flame causes a 
 flicker of the flame, and the flicker of the 
 flame causes an air wave. Two such tubes, 
 if alike, will sing in unison, but by sliding up a paper 
 tube surrounding one, its tube is lengthened, a lower 
 note results and beats are heard. That such a singing 
 flame palpitates is seen by moving the head quickly 
 from side to side while looking at it or by focussing 
 it by a convex mirror upon a screen and turning the 
 mirror quickly but slightly on a vertical axis. The 
 image appears then in different places when of dif- 
 
I2O Practical Physics. 
 
 ferent sizes, so that a uniformly jagged appearance 
 results. 
 
 107. Sinuosities.- The above method of making 
 palpitation visible is only one instance of the device 
 by which a to-and-fro motion is converted into a wavy 
 or sinuous one by combining it with motion of trans- 
 lation. If a piece of elastic wire is fastened to a prong 
 of a tuning-fork and held in such a way that when the 
 fork sounds the wire scratches lampblack off a sheet 
 of glass, the scratch will be a line. But if either the 
 fork is drawn along or the glass shifted, a sinuous line 
 is laid bare. If the relative movement endures for a 
 second, whether that movement be fast or slow, there 
 will be as many crests on one side of the sinuosity as 
 there were complete vibrations. Use has been made 
 FIG. 8 4 . of this method for regu- 
 
 lating forks to agree with 
 a normal fork. Both 
 forks are provided with 
 little styles of bristles. 
 These delay the vibration a little, but affect both 
 forks alike. The styles rest upon a cylinder which 
 is covered with lampblack and can be turned on 
 a horizontal axis which is a screw. In this way 
 the cylinder advances as it turns, and the sinuosities 
 take a spiral form. The number of waves between 
 two lines parallel to the axis is counted, and the fork 
 under trial filed accordingly (see 85). 
 
 1 08. Effect of motion of the source of sound. 
 If we were to begin to move away from a source of 
 sound the moment it began to give forth n vibrations 
 per second, and were to move at the rate of 1,100 feet 
 
Motion of a Source of Sound. 121 
 
 second, it is clear that the sound would never over- 
 take us. If we were to move at the rate of 550 feet a 
 second, at the end of the second we should have been 
 
 overtaken by - sound waves, because the -th sound 
 
 wave would be at 550 from the source. Hearing - 
 
 sound waves in a second, we should hear the octave 
 lower than we should have done had we remained 
 at rest. And inversely, if we started at a distance of 
 1,100 feet from the source of sound, and began 
 moving towards the source of sound at the rate of 
 1,100 feet a second the moment the source of sound 
 began giving off ;/ vibrations, we should hear nothing 
 in the first half-second, or 550 feet. Then we should 
 hear the whole n vibrations in the next half-second, 
 or 550 feet, and reach the sounding body just as it 
 had completed its #th vibration. Evidently, therefore, 
 the pitch of the note which we should hear would be 
 an octave higher than it would have been if we had re- 
 mained at rest. It is also clear that this change of pitch 
 by motion is the same whether we move or whether the 
 source of sound does so. This is shown by fastening 
 a whistle to the end of a long caoutchouc tube, and 
 whirling the tube round while the whistle is sounding. 
 To a person standing at some distance the pitch of 
 the note is heard to become graver as the whistle re- 
 cedes, and shriller as it advances towards him. 
 
 Sympathy. If two solid bodies, such as two 
 strings or taning-forks, are capable of giving out the 
 same note when sounded, the sounding of one alone 
 will cause the other to . sound if the two be in con- 
 
122 Practical Physics. 
 
 nection by any elastic medium. Thus if two tuning- 
 forks placed side by side, facing one another, be 
 related as a note and its octave, and a third fork in 
 unison with one of them be sounded and placed 
 between them at the same distance from each, the 
 unison fork alone will sound. A pellet of wax hung 
 resting against this one will be thrown off, while a 
 similar pellet attached to the other will remain at rest. 
 This may be regarded as an absorption of vibration. 
 
 These experiments are interesting on account of 
 their supposed relationship to similar absorption of 
 light rays, but are here chiefly noteworthy inasmuch 
 as they confirm the assertion that there is little change 
 in the wave length in its passage through the air. 
 
 109. Approach caused by vibration. The air in 
 the neighbourhood of a vibrating body is on the whole 
 somewhat less dense than when the body is at rest. 
 If a mixture of lycopodium and sand be scattered on 
 a vibrating plate (95) which has broken up into 
 FIG. 85. segments (fig. 85), while the sand col- 
 
 , lects on those lines where there is 
 
 least motion, the lycopodium collects 
 in the complementary regions where 
 the motion is greatest. On examining 
 those little heaps of powder the par- 
 ticles are seen to enter the heaps at 
 the base, rise in the middle, and roll down the slope, 
 showing that there is an inrush of air laterally to 
 supply partial rarefaction. Further, if one limb 
 of a large tuning-fork be fastened air-tight in a tube 
 (fig. 86), from which a capillary tube leads into water, 
 when the other limb is bowed the water sinks in the 
 
Approach caused by Vibration. 123 
 
 FIG. 86. 
 
 capillary as though a vibrating fork occupied more 
 room than one at rest. 
 
 Finally, a series of air waves 
 from a fork on striking on a lightly 
 suspended surface, either smooth 
 or rough, cause the surface to 
 approach the fork ; or if the sur- 
 face be fixed and the fork mov- 
 able, the fork approaches the 
 surface. This is the case whether 
 
 the surface be smooth or rough. - 
 
 A toy caoutchouc ball floating I [ 
 
 on clean water shows this effect to 
 
 perfection. 
 
 110. The Phonograph. By speaking on to a 
 stretched membrane, the other side of which carries a 
 style, and moving a smoked glass surface at a uniform 
 rate across the style, a permanent record is obtained 
 of the vibrations corresponding to the words uttered. 
 The logograph is a device of this kind. In the 
 phonograph not only is a similar record preserved, but 
 it is of such a nature as to be usable in the reproduc- 
 tion of the sounds and articulate words. A spiral 
 groove is cut in a revolving drum ( 107, fig. 84), 
 which turns on a screw axis of the same pitch as the 
 groove. Tinfoil is smoothly rolled upon this, so that 
 there is a spiral worm cavity. A little drum, whose 
 sides are of wood and whose membrane is thin sheet 
 iron, has a style fixed to its centre outwards, and this 
 can be brought and fixed so that the style just touches 
 the foil. On turning the cylinder round and speaking 
 into the drum, the style makes a series of indentations 
 
124 Practical Physics. 
 
 on the foil. On passing this series of indentations 
 beneath the style of the same drum, or better, beneath 
 that of a drum made of paper, the style enters the 
 cavities which the first one made, and sets its drum in 
 vibration, which thus reproduces the sounds which 
 the first drum received. The complex vibrations of 
 part-singing can be registered and reproduced. 
 
APPENDIX. 
 
 use of this device for 
 FIG 87. 
 
 ~wo\ 
 
 in. The Vernier. -The 
 
 getting exact measures of 
 distances, heights, and 
 angles, depends upon the 
 fact that it is easier to per- 
 ceive exact coincidence in 
 position than to estimate 
 exactly a difference of po- 
 sition. A vernier is a small 
 scale sliding edge to edge 
 with the main scale, and 
 having its divisions a little 
 further apart than those 
 of the main scale. If the 
 object is to read to tenths 
 of the divisions of the 
 main scale, the length of 
 the vernier is eleven of the 
 divisions of the main scale, 
 and this length is divided 
 into ten equal parts. Each 
 division of the vernier is 
 i~ as long as a division 
 of the main scale. If the 
 main scale is numbered from below upwards, the vernier 
 is numbered from above downwards, its top being marked 
 
 89 
 
 V 
 
 10 Ve. = 11 Sc, 
 
126 Practical Physics. 
 
 o. Thus let it be required to determine the height of the 
 line H, fig. 87, which falls between the 97th and 98th 
 divisions on the scale S. Push up the vernier V till its top 
 or zero line coincides with H. Look down the two 
 scales and you see that 89 very nearly coincides with 8 ; 
 assume that it does so. The height of H is 97 +x scale 
 divisions, and x is of such a length that .*+ 8 scale divi- 
 sions are equal to 8 vernier divisions, or to 8 + ^ scale 
 divisions ; that is, x + 8 = 8 + ~, whence x is ~ of a scale 
 division and the height of H is 97 + ~. 
 
 The divisions on the vernier of a sextant are 
 generally f of the divisions on the main scale ; 
 the latter are arcs representing 20 minutes or \ of a 
 degree : the vernier enables reading to be taken of ~ of \ 
 of a degree, or to one minute. 
 
 112. Parchment paper. Mix slowly two pints of 
 commercial oil of vitriol with one pint of water and cool 
 to about 15. Pour into a shallow basin, and drag 
 through it a sheet of unsized paper (Swedish filtering 
 paper is good) at such a rate that each part of the paper 
 is in contact with the liquid for about five seconds ; 
 plunge the paper immediately into a pail of water and 
 thence after a few minutes into a basin under the tap. 
 After a quarter of an hour's rinsing a drop or two of 
 ammonia may be added and the rinsing continued. 
 The paper should be kept moist. A strip of this paper 
 an inch wide should support at least twenty pounds. 
 
 113. Hints on glass working-. Perhaps the 
 following few hints on working in glass may be useful 
 for the construction of some of the apparatus described. 
 
 To cut a glass tube. Lay the tube over the edge 
 of the table, and tilt it a very little, so that the place 
 where it has to be cut rests on the edge of the table. 
 Hold the tube close to this place, and give one long and 
 Steady cut with a three-cornered file, guiding the file with 
 
Glass Working. 127 
 
 the thumb-nail, If the tube is very thick in the glass as 
 well as in diameter, repeat two or three times in the 
 same place, but don't saw. Hold it horizontally on both 
 sides before the chest, with the cut towards you ; pull, 
 and bend as liitle as possible. The less the bending the 
 cleaner the cut. 
 
 To smooth the ends of tubes. Tubes which have 
 to be passed through corks, or connected by caoutchouc 
 tubing, should have their ends smoothed. Warm the 
 end by passing it through the air-gas burner, then hold 
 it obliquely in the flame, turning it till the edges are 
 rounded : this is seen to happen soon after the flame 
 begins to be coloured yellow by the sodium of the 
 glass. 
 
 To bend tubes. Tubes, unless of great thickness, 
 should be bent with one motion, unless the bend is 
 required to be a gradual curve. The two parts on either 
 side of where the bend is to be are held as near as 
 possible to the centres of gravities, lightly with the same 
 grip as a pen is held, under-handed, thumb upwards. 
 The region being gradually warmed, the tube is held 
 rather obliquely through the solid part of the flame, 
 being constantly turned round. As soon as the flame 
 burns yellow and two or three inches of the tube are 
 found to be soft, the tube is removed from the flame and 
 bent to the required angle. A tube which has been 
 bent so sharply that there is a crease in the bend is 
 pretty sure to break there. 
 
 To close the end of a tube. Tubes not more than 
 half-inch in diameter may be closed over the simple air- 
 gas burner. They should be softened near the end and 
 the end pulled off : this leaves a tail of glass : the root of 
 the tail is heated and again pulled off, and so on till the 
 tail is very slender ; then cut it off and heat the stump 
 in the flame : it will melt and run up, making the end 
 
128 Practical Physics. 
 
 about of the same thickness as the rest of the tube. When 
 the end is red-hot it may be further smoothened by 
 removing it from the flame and gently blowing into the 
 open end. To close a wide thick tube, the table blow- 
 pipe is preferable. 
 
 To fuse platinum Into a glass tube. The whole 
 region being heated, a fine blow-pipe flame is made to play 
 FIG. 88. on tne point, and when this is soft a pla- 
 tinum wire is stuck to it and rapidly 
 pulled away ; this draws out a little tube: 
 ^^^ this tube is cut off as close as possible to 
 the main tube, and the end is heated till 
 its edge shrinks so as scarcely to project 
 upon the main tube. The platinum wire 
 is thrust through the hole, which it should 
 nearly fit ; the glass is softened, and the 
 red-hot wire is worked a little in the hole, both in and 
 out and round about, to enforce complete contact. 
 
 To join tube to tube, end to end. If they are of 
 the same or nearly the same diameter, the ends should be 
 cut clean and flat, but not ground ; the further end of one 
 tube should be closed with a cork. The ends being 
 thoroughly and uniformly softened, are pressed gently to- 
 gether ; for steadiness the wrists may be in contact. The 
 joint is allowed to get sufficiently cool to prevent bending 
 when the whole is held in one hand. A pointed flame of 
 the blow-pipe so made that the tube is not softened all round 
 is applied in succession to three or four points of the 
 join, and air is gently blown in at the open end, not so as 
 to make a bulb but so as to restore the cylindrical form. 
 By this means the appearance of a joint is quite erased 
 beyond a little irregularity. 
 
 If the tubes are of very different diameter the wider 
 one should be drawn out with much heat and little 
 pulling, and constant rotation, so that the glass of the 
 
Glass Working. 129 
 
 neck may be of a reasonable thickness. The neck being 
 cut through, proceed as before. 
 
 To join a capillary tube to another, a bulb should be 
 blown on one end of the capillary tube and then broken 
 and the edge chipped off pretty even. The edge of the 
 so formed tube is allowed to collapse till it is of about 
 the same width as the tube to be joined, they are joined 
 as before. 
 
 To join tubes end to side. One end of each tube 
 being permanently or temporarily closed, a pointed flame 
 is directed upon one side of the tube FlG - 8 9- 
 whose side has to be pierced, and by ~ \\ 
 
 blowing a gentle elevation is produced : 
 this is increased by two or three sub- 
 sequent blowings until by a strong puff " 
 
 of breath the side is blown through. C? 
 
 The remains of the thin glass bulb are U 
 
 removed by pressure, and the edge of 
 
 the hole rounded in the flame ; the edge 
 
 of the other tube is then applied and II 
 
 fused on as above. 
 
 A simple constriction in a tube is made by using a 
 large blow-pipe flame and turning the tube round and 
 round without drawing it out. FIG. 90. 
 
 A bulb is blown on the e v / 
 
 end of a tube by first closing / ^ i 
 
 the end and letting it fall together till a good mass of 
 glass is collected at the end which must FlG 9I . 
 
 be very uniformly hot when the breath 
 is gently forced in at the open end. 
 
 To blow a bulb on the middle of 
 a tube, one end of the tube is closed 
 and the place required is uniformly 
 heated and the ends are gently pushed 
 together while air is blown in at the open end. 
 K 
 
130 
 
 Practical PJiysics. 
 
 If it be required to blow a large bulb of thickish glass 
 on a narrow tube, the narrow tube should be joined to a 
 FIG. 92. piece of wider tube and 
 
 the bulb blown on the 
 latter. 
 
 To cut sbeets of glass 
 with a diamond. The 
 glass should be placed 
 on a piece of cloth and 
 the cut made with a 
 single stroke towards you, 
 taking care to cut quite 
 up to the edge next you. 
 The plate is held in both 
 hands with the thumbs 
 above the glass quite on 
 the edge, one on each 
 side and quite close to the cut. It is then bent upwards. 
 To cut a round piece of glass, such as a flask or 
 beaker, a crack must be made in the vessel by heating a 
 part of it and dropping a drop of water on the heated 
 part. A piece of pointed charcoal or pastile is set on 
 fire and the point moved a little in advance of the crack, 
 which follows it, and may be directed along any dry ink 
 line previously made on the glass. The sharp edge, if it 
 be irregular, as it is apt to be, is chopped regular by 
 a key, between the wards of which the edge is placed ; 
 the fit should be good and only the edge placed in ; the 
 key is turned outwards. 
 
 The end of a tube may be ground off flat by being 
 held against the flat side of a grindstone, using water. 
 It should be finished on a flat sandstone slab. The end 
 of a tube may be at once ground flat on the slab ; the top 
 of the tube being lightly held serves as a pivot : a small 
 circular motion is given to the lower end. 
 
 To bore a hole in glass, an old file is ground to a 
 
Etching on Glass. 131 
 
 three-cornered borer, finished on the hone and hardened 
 by heating it red-hot and quenching it. The file is placed 
 in a handle and worked with the hand or inserted in a 
 watchmaker's drill. The point to be bored through is 
 kept moistened with oil of turpentine, and the glass is 
 fixed immediately beneath it. When the hole is half- 
 way through, the plate is inverted and the hole met on 
 the other side. 
 
 1 14. To etch a scale on glass. Steel millimeter 
 scales are sold, and from these millimeter divisions are 
 easily transferred to glass. The glass is cleaned and 
 heated and covered uniformly, and not too thickly, with 
 melted beeswax and turpentine, 20 of wax to I of tur- 
 pentine ; the scale and the glass are stuck with a little 
 
 FIG. 93. 
 
 soft wax on a table, as in fig. 93. A rod about 2 feet 
 long has two stiff needles driven through its ends, and 
 while one needle is placed in a division of the scale the 
 other scratches the wax off the glass ; and, to prevent the 
 scratched lines being too long, two straight-edges may be 
 fastened along the glass. Figures having been added 
 with a needle-point, the glass is painted over with a solu- 
 tion of hydrofluoric acid. In about half a minute the acid 
 is washed off and the wax removed by spirits of wine or 
 turpentine. A clearer etching is effected by use of the 
 gaseous acid. The glass is then supported with its 
 marked side downwards over a mixture of powdered fluor 
 spar and oil of vitriol contained in a long leaden trough, 
 which is kept for some hours in a warm place. The 
 liquid acid, and especially the gaseous acid, is excessively 
 K 2 
 
132 Practical Physics. 
 
 poisonous, and the etching should be performed where 
 there is thorough ventilation. 
 
 115. The siphon barometer. To make a siphon 
 barometer, a piece of well annealed soft- German or lead 
 glass, about 42 inches long, an inch thick outside 
 and \ inch inside, and of the same bore at both ends, 
 is thoroughly cleaned and dried. The final drying 
 is effected by passing it to and fro through an air- 
 gas flame throughout its whole length, and then heating 
 nearly to softening a spot about 4 inches from one 
 end. Air is drawn through from the other end. The 
 place which was heated strongest is now softened in the 
 blow-pipe flame, and the short end, say 3 inches, is 
 drawn off as quickly as possible, A sharp flame is now- 
 applied to the root of the tail, the tube being continually 
 turned and a fresh piece drawn off, and so on. Finally, 
 the short and slender tail is allowed to fall back upon the 
 glass. The end is then to be rather strongly heated in a 
 larger blow-pipe flame and air gently blown in from the 
 other end. This must be done until the inner surface of 
 the closed end is quite smooth and dome-shaped. The 
 whole of the tube is again to be strongly heated, and, a 
 narrow tube being passed down to the bottom, air is to 
 be drawn through the latter. The narrow tube being 
 withdrawn, the barometer tube is bent in a smooth 
 bend, commencing at about 34 inches from the closed 
 end. The bend is so made that the shorter and open 
 end is as close as possible to the longer limb and parallel 
 
 to it. The tube is now 
 supported on its back, 
 inclined downwards to- 
 wards its closed end 
 and its open limb up- 
 wards. A little funnel 
 has its tube end drawn out and slightly bent down at its 
 
Siphon Barometer. 133 
 
 extremity ; the drawn-out end is inserted into the open 
 limb of the barometer till its extremity is above the bend 
 in the latter, the tube of the funnel having been previously 
 so bent that when it is so inserted the funnel stands 
 upright. The funnel with its tube, as well as the baro- 
 meter, are all dry and warm. Petfectly pure mercury is 
 heated to about 100 C. in a basin and poured into the 
 funnel, which must be kept well filled. The drops of 
 mercury roll down the barometer tube and completely 
 displace the air. As soon as the barometer tube is filled 
 to the bend, the funnel tube is removed and the whole 
 brought gently to the vertical position. Should any 
 minute air-bubbles appear, which is never the case if the 
 above directions are strictly adhered to, the barometer 
 is gently turned completely over, so as not to spill mer- 
 cury, and the closed end is tapped vertically upon 
 with a block of wood. The air-bubbles rise to the free 
 surface. Suppose all the bubbles to be got rid of, the 
 barometer is turned upright and a little more mercury is 
 added to the open end. If the vacuum is perfect, when 
 the barometer is gently inclined the mercury rises to the- 
 top with a sharp click. 
 
134 
 
 ELEMENTARY EXPERIMENTS 
 
 RELATING TO 
 
 SOUND AND WAVES. 
 
 N.B. The numbers in brackets in this list refer to the paragraphs 
 of the list of Apparatus and Materials, pp. 151-154. 
 
 WAVES. 
 
 1. Transmission and Reflection of Transverse Mo- 
 tion in Elastic Cords. An empty vulcanized caoutchouc 
 tube 12 feet long is fastened to the ceiling at one end, 
 and is held at the other in the hand in a nearly vertical 
 position. Strike it with the other hand. A half wave 
 travels along, and comes back reversed (i). 
 
 2. Two similar tubes, equally stretched, are similarly 
 and simultaneously struck ; rate of motion of displace- 
 ment is the same (i). 
 
 3. Stretch one tube more than the other, keeping 
 each at its full length. Compare time of wave from end 
 to end. Compare rate of wave by making the unequally 
 stretched tubes of equal length (i). 
 
 4. Fasten an empty tube and a sand-filled tube side by 
 side. Stretch equally and take equal lengths. Compare 
 rates of wave motion. Stretch sand-filled tube till the 
 rates are equal, taking equal lengths (i). 
 
 5. Fasten an empty and the sand-filled tube end to 
 end and fasten the end of one to the wall. Send a half 
 wave up the other. Notice change of rate and change 
 
Experiments on Transverse Waves. 135 
 
 of amplitude when the half wave passes from one to 
 the other ; also after reflection (i). 
 
 6. Make the half wave with either of the tubes longer 
 and longer by shaking the end more slowly until the front 
 of the reflected half wave meets the front of the next 
 advancing half wave in the middle of the tube. Forma- 
 tion of node in the middle. Wave length equal to length 
 of tube. Formation of one complete stationary wave. 
 With half rate of excitement the tube swings as a whole, 
 and the wave length is double the length of the tube. By 
 quicker motion break up the tube into segments separated 
 by nodes. Repeat with differently stretched and loaded 
 tube (i). 
 
 7. Transmission and Reflection of Transverse 
 Motion in Liquids. Water-Waves. Examine motion 
 of water in trough (2). Fill trough nearly full of water, 
 place chips of cork along edge of water, depress and 
 elevate block (2) at one end of trough and watch the 
 motion of the floating cork chips. Substitute little 
 beeswax balls mixed with iron filings 'till they just float 
 and place them at various depths. Observe the closed 
 curves in which the balls move. 
 
 8. Take the two circular zinc troughs (3). Nearly fill 
 with water. Set the water swinging (oscillating) in 
 various ways in both troughs (a) by tilting them, pro- 
 ducing a nodal line in the middle (b) by moving up and 
 down in the centre some light circular body, such as an 
 empty beaker (3). Show, by counting with a watch, that 
 the number of times the water returns to a given position 
 in a given time is greater in the smaller trough, and that 
 the two numbers are inversely as the square roots of the 
 troughs' radii or diameters. Show, by hanging a bullet 
 from a thread (3) having the length of the trough's radius, 
 that the motion of the water in case (&) is, with both troughs, 
 at the same rate as the pendulum. Examine the motion 
 
136 Practical Physics. 
 
 .of the water in case (b\ and show that a nodal ring is 
 formed nearly at one-third of the radius from the circum- 
 ference, and that the vertical motion at the centre is 
 nearly double that at the circumference. As the wave's 
 path is from the centre to the circumference and back, 
 show that the rate of wave progression is directly 
 proportional to the square root of the wave length. 
 
 9. Air Motion in Mass. Vortex Rings. Fill case 
 (4) with smoke or chloride of ammonium in suspension. 
 Hit the canvas at the back, and examine the motion 
 general and internal of the vortex rings. Blow out a 
 candle 20 feet off. Send one ring to. overtake another, 
 and notice rigidity. 
 
 10. Partial Vacuum on Dispersion. Balance the 
 piece of pasteboard (6) on the point of the finger ; place 
 the disc with the tube over it, and blow through the tube. 
 Notice that the discs adhere together, showing that, by the 
 dispersion of the air column in the tube when it meets the 
 lower disc and passes between the two, the air is rarefied. 
 
 11. Approach caused by Vibration. Float a toy 
 air ball (7) on clear water, and show that when a tuning- 
 fork which has been struck is brought near it, the baH 
 approaches the fork. 
 
 12. Connection between the Volume and Density 
 and the Pressure on or Tension of a Gas. Mercury is 
 poured into the open end of the tube (8) just in sufficient 
 quantity to cover the bottom of the bend. The air in 
 the shorter limb is then exactly at the atmospheric 
 pressure. Any quantity of mercury is then poured in, 
 and the difference .in height between the two columns is 
 measured. The pressure to which the gas is row sub- 
 jected is the atmospheric pressure (for which the 
 barometer is consulted) plus the pressure of the difference 
 of the mercnrial columns. The volume of the air, which 
 may be considered as the length of the air column in the 
 
Compression and Rarefaction. 137 
 
 shorter limb, is found to be in all cases inversely pro- 
 portional to the pressure. 
 
 13. Beat liberated on the Compression and ab- 
 sorbed on the Expansion of Air. Fas' en German 
 tinder to the bottom of the wooden rod in (9) and, placing 
 the closed end of the tube on the table, thrust the wooden 
 rod down. After One or two thrusts the tinder will light. 
 Put a drop of bisulphide of carbon on a pellet of cotton 
 wool and roll it in and out of the tube, then thrust the 
 rod down, the bisulphide will flash. Clean the tube and 
 place in it a pellet of cotton wool moistened with water ; 
 push the rod down to about a quarter the length of the 
 tube from the bottom. After a time pull it up suddenly. 
 Clouds of condensed watery vapour will be formed. 
 
 14. Propagation of Compression and Rarefac- 
 tion through Solids and liquids. Arrange " solitaire " 
 balls or marbles (10) in a groove, and hit the row with 
 one, two, or three, noticing the number which are sent off 
 from the other end. 
 
 15. Strike tuning fork (7) and hold its root on one 
 end of a deal rod (7), and place a board (7) on and off 
 the other end. This shows that the waves of compression 
 and rarefaction travel along the rod. 
 
 1 6. Fasten one end of the sand-filled tube (i) to the 
 ceiling. Fasten a piece of paper near the top. Send 
 a wave of rarefaction up the tube by quickly pulling the 
 free end. 
 
 17. Fill tube (12) with water. Strike fork armed 
 with cork cone (12), and plunge cone into water at top 
 of tube. The sound heard shows that the wave of com- 
 pression travels through the water. 
 
138 Practical Physics. 
 
 SOUND WAVES. 
 
 1 8. Propagation and Reflexion of States of Com- 
 pression and Rarefaction through Air. The tubes 
 ( 1 3) are fitted end to end. A watch is placed at such a 
 distance from the ear as to be inaudible. The tube is 
 placed over the ear and directed towards the watch. The 
 ticking becomes audible. 
 
 19. The tubes (13) are supported horizontally at an 
 angle of 90 with one another. A watch is placed at the 
 end of one, and the ear at the end of the other (the ends 
 furthest apart), and screens are placed between the ear 
 and the watch till the latter becomes inaudible. A piece 
 of cardboard or the hand or a flat flame is placed at their 
 contiguous ends, making 45 with each tube. This 
 makes the watch audible, and proves the law of reflexion. 
 
 20. Destruction of Sound Waves. The tubes (13) 
 are arranged horizontally end to end with an interval of 
 half an inch between. The watch is placed at one end 
 of one tube, the ear at the other end of the other tube, 
 at such distances that the watch is faintly audible. A 
 dry cloth placed between the tubes does not destroy the 
 sound, a wet one does ; so does a current of heated air 
 from a flame. 
 
 21. A watch is loosely wrapped in folds of flannel till 
 it is inaudible. A deal rod with board attached (14) is 
 thrust amongst the flannel till it touches the watch, which 
 then becomes audible. 
 
 22. A hand bell is heated over an air gas burner. 
 At a certain temperature it ceases to ring when stnick. 
 
 23. A glass funnel (16) is stopped at its neck and 
 partly filled with a solution of carbonate of sodium. 
 When struck it rings. Add a- solution of tartaric acid; 
 the effervescence causes a dulness in the sound. 
 
Sound Waves. 139 
 
 24. Refraction of Sound. A toy air-ball (7) is filled 
 with carbonic acid. This is made by putting some 
 marble into the flask (17), putting in the cork, and then 
 pouring water and hydrochloric acid down the straight 
 tube. The air-ball is emptied of air and tied over the 
 end of the bent tube. When filled it is tied off, and 
 hung between the watch and the ear. The watch being 
 two or three feet off and the ball close to the ear, the 
 loudness of the watch's ticking is increased. 
 
 25. Formation cf Notes. The humming-top (18) is 
 spun on a hard surface. A card is held against the 
 toothed wheel. A note is produced, which becomes 
 lower in pitch as the top moves slower. Air is blown 
 through ttie tube (18) on to the outer and on to the inner 
 ring of holes. The note produced by the former is 
 always an octave higher than that by the latter. 
 
 26. Transverse Vibrations of Rods. Verify the 
 generalisation that if the length of a rod fastened at one 
 end is /, and its thickness, in the plane of vibration, is d, 
 all other things being the same, the number n of vibrations 
 per second ^or in a given time) is such that 
 
 n ~ -p and n - d 
 or 
 
 Clamp deal rod (18) flatways (narrow face up) hori- 
 zontally in the vice (18) between two pieces of wood, so 
 that 10 feet are free ; set it vibrating horizontally. 
 Adjust a pendulum bullet (3) so as to oscillate with the 
 rod. Adjust another bullet so as to oscillate twice as 
 fast as the first. It will be found that the second pen* 
 dulum will keep time with the rod (a) if the rod is 10 feet 
 long and turned edgeways, (d) if it is made seven feet long 
 and vibrates flatways (io 2 = 2 x 7 2 nearly). 
 
140 Practical Physics. 
 
 27. Combinations of Motions. Fasten knitting 
 needle (20) in vice (19), and fasten a bright bead on top 
 of needle. View bead by light of one candle or one 
 distant window. Strike or pluck in one direction. The 
 bead will appear a straight line of light. While it is 
 vibrating hit it in a direction at right angles to its motion 
 and it will describe a circle or ellipse. Touch one side 
 of it near the vice with a stiff feather and the ellipse will 
 open and shut. Clamp the rectangular rod (20) in the 
 same way, and the figures obtained are parabolic, or 
 8-shaped. Touch one side with the feather and they 
 vary. 
 
 28. A bright bead being fastened to one end of the 
 spring (21) the other end is clamped at various distances 
 in the vice, and various curves are traced out by the bead 
 on the free end. 
 
 29. Analysis of Vibrations by Sinuosities. Fasten 
 the tuning-forks (7), which are a fork and its octave, in 
 the vice (19), clamping them between two pieces of wood. 
 Fasten with beeswax on to the two prongs on one side 
 two little styles of quill cut to fine flexible points. Soak 
 a little cotton wool in turpentine, put it on a stone and set 
 fire to it. Hold a glass plate (22) over the flame till one side 
 is covered with lamp-black. Set the two forks vibrating 
 with the fiddle bow (22) and draw the smoked face of the 
 glass across the styles, waved lines will be scratched on 
 the glass; and the higher pitched fork produces twice 
 as many waves in the same length as its lower octave 
 fork. 
 
 30. Transverse Vibrations of Strings (Wires). 
 To show that the rate of vibration of a stretched string 
 varies inversely as its length, other things being the 
 same, fasten two similar iron wires to the wood-screws 
 of the monochord (23). Pass the other ends over the 
 brass pulleys and fasten equal weights to them, say 28 Ibs., 
 
Vibrations of Strings. 141 
 
 using the whole lengths of the wires from the fixed bridge 
 to the pulleys. Pluck the wires in the middle, and the 
 same notes will be given. Insert one bridge halfway 
 between the one pulley and the bridge, the corresponding 
 string gives the octave higher than the unshortened 
 string. Insert bridge anywhere in the other string. 
 Make one string half as long as the other, and the 
 shorter string always gives the higher octave or twice as 
 many vibrations in a second as theJonger one. 
 
 31. To show that the number of vibrations varies 
 with the square root of the stretching force or weight, 
 fasten two weights over the pulleys and let one weight 
 be four times as great as the other. The wire with the 
 heavier weight gives the octave higher than the one with 
 the lighter weight. And this is the case if the bridges 
 are inserted anywhere, provided the two are at the same 
 distance from the pulleys. 
 
 32. Combine results 31 and 32. That is, hang any 
 two unequal weights from similar wires over the pulleys, 
 and Use the whole length /of the more weighted wire ; 
 shift the bridge of the less weighted wire till the two give 
 the same note. It is then found that if the wire A has 
 the length / t , and is stretched by the weight w lt and the 
 wire B has the length / 2 , and is stretched by the weight 
 iv^ then when there is unison, 
 
 Verify this by altering the length of A. 
 
 33. From the above equation find out the weight of a 
 lump of iron which is fastened to one wire by obtaining 
 unison on shifting either its bridge or that of the other 
 wire, which is stretched by a known weight. 
 
 34. Show that, other things being the same, the 
 number of vibrations varies inversely with the thickness 
 
142 Practical Physics. 
 
 of the wire. Obtain the relative thicknesses of two iw>n 
 wires by weighing equal lengths of them, and taking the 
 square roots of their weights ; vary the weights which 
 stretch unequal lengths till there is unison. Then find 
 that the square roots of the stretching forces or weights 
 are inversely as the thicknesses. Or that therefore the 
 stretching forces are as the squares of the thicknesses, 
 i>. as the weights of the wires. Take equal stretching 
 forces and vary the lengths till there is unison. Then 
 find that the lengths are inversely as the thicknesses. 
 That is, verify the following : where n is the number of 
 vibrations per second, / the length, s the stretching force, 
 d the thickness of the wire, and w the weight of a given 
 length. 
 
 or if there is unison so that n^ 
 
 or 
 
 35. To obtain the relative diameters of wires of dissi- 
 milar metals, weigh equal lengths and take the square 
 roots of the weights and divide these numbers by the 
 respective specific gravities of the metals. The specific 
 gravity is got by dividing the weight of any piece of the 
 
Vibrations of Strings. 143 
 
 metal by the amount of weight it loses in water (that is 
 by the weight of an equal volume of water). 
 
 36. The ordinary musical scale is as follows for any 
 octave where n is the number of vibrations per second 
 of the lowest note (tonic) : 
 
 Tonic. Second. **ajor Fourth. Fifth. Major Major^ Qc ^ 
 
 n \n |* * \n * ^ 2* 
 
 If the middle C is taken as having 256 vibrations a 
 second, the eight complete notes from this C to its higher 
 octave are 
 
 CDE F G A BC' 
 
 256 288 320 341 -3 384 426-6 480 512 
 
 If the middle C is taken as 264 the numbers are 
 
 CDE F G A B C' 
 
 264 297 330 352 396 440 495 528 
 
 Divide the monochord (23) scale, whose length from 
 the fixed bridge to the peg or pulleys is, say, /, into 
 intervals of the lengths, 
 
 , 8 4, 3, 2 3 8 I 
 
 * 9' 1 ' 4 4 3 ' 5 ' ip 2 
 
 Then whatever be the stretching force, these lengths, 
 when the moveable bridge is placed at the corresponding 
 marks, form a scale. The full length may be tuned by 
 turning the peg or weighting over the pulley till it is in 
 unison with a known fork, say A. 
 
 37. Nodes in Strings and Rods. Slightly stretch, 
 and rigidly fasten in a vertical position, the two ends of 
 an empty caoutchouc tube (i). Slightly pinch (damp) 
 the middle and pluck the tube at a quarter from bottom ; 
 on taking away the damping fingers a node remains 
 
144 Practical Physics. 
 
 there. Damp the tube at one-third and pluck at one- 
 sixth from end, two nodes are formed, and so on. 
 
 38. Use the stretched monochord wire instead of the 
 tube. Place paper riders at every one-eighth of the 
 wire's length. Touch the second one with a stiff feather 
 and gently pluck the wire where the first is. The third, 
 fifth, and seventh will be thrown off, while the second, 
 fourth, and sixth remain. 
 
 39. Fasten a tuning-fork (7) upright in a vice (19), tie 
 a piece of cotton to the top of one prong, prevent its 
 slipping by a little wax. Carry the thread over a smooth 
 ring of wire and fasten a weighed cardboard tray to the 
 other end. Let the two prongs of the fork and the 
 thread be in one plane. Load the tray, and move the 
 ring to and from the fork ; or, keeping the ring fixed, vary 
 the weight till, when the fork is bowed, there is only one 
 segment, that is, the thread swings as a whole. Keeping 
 now the length the same, make the weight (reckoning the 
 tray) only a quarter as great ; two segments are formed. 
 If the weight be one-ninth as great, there will be three 
 segments ; if one-sixteenth there will be four. 
 
 If the string be at right angles to the fork's two 
 prongs the segments formed are always twice as numerous 
 as in the former cases, if the lengths and weights are the 
 same as before. 
 
 40. Hold deal rod (19) upright in hand, and by tilting 
 the hand to and fro less or more rapidly, make one or 
 more nodes. Mark the places of the nodes and measure 
 the segments ; notice that the last division swings free, 
 and is less than half a segment in length. 
 
 41. Cut (24) a strip of window glass about one inch 
 wide and any length / (about six inches), and lay it across 
 two parallel strings at such a distance apart that each 
 string is a little less than a quarter / from the end. Fasten 
 the strings to the glass with a little drop of wax in the 
 
Transverse Vibrations. 145 
 
 middle of the glass. On hitting the glass in its centre a 
 note will be produced resulting from the formation of one 
 
 segment of length rather more than in the middle and 
 two free half segments each rather less than -. Referring 
 
 to 26 for the number of vibrations of a rod, and to 36 
 for the relative numbers of vibration in the gamut 
 
 In the gamut n z = 2# M for the next whole note, 
 
 o 
 
 Similarly for the next whole note 
 
 and so on. 
 
 Calculate these lengths and cut strips of glass accord- 
 ingly. Support and fix them with wax in a row on two 
 horizontal threads making an angle with one another. 
 Compare the motion of such bars with that of the water 
 in a rectangular trough (3) when the central line is ele- 
 vated and depressed. 
 
 42. Hold fork (7) horizontally and bow it ; scatter 
 sand on it All is thrown off. Bow it near the root. A 
 shriller note is produced, and some of the sand rests in a 
 line a nodal line somewhat less than of the fork's 
 length from the end. Prove by monochord that the two 
 notes are nearly as I : 9 (number of vibrations per second). 
 
 43. Remove clapper from hand bell (15) ; fix the bell 
 vertically upside down in vice (19). Hold a pellet of seal- 
 ing wax, the size of a pea, hung from a silk thread, against 
 the edge of the bell. Bow the bell, and move the pellet 
 round, finding the four nodal points and the four regions 
 
 L 
 
146 Practical Physics. 
 
 of greatest motion. Nearly fill the bell with water and 
 bow. Notice regions of comparative rest, and of disturb- 
 ance. Move quickly in and out by the hands two oppo- 
 site sides of an elastic wire (23) hoop. Notice nodes and 
 segments. 
 
 44. Beats. Clamp two similar tuning-forks (7) in 
 vice (19) or screw them into board (n) or monochord 
 (23). Load one near its root with a half dime piece 
 stuck on with wax. Bow both forks. Notice beats. 
 Change half dime for a ten cent piece. The beats be- 
 come more frequent. Move the coin higher up ; the 
 beats become still more frequent. 
 
 45. Determine rate of loaded fork with monochord 
 (23), knowing that of unloaded. Show that the number 
 of beats per second is equal to the difference between the 
 numbers of vibrations per second of the two forks. 
 
 46. Increase the load on one fork till harshness or 
 dissonance ensues. Again compare rates. 
 
 47. Longitudinal Vibrations. Solids. Clamp be- 
 tween edges of wood in the vice (19) in the middle and 
 horizontally the brass tube (25). Rub one end longitu- 
 dinally with wash-leather (25) covered with powdered 
 rosin (25). Hang a pellet of wax touching the other end. 
 Observe how it is thrown off. 
 
 48. Let two glass tubes (25), one twice as long as the 
 other, be held, each in the middle, between finger and 
 thumb, and let one end of each be rubbed with wet 
 flannel longitudinally. The longer tube produces the 
 lower octave of the shorter one. A wave of compression 
 has to travel twice as far from end to end and back 
 in the fc rmer as in the latter case, and therefore takes 
 twice as long ; and accordingly in the same time it re- 
 appears and hits the air half as often. Prove this by 
 stretching equally two pulley wires of the monochord and 
 moving the bridges till the one wire is in unison with the 
 
Longitudinal Vibrations. 147 
 
 one tube, and the other with the other tube. The wires 
 are then found to be in length in the ratio of 2 : i. 
 
 49. Take equal lengths of deal and oak rods (25) ; 
 hold them in the middle and rub ends with rosined 
 leathers. The note from the oak is the deepest. Cut (26) 
 pieces off the oak rod till the notes are in unison. 
 Measure the lengths. The lengths are in the proportion 
 of the rates of progression of the compression wave in the 
 respective rods. Because the compression has to travel 
 from one end to the other, and back again, in order to 
 beat the air once to produce one sound wave. 
 
 50. To find the actual rate, tune, by cutting one of 
 the rods, to a tuning-fork of known rate (No. of vibrations 
 per second). This is best done by augmenting the sound 
 of the fork by holding it over a resonant jar or cavity (see 
 below 55). If the fork gives ;/ vibrations to and fro in 
 one second and the rod is in unison with it, the com- 
 pression in the rod must travel from one end to the other 
 and back (that is, twice the whole length of the rod) n 
 times in I second. Assuming sound to travel in air 1,100 
 feet in i second, it travels in deal about 16,000 feet in a 
 second. 
 
 51. Hold two similar wooden rods, one in the middle, 
 and the other at a quarter its length from one end. Set 
 both in longitudinal vibration, rubbing the shorter end of 
 the second, octaves will be produced. The second rod 
 will have a node at a quarter its length from the further 
 end. 
 
 52. Wrap a piece of thin iron wire (23) tightly into a 
 close spiral round the brass rod (25). Hang the spiral 
 by one end, and hang a little weight at the other. Note 
 with watch the number of jumps the wire gives in a few 
 seconds when pulled out. Vary its length and the 
 weight. Compare with half of longitudinally vibrating 
 rod clamped in the middle. 
 
 L 2 
 
148 Practical Physics. 
 
 53. Fasten rigidly both ends of the wire spiral of 52. 
 slightly stretched and vertical. Set the middle moving 
 up and down. Also damp the middle and pull the 
 centre of the lower half gently down and release it. The 
 middle forms a node. Obtain two automatic nodes in a 
 similar manner. 
 
 5 |. Tubes open and closed at one end. Fasten a 
 piece of glass tubing (27) about 18 inches long vertically. 
 Fit a cork into the bottom. Through the cork pass a 
 narrow piece of glass tubing. Fasten one end of a piece 
 of vulcanized caoutchouc tubing about three feet long (i) 
 to this. To the other end of the elastic tubing attach 
 the neck of a funnel (16). Support the funnel on the 
 filter stand (27). Let the funnel be a little above the top 
 of the tube. Fill both with water. Sound the highest ot 
 the three forks (7). Hold it over the upright tube, de- 
 press the funnel till the fork's note is greatly augmented. 
 Lift the funnel up and down, and fix it when the augmen- 
 tation of the fork's note (resonance) is greatest. Mark 
 the height of the water in the tube exactly. Cut the tube 
 with a file (26) about inch below mark. Grind it down 
 on a wet hearth-stone exactly to the mark. Cut and 
 grind down several glass tubes of this same length. 
 Make caps for the tubes by cutting round discs of 
 card-board as large as the outside of the tubes, these 
 discs can be stuck on to the ends of the tubes with 
 beeswax. 
 
 55. Show that if a fork resounds with a tube closed at 
 one end of length /, it will resound with a tube open at 
 both ends of length 2 /. To show the latter, fasten two 
 tubes together by an inch of india-rubber tubing (27). 
 
 56. Show that if a fork resounds with a tube of length 
 / closed at one end it will resound with tubes closed at 
 one end whose lengths are 3 /, 5 /, 7 /, etc. 
 
 57. Show that if a fork resounds with a tube open at 
 
Vibrations of Air in Tubes. 149 
 
 both ends of length /j it will resound with tubes open at 
 both ends whose lengths are 2 / 3 / : , 4/,, etc. 
 
 58. Show, as far as the forks at disposal will allow, 
 that if a fork resounds with a tube closed at one end, 
 those forks will resound with the same tube whose notes 
 are the next harmonic but one, the next but three, and so 
 on, above that of the first fork. 
 
 59. Show that if a fork resounds with an open tube all 
 forks will do so whose notes are higher harmonics of the first. 
 
 60. Admitting that for all notes 
 
 wave length in feet- number of feet traversed in i^ 
 number of waves generated in i ' 
 
 and admitting that the resonant tube closed at one end is 
 \ the wave length of the wave system of the lowest note 
 which resounds in it, deduce (a) the rate of transmission 
 of sound through air, knowing the number of vibrations 
 of a fork and the length of the air column closed at one 
 end or open at both, which resounds with it ; (b] deduce 
 the wave-length, assuming the rate of propagation to be 
 1,100 feet a second, and knowing the pitch of the fork ; 
 (c) deduce the pitch of the fork, knowing the rate of pro- 
 pagation and the length of the resonant column. 
 
 61. Heat a closed tube, which resounds with a given 
 fork, over an air gas flame. Show that it no longer re- 
 sounds. Invert the tube, and fill it with coal gas. It no 
 longer resounds. Use apparatus in 54. Get the tube 
 when containing air to resound to a fork ; fill it with car- 
 bonic acid (17) by displacement ; show that the column 
 must be shoitened to resound and compare lengths. This 
 should verify the generalisation that when d is the density, 
 
 62. Effect of Relative Motion between Origin of 
 Sound and Ear. Fasten a whistle (29) in one end of a 
 
150 Practical Physics. 
 
 caoutchouc tube about 6 feet long. Sound the whistle 
 by blowing into the other end. Whirl the tube round 
 while continuing to blow, and notice the alteration of 
 pitch at different pkces. This is best heard at a 
 distance. 
 
 63. Singing Flames. Draw out a piece of glass 
 tubing till the opening at the end is about as wide as a 
 pin. Fasten to gas pipe, place vertically, and light. Re- 
 duce the flame to the height of about | to \ inch. Clamp 
 over it a glass tube so that the flame is about a quarter 
 of the tube's length up the tube. The air in the tube will 
 give a note. Place a similar jet and tube side by side 
 with the former one. Provide each tube with a little 
 sliding tube of paper so as to be able to alter the lengths, 
 obtain perfect unison, and various beats. Show that the 
 singing of the flame immediately begins if the voice is 
 pitched to the note which the flames would give. Also 
 start by a consonant tuning-fork. 
 
 64. Artificial larynx. Grind off the top of a glass 
 tube (27) in two planes at an angle of about 60. Stretch 
 across the top two pieces of vulcanized caoutchouc (29) 
 in such a manner that there is a slight crack between 
 them, bind the caoutchouc on to the tube with silk, and 
 blow through. 
 
APPARATUS AND MATERIALS FOR 
 EXPERIMENTS IN SOUND AND WAVES. 
 
 (1) Three similar vulcanized caoutchouc tubes, each 
 about inch wide and 12 feet long. One filled with 
 sand and tied up at the ends. A piece of similar tubing 
 6 feet long. 
 
 (2) A long narrow wooden trough 4 feet x 6 inches x 
 6 inches caulked with marine glue, and painted inside. 
 Preferably with one long face of glass. A block of wood 
 5f inches x 4 inches x 4 inches, with handle perpendicular 
 from middle of one long face. Balls of wax mixed with 
 iron filings so as just to float. 
 
 (3) Two cylindrical zinc troughs about 2 feet and 18 
 inches diameter, and 18 inches deep. A rectangular 
 trough 2 feet x i foot x 18 inches. Silk thread, leaden 
 bullets. A beaker with bottom about 3 inches diameter. 
 
 (4) A box about 18 inches cube, one side removed and 
 replaced by sailcloth nailed tight on. The seams of the 
 box made tight by paper pasted on the inside. A circular 
 hole in the side of the box opposite to the canvas. The 
 hole can be covered by a plain piece of cardboard. Two 
 holes, side by side on one side of the box, into which pass 
 glass tubes bent at right angles, the other ends of which 
 pass through corks in the necks of two flasks, one con- 
 taining ammonia and the other hydrochloric acid. 
 
 (5) Two air gas burners with tubes. 
 
 (6) Fasten a tin or glass tube, inch diameter, to the 
 middle of a circular plate of tinplate or cardboard about 
 6 inches in diameter, with a hole in the middle in which 
 the tube fits. A circular piece of cardboard somewhat 
 less than the disc. 
 
152 Practical Physics. 
 
 (7) A toy air-ball, the larger the better. Three tuning- 
 forks, two alike and one an octave higher. 
 
 (8) A glass tube about | inch internal diameter and 50 
 inches long, smoothly and as flatly as possible closed at 
 one end. The tube is bent into two parallel limbs at a 
 distance of about 10 inches from the closed end. It is 
 fastened to an upright board upon which are ruled hori- 
 zontal lines ^ i nc h apart. Enough mercury to fill the 
 tube. 
 
 (9) A stout glass tube about \ inch internal diameter 
 and 6 inches long, closed at one end by a cork which is 
 made air-tight by sealing-wax. A cylindrical wooden 
 rod just passing into the tube, wrapped round at one end 
 with silk thread, till it just fits the tube. The silk is oiled 
 or covered with glycerine. A piece of German tinder. 
 A little bisulphide of carbon. 
 
 (10) A dozen marbles or f solitaire ' balls. 
 
 (n) A deal rod, any shape, 12 feet long, covered with 
 list, hung from threads or clamped horizontally. A 
 square thin deal board, not cracked, about 2 feet square. 
 
 (12) A glass tube about 18 inches long and | inch 
 wide, closed at one end, is fastened perpendicularly by a 
 little wax to the board (in n), which is supported on three 
 corks. The tuning-fork (7) has a little cone of cork 
 fastened to one face of one prong by beeswax. 
 
 (13) Two tinned iron tubes, each about 3 feet long and 
 4 inches diameter ; the end of one fits into the end 
 of the other. 
 
 (14) A pointed deal rod, about 6 inches long, fastened 
 to a square light deal board 5 inches square. 
 
 (15) A hand bell, the larger the better. 
 
 (16) A glass funnel about 4 inches in diameter. A cork 
 to fit its neck. A clamp or support for the funnel. Car- 
 bonate of soda, tartaric acid. 
 
 (17; A i Ib. flask, fitted with a cork through which 
 
Apparatus and Materials. 153 
 
 pass air-tight (a) a straight tube reaching to the bottom 
 with a funnel at the top, (b) a tube bent at right angles, 
 which just passes through the cork. Pieces of marble. 
 Hydrochloric acid. 
 
 (18) A large humming-top with a smooth but' on 
 driven into its peg. Filled with sand and closed. Resting 
 upon the body of the top and fastened to it is a horizontal 
 dis<: of thin iron plate, having 200 or 300 teeth in its cir- 
 cumference. Also two rings of holes near the circum- 
 ference. One ring having twice as many holes as the 
 other. A piece of quill glass tubing bent to 135 at one 
 end. 
 
 (19) A deal rod, about 12 feet long, i inch wide, and \ 
 inch thick. The ratio of width to thickness should be 
 very exact. A table vice. 
 
 (20) A round knitting needle. Some hollow silvered 
 glass beads. A square steel rod, about 8 inches long, 
 and ^ inch square. A rectangular steel rod, about 8 
 inches long ; one side i inch, the other ^ j nc h. The 
 ratio should be very exact. 
 
 (21) A straight piece of clock spring about I foot lonj 
 is softened in the middle in the flame of an air-gas 
 burner, and twisted so that the planes of the two parts 
 are at right angles to one another. 
 
 (22) A fiddle bow. Some sheets of glass, 3 inches x 
 4 inches. Some oil of turpentine. 
 
 (23) Monochord, etc. An inch deal board, 3 feet long, 
 9 inches wide. Two pieces of wood, 6 inches x i inch x i 
 inch, screwed on across ends to form supports. Three 
 long wood screws driven in obliquely (slanting outwards) 
 at one end at equal distances. At the other end, opposite 
 one screw, is a pianoforte peg, at an angle of 45. Oppo- 
 site the other two screws are two brass pulleys (window- 
 blind pulleys) on stems which are driven in at an angle of 
 45. A bridge, that is, a triangular wedge of hard wood, 
 
154 Practical Physics. 
 
 9 inches long, \ inch wide at base, and as high as the 
 pulleys. This is screwed from below across the board 
 about 3 inches from the wooden screws. Three other 
 little moveable bridges about I inch long, as high as the 
 pulleys, are provided. A variety of weights and hooks. 
 A pair of pliers. Several yards of iron wire (pianof rte 
 wire) of different thicknesses. Brass wire, seme of which 
 has the sa ( ne thickness as some c f the iron wire. The 
 ends of three pieces of wire are twisted into loops and 
 passed over the screw heads. One of the other ends is 
 passed through the pianoforte peg, which is then twisted 
 round by the pliers. The other two have loops twisted 
 in them, and passing over the pulleys carry weights. A 
 sheet of paper is gummed to the board having lines at 
 every inch, and thinner ones at every T T 5 th inch. Mark 
 with o the line beneath the pulleys and at the pianoforte 
 peg. 
 
 (24) A sheet of window glass. 2 square feet of patent 
 plate glass. A glazier's diamond or steel wheel-glass- 
 cutter. 
 
 (25) Several round deal and oak rods, 6 feet long, 
 inch diameter. One brass rod or tube inch diameter, 
 3 feet long. Glass tube, % inch diameter, 3 feet long. A 
 square foot of flannel. A piece of wash-leather. Some 
 powdered rosin. 
 
 (26) Small hand-saw. Small triangular file. 
 
 (27) Twelve feet stout glass tubing, f inch internal 
 diameter. A few inches of inch tubing. A filter stand 
 and a retort stand. A few feet of vulcanized caoutchouc 
 tubing, inch internal diameter. 
 
 (28) A dog whistle without the pea. 
 
 (29) A few square inches of thin vulcanized sheet 
 caoutchouc. 
 
INDEX. 
 
 The nuvtbers refer to the paragraphs. 
 
 ABS 
 
 ABSORPTION (of gases by li- 
 quids), 36, 37 
 Approach caused by vibration, 109 
 
 BAROMETER siphon, 115 
 
 Beats, 103, 104 
 
 Bell, 92 
 
 Breath pictures, 42 
 
 Bubbles, 14-18 
 
 CAPILLARITY, 24-29 
 
 Closed and open pipes, 96-98 
 Cohesion of gases (viscosity), 19 
 
 liquids, 8-18 
 
 liquids affected by adhesion to 
 
 solids, 24-29 
 
 solids, 1-7 
 
 solids affected by adhesion to 
 
 liquids, 30-32 
 
 Colloids, vapour tension of, 55 
 Condensation of gases on solids, 
 
 38-42 
 Conversion of sound into notes, 80 
 
 DENSITY, 60-73 
 
 Detection of sound, 81 
 
 Dialysis, 57, 58 . 
 
 Diffusion of gases into gases, 43-46 
 
 into liquids, 36-37 
 
 into solids, 38-41 
 
 liquids into gases, evaporation, 
 
 49 
 
 liquids into liquids, 33-35 
 
 liquids into solids, 56 
 
 Drop size, 12, 13 
 
 EFFUSION of gases, 47 
 Elasticity of gases, 21-23 
 
 PHON 
 
 Elasticity of solids, 4-7 
 Etching on glass, 114 
 Evaporation of liquids into 
 49 
 
 GAS- WAVE, 96-99 
 
 Glass etching, 114 
 
 Glass working (hints on), 113 
 
 HARDNESS of solids, i 
 INTERFERENCE, 103-106 
 JETS (Liquid), 10 
 
 LIQUID waves, 76-78 ' 
 Longitudinal vibrations of liquids, 
 
 100 
 Longitudinal vibrations of solids, 
 
 100-112 
 
 MOTION (effect of on sound), 108 
 Musical scale, 90 
 
 NODES, in pipes. 98 
 --- plates, 93-95 
 -- rods, 91 
 
 -- strings. 86-88 
 Notes derived from sound, 80 
 
 OCCLUSION, 40, 41 
 
 Open and closed pipes, 96-98 
 
 Origins of sound waves, 84 et sef. t 
 
 89 et seq. 
 Osmose, 56 
 
 PARCHMENT paper, il* 
 Phonograph, no 
 
IS6 
 
 Index. 
 
 REFL 
 
 REFLEXION of sound, 82 
 Reflexion of water-wave, 77-78 
 Refraction of sound, 83 
 Resonance, 99 
 Rods, transverse vibrations of, 84-85 
 
 SENSITIVE flame, 81 
 
 Singing flame, 106 
 
 Sinuosities, 107 
 
 Siphon barometer, 115 
 
 Solids, longitudinal vibrations of, 
 
 ICX>-I02 
 
 Solution (of solids in liquids), 30-32 
 Specific gravity, 60-73 
 
 of liquids, 67-70 
 
 of solids, 62-66, 71-73 
 
 Stationary water-waves, 77-78 
 Strings (transverse vibrations of), 
 
 86-89 
 Sympathy, 108 
 
 WAV 
 
 TENACITY, 2-3 
 
 Thunder, 92 
 
 Torsion, 4-6 
 
 Transpiration, 59 
 
 Transverse vibrations of rods, 84, 85 
 
 strings, 86-89 
 
 VAPOUR tension, 51-55 
 
 Vernier, the, in 
 
 Vibrating strings as source of sound, 
 
 89 
 
 Vibration of rods (transverse), 84, 85 
 Volume hardness, 20-23 
 Vortex rings, 74 
 
 WATER-WAVES, 76-78 m 
 Waves governed by elasticity, 79 
 
 gravity, 76-78 
 
 in general, 75 
 - liquid, 76-78 
 
UNIVERSITY OF 
 
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