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PAPERS



ON



MECHANICAL AND PHYSICAL

SUBJECTS.



C. J. CLAY AND SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MAEIA LANE.

50, WELLINGTON STREET.




Eeipjtg : F. A. BROCKHAUS.
gork: THE MACMILLAN COMPANY.
E. SEYMOUR HALE.



PAPERS



ON



MECHANICAL AND PHYSICAL

SUBJECTS



BY



OSBORNE REYNOLDS, F.R.S., MEM. INST. C.E., LL.D.,



REPRINTED FROM VARIOUS TRANSACTIONS AND JOURNALS.

VOLUME I

18691882




LDGE:
AT THE UNIVERSITY PRESS.

1900

[All Eights reserved.]



Cambridge:

PRINTED BY J. AND C. F. CLAY,
AT THE UNIVERSITY PRESS.



PEE FACE.

TTAVING found the various reprints of papers by the same author,
which have been published during the last thirty years, of the
greatest assistance, and being assured that it would be a convenience
to some of my scientific friends if the papers on mechanical and physical
subjects, which I have communicated to various societies and scientific
journals, were published in a collected form, also having secured the able
assistance of Mr Charles B. Dewhurst, M.Sc., in collecting and arranging
the papers and correcting the press, I gladly availed myself of the oppor-
tunity afforded me by the liberality of the Syndics of the University
Press of having papers I have written between the years 1869 and 1900
reprinted in a collected form. These include all the papers which I have
published in the transactions and journals, with the exception of certain
abstracts of papers which were printed in full at somewhat later dates, six
short papers of only temporary interest, and a Memoir of James Prescott
Joule which is published separately, being Vol. vi. Fourth Series of the
Memoirs and Proceedings of the Manchester . Literary and Philosophical
Society. The titles and text of the first forty of these from 1869 to 1882
are included in this volume.

In reprinting the papers errors resulting from inadvertence have been
corrected, where discovered; but otherwise there have been no alterations
nor have any notes been added.

The chronological order has been followed in arranging the papers
notwithstanding that it entails a somewhat excessive amount of discon-
tinuity in the sequence of papers on the same subjects. With a view



Vlll PREFACE.

to obviate the inconvenience of this discontinuity, in addition to the
references back to the earlier paper, references forward to the papers in
which the subjects are continued have been added.

As affording some explanation of the absence of any connection between
many of the subjects in this collection of papers it may be pointed out
that these subjects have not been determined by arbitrary selection,
neither have they been the result of following up one line of research.
They have, for the most part, been suggested by the discrepancies between
the actual results obtained in definite mechanical arrangements, such
as occur in some parts of the large field of practical mechanics, and the
conclusions arrived at, as to what these results should be for the same
circumstances, by means of geometrical and physical analysis as far as
this analysis was developed at the time.

When such discrepancies occur, if the experimental results are consistent
and approximately accurate, they afford evidence that some circumstance
has not previously been taken into account in the general theoretical
analysis, and thus indicate the necessity for its further extension. Such
discrepancies may also afford a suggestion or clue, and when this occurs
the extension of the theoretical analysis necessary to remove the discrepancy
is in general not difficult to find, and requires only a short paper for its
exposition. But when this has been accomplished, further consideration
may show that these extensions of the analysis have a more general
application than to the immediate circumstances which led to their
recognition, the study of which demands further research and exposition,
which require time, and before this is ready some other discrepancy in
another part of the field of practical mechanics has appeared and secured
precedence.

OSBORNE REYNOLDS.

MANCHESTER,

March, 1900.



CONTENTS OF VOL. I.



1. On the Suspension of a Ball by a Jet of Water ...,, . 1 6

The effect of air currents analysis of forces acting determination of
position of equilibrium experimental verification.

2. The Tails of Comets, the Solar Corona, and the Aurora,

considered as Electrical Phenomena .... 7 14

Part I. Tails of comets either material appendages of the nucleus or
matter existing independently of the comet reasons for rejecting
last hypothesis the analogy between comets, the corona, and the
aurora. Part II. Explanation of the supposed electrical action as due
to the action of the sun.

3 A. On Cometary Phenomena . . ... . . 15 21

The difference of evaporation on a comet and on a planet a sufficient
cause for the electric phenomena on the comet.

SB. On an Electrical Corona resembling the Solar Corona . 22 26

A corona may be produced by discharging electricity from a brass ball
in a partially exhausted receiver.

4. On the Electro-Dynamic effect which the Induction of

Statical Electricity causes in a moving body . . 27 29

This induction on the part of the sun a probable cause of terrestrial
magnetism.

5. On the Electrical Properties of Clouds and the Phenomena

of Thunderstorms ........ 30 34

The inductive action of the sun shown to be a sufficient cause for
the production of thunder clouds.

6. On the Relative Work spent in Friction in giving Rotation

to Shot from Guns rifted with an increasing, and a

uniform twist 35 40

The work spent in friction inversely proportional to the angle turned
through by the shot in the gun hence the energy wasted with
parabolic grooves between three halves and twice as much as with
plane grooves.



CONTENTS.



7. On the Bursting of Trees and Objects struck by Lightning . 41 42

An experiment showing the explosive effect of lightning to be probably
due to the conversion of moisture into stearn.

7 A. On the Destruction of Sound by Fog and the Inertness of

a Heterogeneous Fluid 43 47

The greater resistance to motion of air charged with small drops an
explanation of the destruction of sound by fog.

8. On the Effect of Acid on the Interior of Iron Wire . 48 50

The effect of acid in causing soft ductile iron wire to become short and
brittle shown to be due to the hydrogen in the acid having combined
with the iron.

9. The Causes of the Racing of Screw Steamers investigated

Theoretically and by Experiment 51 58

Insufficiency of the mere exposure of the screw to account for the
phenomena racing occurs when the screw is immersed slightly beneath
the surface the cause shown to be the admission of air to the screw
explanation of the way in which the air acts to diminish resistance of
screw.

10. The Condensation of a Mixture of Air and Steam upon

Cold Surfaces 5966

The rate of condensation of pure steam very great measurement of the
effect of different proportions of air great effect of a small quantity
of air in retarding condensation, diminution of condensation, rapid and
nearly uniform as the pressure of air increases from two to ten per
cent, that of the steam then less rapidly up to thirty per cent., and
nearly constant for greater proportions.

11. On the Forces caused by Evaporation from,, and Condensation

at, a Surface 67 74

Experiments to show that evaporation from a surface causes a force
tending to drive the surface back, and a condensation, a force tending
to draw the surface forward explanation of these effects only partially
accounted for by the visible motions the main cause explained by the
kinetic theory of gases expression for the force exerted /= w*J'3p/gd
application of the theory to Mr Crooke's experiments a similar effect
produced by communication of heat from a hot surface to a gas.

12. On the Surface-Forces caused by the Communication of Heat 75 77
These forces affording a simpler explanation of Mr Crooke's experiments.

13. On the Effect of Immersion on Screw Propellers . . 78 80

Experiments showing how far the depth of immersion affects the resis-
tance encountered by a screw when travelling forward the resistance
independent of the depth of immersion so long as the screw is not
frothing at or below the surface.



CONTENTS.



14. On the Extent and Action of the Heating Surface of Steam

Boilers . . . . . . .... 81 85

The heat carried off by a fluid from a surface proportional to the internal
diffusion of the fluid near the surface the two causes natural diffusion
of the fluid at rest, and the mixing due to the eddies caused by visible
motion the combined effect expressed by: H=At+Bpvt this afford-
ing an explanation of results attained in Locomotive Boilers experi-
mental verification.

15. On the Action of Rain to Calm the Sea . ' . . . 86 88

The vortex rings produced by the drops of rain tend to destroy wave-
motion.

16. On the Refraction of Sound by the Atmosphere "''.'"" . 89 106

The effect of wind upon sound mainly due to the difference in the

velocity of the air at the surface of the ground and at a height above /

it the wind lifts the waves which proceed to windward and brings

down those which move with it the effect of the elevation of the

observer and the sound-producing body result of experiments the

effect of variations of temperature to cause the sound waves to rise

the experiments of Prof. Tyndall explained by the theory.

17. On the Efficiency of Belts or Straps as Communicators of

Work . . . . . . . . . ". . 107109

The stretching of an elastic belt being proportional to its tension the
velocities on the tight and slack sides are different the waste of energy
due to the consequent " creeping " round the pulleys explanation of
the slipping of wheels having elastic tires.

18. On Rolling-Friction . . . . .. . . . 110133

Inaccuracies of the surface and crushing under the roller insufficient
to explain the whole resistance to rolling oscillations of a roller
slightly disturbed the creeping of belts the deformation of the
roller and the surface effect of the relative hardness of the roller
and surface on the distance rolled through effect of the diameter of
the roller the slipping between the surface of the roller and that of
the plane the friction and its action to prevent deformation these
actions explained by the case of a soft bar between hard plates effect
of friction during contraction and expansion the direction of friction
the deformation caused by the roller the actual and apparent slipping

experiments to show the effect of oiling the surface the tendency to
oscillate the effect of softness of the material experiments to find
the extent of the slipping effect of heat and viscosity to cause friction

explanation of the scaling of steel and iron rails.

19. On the Steering of Screw Steamers . . . . * . 134 140

The uncertainty of the steering when starting or stopping the accident
to the 'Bessemer' in Calais Harbour the models used in the experi-
ments effect of reversing the screw on the steering of the models
the result when the model is driven slowly forward by the paddles and
the screw is reversed general conclusions : that with the screw acting
against the motion of the vessel the rudder will act as if the vessel
were going in the direction of the screw the effect of the screw to
turn the boat independently of the rudder the effect of racing
results of experiments confirmed by instances of the behaviour of
vessels that have been in collision.



Xll CONTENTS.



PAGES



20. Improvements in Turbines and Centrifugal Pumps . . 141 148

A method of using two or more Turbines or Pumps in combination, the
fluid (which may be either water or gas) passing through them
successively.

21. On the Unequal Onward Motion in the Upper and Lower

Currents in the Wake of a Ship ; and the Effects of this

Unequal Motion on the Action of the Screw-Propeller . 149 156

The relative speed of the upper and lower currents in the wake the
actual velocity of the wake the effect on the screw the tendency to
cause vibrations effect on the efficiency disadvantage of large screws.

22. On, the Refraction of Sound by the Atmosphere . . 157 169

The effect of variation of temperature to incline the fronts of the sound
waves experiments with rockets experiments in Lynn Deeps the
great distance at which sounds are sometimes heard Arago's experi-
ments the heterogeneity of the atmosphere.

23. On the Forces caused by the Communication of Heat between

a Surface and a Gas ....... 170 182

Experiments on the Light-mill the force which turns the mill not
directly referable to radiation Dr Schuster's determination of the
magnitude of the force theoretical difference of temperature
dp/p-dT/4r actual difference of temperature a new Photometer
Mr Crooke's experiments on a Light-mill floating in water.

24 and 25. On various Forms of Vortex Motion . . . 183 191

Description of a method of rendering the internal motions of fluid visible
by means of colour bands.

26. On the Investigation of the Steering Qualities of Ships . 192 197

The experiments of a Committee of the British Association confirm the
theory (paper 19) on the effect of reversing the screw on the steering
of a vessel.

27. On the Rate of Progression of Groups of Waves and the

Rate at which Energy is Transmitted by Waves . 198 203

Two kinds of waves, those that transmit energy and those that travel
through a medium without transmitting energy mathematical inves-
tigation of the rate at which energy is carried forward by waves in
deep water.

28. On the Effect of Propellers on the Steering of Vessels . 204 213

Further experiments on large vessels by a British Association Committee
trials of the S.S. 'Hankow' by Commander Symrnington experi-
ments on H.M.S. 'Speedy' by Captain Waddilove.

29. On the Manner in which Raindrops and Hailstones are

formed 214222

Hailstones formed by aggregations of small frozen particles imitation
hailstones formed in Plaster of Paris, raindrops formed by aggregations
of small particles of vapour.



CONTENTS. xiii

PAGES

30. On the Formation of Hailstones, Raindrops, and Snowflakes 223 230

Aggregation resulting from the more rapid descent of the larger particles
the shape and structure of ordinary hailstones artificial hailstones
produced by means of an ether spray snow crystals.

31. On the Internal Cohesion of Liquids and the Suspension of

a Column of Mercury to a height more than double that

of the Barometer 231243

Surface tension and cohesion the effect of vapour experiments.

32. On the Steering of Screw Steamers . . . . . 244 256

Further experiments on large vessels on the effect on the steering of
reversing the screw.

33. On certain Dimensional Properties of Matter in the Gaseous .

State . . 257390

PART I. (EXPERIMENTAL).
Section I. Introduction.

General description of the phenomenon of thermal transpiration
correspondence of the results from plates of different coarseness when
the densities of the gas are inversely as the coarseness of the plates
proof that gas is not a continuous plenum the results deduced from
the kinetic theory impulsion or the phenomena of the radiometer
arrangement of the paper statement of the laws established by
experiment 257 264

Section II. Experiments on thermal transpiration.

Description of the apparatus and tests applied drying the gas differ-
ences of temperature the porous plates the first results with air
hydrogen maximum difference of pressure carbonic acid stucco
plates corresponding pressures with stucco and meerschaum log-
arithmic homologues a method of reducing the experimental results
comparison of the results with the laws stated in Art. 9 ... 264 290

Section III. Experiments on transpiration under pressure.

Graham's results necessity for further experiments the apparatus
equal volumes measurement of the time purity of the gases ex-
perimental results comparison of logarithmic homologues relative
coarseness of the meerschaum and stucco plates corresponding results
at densities corresponding to the fineness of the plates Graham's
results reconciled verification of Law 1, Art. 9 290 299

Section IV. The radiometer with very small vanes.

The apparatus fibre of silk effect of elevating the heater bending of

the fibre spider-line agreement of the results with the theory . . 299304

PART II. (THEORETICAL).
Section V. Introduction to the theory.

The necessity for a limited surface no force on an unlimited surface
illustration from two opposite batteries prefatory description of the
mathematical method . . 304 312



XIV



CONTENTS.



Section VI. Notation and preliminary steps.

Explanation of the symbols <r"(#), A, 8, C, D, E, F, G, #- the rates at
which mass, momentum, and energy are carried across a plane by any
one of the groups A, B, (7, &c., in a uniform gas Maxwell's law of
distribution of velocities in a uniform gas Restriction to gases of
uniform texture, such as air or hydrogen Table XX. Values of a (Q) 312 318

Section VII. Foundations of the theory. The mean range.

The condition of the gas varying from point to point line of thought
sketch of the method by which the fundamental theorems are deduced
the mean component velocities of the molecules which pass through an
element limitations and definitions condition of the gas resultant
uniform gas inequalities fundamental assumptions fundamental
theorems (I. and II.) corollaries the mean range s the mean com-
ponent values of s general expressions for (r(Q) when the gas is
continuous a- (Q) in the neighbourhood of a solid surface . . . 319 340

Section VIII. Equations of motion.

Equations of steady condition steady density, momentum, and pressure

conditions of no tangential stress in the gas or on a solid surface . 340 342

Section IX. Application to transpiration and thermal transpiration through a tube.

Equations of steady condition transpiration under pressure when s is
small compared with c, the distance across the tube relation between
*, /x, and other quantities general case of transpiration and thermal
transpiration the value of s a s 2 near a solid surface the velocity of
the gas and the friction at a solid surface the equations of motion as
affected by discontinuity general form of * x ' 2 ' general equation of
transpiration ...........



Section X. Verification of the general equation.,

Statement of experimental results application of the general equation
to the transpiration of a gas of uniform texture application of the
general equation to transpiration arising from varying molecular
texture

Section XI. Application to apertures in thin plates and impulsion.

Equations of motion condition of the gas thermal transpiration through
an aperture in a thin plate thermal impulsion near a surface between
two surfaces general equation of impulsion

Section XII. Application to the fibre of silk and the radiometer.

Corresponding results when the density is proportional to the smallness
of the vane other results author's earlier conclusions confirmed in so
far as they went force depends on the divergence of the lines of flow
as well as on the heat communicated, figs. 12-14 figures indicate the
divergence of the lines of flow and the force in the radiometer
stability of the equilibrium the motion other points action does
not depend on the distance between the hot and cold plates

Section XIII. Summary and Conclusion.
General summary dimensional properties of gas conclusion

APPENDIX.

"Dber Thermodiffusion von Gasen (Pogg. Ann., 1873, p. 302), by
W. Feddersen on the name " thermal transpiration " addition to
Art. 7 addition to Arts. 41 and 104 addition to Art. 119 .



342352



352362



362371



371378



378381



381383



CONTENTS. XV

PAGES

34. Note on Thermal Transpiration ..... 391 393

The author's method, and the method of Prof. Maxwell.

35. Some Further Experiments on the Cohesion of Water and

Mercury 394398

36. On the Bursting of the Gun on Board the ' Thunderer ' . 399402

The bursting explained by supposing double loading and the powder of
the second charge converted into a high explosive by compression.

37. On the Steering of Ships . . . . . . . 403408

Experiments on H.M.S. 'Minotaur' and ' Defence.'

38. On the Effect of Oil in destroying Waves on the Surface

of Water 409

39. On Surface Tension and Capillary Attraction . . . 410 412

40. On the Floating of Drops on the Surface of Water depending

only on the Purity of the Surface .... 413 414



Page 58, paper 9 depth than a single screw.

(add) For continuation see paper 13, page 78.

Page 245, 6th line, in place of (see Report, 1875, I. p. 145)
insert (see paper 19, p. 134).




1.

ON THE SUSPENSION OF A BALL BY A JET OF WATER.



[From the Fourth Volume of the Third Series of " Memoirs of the Literary
and Philosophical Society of Manchester." Session 1869-70.]

(Read March 8, 1870.)

WHEN a ball made of cork, or any very light material, is placed in a
concave basin, from the middle of which a jet of water rises to the height of
four or five feet, the jet maintains the ball in suspension ; that is to say, it
takes and keeps it out of the basin. The ball is not kept in one position, it
oscillates up and down the jet ; nor is its centre kept exactly in a line
with the jet, it often remains for a long time on one side of it. In fact, the
ball appears to be in equilibrium when it is struck by the jet in a point
about 45 below the horizontal circle. In this way, for some seconds at
a time, the ball appears as though it were hanging to the jet, and then
oscillates in an irregular manner about this position. If its oscillations
become so great that it leaves the jet, it instantly drops, but in descending
it generally comes back into the jet before it reaches the basin. The friction
of the water causes the ball to spin rapidly ; and as it moves about the jet,
it spins sometimes in one direction, sometimes in another, always about a
horizontal axis. Of the water which strikes the ball, part is immediately
splashed off in all directions, part is deflected off at the tangent, and part
adheres to the ball, and is carried round with it, until it is thrown off by
centrifugal force.

The only explanations of this that appear to have been offered are based
on one or the other of the following assumptions, viz. that the centre of
gravity of the ball remains directly over the jet, or that the jet is accompanied
by a current of air which tends to carry the ball into it. With respect to
these assumptions, the fact that the ball will come back again into the jet
when driven entirely away from it must upset the truth of the first, and
^L o. R. 1



2 ON THE SUSPENSION OF A BALL BY A JET OF WATER. [1

at the same time it appears to establish the truth of the second. However,
some experiments, which will be subsequently described, made with a view
to ascertain if this current exists, show that it does not. Besides which,
Mr Routledge and Mr Wild have made some experiments. The former
found that when the jet, directed horizontally to avoid the influence of the
falling drops, was brought very near to a light ball suspended by a thread,
the ball showed no tendency to move towards the jet ; and Mr Wild settled
the point by showing that the action of the ball is the same in a vacuum
as it is in air. It appears, then, that neither of these assumptions is
satisfactory.

Now, of the forces which act on the ball, its weight acts at its centre in
a vertical line, and is the only force which is not due to the action of the
water. When the jet strikes the ball directly underneath, it will produce
a force acting upwards in a vertical line, the magnitude of which depends
on the height, and may therefore balance the weight of the ball. In this
position the ball is, by the action of these two forces, in equilibrium, in the
same manner as if it were balanced on a point. The slightest deviation in
the jet will upset it ; and then the jet will strike it on one side of the
vertical line through its centre: when so struck, the forces at the point
of contact may be resolved into two, of which one acts along the normal
to the surface, or through the centre of the ball, and is due to the impulsive
action of the water (this is called P'), and another in the tangent plane at
the point of contact (p) (this is due to the friction of the water, and is
called R). If W be the weight of the ball, then P', R, and W are the only
forces which at first sight appear to exist; and the question is, can the
ball be in equilibrium under the action of P', R, and W? This question



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