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No 2556 | HYDROGRAPHIC OFFICE |=.
Cc. BOOK DIVISION
OCHAN CURRENTS
AND THE
SYSTEM OF THE WORLD
“PRINTED BY
SPOTTISWOODE AND CO., NEW-STREET SQUARE
LONDON
mania
ne
oe
CHART
Showing the course of the pr
SURFACE CURRENTS
which the conflicting action of tral
the Earth's rotation the water is raised to
level 13 miles higherin the equatorial than
in the polar regions and this chart shows
the surface currents of the circulation caused
hy the forces of gravitation which hold the
and Terrestrial Gravitation’ caused by
the Earth's axial rotation tends to
Under currents rise to the surface m the polar
regions and form a general surface flow “a
temperate zones.
Surface currents from the equator and the Fs
meet in each of the temperate zonos and sink
dovnwards with a general motion eastwards.
ocean in equilibrium im that position.
Under currents rise to the surface in the equatorial
regions and diverge with a general motion west~
awards The tendency of these under currents is to rise
to the surface chiefly in the eastern part of each
ocean, but their course must be in some measure
“determined by the inequalities in the depth
of the ocean, and by its general configuration.
Plate VIL
VERTICAL SECTIONS OF THE DISTRICTS SHOWN IN PLATE It
B
Water running trom Waster
the Equanie. wer prewar
te ame AD Papel tons
Se —s.
poe a hy
Section of Equatorial Districts
A
B
——
| Water mining trom hee
, the Poles. over arom feet
the ane AB f. ‘ed
3 Ao ane AB
Section of Polar Districts
Each of the two lassen Antarctic Districte Rae its aunis incined tn
the cpporite directim Ww that in the Section, bust tn gach the water
moving than the Bote paseee wver the axa, and that moray tomes
OsPide peer under Dhe xis, just ea wa the ether Polar Dietits
Bi Shaye the position of Courter Gurren Plate VII (a
HORIZONTAL SECTION, APPLICABLE TO EITHER THE ATLANTIC OR PACIFIC DIVISION
DF CURRENTS SHOWN IN THE CHART TAKEN HALFWAY BETWEEN THE SURFACE
ANO THE BOTTOM OF THE OCEAN.
a
Z Water running West and ~
7 Tay pours
Wire murning sFousth
ater the ans
{
((
SS w raang upeara
ESE
Parr I1.—Evidences of the Equilibrium of the . Tides 2 Le
Part I1J.—Evidences of the Convergence towards the
Equator ; : : : er fee
CHAPTER XIV.
EVIDENCES OF THE TIDAL ACTION DESCRIBED IN CHapTerR IX. 158
X1l CONTENTS.
BOOK VII.
REFUTATION OF OBJECTIONS TO THE FORE-
GOING VIEWS.
CHAPTER XV.
PAGE
REFUTATION OF OBJECTIONS ON 4d PRIORI GROUNDS AGAINST
THE POSSIBILITY OF THE EXISTENCE OF THE ACTION OF
Vis-INERTIZ DESCRIBED IN Boox II. as CIRCULATING
THE OCEAN . : ; : ; S : . 165
CHAPTER XVI.
REFUTATION OF A SUGGESTED SUSPENSION OF THE ACTION OF
GRAVITATION . ; ‘ ai fente us é 5 f . Ie
BOOK VIII.
REFUTATION OF ACCEPTED THEORIES BY
WHICH EXPLANATIONS OF THE MOVEMENTS
OF THE OCEAN AND ATMOSPHERE HAVE
BEEN ATTEMPTED.
CHAPTER XVII.
OBSERVATIONS ON THE RELATIVE CuRRENT-CREATING ACTION
oF THE TIDES, THE WINDS, DIFFERENCES OF TEMPERATURE
AND VIS-INERTIE . , : ; : : : Be ke)
CONTENTS, Xill
BOOK IX.
THE MOVEMENTS AND CONFIGURATION OF
THE SURFACE OF THE EARTH.
CHAPTER XVIII.
PRELIMINARY ‘ : : ; : ? 3 ; a Lae
CHAPTER XIX.
THE AcTION OF Vis-INERTIZ ON THE SURFACE OF THE EartH 205
BOOK X.
THE ACTION OF VIS-INERTILEZ IN THE
HEAVENS.
THE SYSTEM OF THE WORLD.
CHAPTER -XX.
PRELIMINARY ‘ ; : 5 F ‘ : z 5 PAL
CHAPTER XXI.
THE Morions oF THE PLANETS . 5 ; : : . 223
CHARTS AND DIAGRAMS.
PLATES.
PLATE
I. Cuart or Surrace Currents . To face the Titlepage
II. SketcH or OcrEsANn CURRENTS CAUSED
BY THE Eartu’s Roration . . To face Chapter I.
III. Roration causep By ARRESTED Motion 70 face page 18
IV. Formation oF CURRENTS . 2 Sees oh 21
V. VERTICAL CIRCULATION . : Se rae aes eLemoe
VI. HorizontTat CIRCULATION . : Sato. - 29
VII. EquaTorIAL COUNTER-CURRENTS . .,, sea
VIII. Verricat Sections or Districts or
Roration . ; ; : . Annexed to Plate I.
VIIa. Horizontau SECTION OF SAME . : 3 2
IX, Surrace or District oF Rotation . Z’o face page 35
pag
X. Arctic CURRENTS . : : : a » 42
XI. Antarctic CURRENTS . : bie * 5. eae
XIa. 3 ‘ ; é if Brena a: Ss
XII. Newrton’s ILiustRatTioN oF ORBITAL
Motion . : : : ee y ‘5 70
XIII. Tur Trpss : ; : : : a eo 108
XIV. THe Tipes . : : : Sees r Pee old
SKETCH OF THE CURRENT-CREATING
ACTION OF Vts-INERTIZ IN THE
ATLANTIC OCEAN .. A : : a qanlag
XV
XVI
PLATE
CONTENTS.
XVI. THE CoNnFIGURATION OF THE Eartu. To face page 211
XVII. OrpitaL Motions or Mercury AnD
THE KARTH ; ‘ : aiots = op
XVIII. Toe Spinnine Tor . : : ‘ - “5
FIG.
WOODCUTS.
THE AcTION oF ASTRAL GRAVITATION . ; ,
THE RETARDATION OF THE NORMAL EQUATORIAL
VELocITY OF ROTATION § : : : ‘
NorMAL VELOCITIES AND RETARDATION . inets
MERIDIONAL AND VERTICAL CIRCULATION OF THE
OcEAN AND ATMOSPHERE . : : : nee
EAstwaARD MoTIoN ALONG THE TEMPERATE ZONE .
223
255
BOOK I.
PRELIMINARY
oe
; Peale
CHAPTER I.
ON THE NATURAL COURSE OF AN INVESTIGATION OF
THE CAUSES OF THE MOVEMENTS OF THE OCEAN.
BrsipEs the waves, which rise wherever the surface
of the water is ruffled by the wind, two apparently
distinct kinds of movement are observable in the
ocean: the one a streaming onwards of parts of the
ocean through itself, which is taking place more or
less in all parts of it, and forms the ocean currents ;
the other, a movement by which its level is con-
stantly changing—rising in one part as it falls in
another. This latter forms the tides, and is an
alternate piling up and subsiding of the water, and
not a current except where the coast line offers such
obstruction as to cause a rush of water.
The first impulse of practical inquirers regarding
the causes of ocean currents seems to have been to
attribute them to the winds, as ocular demonstration
of their action is evident to anyone who watches the
ocean waves which are rolled along by every breeze.
This apparent action of the winds, together with the
general accordance of many of the broad features of
B2
4 THE OCEAN. [Boox I.
aerial and oceanic circulation, led the first investigators
of the subject to regard them as cause and effect-; but
difficulties met with by subsequent inquirers en-
deavouring more accurately to reconcile the observed
effects with this suggested cause, led to the con-
sideration that as the burning rays of the sun are
constantly pourig down on the equatorial waters,
leaving those of the polar regions icy cold, the
differences of temperature resulting from this must
also to some extent tend to cause currents, as the
water endeavours to maintain its equilibrium. ©
Those investigators who came to regard the force
or the direction of the winds as not forming a sufii-
cient explanation of the observed circulation of the
ocean, suggested, as above stated, that differences of
temperature must tend, by disturbing the equilibrium
of the water, to cause a constant circulation between
the equator and the poles; and have by various
theories endeavoured to explain the action of this
effect in such a manner as to reconcile it with what is
known of the actual circulation.1 According to the
most popular form in which the temperature theory has
been propounded, polar cold causes the water to sink in
those regions, and thence to travel along the bottom
1 Maury, as a practical investigator, was compelled to abandon
the idea of the circulation of the ocean being caused by the winds,
and therefore turned his attention to the current-creating action
of differences of temperature, but he has not attempted systemati-
cally to trace the connection between the observed effects and the
suggested cause.
Cuapr. I.] INERTION,
ca
of the ocean to the equatorial regions, there to rise and
return to the poles as surface water. Recent researches
have, however, practically refuted that theory.’
Neither of the foregoing causes has, however, at
any time obtained general acceptance among men
practically acquainted with the movements of the
! The above paragraph has been added to this edition, and
the manner in which the theory alluded to has already been
refuted by recent researches, may be judged of by the following
extracts :—
‘From the drift of this disrupted ice we have fair evidence of
a great bodily movement of the water northward ; for it must be
remembered that icebergs have been fallen in with in the entire
circumference of the Southern Seas, and that they are pushed in
the South Atlantic ocean as far as the 40th parallel of latitude; in
the South Indian to the 45th parallel; and in the South Pacific
to the 50th parallel.
‘In the discussion of oceanic circulation, it has been assumed
that water flows from Equatorial into Antarctic areas; there is no
evidence, so far as I am aware, that warm surface water in the
sense implied is found south of the 45th parallel.’—Address to the
british Association, September 1876, by F. J. Evans, C.B., F.R.S.,
Captain R.N., and Her Majesty’s Hydrographer.
The motion of icebergs, above alluded to, from the pole to the
temperate zone is against the average direction of the winds.
‘I have never seen, whether in the Atlantic, the Southern
Sea, or the Pacific, the slightest ground for supposing that such a
thing exists as a general vertical circulation of the water of the
ocean depending upon difference of specific gravity.’-—Professor
Sir Wyville Thompson’s Report to the Admiralty, December 5,
1875.
For further consideration of the above question see Chapter
VIL. of The New Principles of Natural Philosophy. As heat
acts chiefly by creating differences of specific gravity, the above
quotation from Sir Wyville Thompson shows that the connection
between its action and the existing circulation is not easily to be
traced.
6 THE OCEAN. (Boox I.
ocean. Opinion has always been divided on the sub-
ject ; and some investigators, considering that neither
of the foregoing causes satisfactorily explains the
observed circulation of the ocean, have attributed the
ocean currents to the axial rotation of the earth, or
have endeavoured to connect them with the tidal
action of the sun and moon. :
All the foregoing views appear to have forced
themselves upon the consideration of practical inves-
tigators. But since the days of Newton, the gene-
rality of men most abstrusely acquainted with what
are regarded as the higher branches of scientific
knowledge, have absolutely rejected the tides and the
earth’s rotation from among the possible causes of
ocean currents, considering their current-creatine —
action incompatible with the accepted laws of motion.
The laws on which their philosophy is based thus
compel those who understand and accept those ‘ laws
of motion’ to conclude that either the winds, or
unequal specific gravity resulting from difference of
temperature or otherwise, or those two causes com-
bined, must necessarily in some manner explain the
circulation of the ocean.
It is, however, evident that whatever may be the
current-creating action of-the forces above alluded
to, the fact of the tides being clearly dependent on
the apparent motions of the sun and moon, shows
that a full solution of the movements of the ocean
cannot be attained through the consideration of merely
Cua. 1] INERTION. 7
local causes, but requires the study of cosmical laws.
These we will therefore take into consideration first.
By the force of gravitation drawing towards the
centre of the earth, the ocean is held down in the
hollows of the earth’s undulated surface, and kept
from overwhelming what is at present dry land.
The level of the ocean is not, however, determined
solely by this direct force of the earth’s gravitation ;
for it is well known that the spherical form which
that force tends to cause is changed by the earth’s
axial rotation to an oblate spheroid. It is therefore
evident that the ocean does not partake of the earth’s
rotation by any spontaneous tendency ; but that it is
dragged round by the surface on which it rests.’
As this is an unchanging influence, unceasingly act-
ing in the same manner, its effects naturally claim
a careful consideration before attempting to unravel
the intricacies of those resulting from ever-changing
causes.” And it is well, before entering on a discus-
1 In the Treatise on Vis-Inertie the question of the existence
or non-existence of any action of that force in the ocean is treated
as a question to be solved; whereas in this work the oblate
spheroidal form of the earth is accepted as a sufficient demonstra-
tion of its action in the ocean and on the surface of the earth,
leaving only the further amount and nature of that action to be
ascertained.
2 Not only is the tidal action of the sun and moon an ever-
changing influence in respect to any given part of the ocean, but
it is also very slight in comparison with the action of the earth’s
rotation ; for the extreme effect of that tidal action is to cause,
over a very limited area, a rise and fall of about 120 feet, where-
as the earth’s rotation maintains a constant difference of level
8 THE OCEAN. [Boox I,
sion of effects resulting from the earth’s motion, to
commence by recalling to mind what our knowledge
of that motion is.
It is only recently in the historical period that
the fact of the earth being in motion at all has been
clearly realised. Scarcely more than three hundred
years ago its immobility was regarded as an obvious
fact. That the position of the earth was fixed and
unchanging was supposed to be demonstrated by the
clear and simple evidence of the senses, and the idea
of its being in motion was regarded as an offspring
of intellectual aberration.
It is true that nearly two thousand years before
the period just mentioned some keen observers of
natural phenomena perceived that the earth was
actually in motion ;’ but, though this truth was so
between the equator and the poles amounting to about thirteen
miles ; thus giving what may practically be regarded as an @ prioré
Homonetr ation of its paramount influence.
1 «Tt was the ancient opinion of not a few, in the earliest ages
of philosophy, that the fixed stars stood immovable in the highest
parts of the world; that under the fixed stars the planets were
carried about the sun; that the earth, as one of the planets, de-
scribed an annual course about the sun, while, by a diurnal motion,
it was in the meantime revolved about its own axis; and that the
sun, as the common fire which served to warm the whole, was
fixed in the centre of the universe.
‘This was the philosophy taught of old by Philolaus, Aris-
tarchus of Samos, Plato in his riper years, and the whole sect of
the Pythagoreans; and this was the judgment of Anaximander,
more ancient than any of them; and of that wise king of the
Romans, Numa Pompilius, who, as a symbol of the figure of the
world, with the sun in the centre, erected a temple in honour of
Cuaap, I.] INERTION. 9
long ago apparent to the bright genius of those
ancient philosophers, it was at variance with the
common sense of mankind, and was therefore dis-
carded as a fanciful delusion until, in the sixteenth
- Vesta, of a round form, and ordained perpetual fire to be kept in
the middle of it.
‘The Egyptians were early observers of the heavens ; and from
them, probably, this philosophy was spread abroad among other
nations ; for from them it was, and the nations about them, that
the Greeks, a people of themselves more addicted to the study of
philology than of nature, derived their first, as well as soundest
notions of philosophy: and in the vestal ceremonies we may yet
trace the ancient spirit of the Egyptians; for it was their way to
deliver their mysteries, that is, their philosophy of things above
the vulgar way of thinking, under the veil of religious rites and
hieroglyphic symbols.
‘It is not to be denied but that Anaxagoras, Democritus, and
others, did now and then start up, who would have it that the earth
possessed the centre of the world, and that the stars of all sorts
were revolved towards the west about the earth, quiescent in the
centre, some at swifter, others at a slower, rate.
‘ However, it was agreed on both sides that the motions of the
celestial bodies were performed in spaces altogether free and void
of resistance. The whim of solid orbs was of later date, introduced
by Eudoxus, Calippus, and Aristotle ; when the ancient philosophy
began to decline, and to give place to the new prevailing fictions
of the Greeks.-—Newton’s System of the World.
It has been said that the Druidical ruins in Britain show that
their builders knew of the true arrangement of the solar system ;
but, as far as I am aware, this idea is not supported by sufficiently
reasonable arguments to allow of its being regarded as more than a
vague conjecture. It must, however, be admitted that the ignorance
which subsequently prevailed throughout the country is not a valid
argument against antecedent knowledge ; for we see that the degene-
racy of knowledge in Rome was such, that the successors of Numa
Pompilius imprisoned Galileo and others for asserting the truths
which formed the basis of the ceremonies for the celebration of which
the temple of Vesta, in the same city, was built by that ‘ wise king.’
10 THE OCEAN. [Boox I.
century, Copernicus published his cosmical theory,
maintaining that the earth rotates each day on its
axis, and revolves each year round the sun.
Even then these views met with no ready accept-
ance. And after the publication of the theory of
Copernicus, one of the greatest of philosophers, Des-
cartes, was at great pains to explain how, when, in
describing his system of the world, he spoke of the
earth moving, he did so improperly, and only for the
sake of simplifying the explanation of an hypothesis :
and he argued that, even supposing his cosmical
hypothesis to be true, even then, speaking in a proper
sense, the earth did not really move.
These men, with Kepler, Galileo and others, paved
the way for Newton, who, immediately after Descartes,
enforced the theory of the axial rotation and orbital
revolution of the earth with such clearness and pre-
cision that the belief in these motions gradually
extended until they at length became generally
accepted as incontrovertible facts.
These two motions of the earth, re-discovered by
Copernicus—namely, the diurnal motion of rotation
on its axis, and the motion by which it is annually
revolved in its orbit round the sun, are the only
ereat movements of the earth of which we have,
even at the present day, a definite knowledge. But
besides these motions, a third great movement was,
towards the close of last century, pomted out by Sir
William Herschel, who showed that not only is the
Cuap. 1] LNERTION. 11
earth moving round the sun, but that the sun, carry-
ing with it the earth and the whole solar system, is
itself moving along among the fixed stars. But
though astronomical observations have demonstrated
the existence of this motion, neither its direction nor
its velocity has been clearly defined ; and as regards
any motion which the solar system may, for aught
we know to the contrary, partake in common with
the stellar system, the distance to which our range
of vision has been extended by the telescope is not
sufficient to enable us to obtain any direct informa-
tion from the science of astronomy.!
‘In the treatise on Vis-Inertie already alluded to, as also
in this work, it is, however, shown that the evidences of the action
of vis-inertiz in the ocean indicate a motion of the earth south-
wards ; and that the indications of the action of that force in the
outer crust of the earth corroborate the evidence of the ocean
currents. Those effects may be treated as if resulting from the
motion of the solar system. For, the effects of motion as shown
by tides, currents, and winds, will be the same whether those
effects result simply from a motion of the solar system in the
direction of the south pole, or be the average result of a
motion of the solar system in the direction of the north
pole combined with a motion of a more extensive system
with a greater velocity in the opposite direction. That is to
say, as far as the present question is concerned, those effects
might either result from a motion of the solar system by which
the earth is moved together with that system; sweeping along
among the stars which compose the visible part of the universe,
and so changing its position among those stars; or, they might
be the result of a motion of the whole stellar system, in which
the earth, the sun and the stars, equally partake as particles of
that system ; the motion demonstrated in the direction of the
south pole being, in such case, a majestic movement in which the
whole visible universe is travelling onwards in that direction.
12 THE OCEAN. [Boox I.
For the elucidation of the effects of the motion of
the earth, we have the well-known fact that when-
ever a vessel containing water is set in motion, the
water which it contains has a tendency to move along
its surface in the opposite direction to that in which
it is moved.?
And, since astronomical observations appear to have shown that
the solar system has a motion among the stars by which it is
carried along in the direction of the northern hemisphere, we are,
if those observations be reliable, compelled to the conclusion that
in the same manner as that in which, when the moon is inside the
earth’s orbit, the lesser velocity of its orbital motion round the
earth is lost in the greater velocity of the orbital motion in which,
together with the earth, it is carried round the sun ; so also, ina
similar manner, must the velocity of the motion in which the solar
system is carried northwards among the stars, be lost in the
greater velocity of a motion in which, together with the stars, it is
moving southwards.
1 The argument of the Treatise on Vis-Inertie does not allow
of this illustrative case being assumed to be analogous to that of the
earth and its ocean ; and though I have in the present work con-
sidered it reasonable to admit, as stated on page 4, that the oblate-
spheroidal shape resulting from the earth’s rotation is evidence of
the conditions in the two cases being analogous, the demonstration
required, as stated in the following extract from the first chapter
of the above-mentioned treatise, is in fact given in this work
also ; and the Second Part of that demonstration has been given in
much more detail in The New Principles of Natural Philosophy :—
‘As we do not know in what manner the force which causes
any known motion of the earth acts upon the earth, we cannot
assume that by that motion any action of vis-inertie is brought
into play in the ocean, but the very existence of such action
is necessarily a subject for demonstration, and cannot logically be
inferred or denied, by analogy, from any known phenomena.
‘The subject, therefore, naturally divides itself into two parts.
‘ First, by theoretical deduction to demonstrate hypothetically
the action of vis-inertie :
oe
Guar. 1] | INERTION. 13
This is a simple law of nature :—though the'vessel
containing the water is set in motion, the water tends
to maintain its position, and therefore has a relative
motion over the surface of the vessel in the opposite
direction to that in which the vessel is moved.
We need not immediately investigate the abstract
nature of the force which tends to cause this relative
motion of the water, for it is sufficient, as far as our
present purposes are concerned, that it is a simple
matter of fact that, in the case just mentioned, the
water has a tendency to maintain its position ; and
that therefore, when the vessel which contains it is
moved, the force which tends to hold the water in
that position tends also to cause it to move along the
surface of the vessel in the opposite direction to that
in which the vessel is moved ; and that this foree—
which indisputably does exist, be its abstract nature
what it may—is termed vis-inertiz.
In the consideration of the forces which keep the
ocean in motion, we are, for the reasons given above,
called on to give precedence to the action of this
force of inertion, or vis-inertiz.
‘Secondly, by practical investigation to ascertain whether or
not there exist in the ocean such movements as may, in the first
part, be demonstrated to be the natural result of the action of vis-
inertie.
‘If the practical investigations show the existence of move-
ments in the ocean clearly according with the theoretical deduc-
tions, we may then, in the absence of any other reasonable cause
being adduced, conclude that vis-inertie is the cause of those
movements.’
‘
a,
A
a
BOOK II.
EFFECTS OF THE MOTIONS OF THE EARTH.
THEORY OF OCEAN CURRENTS.
Ree he:
; pap.
RENT CREATING ACTIO}
OF THE
- EARTHS AXIAL ROTATION,
discarding the effects of onward motion,the Winds,
differences of temperature, the tidal action of the
San & Moon, and derangements caused by islands
and mountain ridges below the surface of the ocean,
except that,to illustrate the latter derangements,
an island has been inserted in the North Pacific
and another in the Antarctic Pacific District.
ace
‘ly proved by the recent explorations as also that of several
of the counter aorents E.H. and under currents OR.
le
17
CHAPTER II.
EFFECTS OF THE EARTH’S AXIAL ROTATION.
PART I.
GENERAL EFFECTS.
SincE the motion of the earth’s surface round its axis
is from west to east, any existing action of vis-
inertiz must therefore, according to the foregoing
illustration, tend to cause the water which lies on the
surface to move along that surface from east to west.
That is—a pressure is created acting in the opposite
direction to that in which the surface of the earth is
moving, giving the water a tendency to stream round
the earth from east to west.
This westward pressure, imparted to the ocean
by the rotation of the earth eastwards on its axis,
is obviously a fixed and unchanging influence ; for
the earth is constantly rotating at the same rate and
in the same direction round its axis of rotation.
And, since the speed at which the surface of the
earth rotates at the equator is more than a thousand.
miles an hour and at the poles nothing, all interme-
diate gradations of speed lying evenly between the
C
18 THE OCEAN. (Boox II.
equator and the poles, it is obvious that the force of
westward pressure imparted to any given mass of
water lying about the equator is greater than that
imparted to an equal mass of water lying about the
poles. |
And also, since the velocity of rotation at the
surface of the ocean is greater than at the bottom ;
therefore in all parts of the ocean the westward
pressure imparted to the water at the surface is
greater than that imparted to the water lying be-
neath it.
In order to illustrate the action of these unequal
forces when brought into conflict, let it be observed
that: if an ordinary globe be held by its stand and
be, with a rapid motion, moved in a curve line in a
plane at right angles to the axis of its poles, as
from p to E in Plate III., then, if the onward motion
be suddenly arrested, the globe will rotate on its
axis; the axial rotation being in the direction AHBL.
This motion of rotation results from the in-
equality of the forces of onward impetus generated
on the sides A and B by the movement of the globe
in a curve line from D to E.
For the curve line a 4 is similar to, but greater
than, the curve line BB: and, as the point A describes.
the curve line A A in the same time that the point,
describes the curve line BB, therefore the velocity of
the point A is greater than that of the point B; and
)
on the onward motion of the axis being arrested, the
Platell.
London, Longmans & Co.
Cuap. IT.} ; INERTION. 19
momentum which has been generated by that motion
tends to carry the point A round the axis in the di-
rection AH BL ; the momentum generated at the point
B tending at the same time to carry the point B
round the axis in the opposite direction, that is, in
the direction BHAL. The forces generated on the
sides A and B are thus brought into conflict: the
lesser force, B, must of necessity yield more or less,
in accordance with the relation which the opposing
forces bear to each other: and thus the greater force
of the side A imparts a motion of rotation to the
globe in the direction AHBL.
Also : since in streams of water the greatest force
is in the central parts of the streams; therefore,
wherever a stream is obstructed, the greater force of
the central part of the stream overwhelms the lesser
forces on each side; so that the stream divides,
branching off right and left from the point of ob-
struction.
And for the same reason, also, when two streams
meet, there must be offsets branching off in opposite
directions from the meeting-points.
In the case of the overwhelming of lesser forces
by greater forces, exemplified above in connection
with Plate III., the check to the onward motion is
given at the central axis ; so that the quantities of
motion brought into conflict are of necessity unequal ;
for the masses of matter brought into conflict may,
G2
20 THE OCEAN. . [Boox. II-
as far as our present purposes are concerned, be con-
sidered equal in volume, and the velocity of one of
those equal masses is greater than the velocity of the
other.
But, in the case of a stream of water meeting with
an obstruction in its course, where the different parts
of the water are moved with unequal velocities ; the
check given to the onward motion which brings those
unequal velocities into conflict, is not given as in
Plate III. at a central axis, necessarily bringing a
volume on one side of the axis into conflict with an
equal volume on the other side, but this check is given
at the end of each line of motion ; so that, although
unequal velocities are brought into conflict, yet, as
far as the demonstration in connection with Plate III.
is concerned, there might nevertheless be no over-
whelming of lesser forces by greater forces ; because,
by a greater volume of the water moved at the lesser
velocities opposing itself to a lesser volume of that
moved at the greater velocities, the quantities of
motion brought into opposition might be equalised ;_
thereby preventing the overwhelming of lesser forces
by greater forces in the manner demonstrated in
connection with Plate III.
But that, though the onward motion of the fluid
be checked at the end of each line of motion, there
will nevertheless be an overwhelming of lesser forces
by greater forces, may be demonstrated by holding a
goblet containing water in an inclined position, as in
ete
S J
af Ds Mi
get. 4 —
Cuar. II.] INERTION, 21
Plate IV. figure 1, and then, with the point A as a
pivot, bringing it into an upright position as in figure
2. In this case the central line of motion, B C, over-
whelms the lines of lesser force, FG and HI in
figure 3, on each side; and sets the fluid in motion
in the directions BCGFB and BcrHB. And also,
the surface line of motion, Bc, overwhelms the line
of lesser force, D E, in figure 2, at the bottom of the
fluid; causing a motion in the direction BcEDB. It
is then evident that where unequal forces are brought
into conflict the lesser force must yield. And we
have seen that the force of westward pressure is
greater in equatorial than in polar regions ; and also
greater at the surface than at the bottom of the
ocean. These inequalities in the force of westward
pressure result from the inequalities in the velocity
of rotation in those parts of the ocean. And we will
now consider how these unequal forces are brought
into conflict, and what movements result from their
conflicting action.
This westward pressure would obviously give the
water a tendency to change its meridian westwards
by the shortest route; that is, to make as much
westing as possible in any given space traversed.
And, as the earth’s equatorial diameter is greater
than its polar diameter, this shortest route westwards
is not in lines running due west, but in lines diverg-
ing from the equator somewhat northwards and
to
ho
THE OCEAN. (Boox If.
southwards. This divergence from the equator im-
plies a change of latitude: therefore a tendency to
cause a change of latitude is an attribute of west-
ward pressure.
And change of latitude has itself two important
attributes whose action in the atmosphere was clearly
recognised by George Hadley as affecting the course
of the Trade Winds; but whose action in the ocean
appears to have been first pointed out by Captaim
Maury, as affecting the course of the Gulf Stream :
that is, that a tendency to change of meridian east-
wards is an attribute of such change of latitude
as causes an increase of equatorial distance ; and
that a tendency to change of meridian westwards
is an attribute of such change of latitude as causes
a decrease of equatorial distance.
For, since the velocity with which the surface of
the earth rotates at the equator is upwards of a
thousand miles an hour and at the poles nothing,
therefore, in any change of latitude in a direction
leading from the equator towards either of the poles,
that which changes its latitude has a faster eastward
momentum than that which belongs to the latitude
into which it enters, and will consequently have a
tendency to change its meridian eastwards. Whereas
in any change of latitude in a direction leading from
the poles towards the equator, that which changes
its latitude has not so fast an eastward momentum
as that which belongs to the latitude into which it
St Br ah a
Cuap. II.) INERTION. 23
enters, and it will consequently have a tendency to
change its meridian westwards.
In the former case, that which changes its latitude
rushes on in advance of the latitude entered ; and
in the latter case, the latitude entered rushes on in
advance of that which enters it. The former may be
called a tendency to run eastwards, and the latter
a tendency to fall westwards.
The change eastwards is in fact a tendency of the
water to part from, or run on in advance of, a surface
of less velocity ; and the change westwards, a falling
of the water against a surface of greater velocity with
which the change of latitude brings it into contact.
1 It is greatly to be regretted that it has become customary to
use terms, in reference to the direction of ocean currents, in exactly
the opposite sense to that in which the same terms are used in re-
ference to the winds. This custom is so firmly established that,
as the advantages to be gained by altering it are not perhaps
sufficient to repay. the temporary confusion consequent on a change
in the use of terms, the idea of changing the custom cannot perhaps
be entertained ; though a judicious use of terms has more to do
with the progress of any science, than is perhaps generally supposed.
In speaking of the wind, the terms used denote the direction from
which the wind blows; whereas, in speaking of ocean currents, the
terms used denote, not the direction from which the current runs,
but that towards which it runs. Thus an easterly wind denotes a
wind running from east to west, but in the ocean an easterly current
denotes a current running from west to east. In order, in some
measure, to obviate the confusion which this injudicious use of
terms tends to cause, I have invariably used the termination ‘ ward’
instead of ‘ Zy,’ in reference to ocean currents, so that as an easterly
wind denotes a wind running from the east, an eastward current
denotes a current running towards the east. The ordinary use of
these terms has been so confused, and their relative meanings so
24 THE OCEAN. [Boox II.
PART II.
EFFECTS IN AN OCEAN COVERING THE EARTH.
Let us now consider the action of a westward
pressure of the nature we have described, if acting
in an unbroken expanse of water covering the surface |
of the earth and unobstructed anywhere by land.
Its tendency is to set the water in motion from east
to west. And we have shown that the water thus set in
motion tends to diverge from the equator on both sides.
If there be no obstruction in its course, this
tendency to diverge will be equal at all points of the
equator.
But it is clear that no stream can diverge from
the equator unless a supply be brought to the equator.
There cannot at any point be diverging streams
unless at some other point there be converging
streams. And if the diverging tendency be equal
on every meridian, there is no reason why any one
meridian should yield rather than any other. And
therefore, unless it be possible to obtain a supply for
diverging streams by some other means than the
yielding of the diverging tendencies of one meridian
ill-defined even by the best authorities, that the distinction which I
have here made does not interfere with any previous definition of
their relative significations.
For the sake of further distinction and clearness in the use
of terms, I have used the termination ‘wards’ instead of ‘ ward’
when referring adverbially to the course of the currents,
Cuap. II.) INERTION. 25
for the supply of those of another, the streams must
run due west right round the world in every lati-
tude. In such case westward pressure would be
acting due west in all parts of the ocean, and none
of its attributes would be brought into play.
Since, however, we have shown that lesser forces
must yield to greater forces, and, since the force of
westward pressure is greater at the surface than at
the bottom of the ocean, therefore, though no one
meridian will yield to any other, the diverging ten-
dency of the lower strata of water must yield on
every meridian to the greater force of the upper
strata; so that the lower strata would consist of
converging streams, which, at the point of conver-
gence, must rise upwards to supply the diverging
streams of the upper strata.
Thus in the lower strata converging streams
would be running towards the equator at all points
from the north-east and south-east, and in the upper
strata diverging streams would be running from all
points of the equator towards the north-west and
south-west.
Tt is clear that the streams of the upper strata
must supply those of the lower. Let us consider
what course they must pursue between their depar-
ture from and their return to the equator.
It is obvious that the streams of the upper strata,
running from the equator at all points, must, as they
proceed on their course, become compressed in con-
26 THE OCEAN. {Boox II.
sequence of the decrease in the circumference of the
earth in the latitudes which they are simultaneously
entering. Now, as far as the forces at present under
consideration are concerned, there is no reason why
the stream on any one meridian should yield rather
than that on any other meridian ; and therefore, the
only manner in which the course from the equator
could be continued would be by an increase in either
the depth or the velocity of the strata in inverse
proportion to the decrease in the circumferences of
the consecutive latitudes. But gravitation will
obviously prevent an increase of depth more than
sufficient to carry the streams onwards a moderate
distance beyond the latitude at which compression ~
commences ; and that tendency to run eastwards,
which increases in proportion with any increase of
velocity, will just as obviously prevent the increase
in the velocity of their course from the ‘equator
which would be necessary to carry the whole volume
of the streams onwards towards the poles. And
therefore, since there cannot be either an increase of
depth, or an increase of velocity sufficient to carry
the streams onwards towards the poles, and since the
stream on any one meridian will not yield to allow
of that on any other meridian proceeding, the pole-
ward course of the upper strata must cease equally
on every meridian. The streams of the upper strata
must gradually descend on every meridian into the
lower strata, where, on reaching the surface of the
Cuar. I1.] INERTION. 27
earth, they must divide in opposite directions. The
one division in each hemisphere will obviously form
the streams which in the lower strata run towards
the equator at all points from the north-east and
south-east ; and the other division in each hemi-
sphere, turned towards the poles, bemg under that
influence of change of latitude which tends to carry
it eastwards, forms streams in the lower strata flow-
ing through the temperate zones, and curving east-
wards in their course towards the poles—that is,
forming currents running from south-west towards
north-east in the northern hemisphere, and from
north-west to south-east in the southern hemisphere.
Now it is clear that the decreasing circumference
of the earth must sooner or later act upon these
streams running from the temperate zones towards
the poles in the lower strata, in the same manner
as upon the streams running from the equator to-
wards the poles in the upper strata, and therefore
they must gradually, having no other means of pro
gressing, turn upwards into the upper strata, through
which they must return southwards, until, meeting
with the streams flowing from the equator in that
upper strata, they form complete circuits of rotation
between the temperate zones and the poles—the
streams of the lower strata running eastwards in
their course towards the poles, and those in the
upper strata running westwards in their course from
the poles.
28 THE OCEAN. [Boox Il,
Thus there would be formed two great zones of
currents in each hemisphere, as shown on Plate V.,
in which figure 1 represents the currents of the upper
strata, and figure 2 those of the under strata.'
The under strata in the equatorial zone run
towards the equator at all points from north-east
and south-east ; and in each polar zone run towards
the pole from south-west in the northern, and from
north-west in the southern hemisphere.
And in the upper strata, the great westward
current of the equatorial zone diverges from the
equator on both sides ; the diverging streams tending
in their course more and more directly towards the ~
poles, and then eastwards, until meeting with the
streams running from north-east in the north polar
zone and from south-east in the south polar zone.
PART IIT.
EFFECTS IN AN OCEAN SURROUNDED BY LAND.
Section I1.—Lquatorial and Polar Districts.
The course of the currents just described is that
which would result from the action of westward
pressure if acting in an ocean covering the surface
of the earth and unobstructed anywhere by land.
1 This circulation is demonstrated by a shorter mathematical
argument in Chapter III. of Zhe New Principles of Natural
Philosophy; which does not, however, so well serve as a basis
for the subsequent details. See also, farther on in this volume,
Chapter XXI., Proposition XX VII.
Plate V.
itt
URS
Me
ESS /
a.
’
w
Es a
Plate VL
London, Longmans & Co.
Cuar, IT. ] INERTION. 29
We will now, before applying its action to the
ocean as it actually exists, consider its effects if acting
in an ocean running north and south from pole to
pole, and bounded east and west by an unbroken
barrier of land. And we will first consider the
effects resulting in such an ocean from the obstruc-
tion formed by the barrier of land, apart from the
effects resulting from the difference in the relative
forces at the surface and bottom of the ocean, and
also all effects of friction.
Let Nwse, in Plate VI., be such an ocean as
above described, Ew the line of the equator, n the
north pole, and s the south pole.
Now, if the forces of westward pressure were
equal on each parallel of latitude, it is obvious that
the only effect which could result from its action
would be a change in the position of the water—
that is, the level of the ocean would be depressed on
the eastern and raised on the western side of the
ocean.
Since, however, the force of westward pressure
is greatest at the equator, and decreases from the
equator towards the poles in proportion with the
decreasing circumference of the parallels of latitude,
and since lesser forces must yield to greater forces ;
therefore, the force of westward pressure created in.
the equatorial regions must overwhelm the lesser
forces north and south, and drive the water eastwards
through latitudes at some certain distance from the
30 THE OCEAN. [Boox II.
equator on both sides. And this water, by returning
to the equator from the north and south on the
eastern side of the ocean, would form a supply for the
sreater force of westward pressure about the equator.
Thus the waters of the ocean would be set in mo-
tion westwards in the equatorial regions ; northwards
and southwards from the equator towards the tem-
perate zones on the western side of the ocean ;
eastwards through the temperate zones ; and from the
temperate zones towards the equator on the eastern
side of the ocean.
The action of westward pressure, under con-
sideration, would not, however, simply tend to form
these two revolving currents—one lying on each side
of the equator ; for, the water turned northwards and
southwards from the equator on the western side of
the ocean, comes under the influence of change of
latitude, which, as it is increasing its equatorial dis-
tance, gives it a tendency to run eastwards ; and
therefore, instead of sweeping from the equator all
along the western coast, and then back to the
equator along the eastern coast, 1t must, at some
certain distance from the equator, diverge eastwards
from the western coast and flow through the ocean
to strike upon the eastern coast. Dividing upon the
eastern coast, one portion in each hemisphere forms
the stream running from each temperate zone towards
the equator ; and the remainder in each hemisphere
is turned along the eastern coast from each of the
Cuap, II.) INERTION. 31
temperate zones towards the poles. These streams
on the eastern side of the ocean, flowing from the
temperate zones towards the poles, are under that
influence of change of latitude which tends to carry
them eastwards, and they must therefore tend to
follow the course of the coast, until, after sweeping
through the polar regions, they appear on the western
side of the ocean as streams flowing from the poles
towards the equator. And as on the western coast,
flowing towards the equator, they come under that
influence of change of latitude which tends to carry
them westwards, they must therefore tend to follow
the course of the western coast, until they meet the
streams flowing from the equator on that coast.
Thus the streams turned polewards from the tem-
perate zones, on the east side of the ocean, rejoin
their parent streams on the west side of the ocean,
forming continuous streams encircling each of the
polar districts of the ocean. And thus, therefore,
the ocean is divided, as far as its currents are con-
cerned, into four separate districts, each encircled by
a revolving current—an equatorial and a polar dis-
trict being formed on each side of the equator, as
shown in Plate VI.
Section II.—Hguatorial Counter-Currents.
We have, however, as yet, in this ocean, applied
only that action of westward pressure which results
from the difference in the relative forces of that
82 THE OCEAN. [Boox IL,
pressure acting along the different parallels of lati-
tude, leaving out of consideration altogether the
difference between the forces acting at the surface
and at the bottom of the ocean. Let us now con-
sider the effects of the opposing action of these latter
unequal forces. Their tendency is to cause the
great westward stream in the equatorial regions to
diverge from the equator on both sides; and there-
fore, that stream may be considered as consisting of
two separate portions, the one tending to run west-
wards and northwards, the other westwards and
southwards. And, therefore, on meeting with the
obstruction on the western side of the ocean, it is In
fact not one stream but two streams; each of which
streams must, on meeting with the obstruction, divide
to the right and left ; so that the left-hand division of
the northern and right-hand division of the southern
stream would meet and turn each other back east-
wards, as shown in Plate VII. And this current
running from west to east would, for whatever dis-
tance it might run, divide the northern from the
southern portion of the great equatorial current
running from east to west, and would to some extent
supply the diverging tendencies of that stream.
Thus the inequality between the forces of the
upper and under strata tends to cause a counter-cur-
rent to run eastwards, dividing the north from the
south equatorial district.
Mile haa TOL
Cwar. IL] INERTION.
co
co
Seorion ITI.—Jnelination of the Axis of Rotation.
But it is clear that the effects resulting from the
inequality between the forces of the upper and under
strata cannot possibly be such as to tend in any way
to obliterate or even to change the positions of the
districts shown in Plate VI. and just described in this
chapter ; for those districts are precisely analogous
to those which would be formed by a system of upper
and under currents if westward pressure were not
deflected by obstructions lying in its course. That
is to say, they are analogous to the polar and equa-
torial zones described in the second part of this
chapter and illustrated in Plate V. Those zones
“result from a necessary overwhelming of the lesser
forces of the lower strata by the greater forces of the
upper strata, in case of no obstruction occurring to
deflect westward pressure from its natural course.
And, in fact, since the deflection of that pressure
does not change the relation of the forces of the
upper and lower strata to each other, therefore the
fact of westward pressure being deflected by the
obstruction formed by coast-lines will not obviate
the necessity of an overwhelming, to a greater or
lesser extent, of the lesser forces of the lower strata
by the greater forces of the upper strata ; and there
must therefore be formed, notwithstanding the de-
flection of westward pressure, in every ocean, a
system of upper and under currents analogous to
D
34 THE OCEAN. [Boor II.
that exemplified in Plate V. And, since the de-
flection of westward pressure by coast-lines must
cause an overwhelming of the lesser forces of the
polar regions by the greater force of the equatorial
regions, there must therefore, in every ocean, be a
combination of these two systems of circulation.
That is to say, there must be a horizontal circula-
tion resulting from the overwhelming of the forces of
the polar regions by the force of the equatorial re-
gions ; and also a vertical circulation resulting from
the overwhelming of the force of the lower strata by
the force of the upper strata. As the one system
tends to cause each district to rotate round a vertical
axis, and the other system tends to cause it to rotate
round a horizontal axis, their combined action must
cause it to rotate round an inclined axis; and the
inclination of this axis will incline more towards
either a vertical or a horizontal line, according as
the relative force of the one or the other system of
circulation may preponderate in any district. Since
the currents west of the vertical axes conform to
those above the horizontal axes, and the currents
east of the vertical axes conform to those below the
horizontal axes, the inclination of the axes resulting
from their combined action must therefore be from
west at the bottom of the ocean to east at the surface,
as shown in Plate VIII. And, in this inclined cir-
culation, since the ocean must preserve its level, the
inclination of the axes necessitates an elongation of
op Sas
6 a
pi the
Bris
ile
m. nara i x
i
\
lL ied Ba
i. ies
bn Deb oe & O
F a Fa
sine
a) ‘ah Wks ‘
a ‘8.- is N i
Pi ae A me hs
q ial Fe
, 4 ¥
4
wt
rie) 3
We
' ‘
:
ey
A r
j
Cuar. II. } INERTION. 35
the circles of rotation in the direction in which the
axes are inclined. And, since this inclination of
the axes is from west at the bottom of the ocean
to east at the surface ; therefore, the elongation of
the circles of rotation is westwards from the axes
at the surface of the ocean, and eastwards from the
axes at the bottom of the ocean. And thus, instead
of the circles of rotation resulting from either the
horizontal or the vertical forces, their combined action
causes the revolving currents enclosing each district
to tend to describe ellipses of rotation.
Tt thus appears that, setting aside the contortions
caused by coast-lines, the combined action of the
forces of vertical and horizontal circulation gives
the currents which encircle each district a natural
tendency to revolve in elliptical courses.
Section [V.—Surface Currents within the Districts.
Let us now consider how the combined action of
these forces will affect the surface currents contained
within each district.
Let NWSE, in Plate I[X., figure 2, be a north
equatorial district.
Under the sole influence of the horizontal circu-
lation, the currents would all simply describe con-
centric circles of rotation round a central axis.
And, under the sole influence of the vertical cir-
-- culation, the entire surface of the district would
consist solely of currents running in parallel lines
D2
36 THE OCEAN. [Boox II.
from the equator; the circles of rotation being
completed by under currents flowing towards the
equator.
But, under the combined action of the forces
which tend to cause these systems of circulation, the
water which on the west of the district is turned
from the equator by the horizontal force, necessarily
comes into conflict with that tending to diverge all
along the line of the equator under the action of
the vertical force. The streams oR, in figure 1,
diverging under the action of the vertical force, must
then be borne back by that under the action of
the horizontal force ABC, until, by the accumulation
of the streams oR, they form a stream equal in force
to ABC.
Let the point x, in figure 2, be the meeting-point
of the opposing streams thus formed.
Then the stream ABC meets the stream OR at Xx;
and from the meeting-point at x the offset p falls
into the course of the rotation of the district swNE;
but the offset E, running in the opposite direction,
must come into conflict with that course of circu-
lation.
Let y be the point at which the stream Er meets
the stream SWNE.
Then from the meeting at y the offset F falls into
the course of rotation SWNE; but the offset 4,
running in the opposite direction, must come into
conflict with the course of rotation $ WN E.
Cuap. II.) INERTION. 37
Let z be the point at which the stream H meets
the stream S W NE.
Then from the meeting at z the offset 1 falls into
the course of rotation SWNE; and the offset R falls
into the course of the stream or, forming an un-
broken course of circulation, which may be termed
the natural course of the surface currents within each
cistrict.
Since the streams ABC and oR both tend east-
wards in their course from the equator, and the stream
EH tends westwards in its course to the equator, the
latter must, sooner or later, after leaving the point x,
be thrown against the stream ABC, and then be
forced eastwards, running counter to that stream as
far as the point at which the stream or diverges
from it.
Section V.—Vertical Circulation within the Districis.
Now the axis of this district being inclined as
before described, it is clear that about the central
_ parts of the district an under current must be run-
ning southwards, whilst the surface above it is flow-
ing northwards. Let us consider how this is effected.
The point x (Plate IX., figure 2), as already de-
scribed, is that at which the opposing streams ABC
and 0 R meet with equal force as surface currents.
But, since the stream ABC is that which is de-
flected by the coast-line, which deflects the whole
mass of water from the surface to the bottom of the
38 THE OCEAN. [Boor IT.
ocean ; whereas the stream 0 R results from the yield-
ing of the lesser force of the lower strata to the
greater force of the diverging tendency of the upper
strata ; therefore, although at the surface of the ocean
the stream ABC is effectually resisted by the stream
OR, it will nevertheless meet with no such resistance
in the lower strata ; but, in proportion as the force
of the stream oR diminishes beneath the surface, —
it will be underrun by the stream aBc; and at the
bottom of the ocean, not only will the stream a BC
meet with no resistance from or, but under the
action of the vertical forces of circulation, its south-
ward course as an under current will be accelerated
until it completely underruns oR, and reappears at
the surface in the equatorial regions.
Section V1.—Under-Currents within the Districts.
Thus, whilst opposing the stream o R on the sur-
face of the ocean, the stream A BC joins the course of
the streams flowing towards the equator at the bot-
tom of the ocean. But though a Bc joins the course
of those streams at the bottom of the ocean, they are
thrust away by it from the western part of the dis-
trict just as the streams oR are on the surface ; and
therefore by this conflicting action a counter-current
must be formed at the bottom of the ocean, running
counter to the stream NESW, under the axis of
rotation inversely as EH runs counter to it on the
surface.
—
Cnap. I.) INERTION. 39
Section VII.— Difference in the Action of Counter-Currents
in Equatorial and Polar Districts.
The conflicting action of the forces of vertical
and horizontal circulation in the polar districts must
tend to form counter-currents analogous to those of
the equatorial districts ; but in them those currents
will tend to run against the central streams instead
of against that which encircles the district.
Section VIII.—Connecting Currents between Equatorial and
Polar Districts.
Referring to Plate VI., it will be seen that the
equatorial stream A BC meets a polar stream pouring
down upon it from the north in the neighbourhood
of c; so that, in fact, as the stream ABC opposes OR
on one side, it also opposes the polar stream EC
(Plate VI.) flowing from the opposite direction on the
other side. The southward course of the polar
stream EC (Plate VI.) is obstructed on the surface
of the ocean by the equatorial stream aBc; but we
have seen that,in consequence of the action of the
vertical force of circulation, the equatorial stream
ABC offers no obstruction to the southward course
of the polar stream in the lower strata. The lower
strata of the polar stream Ec (Plate VI.) must there-
fore continue their course southwards as an under
current ; to some extent joining the lower strata of
the stream ABC as it underruns the course of the
surface stream OR, in the opposite direction, and
40 THE OCEAN. [Book II,
rising to the surface ini the equatorial regions under
the action of the force of vertical circulation ; which
latter necessitates a circulation from the equator at
the surface and towards the equator at the bottom of
the ocean in the central parts of the district swN bk,
in Plate IX., just as the horizontal force necessi-
tates a circulation from the equator on the west and
towards the equator on the east side of the district.
Thus a constant circulation between the equa-
torial and polar regions is caused, for as the polar
stream ECD is carried southwards, displacmg the
stream ABC in the lower strata, an equal volume of
the stream ABC must be thrown into the course of
the stream C DE in the upper strata.
Section [X.—Subdivision of Districts.
The course of the currents which we have
described in connection with Plate IX. we have
termed the natural course of the currents within the
district; but in fact it is clear that instead of the
horizontal force of circulation being contained in one
stream and meeting the vertical force, also in one
stream, as at x, there might, by the horizontal force
being partially deflected by obstructions in its course
before reaching the west side of the ocean, be many
such meeting-points formed within a district, all
being nevertheless of a similar nature: but, since the
number of these meeting-points in any district must
be determined by the configuration of the coast-lines
Cuapr. IL. ] INERTION. 41
and bottom of the ocean, this is a question to be con-
sidered in the practical investigation of the move-
ments of the ocean.
PART EV.
EFFECTS IN THE OCEAN AS IT IS.
In the actual configuration of land and water on
the surface of the earth, there are, as far as westward
pressure is concerned, two great force-creating re-
gions in the ocean—one the equatorial region of the
Atlantic, the other that of the Pacific and Indian
Oceans. The Pacific and Indian Oceans, being con-
nected in the force-creating regions, must be re-
garded as subdivisions of the same district: and, as
poimted out in the preceding part of this chapter,
barriers of islands, or ridges over which the water is
comparatively shallow, form other subdivisions, theo-
rectically similar, though not so distinctly marked as
that which forms the Indian Ocean.
In the northern hemisphere, the comparatively
unimportant opening of Behring’s Strait being the
only communication between the Pacific and Atlantic
Oceans, we have two oceans which, as shown in the
chart on Plate II., should each contain an equatorial
and a polar district of currents analogous to those
whose formation has been described in Part III. of
this chapter, and illustrated in Plate VI.
49 THE OCEAN. [Book Il,
The basin of the Arctic Ocean thus forms a part
of the Arctic district of the Atlantic Ocean: and,
therefore, the stream which on the eastern side of
the Atlantic flows northwards from the temperate
zone enters the Arctic Ocean on the eastern side of
the Atlantic, and flows from the Arctic Ocean on the
western side of the Atlantic. And, in consequence
of the inclination of the axis of the district before
explained, the stream which enters the Arctic Ocean
passes under the axis, and that which flows from the
Arctic Ocean passes over the axis; and therefore, all
along the coast which lies east of the entrance from
the Atlantic to the Arctic Ocean, the surface water
sets from the coast ; and, all along the coast which
lies to the west, the surface water sets against the
coast : this is so because the stream which enters
the Arctic Ocean is naturally an under current, and
is forced to the surface by the obstruction formed
by coast-lines, as shown in Plate X.
In the southern hemisphere the oceans communi-
cate freely through the comparatively wide and deep
expanse of water lying between Cape Horn and the
South Shetlands in the one direction, and in the
other direction the communication beyond the tropics
is still more free. Besides this, there is a vast extent
of earth’s surface in high southern latitudes which
has not yet been explored, and which may therefore,
as far as our knowledge from actual observation is
concerned, consist of either land or water. Since,
«
Be ef
Lbrw thrid dry Jenne © Ala |
prow Wis Cu .
Note.
The normal circulation of the polar regions which the Earths rotation tends to cause is north eastwards towards the pole in the under strata and south westwards fiom the pole on the
surface of the ocean.But the chart was drawn in 1866 on the supposition that the flow of water northwards from the Atlantic in the under stvata,not meeting an equal flow towards the pole
from the opposite direction,flows onwards to rise to the surface against the northern shores of Asia,and the red and blue arrows have now (1877) been added in accordance with that
supposition.the extent to which the normal circulation of’ the polar region is deranged by the ee of the influx of water from the Adantic side is a question to be determined by
practical observation.The letters refer to PlatesIX and I[the red being under currents, and the blue surface currents,as in the latter Plate. ae m
The normal surface pressure from the north east may be the preponderating’ force in higher latitudes than have yet been explored, but it is not the preponderatmag force m the Arctic
Ocean, for it tends to carry the ice of the Paleocrystie Sea westwards.
Baw* Weller. *
London.Longmane & Cx.
W.L.Jordan
Cuar, IL.) INERTION. 43
however, the Antarctic voyages of discovery under
Sir James Ross and Captain Wilkes have shown the
existence of a considerable tract of land in high
southern latitudes, I will proceed with this _theo-
retical consideration of the action of vis-inertiz
under the supposition of an Antarctic Continent of
considerable extent existing in the south polar
regions.
Let the streams marked Atlantic and Pacific in
Plate XIa. be streams flowing towards the Antarctic
Continent £, from separate equatorial regions. These
streams have a tendency to run eastwards in their
course from the equator towards the pole. In their
course towards the pole they are obstructed by the
continent E. On meeting with this obstruction, each
stream must divide right and left; one portion of
each stream being turned westwards, and the other
portion of each eastwards. The westward division
of each stream must, as it flows on its course, meet
the eastward division of the other stream: so that
the Atlantic and Pacific streams meet each other in
both directions on opposite sides of the Antarctic
Continent. From each of these meeting-points, the
streams must branch off in opposite directions: so
that one branch from each meeting-point must fall
against the Antarctic Continent, and the other branch
from each of the two meeting-points must flow north-
wards towards the equator.
Let any points 4 and B, on opposite sides of the
A4 THE OCEAN. [Boox II,
Antarctic Continent, be the points at which the
Atlantic and Pacific streams meet.
Then in each ocean a stream flowing southwards
and eastwards from the equatorial regions meets a
stream flowing westwards and northwards from the
polar regions, as shown in the plate: and, from the
meeting-point in each ocean, one branch flows north-
wards towards the equator, and the other branch
sweeps the shores of the Antarctic Continent, and
then forms the stream which flows westwards and
northwards from the polar regions in the opposite
ocean.
The Antarctic Continent must cause a subdivision
of each of the Antarctic districts as shown in Plates
XI. and OWE because the stream turned south from
each meeting-point must redivide on striking the Ant
arctic coast, and then the portions turned eastwards
must recoil upon their parent streams, forming separate
districts of rotation ; and forming also, at the pomts
c and p at which they meet the parent streams, an
interlacing of currents with revolving fragments
similar to that which occurs where a polar stream
rejoins the equatorial stream from which it has its
source, as at F and G.
The meetings at a and B are meetings of inde-
pendent streams, from separate force-creating regions,
and therefore they mutually repel each other until
an equilibrium of force is established between them.
But the meetings at Cc, D, F, and G are formed by the
Caar, IT.] INERTION. 45
recoiling of branch streams upon the parent streams,
through which they derive the force which keeps
them in motion; and each of the branch streams
must therefore, as far as the action of the horizontal
force of circulation is concerned, be gradually re-
drawn into the course of its parent stream through
a series of rebounds against it.
From the arguments contained in this chapter, it
appears that, as far as the currents resulting from
axial rotation are concerned, the ocean is divided
into two divisions : the one division consisting of
currents which are kept in motion by force created
in the equatorial regions of the Atlantic Ocean ; the
other, of currents which are kept in motion by force
created in the equatorial regions of the Pacific and
Indian Oceans. And these divisions being analogous
to each other—each being subdivided into equatorial
and polar districts analogous to each other—form
together the ten principal districts shown in the
chart on Plate II. : namely—
Two North Equatorial,
Two South Equatorial,
Two Arctic, and
Four Antarctic districts.
This subdivision of the Antarctic districts de-
pends, as before stated, on the existence of an Ant-
arctic Continent about the south pole. And I have
described the action of vis-inertiz in those regions
under this supposition, because the information gained
46 THE OCHAN. [Book Il.
in the voyages of discovery already alluded to, and
also the actual currents, as far as their course has
been ascertained, appears to be in accordance with
it. The correctness of this is, however, a question
to be determined in the practical investigation of
the subject.
47
CHAPTER III.
EFFECTS OF THE EARTH’S ONWARD MOTION.
PARTE
EFFECTS OF ORBITAL MOTION.
Accorp1né to the foregoing the action of vis-inertix
in causing currents results from inequality of oppos-
ing forces; and therefore, as regards the orbital
motion of the earth, since its velocity is the same at
all parts of the earth, it is obvious that its action in
causing currents can result only from the greater
facility with which water yields to the action of vis-
inertiz in one part of the ocean than in another part.
And, that the water tends to yield more readily in
some parts of the ocean than in others to the action
of any force which may tend to set it in motion, may
be illustrated by the well-known phenomenon that
in any river or stream the water at the surface of
the deep and central parts tends to move more
rapidly than that in shore or at the bottom of the
stream ; because the friction of the ground over
which it runs checks the progress of the water,
leaving that at the surface of the deep and central
parts of the stream comparatively free to run its
48 THE OCEAN. [Boox II.
course under the action of the force of gravitation.
This force of gravitation acts with equal force upon
all the particles of the stream, but those at the sides
and bottom of the stream are checked by friction,
which is therefore a force acting in opposition to that
force of gravitation which tends to draw the stream
onwards; and it is because the particles at the
surface of the deep and central parts of the stream
are comparatively free from the opposing action of
this friction that they are drawn onwards more
rapidly by the force which impels the stream on its
course. We need not here investigate the abstract
nature of the force which causes the particles near
the sides or bottom to resist more than those at the
surface of the deep and central parts of the stream,
the force which tends to set them equally in mo-
tion. We are here only concerned with the fact
that it is a force which opposes the action of any
force which may tend to set the water in motion.
It is for the present sufficient that the force de-
scribed as friction tends at the sides and bottom
of the ocean to check the action of vis-inertize in
those parts, leaving it comparatively unobstructed
at the surface of the deep and central parts of the
ocean; and that therefore the unobstructed ac-
tion of vis-inertize at the surface of the deep and
central parts of the ocean, being a greater force,
must overwhelm, to a greater or lesser extent, the
lesser forces near the shores and bottom of the ocean.
Cuap, ITI.) INERTION, 49
Therefore the action of vis-inertia must tend to
circulate the water by a stream running through the
deep and central parts of the ocean in the opposite
direction to that of the earth’s motion, and along the
shores in the direction of the earth’s motion.
But as regards the action of vis-inertiz resulting
from the axial rotation of the earth, not only is there
this difference in the effective force acting in dif-
ferent parts of the ocean, proportioned to the relative
freedom from friction; but also, besides this, the
actual velocity of the motion is not the same in all
parts of the ocean, but is greater at the equator, de-
creasing gradually towards the poles ; and is greater
at the surface, decreasing gradually towards the
bottom of the ocean : and therefore, the actual action
_of vis-inertiz is greater in equatorial than in polar
regions, and greater in the upper than the lower
strata of water, in proportion with the difference in
the velocity of the motion of axial rotation in dif-
ferent latitudes, and at different depths of the ocean.
And thus, therefore, notwithstanding that the velocity
of the orbital motion of the earth, as also probably
that of the motion of the solar system, is far greater
than the velocity of the motion of axial rotation at
any part of the earth’s surface, by the latter motion
a far greater amount of force effective in causing
ocean currents may—indeed almost obviously must
—be brought into play than can be brought into
play by the orbital motion of the earth, or by any
E
50 THE OCEAN. [Boor It.
simply onward motion of the earth through space.
And therefore, in consequence of the difference in
the velocity of rotation in different latitudes and at
different depths of the ocean, the current-creat-
ing action of vis-inertie brought into play by the
axial rotation of the earth is the great paramount
force ; and that which is brought into play by the
orbital motion of the earth—as also that brought
into play by the motion by which the earth is carried
along through space with the solar system—simply
causes deviations or variations from that which
would be the course of the currents of the ocean if
under the sole influence of the axial rotation of the
earth. |
We have seen that the westward pressure result-
ing from the axial rotation of the earth is fixed and
unchanging in its action. But as regards any in-
fluence which may result from the orbital motion of
the earth, such influence will obviously be not only
itself a variable influence, acting at one season of the
year with greater force than at another season ; that
is, acting with its greatest force in December, when
the speed of the earth in its orbit is fastest, and with
its least force in June, when that speed is slowest ;
all intermediate gradations of speed intervening :
but also, it will be constantly changing its direction
on any given point of the earth’s surface, for at
one season of the year the northern hemisphere, and
at another season the southern, is inclined in the
oe sis 4
--—
eae ay ba
Cuar, III.) INERTION. 51
direction in which the earth moves in its orbit ; and
also, on the side of the earth turned from the sun
the motion of axial rotation is in the same direction
as that in which the earth is moving in its orbit, and
on the opposite side of the earth in the reverse direc-
tion; so that in March at midday this force acts
about ENE.-wards, and at midnight about WNW.-
wards ; whereas in September, at midday it acts
ESE.-wards, and at midnight WSW.-wards; all
intermediate degrees of variation lying evenly be-
tween the extremes of daily and annual variation
respectively. Thus, this force always acts eastwards
in the daytime, and westwards at night, and always
northwards in March and southwards in September ;
oscillating continually backwards and forwards be-
tween the extremes of daily and annual variation
respectively. The annual variation is confined within
about four points of the compass; that is, between
233° north and 232° south, and the daily variation
extends over about fourteen points of the compass ;
that is, from 664° east to 663° west, the greatest
combined variation being from any one point to the
opposite point of the compass, that is, the sixteen
points.
In the annual variation this force turns more and
more northwards from the 28rd of September to
the 20th of March, and then from the 20th of March
to the 23rd of September it turns more and more
southwards. And in the daily variation the change
BE?
OX
bo
THE OCEAN. {Boox Il.
from an eastward to a westward direction occurs at
6 p.m., and that from a westward to an eastward
direction at 6 A.M.
PART II.
EFFECTS OF THE MOTION OF THE SOLAR SYSTEM.
As regards the motion of the Solar System through
space, of which a series of astronomical observations,
originated by Sir William Herschel, has given us a
partial knowledge ; although, reasoning from analogy,
any influence resulting from that motion will pro-
bably be among the forces which are subject to
cyclical changes, yet, considering the enormous periods
embraced in those cycles, the action of such forces
may, as far as our present purposes are concerned, be
regarded as fixed and constant at all points of the
surface of the earth.
We have not, however, in this case, a knowledge
of the motion from which to deduce effects, but the
motion itself must be demonstrated by induction
.from its effects, if, reasoning from analogy, the
existence of effects consistent only with some as
yet unknown motion be demonstrated. And also it
must be observed that any motion which may thus
be demonstrated by the action of vis-inertie does
not necessarily indicate simply a motion of the Solar
System ; for, as far as the evidence deducible from
Onap. III. ] INERTION. 53
the action of vis-inertiw is concerned, the motion
demonstrated might be the average result of a com-
plication of various motions in different directions.
It is obvious that since we have no definite @ priori
knowledge of such motion, we cannot do more than
point out what the different possible effects of that
motion might be ; and if, after determining the effects
of the rotation of the earth on its axis, and its mo-
tion in its orbit round the sun, we find in fact such
deviations from the effects which those motions
should cause as are in accordance with any one of
the presumable motions of the Solar System through
space, we shall then, from those effects, obtain a
knowledge of the motion which causes them. And,
in investigating the action of vis-inertiz, it is not
necessary to decide whether the motion demonstrated
be a simple motion of the Solar System, or the
average of acombination of various motions of which
that system may partake.
If the course of this as yet unknown motion of
the earth through space be in the plane of the
ecliptic, it will then at one period of the year be in
conjunction with the orbital motion of the earth, and
at the opposite period of the year in opposition to
that motion ; gradually changing in the course of
each year from complete conjunction to complete
opposition, and again from opposition to conjunction. ,
So that, apart from a knowledge of such motion,
effects of vis-inertiz observed in the ocean at any
54 THE OCEAN. [Boox I.
one period of the year would appear inconsistent
with effects observed at any other period of the year.
Tf, on the other hand, the course of this unknown
motion be in the line of the poles—then, if in the
direction of the north pole, the action of vis-inertiz
would appear southwards at the surface of the deep
and central parts of the ocean, and northwards along
the shores ; and if in the direction of the south pole,
then its action would appear northwards at the sur-
face of the deep and central parts of the ocean, and
southwards along the shores.1 And the action of vis-
inertizee will deviate more or less from the courses
here described, according as the line of motion may
deviate more or less from the line of the poles, or
from the plane of the ecliptic.
It is evident that by the action here explained a considerable
amount of warm surface water might be transferred across the
equator, counterbalanced by a flow of cold water in the under
strata. Mr. Croll points out that if oceanic circulation were
caused by differences of temperature it would tend to equalise the
temperature of the opposite hemispheres, whereas if caused by
the winds it would tend to increase any existing difference. And
to this latter action he attributes alternate glacial epochs in the
northern and southern hemispheres. As a circulation caused by
vis-inertie might have that same effect, the suggested glacial
epochs are not a valid argument in favour of the circulation being
caused by the winds rather than by vis-inertie. This subject is
further discussed in Chapter IV. of The New Principles of Natural
Philosophy.
BOOK II.
THE ABSTRACT NATURE OF THE FORCE WHOSE
QURRENT-CREATING ACTION IS DESCRIBED IN |
BOOK ILE.
VIS-INERTIA& AND GRAVITATION.
or
~s
CHAPTER IV.
GRAVITATION AND VIS-INERTIZ ARE CONVERTIBLE
TERMS AS FAR AS THE MOVEMENTS OF THE OCEAN
ARE CONCERNED,
Let us now proceed to consider what the forces
whose action we have described are in their abstract
nature, and what relation they bear to the forces
which cause the tides.
According to Kepler’s first law of gravitation,
enforced by Newton’s demonstrations, the force of at-
traction proceeding from any body in space decreases
in proportion as the square of the distance from which
it acts increases ; and if this be so, then, since the
superficies of spheres increase in proportion as the
squares of their radii increase, therefore, the force of
attraction proceeding from any centre of gravitation
must be exactly equal in the superficies of all spheres
described from that centre of gravitation ; and,
therefore, though the relative force of that attraction,
as regards other forces of attraction, must decrease
with an increase of distance from the centre from
which it proceeds, and a decrease of distance from
other centres of attraction, and the individuality
of its effects be overwhelmed by being rendered
58 THE OCEAN. [Boox TIL.
comparatively infinitesimal in comparison with the
greater force proceeding from other centres of attrac-
tion ; it must nevertheless, of necessity, be a power
acting throughout the universe, modifying more or
less the effects of other forces of gravitation.
If this be not so, then the law of gravitation
above mentioned is not true ; for that law is an effect
necessarily resulting from this as a cause. They are
inseparable as cause and effect. It is the fact of
gravitation being of the nature described which
necessitates that the force of attraction proceeding
from any power of gravitation must be inversely as
the square of the distance from which it acts. And
since this law could no more exist without gravita-
tion being of the nature above described than gravi-
tation could be of that nature without causing this
law, it must be admitted that any given particles
of the ocean are acted upon by forces of attraction
proceeding from every power of gravitation in the
universe.
Let us suppose those particles to be at any given
time or place in the position in which the joint action
of all powers of gravitation tends to hold them.
The particles in question are held by the earth’s
gravitation, as well as by universal gravitation ; and
therefore, when the earth moves it tends to draw
those particles with it: but, since those particles are
in the position in which universal gravitation tends
to hold them, the action of the earth is, therefore,
Cup. IV.] GRAVITATION AND INERTION, 59
in the opposite direction to that of the combined
action of all other forces of gravitation. Thus, as
the earth moves, tending to carry the particles in
question with it, the action of the foreign force of
gravitation necessarily tends to draw the particles in
exactly the opposite direction to that in which the
motion of the earth tends to carry them.
This latter is precisely the action of vis-inertiz
which we have described in the preceding Book ;
for those particles of the fluid on the surface of the
deep and central parts of the ocean, being the least
closely held to the surface of the earth, are most
free to move in the direction in which the foreign
force of gravitation tends to draw them ; and those
particles which, in consequence of their position, are
more closely held to the earth’s surface, and there-
fore offer more resistance to the action of the foreign
force of gravitation, being under the dominion of
the earth’s power of gravitation, are by that power
drawn into the positions vacated by those set in
motion (in relation to the surface of the earth) by
the foreign force of gravitation : and thus, as long
as the motion which causes this opposing action of
gravitation lasts, a constant circulation is effected.
- The opposing forces are—the earth’s power of gravi-
tation acting in one direction, and the combined
action of all other powers of gravitation acting in the
opposite direction.
Thus, the currents through the deep and central
€O THE OCEAN. -[Boox III.
parts of the ocean are caused by the action of the
foreign force of gravitation, just as the counter-
currents are caused by the earth’s gravitation. The
ocean, as a Whole, must maintain its position in re-
lation to the conflicting forces. And if, on the one
hand, it may be said that the vis-inertie of the
ocean, opposing the earth’s tendency to carry it from
its position, causes a current in one direction, and
that the earth’s gravitation draws counter-currents
in the opposite direction ; so also may it, with equal
propriety, be said that the vis-inertiz of the ocean
opposes the action of the foreign force of gravitation,
and, as the attraction of the latter tends to draw it
from its position, and draws a current through those
parts of the ocean most free to follow its attraction, _
the vis-inertiz of the ocean maintains its position
as a whole by means of counter-currents through
those parts of the ocean which are least free to fol-
low the attraction of the foreign force of gravitation. _
That which is the vis-inertiz current, in relation to
the earth’s gravitation, is the attraction current in
relation to the foreign force of gravitation ; and those
which are attraction currents in relation to the earth’s
oravitation are vis-imertie currents in relation to the
foreien force of gravitation.
Thus the vis-inertiz which draws the currents
westwards in the equatorial regions is, in fact, at-
traction proceeding from the joint action of all foreign
powers of gravitation; and the earth’s power of
Cuap. IV.] GRAVITATION AND INERTION, 61
gravitation maintains the equilibrium of the ocean
as a whole, by drawing an equal volume of water
eastwards through the temperate zones : but, in fact,
this latter movement, when considered in relation to
the joint action of all foreign powers of gravitation,
is just as truly a movement resulting from the vis-
inertiz of the ocean.
Vis-inertiz and gravitation are, therefore, as far as
the arguments hitherto adduced are concerned, con-
vertible terms. Any effect termed an action of vis-
inertiz in relation to any given power of gravitation,
is, in fact, the direct result of some other power of
gravitation ; and, inversely, any effect caused directly
by any given power of gravitation is an action of
vis-inertiz in relation to some other power of gravi-
tation.
The action of vis-inertiz in the ocean and atmo-
sphere can, therefore, with no more reason be denied
than the action of gravitation towards foreign bodies.
To study the movements resulting from the action
of gravitation, or to study those resulting from the
action of vis-inertie, are therefore simply different
modes of studying the same phenomena. A move-
ment of the waters of the ocean caused by the direct
action of the sun’s power of gravitation, tending to
draw the ocean towards it, is, therefore, an action of
vis-inertie in relation to the joint action of all other
powers of gravitation : and the counter-action of vis-
inertie, by which the ocean maintains its position in
62 THE OCEAN. [ Boox III.
relation to the conflicting forces, is just as certainly
the direct action of those other powers of gravitation,
tending to draw the ocean towards the position in
which the combined action of their gravitation tends
to place it.
Therefore, as, when the earth’s gravitation is
considered in opposition to all other powers of
gravitation, the water drawn westwards through
the equatorial regions by the latter is replaced by
an equal volume simultaneously drawn eastwards,
through the temperate zones, by the former power,
so also, when the sun’s gravitation draws a volume
of water to the side of the earth turned towards the
sun, the joint action of all other forces of gravitation
draws an equal volume of water in the opposite
direction, thus preserving the equilibrium of the
ocean in relation to the conflicting forces.
In the consideration of the action of gravitation
in causing the tides of the ocean, we may, therefore,
consider the action of the sun and of the moon, each
singly ; and that of all the other powers of gravita-
tion jointly, under the title of astral gravitation,
which is sufficiently appropriate, though the gravita-
tion of the planets is included in it.
This force of astral gravitation may be defined as
the combined action of the gravitation of the universe,
excepting the force whose action it opposes. And
vis-inertiz is universal gravitation.
Let us now reconsider the nature of the forces
Cuar, IV, ] GRAVITATION AND INERTION. 63
brought into play in the ocean and atmosphere by
the motions of the earth.
As regards the earth’s onward motion through
space, we have shown that, in consequence of the
action of friction along the shores and bottom of the
ocean, vis-inertiz causes a current along the surface
of the deep and central parts of the ocean, where it
is comparatively free from the opposing action of the
force termed friction, in the ordinary acceptation of
the term ; whilst counter-currents return inshore to
the source of action. In this case the vis-inertiz,
which drives a current through the surface of the
deep and central parts of the ocean in the opposite
direction to that of the motion of the earth, is astral
gravitation drawing those particles which, in conse-
quence of their position in the ocean, are most free to
follow the influence of its attraction, towards the
position which its power of gravitation tends to give
them. And the friction which opposes the force of
astral gravitation along the shores and bottom of the
ocean is the earth’s gravitation, which, in consequence
of the particles in those parts of the ocean being
more under its dominion than those at the surface of
the deep and central parts of the ocean, draws them
into the position which it tends to give, and conse-
quently carries them to those positions in relation
to the surface of the earth which the particles most
under the dominion of astral gravitation tend to
vacate.
64 THE OCEAN. [Boox III,
And, as regards the earth’s axial rotation east-
wards, we have shown that, in consequence of the
greater velocity of rotation in equatorial regions, vis-
inertiz causes a current westwards in those regions,
counter-currents running eastwards through the
zones of lesser force in higher latitudes north and
south. In this case, the vis-inertie acting in equa-
torial regions with greater force than in higher
latitudes—in proportion with the greater velocity of
the motion of rotation in those regions compared with
that in higher latitudes—is the force of astral gravi-
tation, which holds all particles equally to the posi-
tion which it tends to give them ; but as the surface
of the earth in the equatorial regions moves more
rapidly than in higher latitudes, the particles in those
regions have a great relative tendency in the oppo-
site direction to that of the surface on which they
rest ; because the surface runs with greater velocity
from under the particles as they move towards the
position which astral gravitation tends to give them.
And over those parts of the surface of the earth
where the action of astral gravitation is less, the
particles, being relatively more under the dominion
of the earth’s gravitation, are drawn into the positions
in relation to the surface of the earth which the par-
ticles most under the dominion of astral gravitation
tend to vacate. Thus, as astral gravitation gives the
water a relative motion in the opposite direction to
that of the surface of the earth in the equatorial
Cap. IV.) GRAVITATION AND INERTION. 65
regions, the earth’s eravitation causes an equal volume
to outrun the surface in higher latitudes, and thus
the equilibrium of the ocean, as a whole, is main-
tained in the position in which universal gravitation
tends to hold it.
Thus, then, the whole system of oceanic circula-
tion which we have shown to result from the action
of vis-inertize—in consequence of the greater force
brought into play in those parts of the ocean which
are moved with greatest velocity overwhelming the
lesser forces in other parts of the ocean, and in con-
sequence of the force acting along the surface of the
deep and central parts of the ocean overwhelming
that acting along the shores—is just as truly the
effect of the opposing action of astral and terrestrial
gravitation, in consequence of the earth in its motion
tending to carry the particles of the ocean from the
positions in which universal gravitation tends to hold
them.
' See also Chapter XXI., Proposition XX VIT.
66 THE OCEAN. [Boox III.
CHAPTER V.
THAT MATTER, BY VIRTUE OF AN INHERENT FORCE
OF INERTION, ENDEAVOURS CONSTANTLY TO BRING
ITSELF TO A STATE OF REST.
WE have seen that, as far as their action in the ocean
is concerned, vis-inertize and gravitation are conver-
tible terms, according as a tendency to move to or
from any given power of gravitation is referred to.
It must not, however, be assumed from this that they
are really in their abstract nature identical.
Newton defines vis-inertiz as ‘an innate force of
matter, or power of resisting, by which every body,
as much as in it lies, endeavours to persevere in its
present state, whether it be of rest, or of moving
uniformly forwards in a right line.’ t
Now, that any bodies have an innate tendency to
move uniformly forwards in a right line is mere
assumption. And this has been assumed to be so
because it was found that the sun’s gravitation is ,
constantly tending to draw the planets towards it ;
but as they do not approach the sun, it is clear that
an equal force tends to carry them in the opposite
1 The Principia, Book L., Definition III.
Cuap. V.] GRAVITATION AND INERTION, 67
direction ; ayd this force, acting in opposition to
solar gravitation, is assumed to be an innate tendency
in the planets to move in straight lines, from which
they are constantly deflected by the gravitation of
the sun. This is mere assumption. It is not based
on any known phenomena.'
It is said that in the simple ease of a ball, thrown
in the air or rolled-on the ground, being set in
motion, its vis-inertie tends to keep it in motion
until it is stopped by the resistance of the air or
the ground against which it runs. This is an error.
It is not the vis-inertie of the ball which tends to
keep it in motion. It is vis-inertie, and vis-inertie
only, which stops, and must in time stop the course
of that ball. Vis-inertie resists the motion of the
ball from first to last. And it is because the force
which set the ball in motion is not continuously
acting, and because vis-inertiz is continuously act-
ing, tending to bring it to rest, that, no matter what
the original velocity of the ball may be, its motion
must at length be spent.
If the force which set a body in motion continue
to act constantly upon it, the motion will be con-
tinued ; but if the motive force be removed, then vis-
inertiz, so far from tending to keep the body moving
onwards in the motion communicated to it, must and
1 The origin of this ‘assumption’ is more fully explained in
Chapters X1I., XVI., and IX. of The New Principles of Natural
Philosophy.
68 THE OCEAN. [Boox III.
will, sooner or later, according to circumstances,
bring the body to a state of rest.
In the case of the ball just mentioned, the ball is
taken from a state of rest ; a certain amount of force
is requisite to take it from that state of rest, and that
force is spent to overcome the vis-inertiee of the ball ;
still more force is requisite to hurl the ball into the
air or along the ground. Here it may be said that,
but for the friction of the air or ground, the ball
would move continuously. This is an error. But
even supposing it were only this friction (unassisted
at all by the vis-inertize of the ball) which stops its
motion, even then, since this friction is the com-
munication of motion to surrounding particles whose
vis-inertize resists the motion, it is the vis-inertiz of
matter which brings the ball to rest.
Let us, however, consider this case on its merits,
apart from any previous arguments. The ball is
thrown through the air. And the reason why the
air tends to resist and check the motion of the ball
is because the ball has to displace particles of the
air in its passage ; and as motion from the ball is
communicated to those particles, less in proportion
remains in the ball. This is the same if the ball be
rolled along the ground. ‘The particles it strikes or
touches, it tends, more or less, to move; but the
vis-inertiz of those particles tends to keep them
at rest, and therefore resists the effort of the ball
to move them ; and thus the ball and the particles
a a
Cuar. V.] GRAVITATION AND INERTION. 69
of air or earth set in motion by the ball are at length
brought to a state of rest by the vis-inertiz of matter.
Now there is certainly no more reason for suppos-
ing the vis-inertize which brings the whole to a state
of rest to reside in the particles of air and earth
set in motion by the ball than in the ball itself set
in motion by the hand. In fact, a certain amount
of force is exerted to overcome the vis-inertiz of
matter, and an amount of motion in the ball and
particles of air and earth which it sets in motion is
caused in proportion to the motive force exerted ;
but, as the motive force is not continuously exerted,
it must at length be exhausted, and the bodies set in
motion be brought to a state of rest by the vis-inerti
of matter.
It thus appears that if in any body whatsoever
there be not some motive force acting continuously
to keep it in motion, its own inherent property of
vis-inertiz must (even if no other cause arise), in the
course of time, bring it to a state of rest.
Let us, however, proceed to consider on what
grounds and by what arguments the motion of the
earth round the sun has been asserted to be main-
tained by an innate property of vis-inertie, in con-
sequence of which it tends to move uniformly for-
wards in a straight line. The force which keeps it
in motion is said to be its innate property of vis-
inertice ; and the force which resists that of solar
attraction, and thus keeps it at its mean distance
70 THE OCEAN. [Boox II,
from the sun, is said to be the tendency of its vis-
inertiz to carry it uniformly forwards in a straight
line.’ The argument, as given by Newton in The
System of the World, is as follows :—
1 The first law of motion was invented after the discovery of
the motion of the earth ; and was invented for the express purpose
of explaining the earth’s continuous motion.
No proof of that law can be given by physical phenomena
about the earth.
Newton accepted it as a necessity for the purpose of explaining
not only the continuous motion of the earth, but also its resistance
to the centripetal force.
This latter was the purpose which made the law most imme-
diately requisite to him. The New Principles of Natural Philosophy,
p. 235.
Kepler first asserted the onward motion of the earth to be due
to an axial rotation of the sun. But he then knew nothing of
the laws even of the direct action of gravitation, and had not the
slightest idea of the revolving action of gravitation exerted by the
sun.
When Newton discovered the laws of gravitation, Kepler's idea
was abandoned by every philosopher, as being incompatible with
the laws of gravitation as far as they were then understood.
Newton himself says, regarding this point: ‘Though gravity
might give the planets a motion of descent towards the sun,
either directly or with some little obliquity, yet the transverse
motion by which they revolve in their several orbs, required the
Divine Arm to impress them according to the tangents of their
orbs.’ !
And elsewhere he says: ‘I do not know any power in Nature
which would.cause this transverse motion without the Divine
Arm.’ ?
It was for the purpose of explaining this ceaseless motion of
the earth without loss of velocity, that the idea was first conceived
of matter having, when once in motion, an inherent tendency to
continue perpetually in motion. Jdem, p. 309.
1 Letter to Dr. Bentley, dated Cambridge, February 11, 1693.
* Letter dated January 17, 1693.
Plate XI.
London, Longmans & Co.
Cuap. V.] GRAVITATION AND INERTION, 71
‘Let Ars (Plate XII.) represent the surface of the
earth, c its centre, VD, VE, vF, the curve lines which
a body would describe, if projected in a horizontal
direction from the top of a high mountain successively
with more and more velocity ; and, because the celes-
tial motions are scarcely retarded by the little or no
resistance of the spaces in which they are performed,
to keep up the parity of cases, let us suppose either
that there is no air about the earth, or at least that it
is endowed with little or no power of resisting : and
for the same reason that the body projected with a
less velocity describes the lesser are vp, and with a
greater velocity the greater arc v £, and, augmenting
the velocity, it goes. farther and farther to F and g ;
if the velocity was still more and more augmented, it
would reach at last quite beyond the circumference
of the earth, and return to the mountain from which
it was projected.
The body is supposed to be projected with a hori-
zontal force from v sufficient to carry it as far as D ;
then with a force sufficiently increased to carry it as
far as E; then as far as F, and so on toa. Now,
even admitting that each increase in the projecting
force will carry the body still farther round the earth
Dr. Playfair tells us that but for the discovery of the motion of
the earth, that law might have remained for ever unknown.!
I have shown that in the heavens that law is no longer required
for the purpose for which it was invented. Jdem, p. 245.
! Encyclopedia Britannica, 8th Edition. Fourth Dissertation.
—T
bo
THE OCEAN. [Boox III.
(supposing it to be free from the action of foreign
forces of gravitation), and that it may be so increased
as to carry the body quite round the earth, or an
indefinite number of times round the earth, even
then, that the body can twice return exactly to the
point v, from which it started, or that it must not
necessarily, sooner or later, in the course of time
come to the surface of the earth just as certainly as
that projected from Vv to D,—is not shown. And, in
fact, it is certain that no increase in the amount of the
projecting force can prevent the body from being
gradually more and more deflected from the horizontal
line, until it at length be brought to the surface of the
earth. For the force with which the body is projected
in the horizontal line is supposed to resist the force
with which the earth draws the body towards its sur-
face ; but in resisting this tendency of the earth to
draw the body towards it, a greater or lesser amount
of force is necessarily spent. And as the force with
which the earth draws the body towards it is con-
tinuous, which the projecting force is not, this latter
must at length be spent by the constant resistance of
the former ; and the body, therefore, must at length
be brought to rest on the surface of the earth, just as
certainly, and for the same reasons, as in the case of
the ball rolled along the ground. In both cases a
certain amount of force is expended to set bodies in
motion ; and as the force is not continuous in its
action, it is at length spent by the constant resistance
Cuar. V.] GRAVITATION AND INERTION. 73
of the vis-inertie of matter. The force of friction
which retards and at length stops the course of the
ball rolled along the ground is (as we have before
shown) exactly of the same nature as the force which
resists that by which the body is supposed to be pro-
jected from v. The latter is the force of attraction
caused by gravitation drawing towards the earth, and
the former is the force of friction, in the ordinary
acceptation of the term: but both these forces we
_ have shown to be, in fact, simply efforts of vis-inertiz
constantly tending to bring matter to a state of rest.
It is then evident that in the case of the ball thrown
in the air, or rolled along the ground, as in the case
of the moon revolving round the earth, there is no
intrinsic difference in the nature of the force which
tends to bring them to a state of rest on the surface
of the earth.!
1 The ‘ Laws of Motion’ are more fully discussed in The New
Principles of Natural Philosophy,” especially ‘in ‘Chapters ,TX.,
XII., and XVI. ; and partially in the Challenge-Lectures forming
Chapters VI. and VII. of that work.
74 THE OCEAN. [Boor III.
CHAPTER VI.
THAT THE MOON’S ORBITAL’ MOTION IS CAUSED BY
THE EARTH'S ROTATION, AND ITS APPARENT LAG-
GING MOTION BY ASTRAL GRAVITATION.
We have already observed that the idea of any
body having an innate tendency to move uniformly
forwards in a straight line is mere assumption. No
such innate tendency can, in the present state of know-
ledge, be demonstrated to exist in any known pheno-
mena. And we have shown that if any body really
has a tendency to move uniformly in a straight line, it
certainly is not in consequence of an innate property
of vis-inertize, because we have shown that its innate
property of vis-inertiz constantly tends to bring it to
a state of rest: and therefore, if this tendency to move
uniformly in a straight line exist, it must be in con-
sequence of some force acting continuously with suffi-
cient power to overcome the vis-inertie of the body
set in motion.
The cause of the moon’s motion is a question
which has not hitherto been solved; and we have
shown that the idea of the moon or any of the planets
having a tendency to continue to move uniformly
for wards ina straight line in consequence of an innate
Cuar. VI.] GRAVITATION AND INERTION, 75
property of vis-inertiz is erroneous : and, therefore—
comparing the motion of the moon in its orbit to that
of the stone swung round in a sling, and tending
constantly to fly off at a tangent from its course—it
is evident that an innate property of vis-inertie, tend-
ing to carry the moon onwards in a straight line, is
not the force which resists the earth’s gravitation
drawing towards the earth.
Now, since the earth’s attraction tends to draw
the moon to the earth, and the action of vis-inertiz
tends to bring the moon to a state of rest, just as in
the case of a stone thrown in the air or rolled along
the ground ; and as we have shown that the idea of
any body having an innate tendency to move uni-
formly forwards in a straight line is a mere assump-
tion : let us consider whether the fact of the moon
not being drawn to the surface of the earth, and the
fact of its moving continuously onwards in its orbit,
cannot be explained without assuming the existence
of any laws or forces whose action cannot be illus-
trated by analogy with known phenomena. The
stone thrown in the air is drawn to the ground by
the earth’s attraction, whereas the moon is not. But
then, as the moon is farther removed from the action
of the earth’s gravitation, and is therefore relatively
more under the dominion of some other force of gra-
vitation, it may, in the absence of any other reason-
able cause being assigned, be inferred that the moon
is held in equilibrium between the attraction of the
76 THE OCEAN. [Boox IIL,
earth’s gravitation and that of other forces of gravita-
tion ; so that, as the earth’s attraction tends to draw
the moon to the earth, those other forces tend equally
to draw it in the opposite direction. Then the stone
is drawn to the earth, but the moon is not, because
the stone is within the sphere in which the force of
attraction drawing towards the earth is greater than
that drawing towards the position which any other
force of gravitation tends to give it ; whereas the moon
is just so far removed from the earth as to be held in
equilibrium between a tendency to the position which
the sole action of the earth’s gravitation would give
it if unopposed by other forces, and a tendency to
the position which, if the earth’s force of gravitation
were withdrawn, the combined action of all other
forces of gravitation would give it.
This, however, accounts only for the moon with-
standing the attraction towards the earth, whereas”
the theory which assumes an innate tendency to
move uniformly forwards in a straight line accounts
also for the moon’s onward motion in its orbit. A
cause for the onward motion of the moon, according
with the action of well-known laws, is, however,
indicated by the tides: for the moon tends to raise
a mass of water, or tide, on the earth’s surface be-
neath it ; and, as the earth’s surface rotates eastwards
it tends to carry that mass of water or tide with it ;
and therefore, as the moon tends to hold the tide
beneath it, the rotation of the earth eastwards must
Cap. VI.] GRAVITATION AND INERTION. rg
just as certainly tend to carry the moon eastwards as
to carry the tide eastwards.
The earth’s gravitation, then, is constantly tend-
ing to draw the moon to the earth, and to carry the
moon eastwards with the earth’s axial rotation. But
the moon is not drawn to the earth ; and, as regards
the earth’s axial rotation, the moon is constantly
lagging behind, or falling westwards.
The force by virtue of which the moon resists the
motions which the earth’s attraction tends to give it
obviously accords with that which we have defined
as its innate property of vis-inertiw, by virtue of
which it tends to maintain itself in a state of rest.
And this vis-inertiz we have shown to be universal
gravitation.
The earth’s gravitation tends to draw the moon to
the earth, and the moon’s gravitation tends to draw
the earth to the moon, but by opposing forces of
astral gravitation they are held in equilibrium. By
some force (with whose nature we are not here con-
cerned) the earth is caused to rotate eastwards on its
axis, and as it rotates, its gravitation tends to carry
the moon eastwards with that same motion ; but the
moon’s vis-inertiz resists this motion in precisely the
same manner as that in which we have described the
current-creating action of vis-inertiz in the ocean, for
the forces in play are precisely the same as those
acting on any given particles of water. The earth
tends to draw the moon to the position which the
78 THE OCEAN. [Boox III.
earth’s gravitation tends to give it ; but the moon is
already held in equilibrium by universal gravitation,
and therefore, as the earth tends to draw it in any
direction from that position, astral gravitation, or the
combined action of all other forces of gravitation,
tends to draw it in the opposite direction.'
' See The New Principles of Natural Philosophy, Chapter ITT.
79
CHAPTER VII.
THAT THE CURRENT-CREATING ACTION OF VIS-INERTIA,
DESCRIBED IN BOOK II., IS CORROBORATED BY THE
MOTIONS OF THE PLANETS.
THAT the earth’s surface, in some manner, tends to
carry the moon eastwards is indicated, as pointed out
in the foregoing chapter, by the fact that the action
of the moon’s gravitation raises a tide which goes
round with the moon, whilst the earth’s surface rolls
on eastwards under them. And, since the moon’s
gravitation drags westwards on the earth’s surface
(for it drags the tide westwards with it), that surface
must, since the action of gravitation is reciprocal,
tend to drag the moon eastwards. This reciprocal
action of gravitation is inseparable from the existence
of that force which, by Newton’s demonstrations,
may be said to have been removed from the domain
of theory by being incontrovertibly established as a
simple fact. And, therefore, the assertion that the
earth’s surface drags the moon eastwards is not only
in accordance with Newton’s laws of gravitation, but
80 THE OCEAN. | [Boox III.
it is, in fact, an inseparable corollary from them ; so
that its refutation, of necessity, involves the denial
of the existence of the force of gravitation. This
being so, then any definitions or axioms invented to
explain the onward motion of the moon and other
heavenly bodies are, if at variance with the assertion
that the earth’s surface tends to drag the moon east-
wards, of necessity false.
But if the moon is really carried round by the
earth’s surface rotating below it, then the far side of
that surface, moving in the opposite direction, must
tend to check it; and, therefore, the velocity of its
motion must depend on the amount by which the
dragging power of the nearer exceeds that of the
remoter part of the earth.
This argument, and with it the whole theory of
the current-creating action of the earth’s rotation,
can be brought to a crucial test. For, if the motion
of the moon in its orbit round the earth is caused by
the earth’s rotation, then it is to be presumed that
the motions of the planets round the sun are caused
by a rotation of the sun in the same direction as that
in which the planets revolve ; and, therefore, accord-
ing to the above argument, the relative velocities of
the planets must show a dependence on the relative
amounts by which the force of the gravitation of the
nearer exceeds that of the remoter part of the sun in
their respective orbits.
Cuar. VII.] GRAVITATION AND INERTION. 81
The exact relative amount of the revolving force
in each orbit depends on the thickness of the surface
whose gravitation causes the revolving action, and of
this we have no definite knowledge. But, by taking
the amount by which the force of the nearest exceeds
that of the remotest part (or any other corresponding
points in the opposite hemispheres) an approximation
can be obtained, which is sufficiently accurate for our
present purpose.’
The apparent motion of the spots upon the sun
has long been supposed to indicate a motion of
rotation in the direction above suggested. And the
following tables show it to be a mere matter of fact
that in the different orbits of the planets the fractions
by which the force of the gravitation of the nearest
part of the sun exceeds that of the remotest are such
that their square roots represent the actual relative
velocities with which the planets move in their orbits
round the sun.
Taking the sun’s diameter as 888,000 miles, the
relative distances from the nearest and remotest
parts of the sun respectively are approximately
as in the first column of the following table, in
which that diameter is taken as the unit of measure-
ment :—
' See Table of Forces, Proposition XIX., Chapter X XI.
Relative distances from
nearest and remotest
parts of sun, in solar
diameters
Mercury 41 42
Venus . ww we
Harth . 106 107
Mars 164 165
Jupiter 556 557
Saturn. 1,020 1,021
Uranus 2,051 2,052
Neptune 3,212 3,213
THE OCEAN.
Inverse squares of distan-
ces give the proportion
which in each orbit the
gravitation of the re-
motest bears to that of
the nearest part of the
sun
Fraction of direct force
which acts as a re-
volving force
1,681 1,764
5,929 6,084
11,236 11,449
26,896 27,225
309,136 310,249
1,040,400 1,042,441
4,206,601 4,210,704
10,316,944 10,323,369
3, = 024092
338, = 012902
si. = 009315
822, = 006078
813, = 001796
wae; = -000979
44293; = 000487
reer: = 008i
[ Boox ile
Sq. Roots
of fore-
going
fractions
give re-
lative
veiocities
1552¢
“1135+
0965t
‘O779T
0423t
0312+
0220f
01763
The lengths of the orbits increase as the distances
from the centre increase. And the relative lengths
of the orbits, divided by the relative periods of orbital
revolution, give the relative velocities of the orbital
motions, as follows :—
Relative periods of re- | Relative velocities of
Relative lengths of orbits
volutions orbital motions
Mercury 413 88 “A715t
Venus 77s 225_ *3444f
Harth 1063 365 29177
Mars 1643 687 “23941
Jupiter 5564 4,333 1284¢
Saturn ; ; EO205. 10,759 “0948t
Uranus 3 . 2,0514 30,687 0668t
Neptune . . . 93,2123 60,127 "05342
Tt These decimals are all a fraction larger if extended. The
least velocity is extended a figure farther to give greater precision
when used as a divisor in the third table. The distances of the
planets from the sun and the relative lengths of the orbits given
above are based on the distances given in Mitchell’s Popular
Astronomy, discarding fractions of the solar diameter used as the
unit of measurement, and the relative periods of revolution are,
within half a day, the actual periods.
Car. VIL.) GRAVITATION AND INERTION. 83
These actual velocities, deduced from the approxi-
mate measurements of the relative distances and
periods, are the same as those in the theoretical
table ; for :
By actual measurement | Taking Neptune’s velocity
The relative velocities by the they are, according to as 10, both tables give,
theoretical table are as under: the preceding table, as excepting fractions, the
under :— same velocity, as under :
Mercury ; . 15,520 47,150 88
Venus . 5 . 11,350 34,440 64
Harth . : . 9,650 29,190 54
Mars. : 5 as) 23,940 44
Jupiter . - . 4,230 12,840 24
Saturn . : . 93,120 9,480 17
Uranus. E . 2,200 6,680 12
Neptune - . 1,763 5,342 10
The first of the foregoing tables shows that the
fraction of the sun’s direct force which acts as a
revolving force is, approximately, inversely as the
distance from the sun. And, as the total of the
direct force is itself inversely as the square of the
distance, the revolving force of the sun’s gravitation
is, therefore, inversely as the cube of the distance
from the sun, approximately ; and, this being so, it
is then a mere matter of fact that the square roots
of the revolving forces in the different orbits of the
planets represent, approximately, the actually appa-
rent velocities with which, if viewed from the sun,
they would be seen to move, threading their way east-
wards among the fixed stars. Or, in other words,
the rapidity with which an orbital revolution is
accomplished increases or decreases directly as the
&é 2
84 THE OCHAN, [Boox III.
square root of the revolving force of the sun’s gravi-
tation.
The revolving force of the sun’s gravitation is,
therefore, as the square of the angular velocity of
the motion—that is, the velocity as measured on the
surface of the sun which causes the motion.’
Now, since, according to the foregoing chapters,
the earth is held in equilibrium between opposing
forces of gravitation, therefore the retarding force
of astral gravitation increases as the square of the
velocity of the motion which it opposes (for the
revolving force increases in that proportion).
The action of this retarding force of astral
gravitation then makes the squares of the velocities
of necessity inversely as the cubes of the relative dis-
‘tances ; because, suppose the revolving force to be
increased, then there is a corresponding increase in
the opposing force of astral gravitation without any
increase in the direct force of the sun’s gravitation,
and astral gravitation would then carry the earth
back at a tangent to the orbit in which the revoly-
ing force tends to carry it, until, in consequence of
the revolving force decreasing as the cube, and the
direct force only as the square of the distance increased,
the equilibrium between the force of astral gravitation
drawing from the sun, and that of the direct force of
the sun’s gravitation, would be restored.”
1 See also Proposition XVII., Chapter X XT.
2 See Proposition XXV., Chapter XXI.
:
a
Cuar. VIL.] GRAVITATION AND INERTION. 85
Now it must be observed that, in treating of the
action of vis-inertize in causing currents in the ocean,
we have been driven to the conclusion that the moon
must be acted on by the same forces that impel any
given drop of water through its circulation. That is
to say, the revolving force of the earth’s gravitation
is constantly dragging them eastwards, whilst their
own inherent force of inertion is constantly opposing
that motion and causing them to lag westwards.
And then we have naturally inferred that the sun,
by a motion of rotation, must tend to carry the
planets round with it, just as the earth tends to carry
along the water and the moon.
To test this we have calculated the relative force
of the sun’s revolving action in the orbits of the
planets, considering that the nearest part of the
surface tends to carry them in one direction, whilst
the farthest part tends to carry them in the opposite
direction, and we have found that the actual relative
velocities with which the planets move round the sun
bear a fixed ratio to the relative amounts by which
the force of the gravitation of the nearest exceeds
that of the remotest part of the sun in their respec-
tive orbits.
When a theory which explains the movements of
the ocean and atmosphere—as shown in Vis-inertic,
and farther on in this volume—is corroborated
like this by the motions of the heavenly bodies,
and wherever extended finds nothing in nature at
86 THE OCEAN. [Boox III.
variance with it, of what avail is it to oppose it with
ideas which, though asserted to be laws of motion,
are merely theoretical, for they are not corroborated
by phenomena observed in nature. The more clearly
those so-called laws are shown to be at variance
with the theory substantiated by natural phenomena
throughout the visible universe, the more certain and
complete must be their destruction.
According to the above-mentioned laws the
moon’s orbital motion is maintained by its inherent —
tendency to keep itself in motion—that motion having
been communicated to it at some unknown period,
by some unknown cause: and then the force which
resists the earth’s gravitation is said to be the ten-
dency of that motion to carry it onwards at a tangent
from its orbit, like a stone from a sling. Whereas,
according to the arguments in the foregoing Chapters -
of this Book, the earth’s gravitation is the motive
force which draws the moon onwards in its orbit, and
the centripetal and centrifugal forces, which by their
opposing action keep it at its mean distance from the
earth, are—the former terrestrial and the latter astral
gravitation. These centripetal and centrifugal forces
are of a very different nature from those in the case
of a stone swung round in asling. Let us consider
what the difference is.
As regards the centripetal force: the string hold-
ing the stone in its course has been compared to the
earth’s gravitation holding the moon in its course.
Cuar. VII.} GRAVITATION AND INERTION, 87
The string certainly holds the stone in its course as
long as the motion lasts, but there the analogy ends.
And as regards the centrifugal forces there is no
analogy in the two cases, excepting the fact of both
tending to carry the revolving body from the centre
round which it revolves. In the case of the stone,
the centrifugal force gives the stone a tendency to fly
off at a tangent from the circle in which it is revolved,
in the direction of its motion. But, as regards astral
gravitation, considered as the centrifugal force which
opposes the centripetal force of the earth’s gravita-
tion : if the moon were not acted on by the revolv-
ing force of the earth’s gravitation, but only by
the direct force, then astral gravitation would tend
to carry the moon directly from the earth, not at a
tangent to any part of its orbit: and when in
motion, astral gravitation tends to carry the moon
off at a tangent from its orbit certainly, but im
the opposite direction to that of its motion. ‘The cen-
trifugal force endeavours to place the moon at c in
the higher orbit, c D E, instead of at B; to which
latter it is carried by the revolving force along its
orbit from a.’ (Fig. 19, p. 88.)
1 The reader will observe that the theory of counter-attraction,
or astral gravitation, need not be considered to supplant the New-
tonian theory of centripetal and centrifugal forces, but rather to
define the nature of the latter force ; showing that it is similar to
the former : both being gravitation caused by vis-inertix, which is
just as much the primary cause of the centripetal as of the centri-
fugal force.
The effects are matters of observation, so that the point at
88 THE OCEAN. [Boox III.
The force of universal gravitation in fact opposes —
the motion of the stone in the sling just in the same
manner as that of astral gravitation opposes the
motion of the moon ; but there is this radical differ-
UI
T/
d
Fic. 19.
ence between the case of the stone revolved in the
sling and that of the moon revolving round the earth.
issue is as to how those effects are caused; and I maintain that
vis-inertiz holds the planets in equilibrium, the centripetal force
of the sun’s gravitation being a part of the action of the planet’s
vis-inertiz just as much as the centrifugal force. The error lies
in the cause to which the tangental effort is attributed; and I
have endeavoured to show that that effort is not caused by the
vis-inertiz of the planet tending to carry it onwards along the
tangent, but by astral gravitation (a part of the action of vis-inertiz)
retarding it, and tending to draw it backwards farther and farther
from the successive positions to which the revolving force carries
it along its orbit.
Vis-inertie is the combined action of universal gravitation,
which actually does keep the planet on the line of its orbit;
opposing any tendency from, as much as towards, the sun.—The
Elements, Preface, Vol. I. London, 1866.
Cuap. VI] GRAVITATION AND INERTION. 89
In the former case it is the motiun of the stone which
tends to carry it out of the circle in which it is re-
volved: whereas in the case of the moon, as we
_ have shown that the motion is caused by the earth’s
gravitation, it cannot tend to carry the moon onwards
at a tangent from its orbit, nor indeed can it tend to
carry it out of its orbit at all.. The root of the differ-
ence is this: the force by which the stone is set in
motion is an illustration of the direct action of the
forces ordained to control matter; whereas, in the
case of the moon, the motion is caused by gravitation,
an attribute of vis-inertize
the mode, in fact, in which
vis-inertiz manifests its resistance to the motive force.
The motion of the moon in its orbit may rather
be compared to that of a cork floating in a basin of
water, in which, by rotating any object rapidly in
the centre of the basin, the whole mass of water is
caused to rotate, carrying the cork along with it.
The motion of the moon and that of the cork are
analogous, inasmuch as both are caused by gravita-
tion, this gravitation being an effect resulting from
the resistance which the vis-inertie of matter pre-
sents to the action of the force by which the object
in the centre of the basin is made to rotate. This is
so because, in consequence of its property of vis-
inertiz, the water in the basin tends to maintain itself
in a state of rest ; and therefore, resisting any force
which may tend to set it in motion, it endeavours
to maintain its position and that of its parts in
90 THE OCEAN. [Boox IIL.
relation to each other. When, then, the object in the
centre of the basin is made to rotate, those particles
of water adjoining the rotating surface endeavour to
maintain their position in relation to the part of the
rotating surface against which they rested, and also
in relation to those particles next beyond them ; and
therefore draw towards the part of the surface caused
by. the action of the extraneous force to tend from
them, and also towards those particles next beyond
them, these latter towards those next them, and so
on; and thus all. the particles, each endeavouring to ~
maintain its connection with those next to it, draw
or gravitate towards each other. Thus the gravita-.
tion of the particles one towards another draws the
whole mass onwards in a motion of rotation, each
endeavouring to maintain its position in relation to
the particles set in motion by the action of the ex-
traneous force: and therefore, as the object in the
centre of the basin is made to rotate, the force of
eravitation causes the cork to revolve in the same
direction. This is analogous to the motion of the
moon revolved eastwards in its orbit by the force of
its gravitation towards the surface of the earth ro-
tating eastwards. In the case of the moon, as in the
case of the cork, the motion is caused directly by
gravitation, which is the effort of vis-inertie to
maintain matter in a state of rest :—1it is the force
exerted in the endeavour to resist the action of any
forces which tend to cause a change of form or posi-
Cuar. VII.) GRAVITATION AND INERTION. 91
tion. These motions result from the efforts of the
particles of matter to maintain the positions in rela-
tion to each other which the extraneous force dis-
turbs ; whereas the motion of the stone in the sling
is caused directly by the extraneous force carrying
the stone onwards in accordance with its laws, in
spite of the resistance of vis-inertiz. The stone is
hurled through the air in direct opposition to the
force of gravitation ; and after it is released from
the sling the motion communicated to it must, sooner
or later, be spent by the continuous resistance of
vis-inertix.
An increase of the velocity of rotation which
revolves the cork and the water above mentioned
will cause the particles of water and the cork to
recede from the centre along tangents backwards from
the successive points to which the revolving force en-
deavours to carry them in the circles of revolution
(as shown by the diagram on page 88); because,
as has been shown in the preceding chapter, the
retarding force of astral gravitation increases as the
square of the velocity of the motion which it resists ;
and it will therefore carry the revolving particles
backwards from the centre of revolution until the
disturbed equilibrium is readjusted in consequence
of the revolving force decreasing as the cube of the
distance from the centre increases.
As the water recedes along the tangents it exem-
plifies the overwhelming of lesser forces by greater.
vo)
i)
THE OCEAN. [Boox III.
For the revolving force increases towards the centre,
and as any particle is carried onwards by it, the par-
ticle next outside it is carried relatively in exactly
the opposite direction by the force of astral gravita-
tion, the action of which is relatively greater, as re-
gards the revolving force, on it than on the particle
nearer the centre of rotation. Its motion backwards
along the tangent results from the effort of vis-
inertiz to maintain the equilibrium destroyed by the
particles nearer the centre of rotation being carried
in the opposite direction.
The above argument is equally applicable to the
moon ; for, suppose the latter to be lying loosely on
the surface of the earth, and let a motion of rotation
be generated in the earth, and then, as that motion
carries the surface on which the moon rests onwards,
astral gravitation, whose action, compared with the
revolving force, is relatively greater on the moon
than on the surface below it, maintains the equili-
brium of gravitation by carrying the moon in the
opposite direction, which is backwards along the tan
gent to the surface on which it rested. And it will
continue to recede along that tangent as long as the
disturbed equilibrium is more readily restored by
that motion than by the motion of the opposite side
of the rotating surface, or of some other body in the
same direction. At the distance thus determined it
would revolve with the rotating surface, though con-
stantly lagging backwards over it under the action
Cuap. VIL] GRAVITATION AND INERTION. ~ 93
of astral gravitation. Thus the force of astral gravi-
tation, opposing that of the earth’s gravitation, is
constantly endeavouring to draw the moon out of its
orbit, and the earth’s gravitation revolves it in the
orbit in which it is held by those opposing forces.
The foregoing shows that it is an error to sup-
pose the orbital motion of the moon to be analogous
to that of a stone swung round in a sling. Because :
it is the motion of the stone which tends to carry it
out of its orbit ; that motion tends to carry it on-
wards at a tangent to its orbit in the direction in
which it is revolved ; and the motion is caused by a
force which moves the stone in spite of the resistance
of vis-inertiz. Whereas: it is the force which op-
poses the motion of the moon that tends to carry it out
of its orbit ; that force tends to draw it backwards
in the opposite direction to that in which it is re-
volved ; and the motion of the moon is caused by
gravitation, which is the effort of vis-inertix to bring
matter to a state of rest. For the motion of the
moon is its effort or gravitation towards the nearest
part of the surface of the earth which is constantly
rolling from it. An increase of the velocity with
which that surface moves would increase the distance
to which the moon is drawn from it; because the
force of astral gravitation which prevents the moon
from keeping pace with the surface increases as the
square of the velocity of its motion.
To make this clearer we may recapitulate :
94 THE OCEAN. [Book III.
As the ratio in which the force of astral gravita-
tion increases or decreases is dependent on that of the
revolving force ; and as the latter is inversely as the
cube of the distance, whereas the direct force is
inversely as the square of the distance from the earth,
therefore, however great the revolving force may be
at the surface of the earth, the opposing force of astral
gravitation which carries the moon backwards from
the position to which the revolving force tends to
carry it must at some certain distance become equal
to the direct force of the earth’s gravitation ; and
there the moon would be revolved in equilibrium
between the force of astral gravitation tending to
draw it out of its orbit from the earth and that of
the earth’s gravitation tending to draw it to the
earth.
In the case of the stone, the motive force tends to
carry it off at a tangent to the circle in which it 1s
revolved in the direction of its motion, in spite of the
resistance of vis-inertize, which tends to bring it to a
state of rest: whereas the moon is held in equili-
brium by vis-inertiz, or universal gravitation, whilst
the force of astral gravitation tends to carry it from
the earth, and the earth’s gravitation tends to draw it
to the earth ; and its motion is constantly restoring
the equilibrium of gravitation towards it as fast as that
equilibrium is disturbed by the action of the force
which causes the earth to rotate.
The motion of the stone disturbs the equilibrium
Caap. VII.) GRAVITATION AND INERTION. 95
of gravitation, whereas the motion of the moon main-
tains it.
1 Newton erred in assuming the centrifugal force which op-
poses the centripetal force of solar gravitation, and holds the planets
at their mean distances from the sun, to result from an innate
tendency to move uniformly forwards in a straight line: and he
doubly erred in assuming this asserted tendency to move uniformly
forwards in a straight line to result from innate vis inertiz, by
virtue of which any body once set in motion tends to continue that
motion uniformly forwards in a straight line until other forces from
without stop it. For, first, I have shown that vis-inertize opposes
motion in everything, and that its own inherent property of vis-
inertize must tend to bring a body to rest, under any circumstances
whatever, just as much, and in the same manner, as the action of
any force from without. And, secondly, I have shown that, as
regards the motions of the planets in their orbits, the centrifugal
force which opposes the centripetal force of the bodies which com-
pose the solar system one towards another, and all towards their
common centre of gravity, is the force of astral gravitation oppos-
ing that of solar gravitation ; so that, in their courses, they are
borne smoothly along the lines of equilibrium lying between
opposing forces of gravitation. This subject is more fully discussed
in The New Principles of Natural Philosophy.
96 THE OCEAN. [Boox III.
CHAPTER VIII.
THE MOTIVE FORCE.
Tue foregoing chapters of this Book have shown
that vis-inertiz is a really mherent property in
matter, by virtue of which it endeavours to be just
what it is and where it is; and that gravitation is
simply an effect of vis-inertia—this effect of vis-
inertize being brought into existence in consequence
of the action of some other force tending to cause a
constant change of form and place.
They have also shown that this motive force acts
from the central parts of the sun, causing the latter
to rotate and to revolve the surrounding planets
with it. And that a similar motive force acts from
the central parts of the earth, causing it to rotate and
to revolve the moon in the same direction.
Whatever be the source or abstract cause of the
force which rotates the earth and the sun as above
shown, the term evanescence may appropriately be
applied to it in a limited sense, and even a com-
prehensive signification of the term may be shown
to be not inappropriate. or the tendency of the sole
action of gravitation would be to consolidate the
universe into one motionless mass ; but if evanescence
Cuap. VIII. ] GRAVITATION AND INERTION. 97
be brought into play throughout it, then motion is
necessitated ; for evanescence implies a motion of
the evanescing particles, and gravitation, tending to
cause contraction, necessitates a motion of the re-
maining particles : and since contraction is a neces-
sary consequence of evanescence, having effect wher-
ever evanescence occurs, it must act towards every
point from which evanescence acts, and thus divide
the universe into separate masses ; and the motion
resulting from this contraction must be more or less
circular, because the position of every particle is
determined by gravitation, and every division of the
universe must therefore preserve its relative position
as regards the aggregate of the other divisions of the
universe, which necessitates a motion of rotation in
each division ; and the particles rotating must all
move harmoniously, because the force of attraction
acting from all sides prevents the movement of any
one particle unless there be an harmonious movement
of some other particle or particles, so as to preserve
the balance of gravitation.
Even under its most limited signification the
force of evanescence, which vis-inertiz is, by the act
of gravitation, constantly opposing, comprehends the
detailed action of the laws which control matter ;
and the evolution of life upon the earth is therefore
the action of evanescence, which causes it to rotate.
And if accepted in its widest sense, it is then to be
inferred that matter has not always existed, and that
H
98 THE OCEAN. [Boox III.
in the course of time it will cease to exist : presuming,
of course, that it is only reasonable to suppose that
something immaterial pre-existed from which it had
its origin, and that when it has run its course and
ceased to exist, something immaterial evolved from
it will exist after it. We are, however, concerned only
with the forces brought into play by the evanescence
of matter, and not with the immaterialities which
pre-existed, or into which it is in process of trans-
mutation ; and these forces, termed evanescence,
tending to control matter in a constant series of
evolutions through its existence, causing constant
change of form and place, bring into play the force
of gravitation in consequence of the action of vis-
inertiz, by virtue of which matter tends to preserve
its existence, or hold itself together, and continue
~where and what it is.!
1 See Chapter XIX. of The New Principles of Natural Philo-
sophy, ‘Is force inherent in matter? And is matter evanescent
or indestructible ?’
BOOK IV.
y FECTS OF SOLAR AND LUNAR GRAVITATION.
THHORY OF THE TIDES.
101
CHAPTER IX.
NORMAL POSITIONS OF THE TIDES IN RELATION TO
THE FORCES BY WHICH THEY ARE RAISED.
THE position which the ocean would have under the
sole influence of terrestrial gravitation is modified by
the gravitation of other bodies in space, which tend
to draw the water to the parts of the surface of the
earth turned towards them.
The sun, the moon, and the planets all tend, more
or less, to draw the water to those parts of the earth’s
surface turned towards them. And by the earth’s
motions the parts of the surface of the earth turned
towards the foreign bodies respectively are being
constantly changed. The gravitation of those bodies
constantly tends to hold the water in the position
which they tend to give it, whilst the earth’s gravi-
tation as constantly tends to carry the water away
from that position, together with the surface on which
it rests.
Let us now suppose all other bodies of the Solar
System to be so far removed from the earth that the
individuality of their forces of gravitation on the
earth may be lost in that of the remaining force—
which is, in fact, that of the stars, or, as we have
before termed it, astral gravitation.
102 THE OCEAN. [Boox IV.
Discarding in this manner the individual action
of the sun and moon, we have seen that the ocean
has a tendency to maintain the position from which
the surface on which it rests tends to carry it: and
that this tendency results from its property of vis-
inertiz, in the ordinary acceptation of the term ; but
we have also seen that the action of vis-inertiz which
resists motion towards the position which the earth’s
power of gravitation tends to give, is a power of
gravitation drawing towards the position which the
combined action of all powers of gravitation, except-
ing that of the earth, tends to give. To this force
we have applied the term ‘ astral gravitation,’ because
we have ascertained that vis-inertiz is really uni-
versal gravitation, which this force is not.
The oceanic circulation resulting from the con-
flicting action of these forces of terrestrial and astral
gravitation we have described at length in Book IL.,
in which we have shown that, as regards the onward
motion of the earth, in those parts of the ocean least
under the dominion of the earth’s gravitation, a
current is drawn through the ocean, by the attraction
of astral gravitation, in the opposite direction to that
of the motion of the surface of the earth ; whilst in
those parts of the ocean most under the dominion of
the earth’s power of gravitation counter-currents are
drawn through the ocean, by the earth’s gravitation,
in the direction of the motion of the surface of the
earth. |
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Cuap. IX.] SOLAR AND LUNAR GRAVITATION. 103
And, as regards the axial rotation of the earth,
as that rotation is eastwards, the earth’s gravitation
tends to carry the ocean eastwards with the surface
on which it rests ; but astral gravitation, drawing in
the opposite direction, tends to give it a relative mo-
tion westwards over the surface of the earth all round
the earth. But as the stars draw the water west-
wards through the equatorial regions, where the force
of their gravitation, compared with that of the earth,
is relatively greater than in the temperate zones, the
earth’s gravitation draws an equal volume eastwards
through the temperate zones, in which the force of
its gravitation is relatively greater than in the equa-
! and also as the stars draw the water
torial regions :
upwards from the surface of the earth in the equa-
torial regions, the earth’s gravitation draws an equal
volume downwards to the surface of the earth in the
temperate zones. From this opposing action of astral
and terrestrial gravitation there results the elaborate
system of oceanic circulation described in Book II.
The circulation there described is quite independent
of the individual action of the sun and moon, though
the gravitation of those bodies is included in the
force of gravitation whose combined action causes
that system of circulation. The opposing forces of
terrestrial and astral gravitation together represent
universal gravitation or the action of vis-inertie.
We have, in Book III., shown that in the same
1 See Chapter XXI., Proposition XXVII., Sect. 6.
104 THE OCEAN. - [Boox IV.
manner as that in which astral gravitation opposes
terrestrial gravitation it must also oppose the action of
solar and lunar gravitation, causing a counter-move-
ment for each movement caused by the latter forces.
The movements and the counter-movements in each
case equally result from the effort of vis-inertix to
maintain the equilibrium of the ocean.
In the same manner as vis-inertiz creates the
movements and counter-movements which circulate
the ocean, as described in Book II., in consequence
of inequalities in the action of terrestrial and astral
gravitation, it must also, as shown in Book IIL,
create movements and counter-movements in conse-
quence of inequalities in the action of solar or lunar
and astral gravitation. The consideration of the
action of vis-inertize thus leads us to a considera-
tion of the effects of solar and lunar gravitation on
the ocean, as forming a part of that action of vis-
inertize.
Let us now consider the effect of the gravitation
of the sun and moon in their actual positions.
For this purpose let s, in Plate XIII., represent the
sun, E the earth, and m the moon. Then, first, as
regards the solar tides: if the sun and earth be at
rest, the sun’s gravitation raises a tide (cD in Fig. 1)
on that part of the earth immediately under the sun,
and astral gravitation raises a tide (F G) on exactly
the opposite side of the earth.
The sun, however, rotates eastwards on its axis,
Cuapr. IX.] ) SOLAR AND LUNAR GRAVITATION. 105
and as it rotates its gravitation tends to carry the
earth with it, the latter endeavouring to maintain its
position in relation to the nearest part of the surface
of the sun. But as the sun’s gravitation endeavours
to carry the earth eastwards, it endeavours to draw it
from the position in which astral gravitation tends to
hold it. And this latter force prevents the earth from
maintaining its position in relation to the rotating
surface of the sun. And though the earth is drawn
onwards in its orbit by solar gravitation, it is, in con-
sequence of the retarding action of astral gravitation,
constantly falling westwards in relation to the surface
of the sun.
As the attraction of solar gravitation draws the
earth onwards in its orbit, it draws the solar tide
(westwards in relation to the surface of the earth) to
that part of the surface of the earth which is in advance
in the earth’s orbital motion. This is a meridian
somewhat nearer that of the sun than the meridian of
6" a.M. Let us, for the present arbitrarily, suppose
this to be the meridian of 63" a.m. And astral gravi-
tation—acting in exactly the opposite direction to that
in which the sun’s attraction tends to carry the earth—
draws the counter-tide westwards, to the part of the
earth opposite that to which the solar tide is drawn.
This is a meridian more remote from the sun than the
meridian of 6° p.M., and doubly remote from that
which is most behind in the central line of the earth’s
orbital motion. The positions of the solar tide c p,
106 THE OCEAN. [Boox IV.
and the solar counter-tide F G, would then be as shown
in Fig. 2.
Then as regards the lunar tides : the action of the
moon on the lunar tides is exactly the reverse of that
just described as the action of the sun on the solar
tides: for the earth is revolved in its orbit round the
sun by the force of solar gravitation, which raises the
-solar tide ; whereas it is the earth’s gravitation which
revolves the moon in its orbit round the earth. But
we may, for the sake of simplifying the question, just
for the present, suppose the earth to be revolved round
the moon in the opposite direction to that of the real
motion of the moon round the earth.
Then, as the moon revolves eastwards round the
earth, the relative positions of those bodies and the
lunar tides are the same as if the earth be supposed
to revolve westwards round the moon. Then, as in
the case of the solar tide, the lunar tide, 1H, in Fig. 3,
is drawn to that part of the earth’s surface which
is in advance in this orbital motion, and the counter-
tide, JK, is drawn by astral gravitation to exactly
the opposite side of the earth.
In consequence of the smaliness of the moon’s orbit,
the lunar tides are drawn more towards the moon’s
meridian than is the case with the solar tides in
relation to the sun’s meridian. Let us, for the sake
of illustration, suppose this difference to be double
that in the case of the solar tides. Then, as there is
a difference of an hour in the relative distances of the
Cap. IX.] SOLAR AND LUNAR GRAVITATION. 107
solar tide and the solar counter-tide from the sun’s
position (those tides corresponding with the meridian
of 63" a.m. and 63° p.m.), there will be a difference of
two hours in the relative distances of the lunar tides
from the moon’s position.
Therefore, though if the sun, moon and earth were
at rest, then the tides raised by the sun and moon
would be in conjunction at the same time as they ;
as the earth and moon are in motion, the tide
raised by the sun’s gravitation as it revolves the earth
round the sun, and that raised by the moon’s gravi-
tation as the earth revolves the moon round it, will
not be in conjunction when the sun and moon are in
conjunction, because the position of the solar tide
being 52° west of the sun’s meridian, and that of the
lunar tide being 5" east of the moon’s meridian (for
the moon follows its tide), therefore the lunar tide
can only be in conjunction with, the solar tile when
the moon is 5" west of the meridian of 63" a.m.—that
is, when the moon is on the meridian of 13" a.m. The
moon reaches this latter meridian in rather less
than two days after being in opposition to the sun.
Therefore, about two days after the sun and moon
being in opposition, the lunar and solar tides will be
in conjunction (as at cD in Fig. 2), their counter-
tides also being at the same time in conjunction on
the opposite side of the earth (as atra). But also
when the moon is at the opposite point of its orbit
(as at N), two days after conjunction with the sun,
108 THE OCEAN, [Boox IV.
the lunar tide will be in conjunction with the solar
counter-tide, and the lunar counter-tide at the same
time in conjunction with the solar tide. Thus about
two days after conjunction, and also two days after
opposition of the sun and moon, their tides (as a
whole) are in conjunction, and not when the sun
and moon are themselves in conjunction and opposi-
tion.
And then the combined action of the sun and
moon endeavours to place the high spring tide on
the meridian of 63° a.M.
Thus, as shown in Fig. 2, the tidal action of the
moon acts in conjunction with that of the sun at the
moment when the earth’s course westwards round
the moon is in conjunction with its course eastwards
round the sun.
The solar and lunar tides are again in conjunction
when the earth’s course westwards round the moon is
exactly in opposition to its course eastwards round
the sun. But in the latter case the solar tide is not,
as in the former case, in conjunction with the lunar
tide, but with the lunar counter-tide ; the lunar tide
being at the same time in conjunction with the solar
counter-tide.
From this it is obvious that the study of the tides
would be simplified and rendered more accurate by
dating the hour of the ‘establishment’ of ports from
the time when the earth’s course round the moon is
in conjunction with, or opposition to, its course round
Cuap. IX.] SOLAR AND LUNAR GRAVITATION. 109
the sun, than by the present method of taking as the
‘establishments’ the hours at which the first high
tide occurs at the various ports after the sun and
moon being in conjunction or opposition.
For the time when the earth’s course round the
moon is in conjunction with its course round the sun
is the normal hour of the monthly conjunction of the
lunar with the solar tide, and therefore the ‘ priming’
and ‘lagging’ of the tides throughout the month
may be calculated in a more simple and accurate
manner by considering this as the commencement
and close of the tidal months, and by reckoning the
cycle of variations in the alternate ‘priming’ and
‘lagging’ of the tides through these intervals, instead
of through the intervals between the times of new
moon.
110 THE OCEAN. [Boor IV.
CHAPTER X.
MOVEMENTS OF THE TIDES IN RELATION TO THE
SURFACE OF THE EARTH.
WE have thus far determined the positions, in rela-
tion to the sun and moon respectively, in which those
bodies tend to raise their tides, supposing the earth
sumply to be moved onwards in its orbit round the
sun, or in an orbit round the moon. Let us now
consider how these positions will be affected by the
earth’s axial rotation, and what course this rotation
will give them over the surface of the earth.
In the position of the tides in Fig. 2, Plate XIIL.,
the effect of the axial rotation of the earth has not been
taken into consideration at all. We have seen that
the solar and lunar tides are in conjunction when the
relative positions of the sun and moon are such that
the earth’s motion eastwards round the sun, or west-
wards round the moon, are in the same line. And
therefore, if the earth did not rotate on its axis, the
solar and lunar tides at the time of conjunction would
be on that part of the earth which is in advance in
those motions, the two counter-tides being together
on the opposite side, as in Fig. 2. But, as the earth
rotates eastwards on its axis, it tends to carry the
Riese
Pest
gy
Whe
Py
Cnar X.] SOLAR AND LUNAR GRAVITATION. 111
tides with it towards the position shown in Fig. 4.
They constantly endeavour to get into the positions
in which the lunar and solar forces respectively tend
to place them ; but the surface of the earth, on which
they rest, as it revolves eastwards, is as constantly
endeavouring to carry the tides eastwards with it.
And therefore, whatever may be the normal
velocity with which water would move through the
ocean under the action of the luni-solar force towards
the meridian on which that force tends to place the
tide, it must be constantly rising towards that meridian
from the east in the equatorial regions, and from the
west in the higher latitudes in which the velocity
with which the surface rotates eastwards is less than
the normal velocity of the tide.
Thus, as shown in Plate XIV., the high spring
tide would he diagonally across the meridian of
63" am., so that in the temperate regions the
surface of the earth would reach it in the early
morning, and in the equatorial regions not until
during the forenoon. And therefore, if an unbroken
expanse of ocean covered the earth, the hours of high
water at different places would increase as the distance
from the equator decreased, for the tide would first
touch the meridian in high latitudes, and then travel
down it from the north and south to the equator, and
then fall on the equator as it rose again along the
meridian in higher latitudes.
Thus the luni-solar tide on the side of the earth
112 THE OCEAN. [Boox IV,
in advance in the orbital motion, and the counter-tide
on the opposite side, would, whilst keeping their
positions unchanged in respect to the forces by
which they are raised, appear to have cyclonic move-
ments, for they would (even if their course were due
west) alternately rise and fall towards and from the
equator along each meridian just as much as east and
west along each parallel of latitude.
The tide, though travelling round the earth from
east to west, would commence on any meridian in
high latitudes in the form of an undulation rising
from the west, and would then converge along the
meridian towards the equatorial regions where the
undulation would be from the east, so having the
apparent motion of a cyclone on each side of the
equator : for, as already shown, the tide is in a chronic
state of trying to place itself on the meridian on
which the luni-solar force tends to raise it; but, as
the earth’s rotation as constantly prevents it from
achieving this, it is for ever rising towards it from
the west in high latitudes, and from the east along
the equator, being upon it only in the intermediate
latitude, in which its normal velocity is the same as
that with which the latitude rotates.
Thus it is evident from the foregoing that, though
the whole tide travels westwards, not only have the
tidal undulations movements in opposite directions
in the temperate and equatorial regions, but, besides
this, recorded times of high water would show a
Cuar. X.] SOLAR AND LUNAR GRAVITATION. 113
regular rise and fall along each meridian, as well as
along the parallels of latitude.
It will be observed that the action here described
harmonises with the views arrived at in Book IIL,
through the arguments in that and the preceding
Books, for though we have here shown that the tide
is carried eastwards in the equatorial regions by the
earth’s rotation, it is just as true, according to the
action of vis-inertize described in the foregoing Books,
that, as in the equatorial regions the tides vibrate
westwards, following the force which raises them,
where its action is relatively greater than the earth’s
gravitation, at the same time, in the temperate zones,
where the earth’s gravitation is relatively greater
than that of the foreign force, it causes an equal
vibration eastwards, and so maintains the equilibrium
of the ocean ; and therefore, though in the ocean as
it exists the tides cannot sweep round the earth with
the regular cyclonic vibrations above described, their
course will be determined by the action of vis-inertix
—for the same counteracting forces are brought into
play in each instance, preserving the equilibrium of
the ocean. If the latter surrounded the earth as an
unbroken expanse of water, then the tides would
simply be excrescences upon the ocean, through which
the circulation described in Book II. would run its
course without being affected by them. And in the
actual ocean, though the fragmentary tides will be
sources of disturbance, as they are broken and .de-
I
114 THE OCEAN. [Boox [V.
flected by the coast-lines, the undulations must never-
theless be under the dominion of the forces there de-
scribed: according to which, as the luni-solar forces
move westwards in relation to the surface of the earth,
they carry the tides westwards with them in the equa-
torial regions, in which the force of their attraction
is greatest; whilst, at the same time, the force of
terrestrial gravitation maintains the equilibrium of
the ocean on the surface of the earth by drawing an
exactly equal mass of the tide eastwards through the
temperate zones, in which the ocean is more under
the dominion of the earth’s gravitation, and less
under the dominion of the forces which raise the
luni-solar tides, than in the equatorial regions. And
thus, therefore, the relative volume of water on
every meridian, and on every parallel, can never
vary.
The position of the ocean in relation to the surface
of the earth is determined by universal gravitation or
vis-inertiz, and is constantly the same both in longi-
tude and latitude. Though the luni-solar forces change
their positions in relation to the surface of the earth,
the volume of water on every meridian and on eyery
parallel remains, nevertheless, constantly the same ;
because this is determined by the combined power of
the gravitation of the universe, and cannot be affected
by the individual action of any of the forces of gravi-
tation within the universe. As the luni-solar forces
move a volume of water from any part of any —
Cuap. X.] SOLAR AND LUNAR GRAVITATION. 115
meridian, the vis-inertie of the ocean carries an
exactly equal volume to some other part of that same
meridian. And so, also, if the luni-solar forces move
a volume of water from any part of any parallel of
latitude, the vis-inertize of the ocean carries an equal
volume of water to some other part of the same
parallel of latitude. Thus, therefore, as the tidal un-
dulations caused by the luni-solar forces rise on any
meridian in the equatorial regions, there is a corre-
sponding fall on that same meridian in the temperate
zones: and as the tide falls on any meridian in the
equatorial regions it rises on the same meridian in
the temperate zones. Thus the action of vis-inertie
resulting from the earth’s axial rotation causes the
tides to move westwards in the equatorial regions and
eastwards in the temperate zones, just in the same
manner as that in which it causes the oceanic circula-
tion described in Book II.
This action is the same as regards both the solar
and the lunar tides, because it acts upon them accord-
ing to their position in the ocean, and is in no way
concerned with the cause of their being raised in
one part of the ocean rather than in another: it simply
determines their movements in relation to the sur-
face of the earth, and is not concerned with what
the cause of the tide may be. And for just the
same reason that any given mass of water which
the earth’s gravitation tends to hold in any part of
the ocean is carried through the oceanic circulation
1 ee
116 THE OCEAN. [Boox IV.
before described, so also that which the gravitation
of the sun or moon tends to place in any given
part of the ocean is carried through the same course
in relation to the surface of the earth. The fact.
of the moon’s gravitation drawing the tide eastwards
from below the moon, and the sun’s gravitation
drawing the solar tide westwards from below the
sun, has nothing to do with the course of the tide
through the ocean after it has been raised by either
of those forces. After it is placed in any part of the
ocean it is carried from that part, through the course
of circulation which vis-inertiz determines, without
reference to whence it came, just as water placed
in any part of the ocean by the earth’s gravitation
is carried through the same course of circulation
without reference to whence it originally came.
- Whatever the positions of the sun or moon in
relation to any given meridian may be, their gravi-
tation forms a part of the current-creating force of
vis-inertie, acting westwards on that meridian just
as much as on any other meridian. The tidal action
of the sun and moon is, therefore quite distinct from
the current-creating action of vis-inertie, though the
gravitation of the sun and moon is merged in, and
forms a part of, this current-creating force of vis-
inertiee.
The tides, as they are broken by the coast-
lines, are constantly being thrown into the course of
the ocean currents resulting from the action of vis-
Cuap. X.] SOLAR AND LUNAR GRAVITATION. 117
inertie, though ocean currents and tides are move-
ments of distinctly different natures.
The ocean currents, as already shown, result
from the great cosmical force of gravitation draw-
ing in all directions from the centre of the earth,
Opposing terrestrial gravitation drawing towards
the centre of the earth; and they form a system
of circulation within the position in which the
ocean is held by gravitation, without tending to
cause any changing of the position of the ocean in
relation to the surface of the earth ; and these ocean
currents would exist even if the earth were not
affected by the gravitation—or by any other influence
—of the other bodies of the solar system: whereas,
the tides result from the disturbing influence of the
bodies within the solar system, which cause a con-
stant changing of the position of the ocean, in accord-
ance with the changes in their positions in relation to
the surface of the earth ; but the movements which
form the tides are undulations or oscillations of the
ocean, and not currents, though, where obstructed
by coast-lines, they form currents about the coast.
The current-creating action of vis-inertie is the
cause of the currents by which the circulation of the
ocean is effected, and must form the basis of any
effective investigation of the tides ; for the study
of the tides is, in fact, a branch of the study of
vis-inertiz, and it is not possible to trace out and ex-
plain the tidal movements of the ocean without the
118 THE OCEAN. [Boox IV.
assistance of the theory of vis-inertie, which must
reveal the course of the earth’s onward motion in
the universe, as it has revealed the abstract nature
of the forces by which it is held in equilibrium as hig
sweeps along the path determined by those forces.
BOOK VY.
AN INVESTIGATION OF OCEAN CURRENTS.
SHOWING
THAT A CIRCULATION ACCORDING WITH THE ACTION OF
VIS-INERTIZ, DESCRIBED IN BOOK IL, EXISTS IN THE
OCEAN,
121
CHAPTER XI.
EVIDENCES OF THE CURRENT-CREATING ACTION OF VIS-
INERTIA, RESULTING FROM THE AXIAL ROTATION
OF THE EARTH.
PART I.
EVIDENCES OF THE EXISTENCE OF THE CURRENTS DE-
SCRIBED AS ENCLOSING THE OCEANIC DISTRICTS SHOWN
ON THE CHARTS ON PLATES I. AND II.
In the equatorial regions, from the eastern parts of
the Pacific Ocean, there is a constant motion of the
ocean westwards ; and the water carried westwards
by this motion is as constantly replaced by currents
flowing towards the equator from the directions of
California and Chili. In the western part of the
Pacific, the water brought to that part of the ocean
through the equatorial regions is poured northwards
and southwards from the equator, a portion also
continuing its westward course through the channels
leading into the Indian Ocean.
The water turned northwards from the equatorial
regions in the western part of the Pacific Ocean
meets, near the Japan Islands, with a stream of cold
122 THE OCEAN. . [Boor V.
water flowing from the north. The supply of water
brought by these streams to the temperate zone on
the western side of the ocean is carried eastwards
through the temperate zone, forming a constant
stream, which, in the neighbourhood of the coasts of
Oregon, divides northwards and southwards; the
former portion flowing towards Russian America, the
latter towards the equator.
In the North Atlantic Ocean the general course
of the currents is similar to that just described as
existing in the North Pacific Ocean:
namely ;: west-
wards in the equatorial regions; northwards from
the equator to the temperate zone on the western
side of the ocean; southwards from the temperate
zone to the equatorial regions on the eastern side of
the ocean; eastwards through the temperate zone.
In the temperate zone on the western side of the
ocean, the warm water flowing from the equatorial
regions meets a stream of cold water flowing from
the north; and the water which flows eastwards
through the temperate zone divides northwards and
southwards in the eastern parts of the ocean—the
one portion flowing southwards past the Cape Verde
Islands, the other flowing northwards to the east of
Iceland.
We have seen that the westward motion through
the equatorial regions of the Pacific is continued in
the Indian Ocean. In this ocean a further supply for
the westward course of the waters in its equatorial
Cuap. XI] OCEAN CURRENTS. 125
regions is brought from the south temperate zone
by a stream flowing northwards along the western
coast of Australia. The water carried westwards
in the equatorial regions flows southwards, on the
western side of the ocean, from the equator towards
the Cape of Good Hope. Near the Cape of Good
Hope it meets cold water from the south. From this,
through the temperate zone, the water flows eastwards
towards Australia, where a portion of the eastward
stream turns northwards, flowing towards the equator
on the eastern side of the Indian Ocean—the re-
mainder flowing on eastwards towards the South
Pacific. Through the temperate regions of the South
Pacific, the water constantly flows eastwards towards
the coast of South America, where, in the neigh-
bourhood of the southern parts of Chili, the stream
divides—one portion flowing northwards towards the
equator, the other flowing southwards towards Cape
Horn, from which it flows northwards and eastwards
into the South Atlantic.
In the equatorial regions of the Atlantic the great
mass of the water heaves westwards as in the Pacific.
In the eastern part of the South Atlantic, as in that
of the North Atlantic, the water flows from the tem-
perate zone towards the equator, forming a supply
for the great westward motion of the water in the
equatorial regions. From the equatorial regions in
the western part of the ocean, in the neighbourhood
of Cape San Roque, the water brought westwards
124 THE OCEAN. [Boox V.
divides northwards and southwards ; the latter flow-
ing from the equator to the temperate zone through
the western part of the South Atlantic, as we have
seen that the portion turned northwards does through
the western part of the North Atlantic. Through
the temperate zone of the South Atlantic the water
flows eastwards, as through the temperate zone of the
North Atlantic.
Thus far we have given the general features of
the circulation of oceanic currents, as far as has been
so clearly ascertained by experience as to be no
longer questions of controversy. And the course of
the currents, as far as described in this sketch, will
be observed to be in close accordance with that of
the currents which, under the theoretical action of
vis-Inertiz described in Book II., tend to form
the oceanic districts shown in the chart on Plates I.
and II. of this volume, and also in Plate VI.
It is well known that in the Great Southern
Ocean a current flows northwards from the Antarctic
regions of the Pacific, bringing with it icebergs,
which, on reaching the eastward current already
described, are carried eastwards towards Cape Horn ;
and a similar movement of icebergs towards the
Cape of Good Hope from the Antarctic regions of the
Atlantic appears to indicate the existence of a north-
ward current from the Antarctic regions of the
Atlantic analogous to that which flows from the
Antarctic regions of the Pacific. Those portions of
Cap, XI.] OCEAN CURRENTS. 125
the Great Southern Ocean which lie just west of each
of these ice-bearing currents are found to be com-
paratively free from ice, as is shown by the useful
and interesting chart of the Antarctic Ocean recently
published by the Admiralty. The absence of ice-
bergs in the parts of the ocean just mentioned
appears to indicate a southward motion of the water
preventing the ice from moving northwards in those
parts of the ocean. The currents, to and from the
Polar regions, which may be inferred from these
movements of the icebergs, are clearly in accordance,
both as regards their relative positions and directions,
with those described theoretically as resulting from
the action of vis-inertiz, and shown in the charts on
Plates I., II., and XI.
As the current which, according to the theoretical
action of vis-inertiz, runs westwards from the Atlantic
to the Pacific has not been found to exist passing
north of Graham Land, it must, according to that
theory, pass through the unexplored regions lying
between Graham Land and the land (supposed to
be portions of an Antarctic Continent) discovered
in the voyages of exploration under Captain Wilkes
and Sir James Ross. The phenomena of the ice-
bergs above referred to clearly accord with that
which is theoretically indicated as the course of the
current in question. It keeps open a comparatively
clear seaway in its course southwards from the At-
lantic to the Antarctic regions, and, after sweeping
126 THE OCEAN. [Boor Y.
the Antarctic coast, it flows northwards into the
Pacific with its temperature reduced, and laden with
icebergs from the frozen regions of the South.
The accordance of the Antarctic currents with
the theoretical action of vis-inertie is further cor-
roborated by the observations of Sir James Ross and
by those of Captain Wilkes. The former found the
current running southwards off the coast of South
Victoria ; and the latter, who sailed westwards in the
Antarctic regions of the Indian Ocean, along what
he supposed to be the shores of an Antarctic Conti-
nent, says that the movements of the ice detached
from the supposed coast-line appeared to indicate a
motion of the water westwards and northwards.
The remarkable accordance of Captain Wilkes’
observations on the movements of the ice in those
regions with what would naturally result from the
action of vis-inertie in case of a coast-line existing
there, appears tome to leave no doubt of the exist-
ence of a sufficient extent of land in those regions to
form an ‘ Antarctic Continent.’
PART II.
EVIDENCES OF THE EXISTENCE OF THE EQUATORIAL
COUNTER-CURRENTS.
We have thus far found the currents which en-
close the districts shown on the charts as theoreti-
cally resulting from the action of vis-inertia to be in
accordance with actual observation.
Cuap. XI.] OCEAN CURRENTS, 127
In Book II. we described the tendency of the
action of vis-inertize to cause a counter-current to
run eastwards in the equatorial regions, dividing the
waters which tend to diverge northwards from those
which tend to diverge southwards from the equator.
In the Pacific, as might be expected from the con-
figuration of the coast on the western side of the
ocean, such a counter-current is clearly developed.
And this Pacific counter-current appears to be a
remarkable illustration of the amount by which the
current-creating action of vis-inertie exceeds that of
the winds ; for, of any quantity of water blown to-
wards the equator from the north-east and south-east
by the Trade Winds, a portion would naturally tend
to return eastwards through the belt of equatorial
calms, where it is released from the action of the
winds which have impelled it westwards: but this
counter-current appears, as far as I have ascertained,
to run through the region of the NE. Trade Wind ;
whereas the action of the winds might have been
expected so to modify the natural action of vis-
inertiz as to compel it to make its way eastwards
through the calm belt, where the action of the winds,
instead of opposing, would rather, as shown above,
tend to assist it on its course.
In the Atlantic, the configuration of the coast
projecting eastwards in the equatorial regions must pre-
vent a counter-current analogous to that of the Pacific
from being developed to more than a very trifling
128 THE OCEAN. [Boox V.
extent ; and if observable at all, it must appear as an
inshore eddy, or as a stream from the Amazon River.
That which is shown as the equatorial counter-current
of the Atlantic is contained within the north equa-
torial district of currents, and is not (as in the
Pacific) a current dividing the north from the south
equatorial district. In consequence of the peculiar
configuration of the coast of Africa, the current which
runs from the temperate zone to the equator on the
east side of the ocean runs eastwards during a great
portion of the latter part of its course to the equator.
And also the difference in the configuration of the
oceans causes an eastward current to be very largely
developed within the North Atlantic district which
is developed to a comparatively trivial extent in the
South Atlantic district. The evidences of the exist-
ence of these eastward currents must, therefore, be
considered in connection with the investigation of
the currents contained within the North Atlantic
— district.
PART III.
EVIDENCES OF THE EXISTENCE OF THE CURRENTS THEO-
RETICALLY DESCRIBED WITHIN THE OCEANIC DISTRICTS.
The chart of the Atlantic given on Plate XV. is
drawn to illustrate the action of vis-inertiz within
the equatorial districts. Let us consider what traces
of the existence of currents of the nature we have
Een |
=
~
-
SS
«
PlateXV.
to Ulustrate the
CU RRENT-CREATING ACTION
°
VIS - INERTLE
Atlantic Ocean.
Cuar. XT.] OCEAN CURRENTS. 129
described have been observed within the North
Atlantic district.
Speaking of the Atlantic Equatorial Current,
Major Rennell says that—‘ At the middle point
between the two continents, and precisely at the
equator, the stream sends off a very large branch
to the north-west, and into the midst of the North
Atlantic ; whilst the main stream turns to the west-
south-west, pointing to the promontory of Cape San
Roque: and, when it approaches that Cape, it sub-
divides ; the largest part passing by the north of the
Cape, towards the West Indies ; the other southward,
along the eastern coast of Brazil.’ !
The stream mentioned in the first part of the
foregoing extract as diverging north-westwards into
the North Atlantic is clearly in accordance with the
current oR, described theoretically in connection
with Plate [X., as resulting from the action of vis-
inertie. Of this current, Major Rennell says farther
on: ‘The north-west branch of the equatorial
current, which separates in about longitude 23°, as
aforesaid, is traced, at common times, as far north as
18°, and sometimes even as far north as 30°. It
appears to be, at least, eighty leagues in breadth, but
not of rapid motion (perhaps less than one knot at a
mean), and runs nearly in the direction which the
' An Investigation of the Currents of the Atlantic Ocean, by
Major James Rennell, F.R.S. (London, 1832), p. 23. All follow-
ing quotations from Major Rennell are taken from the same
work.
K
130 THE OCEAN. [Boox Y.
NE. Trade admits ships to take; in their progress
northwards it is often a great help.’1 And then
Major Rennell remarks: ‘I am unable to account
satisfactorily for the cause of this great derivation
from the great trunk stream of equatorial current,
unless it be to supply the waste of water, by evapo-
ration, within the tract occupied by the warm water
of the Gulf Stream—in effect its recipient—and the
supply of the Mediterranean Sea.’
As the stream here described runs right across
the NE. Trade Wind, it is naturally a stumblinge-
block in the way of a theory which makes the winds
the great prime movers of the oceanic currents ; for,
if a stream of this sort run right across the NE.
Trade Wind, it is not easy to see how the Trade
Winds can be the great prime cause of the Gulf
Stream, which does not itself run with the wind.
Although this stream has not been traced con-
tinuously beyond 30° N., we find, in another part of
Major Rennell’s useful work, further evidences of its
existence in a course coinciding with the theoretical
action of vis-inertize which we have described. Re-
ferring to a Report on Currents, Major Rennell says :
‘An important notice communicated by it is the
proof of a counter-current of warm water, of 13 to
21 miles, running to the westward, and along the
south side of the main stream (the Gulf Stream),
between the parallels of 35° and 86°. This is the
second example of the same kind, Captain Livingston
© Te hI, a
Caap. XI. |] OCEAN CURRENTS. 131
having experienced a like current in latitude 39°,
and between the meridians of 55° and 622° W.’!
And in a note farther on Major Rennell says further
of this current: ‘ A counter-current of warm water,
reported by Captain Livingston, in such a position as
to appear a kind of anomaly, in our present imperfect
state of knowledge, has been already spoken of at
large. From the weight of authority, the fact cannot
be questioned. It may be sufficient in this place to
state that the current, running W. by N. more than
100 leagues, occurred between the parallel of 38° 50’,
long, 622°, and lat. 39° 20’, long. 55°.’ ?
The warmth of the water in this observed current
is of importance, because, but for its temperature, it
would have been at once asserted that it came from
the Azores. It, however, clearly coincides with the
current & (in Plate LX.), diverging westwards, to turn
southwards, from the point x, at which the stream or
meets the stream A Bc. And, in fact, this water
comes from the equator by a shorter route than that
of the Gulf Stream, which it must meet a short
distance west of the longitude in which it was
observed by Captain Livingston. The current here
reported appears to indicate that the main stream 0 R
meets the stream A BC in mid-ocean, east of the
position in which the current in question was ob-
served ; for, as the stream aBo, flowing from the
equator, tends eastwards, and the offset ©, turned
1 Ib, p. 228. 2 1b. p.:253.
132 THE OCEAN. _[Boox VY.
towards the equator, tends westwards, the latter must
tend to run as a counter-current parallel to the course
of the former, until its natural course westwards
towards the equator is at length obstructed by the
course of the stream aBc. The point at which the
obstruction occurs forms the theoretical point y, from
which the offset H is forced eastwards towards the
equator between the main streams 0 R and ABC.
As regards the evidences of the existence of
the theoretical current H on Plate [X., which is also
illustrated in the Chart on Plate XV., Captain Living-
ston, as quoted by Mr. Findlay, says: ‘I have no
doubt that there is a current, or rather offset, from
the Gulf Stream to windward, between Bermuda and
the Bahamas. In the “ Brilliant,” we found ourselves
retarded very much in making westing when run-
nine for the Hole-in-the-Wall, one day, about 30
miles of longitude, by excellent observations, the
truth of which was confirmed by our land-fall. In
the ‘ Dispatch” we got out of the Gulf on the 13th
of March, 1819, when we were at noon, by observa-
tion, in lat. 28° 0’, long., by account, 79° 12’; on the
20th of March, at noon, we were, by meridian altitude,
in lat. 29° 48’, and long., by account, 72° 32’. Obser-
vations by sun and moon, a good lunar of three
sights, altitudes, and distances, and worked three
times, gave 71° 18’ 30”,"!
1 Memoir descriptive and explanatory of the Northern Atlantic
Ocean, by John Purdy. Twelfth edition, by Alexander G. Findlay,
F.R.G.S. (London, 1865), p. 333.
Cuar. XI.) OCEAN CURRENTS. 133
The current here observed by Captain Livingston
must not, without authority from actual observation,
be confounded with an inshore current running from
the Gulf Stream just north of the Bahamas. For
this latter may be an eddy-current, contained within
the theoretical current asc (Plate IX.), and
caused by the islands which divide that current into
two portions ; the greater portion passing south of
the islands, and the other portion north of them—if,
indeed, at any season the volume of ABC be too
great to pass within the islands—in which case, when
the eddy-current exists, then the portion of the cur-
rent ABC, of which the eddy-current is an offset,
should be found running north-westwards between
that and the Bermudas: but this is a question to be
decided by observation, not only in the current itself,
where it is strong enough to make itself manifest,
but also, in order to determine its nature, whence it
comes and whither it goes, the actual course of the
‘principal theoretical current oR and its variations
must be better determined by actual observation ;
for shallow water, if the bottom be rock or firm
ground, may be little less important in determining
the course of the currents within any district than
actual land. And, indeed, by the configuration of
the bottom of the ocean in the neighbourhood of
the Bermudas, a portion of the cold water, which,
under the theoretical action described in Book II.,
endeavours to pass by an under-current from the
134 THE OCEAN. [Book V.
Labrador Current to the eastern part of the equatorial
regions of the Atlantic, appears to be forced to the
surface of the ocean near the Bermudas—thus
appearing at the surface immediately after under-
running the Gulf Stream. Recorded observations,
which we shall have to mention farther on, appear to
show that, in general, the whole volume of the theo-
retical current ABC passes inside the Bahamas,
though not all through the Gulf of Mexico.
The theoretical current H has also been observed
farther on its course towards the equator, though it
has been accounted for by Mr. Findlay in a manner
which, if there were no other reasons for discarding
the theory which makes the action of the winds
the principal current-creating force, would be most
natural. Inthe North Atlantic Memoir, Mr. Findlay
says, ‘It has been found that during calm weather,
even with strong easterly winds, the currents have
sometimes been running for days together to the
eastward, especially in the latter parts of January:
and July, when, by the then prevailing strong winds,
the water is heaped up in a very uncommon degree,
and the inner part of the Caribbean Sea, most
probably overcharged, succeeds in re-establishing its
equilibrium by forsaking the power of its wrathful
driver. In this manner, I think, we ought to recon-
cile those circumstances.’ *
But considering how greatly the action of vis-
| 7b, p. 306.
Cap. XI.] OCEAN CURRENTS. 136
inertize, according to the phenomena before mentioned,
exceeds that of the winds, and the manner in which
its action in the ocean, indicated by the oblate sphe-
roidal form of the earth, is corroborated by the argu-
ments in Book III., it is scarcely too bold to suggest
that this current may at times be found distinctly
running eastwards when there is no eastward current
running from the Caribbean Sea; or even when the
currents are as distinctly running westwards into the
Caribbean Sea through all its western channels. In
this—perhaps an extreme case, and suggested only
for the sake of illustrating the theory—the currents
running westwards into the Caribbean Sea would be
supplied by the equatorial current along the northern
shore of Brazil, and by a current running south-
eastwards from the direction of the Bermudas, and
afterwards curving southwards and westwards to
those channels. These two currents, on uniting to
flow into the Caribbean Sea, would represent the
theoretical current ABC in Plate [X. As to whether
the whole of the theoretical current ABC passes
through the Caribbean Sea, or only a portion of it,
the remainder passing north of the Antilles, is a
question which can be decided only by actual ob-
servation. :
This eastward current (Hu, Plate IX.) is also
mentioned by Captain Richards, in a paper published
by the Admiralty, in which Captain Richards says :
‘To the eastward of 40° W., part of this easterly
136 THE OCEAN. [Book V.
current approaches nearer to the equator, or to about
2° N., and decreases considerably in strength, until
joining the Guinea Current, where it increases again
in velocity as it nears the African shores.’ That the
current observed running eastwards in the western
parts of the ocean is not the same as that which
runs eastwards in the eastern parts of the ocean
appears from what Captain Richards says in the same
paper—namely : ‘ This counter-current has been traced
to extend, at certain months of the year, from the
meridian of 53° or 50° W. to that of about 25° W.,
and thus joining or forming a part of the well-known
Guinea Current. It is seldom experienced to the
southward of 2° N.,’ &c
Now, that this current should have been traced
as far as 25° W., accords perfectly with the current
theoretically described ; and that, when the equatorial
belt of calms is in the same latitude as the eastward
currents in question, water carried westwards towards
the equatorial calm belt by the Trade Winds may
escape eastwards in the belt of calms, and so tempo--
rarily effect a union on the surface of the currents,
appears probable enough ; but that the currents are
intrinsically different and independent of one another
appears from the fact of the existence of the current
described by Major Rennell, branching off precisely
oa the equator north-westwards, in latitude 233° W.
1 Notice to Mariners—Atlantic Ocean Currents near the
Equator. Hydrographic Office, Admiralty (London, 1866).
Cuar. XI.] OCEAN CURRENTS. 137
As this north-westward current branches off from
the great westward current of the equatorial regions,
it obviously divides the counter-current running
eastwards in the western parts of the ocean from
the Guinea Current running eastwards in the eastern
parts of the ocean.
I have noticed that a peculiarity in the configura-
tion of the bottom of the ocean appears to be the
cause of a portion of the great North Atlantic under-
current being forced to the surface of the ocean in
the neighbourhood of the Bermudas. And, con-
sidering the great mass of reported currents men-
tioned in Mr. Findlay’s North Atlantic Memoir, it
would appear that the theoretical current E (Plate
IX.) is displaced from what would otherwise be its
natural course, in consequence of this same obstruction.
This appears to be so for the following reasons.
Speaking of the Sargasso Sea, Mr. Findlay, in the
North Atlantic Memoir, says that he is ‘ assured, from
the comparison of a great number of journals, that in
the basin of the North Atlantic Ocean there exist two
banks of weeds, very different from each other ; the
most extensive is a little to the west of the meridian
of Fayal, one of the Azores, between lat. 25° and
lat. 36° :’ the second ‘ occupies a much smaller space
between the 26° and 22° of latitude, eighty leagues
east of the meridian of the Bahamas.’! Such a
1 Memoir Descriptive and Explanatory of the Northern Atlantic
Ocean, p. 292. ;
138 THE OCEAN. [Boox V.
division of the Sargasso weeds may be taken to indicate
the course of the theoretical stream 0 rR; the central
part of that current making a clear way for itself by
throwing off the weeds on both sides into the more
slowly-moving portions of the rotating currents on
each side of it. If these floatine weeds thus indicate
the course of the stream oR, it must then also be
inferred that the theoretical stream & lies west of the
smaller or western portion of the floating weeds ;
these weeds being encircled by the stream o r, and
the counter-streams E and u. And, in fact, numerous
observations show a setting of the water from the
border of the Gulf Stream south-eastwards towards
the Antilles; though the connected course of the
counter-streams E and H, and the natural position of
the theoretical point Y, appear to be interfered with
by the intruding under-current, which we have men-
tioned above as appearing to be forced to the surface
near the Bermudas. In this case, from the north of
the Antilles, the theoretical current H must continue
its course eastwards and south-eastwards towards
the equator, between the mid-ocean current and
the equatorial current, both running in the opposite
direction.
This gives a circulation in accordance with the
theoretical action of vis-inertiz described in Book II.
in connection with Plate [X., and also in accord-
ance with recorded observations, excepting that the
course of the counter-current is not very satisfactorily
Cuar. X1.] OCEAN CURRENTS. 159
traced from the point x, where the Gulf Stream meets
the mid-ocean stream, to the Antilles; but this I
have suggested is in consequence of the intrusion of
the under-current, which deranges the circulation of
the surface currents in that part of the ocean.
I do not find any recorded observation to indicate
that the current E, at any season of the year, takes
a southward course passing east of the Bermudas ;
and also, if it ever take such a course, a current
running north-westwards midway between the
Bahamas and the Bermudas must almost neces-
sarily be concomitant with it; and for this I find no
authority either.
Let us now briefly recapitulate what, according to
the foregoing investigation, appears to be indicated,
alike by theory and observation, to be the general
circulation within the equatorial district of the North
Atlantic Ocean.
From the equator, in mid-ocean, a stream runs
off north-westwards into the North Atlantic. The
projecting coast of Africa causes the stream which
encircles the district, returning to the equator on
the east side of the ocean, to press down upon the
north-westward stream, which latter forms a barrier
preventing the southward stream from falling west-
wards. The north-westward stream, as it flows
through the ocean, clears a way through the Sargasso
Sea, thrusting the weeds off to both sides of its course.
The current 0 R, diverging north-westwards from the
140 THE OCEAN. [Boox V.
equator, has, as already explained, a tendency to turn
more and more northwards as it proceeds on its
course ; and the current ABC meets it in mid-ocean,
south of lat. 40° N. From the meeting-point (x) the
offset northwards is carried eastwards ; which is the .
course which the current or would itself, sooner
or later, have taken, even if not interfered with by
the current aBc: and the offset southwards (#),
being under that influence of change of latitude which
tends to carry it westwards, runs as a counter-current
along the right-hand side of the stream aBc until
the course of the latter forces it eastwards, forming
the eastward current H from the point y to Z, so that
the streams E and H form acontinuous counter-current,
running from the point x, at which the stream or
meets the stream ABC, first westwards and then
eastwards, along the right-hand side of the stream
ABC to the point z, at which the stream 0 R diverges
from the equator. The connected course of this
counter-current appears to be interfered with by the
upheaval of an under-current, forced to the surface
by some peculiarity in the configuration of the ocean
in the neighbourhood of the Bermudas ; but it has
been recorded running westwards counter to the Gulf
Stream from about mid-ocean south of lat. 40° N.:
then setting south-eastwards, from the Gulf Stream,
between the Bermuda and the Bahama Islands : and
again running south-eastwards, from the direction
of the West Indies towards the equator in mid-
is)
Cuapr. XI.] OCEAN CURRENTS. 141
ocean. It often forms a rapid current, running east-
wards north of the Virgin Islands. These appear
_to be the normal currents within the district, though
varying their position and velocity with the seasons,
and, at intervals, to a greater or lesser extent
obliterated by the action of gales and other causes.
Now, if the currents of the North Atlantic Ocean
are such as here described, then does not that stream
flowing from the equator through mid-ocean towards
the banks of Newfoundland explode the theory which
makes the winds the cause of the great oceanic cur-
rents ? Does itnot explode any theory which makes
the winds the principal cause in determining the
course of the currents,—even supposing the principal
motive force to result from the inequalities in tem-
perature and other conditions between the polar and
equatorial regions ? A theoretical consideration of
the action of vis-inertize shows that it must tend to
cause such a current: and the investigation of
recorded phenomena shows evidences of its actual
existence ; and therefore, as it runs its course and
forms its counter-currents in a manner according with
the laws indicated by that theory, it must be admitted
as a proof of the paramount action of vis-inertix in the
ocean, at least until some other reasonab!e explanation
of its existence be given.'
1 Evidence of the existence of the current E H in the North
Pacific, the South Pacific, and the South Indian Oceans is more
clear than above shown for the North Atlantic.
142 THE OCEAN. [Boor VY.
CHAPTER XII.
EVIDENCES OF THE CURRENT-CREATING ACTION OF
VIS-INERTIZ RESULTING FROM THE ONWARD MOTION
OF THE EARTH THROUGH SPACE.
PART I.
GENERAL EVIDENCES OF ONWARD MOTION.
In the theoretical consideration of vis-inertie, I
have in Chapter III. described the variations in the
direction of the action of the orbital force of vis-
inertie, showing a daily variation through fourteen
points of the compass, and an annual variation through
four points, the daily variation being from an action
westwards in the night-time to an action eastwards
in the daytime, and the annual variation being from
an action northwards in March to an action south-
wards in September.
Now, on examining the actual movements of
the ocean, although there appear such effects as
may be expected, in accordance with the theoretical
action of vis-inertiz, to result from an onward motion
of the earth, these effects do not accord with that
indicated theoretically as the action of vis-inertix
Cuap. XII. ] OCEAN CURRENTS. 143
vo
resulting from the orbital motion. But, variations
in the effects alluded to as being in accordance with
what the theoretical consideration of the action of vis-
inertiz indicates to be the natural result of an onward
motion of the earth, appear to show that the orbital
force is a partial cause of the effects observed.
For instance, the effects apparent in the ocean,
instead of showing an annual change in the action of
vis-inertiz from a northward to a southward direc-
tion, indicate a constant action northwards ; though
at the same time an annual variation in the northward
action, by which its action in March is greater than
in September, appears to show the influence of the
orbital force.
And also, as regards the diurnal variation in the
action of the orbital force, there is not apparent such
a reversal from eastwards in the daytime to west-
wards at night-time as that which the sole action of
the orbital force would tend to cause. But there
are, however, apparent effects which indicate such
a change from an eastward action in the daytime
to a westward action in the night-time as accords
with the onward motion indicated by the north-
ward action and its variation above mentioned.
Because in such case the orbital motion being only a
component of the earth’s true motion, and the latter
being not in the plane of the ecliptic, but inclined
southwards, more in the line of the poles ; then, in-
stead of a diurnal change from east to west through
144 THE OCEAN. [Boox Y.
fourteen points of the compass, the diurnal change in
the action of the force resulting from onward motion
would be less in proportion as the direction of the
motion more nearly coincided with the line of the
poles. Ifthe line of motion coincided exactly with
the line of the poles there would then be no varia-
tions whatever in the action of the force resulting
from that onward motion ; but its action throughout
the year, both by day and night, would be north-
wards through mid-ocean and southwards along the
shores.
In the ocean, effects in accordance with the action
theoretically resulting from an onward motion of the
earth indicate a motion southwards ; and variations
both annual and diurnal appear to indicate that,
though the line of motion does not coincide with the
line of the poles, the divergence of those lines is not
very great.
The action of vis-inertie resulting from the onward
motion of the earth appears to be indicated in the
Atlantic by a greater tendency of the currents in
mid-ocean to run northwards, and of those along
the coasts to run southwards, than accords with the
action of vis-inertize which results from the axial
rotation of the earth. For instance, the current
which diverges northwards from the equator in mid-
ocean under the action of axial rotation, as before de-
scribed, we have found to be clearly recorded ; whereas
Cuar. XII.} OCEAN CURRENTS. 145
I do not find that the analogous divergence south-
wards has been noticed, and it is only by means
of observations which accord with the course of its
counter-currents that I find any recorded trace of its
existence. And, as regards the coasts, the stream
which runs southwards from the Arctic regions on the
west of the ocean shows a remarkably constant ten-
dency to keep inshore during the whole of its course
from the east coast of Greenland to the coast of
Florida: it being, in fact, forced inshore both by the
action resulting from axial rotation and by that
resulting from onward motion. But the stream from
the Antarctic regions, analogous, as far as axial rota-
tion is concerned, to the Arctic stream just described,
appears to be drawn from the direction of Cape Horn
eastwards towards mid-ocean, though the sole action
of axial rotation would tend to throw it inshore from
Cape Horn, and cause it to run northwards along
the east coast of South America! in the same manner
as that in which it tends to throw the Arctic stream
inshore against the coast of North America ; instead
of which the stream from Cape Horn bears eastwards,
leaving a great eddy to run southwards between it
and the shore.
' The ‘Challenger’ exploraticns have shown the existence of
a greater mass of cold water moving northwards below the surface
in that locality than was apparent in 1868, when the above was
published. But the corresponding stream in the northern hemi-
sphere is much more apparent on the surface, as stated in the text
above, which those explorations corroborate.
L
146 THE OCEAN. [Boox V.
The tendency of this Antarctic stream to take its
northward course through mid-ocean, compared with
that of the Arctic stream hugging the shore in its —
southward course, accords with what would naturally
be the action of vis-inertie resulting from a south-
ward motion of the earth. For we have seen that
the action of such a force tends to circulate the
waters northwards through the deep and central
parts of the ocean, and southwards along the shores.
This action appears to be again exemplified on the
east of the ocean by the frequent occurrence of a
stream southwards from the equator along the west
coast of Africa ; the northward stream from the direc-
tion of the Cape of Good Hope being drawn towards
mid-ocean, whilst the southward stream runs between
it and the coast.
PART II.
EVIDENCES OF VARIATIONS ACCORDING WITH THE VARIA-
TIONS IN THE COURSE OF THE EARTH’S ORBITAL
MOTION.
As regards that annual variation in the ten-
dency of northward streams towards mid-ocean, and
of southward streams towards the coasts, which appears
to indicate the influence of the earth’s orbital motion,
tending to make the northward action of vis-inertix
more decided in March than in September : it appears
Cuar. XII.] OCEAN CURRENTS. 147
to be exemplified by the Arctic stream, which runs
southwards on the North American coast, thrusting
the Gulf Stream farther from the coast in March than
in September. These currents have been more elabo-
rately investigated than any other great ocean currents,
and the annual variation here mentioned accords
with the idea of its being influenced by the earth’s
orbital motion ; but I have not met with any other
recorded variations of ocean currents that appear suffi-
ciently definite to be adduced as indicating the action
of the same cause.
As regards the diurnal variation which, if the
line of motion be not coincident with the line of the
poles, must result from the action of vis-inertix
being west of north in the night-time and east of
north in the daytime ;—the phenomena of winds in
given localities having a different average direction
in the night-time from the average direction in the
daytime are in accordance with such a cause ; though
I know of no recorded phenomena that can be clearly
traced in its action, as alterations in the relative
temperature on land and water tend to produce the
same effect. The Straits of Gibraltar appear well
adapted for ascertaining the diurnal variation in the
orbital force of vis-inertie, as the tendency of its
action would be to cause a current westwards from
the Mediterranean in the night-time, and eastwards
from the Atlantic in the daytime; and therefore the
current may be expected oftener to take a westward
Te
148 THE OCEAN. [Boox V.
course from the Mediterranean during the night-time
than during the daytime. On the only occasion on
which I have passed through those straits, instead of
the current usually running eastwards, a strong cur-
rent was running westwards from the Mediterranean,
and that was during the night-time.
These remarks on the annual and diurnal varia-
tions possibly resulting from the action of the orbital
force would not be ventured on but for the clear
manner in which the evidences of the action of vis-
inertiz, resulting from axial rotation and onward
motion, accord with that indicated by the theoretical
consideration of their action.
BOOK V1.
AN INVESTIGATION OF THE TIDES
SHOWING
THAT THE TIDAL MOVEMENTS OF THE OCEAN ACCORD
WITH THE ACTION OF THE FORCES DESCRIBED IN
BOOK IV,
151
CHAPTER XIII.
EVIDENCES OF THE TIDAL ACTION DESCRIBED IN
CHAPTER X.
PART I.
THE MOTION WEST IN THE EQUATORIAL REGIONS AND
EAST IN THE TEMPERATE ZONES.
THE action of the forces described in Chapter X. as
tending to give the tide-waves a motion westwards
in the equatorial regions and eastwards in the tempe-
rate zones, is indicated by the following observations,
in a most useful paper, relating to the subject of the
tides, by the late Admiral Fitzroy.
‘Referring to the times of high water on the days
of full and new moon, and giving all the tidal hours
in Greenwich time, Admiral Fitzroy says : ‘ It is
high water at the east side of the Atlantic, from the
Canary Islands to Scotland, within an hour or two
of the same time, on the salient points of the coast,
| namely at about 4°.’ 1 This clearly accords with the
eastward course of the tide-wave through the tem-
perate zone.
1 The Weather Book: a Manual of Practical Ba eccig c IY;
p. 384. By Rear-Admiral Fitzroy. London, 1863.
152 THE OCEAN. [Book VI.
On the west of the ocean: ‘It is high water
at. about 1" from 30° to 40° N.’1 ‘This accords
with the tide which rolls from the east through
the equatorial regions. But Admiral Fitzroy gues
on to say : ‘The times increase northwards from
40° N. to the Bay of Fundy, and also southwards
from 50° N. to that bay.’* The times increasing
northwards from 40° N. to the Bay of Fundy shows
the eastward motion of the tide in the temperate |
zone, and the times increasing southwards from
50° N. appears to accord with the configuration
of the coast, which causes the portion of the tide
drawn eastwards from the coasts of Labrador to
interfere with that drawn eastwards from the coast
of the State of New York.
‘It is high water at 6" on the coast of Brazil, and
at 9" about Blanco Bay (in 40° 8.).’° This shows
the equatorial tide rolling westwards, and then turned
southwards by the coast.
‘From 50° 8. to near Blanco Bay, in 40° S., the
tide-wave certainly travels along the coast to the
north.’* This accords with the tide which rolls east-
wards through the temperate zone of the southern
hemisphere, and sets northwards along the coast of
Patagonia after rounding Cape Horn, but at the same
time tends to follow its eastward course through the
temperate zone of the South Atlantic Ocean.
Admiral Fitzroy speaks of ‘ the flood-tide moving
1 P. 384. 2 P. 384. Sooo: bed See cto hp
eS 2 ae
Cuar. XIIL.] THE TIDES. © 153
towards the west and south along the coast of Brazil,
from near Pernambuco to the vicinity of the River
Plate,’ and also of ‘ the almost uniformity of the
time of high water along that extent of the coast of
Africa which reaches from near the Cape of Good
Hope to the neighbourhood of the Congo.’* The
former we have already mentioned, as indicating
the equatorial tide moving westwards and then turned
southwards by the coast ; the latter accords with the
tide rolling eastwards in the temperate zone.
‘ Against the supposition that a tide-wave travels
along the west coast of America, from south to north,
are the facts—that the flood-tide impinges upon
Childe and the adjacent outer coast, from the south-
ward of west; that it is high water at Cape Pillar
and at Childe, including the intermediate coast,
almost at one time ; that from Valdivia to the Bay
of Mexilones (differing 18° in latitude), there is not
an hour’s difference in the time of high water ; that
from Arica to Payta the times vary gradually as the
coast trends westward ; that from Panama to Cali-
fornia the times also change gradually as the coast
trends westward ; and that from 40° to 60° N. high
72 These facts accord
water takes place at one time.
with the tides rolling eastwards through both of the
temperate zones of the Pacific.
‘In 50° N. it is high water at Vancouver’s Island
at 9", and at the south extreme of Kamtschatka it
bPoatt. 2 Pasi h
154 THE OCEAN. [Boox VI.
is said to be high water at about 6°; the difference,
nine or three hours, is anomalous—made so, probably,
by a derivative tide, or by a mistake.’* But the
tide which reaches Kamtschatka at 6" must, out in.
the ocean, have then advanced considerably farther
on its eastward course, and therefore the difference of
3" between Kamtschatka and Vancouver’s Island does
not appear improbable.
‘High water takes place at one time (within an
hour) all along the east coast of Africa ’? :—according
with the tide moving westwards through the equatorial
regions of the Indian Ocean.
The paper by Admiral Fitzroy, from which all
the foregoing facts have been quoted, was written for
the purpose of showing how incompatible the actual
movements of the tides are with the theory which
supposes the tides of the Atlantic Ocean to be caused
by simply derivative waves branching off from a
wave rolling through the Great Southern Ocean.
PART II.
THE EQUILIBRIUM OF THE TIDES.
That the tidal undulations—rolling westwards in
the equatorial regions, and eastwards in the temperate
zones—counterbalance each other, and thus preserve
the eqnilibrium of the ocean as a whole, as regards
Pe one: gimlesraietss
Cuap. XIII ] THE TIDES. 155
the surface of the earth, appears to be indicated in
the North Atlantic Ocean by the great height of the
tides in the temperate zones compared with the rise
and fall in the equatorial regions. For the water
moved eastwards in the temperate zones is a counter-
poise to that moved westwards in the equatorial
regions by the same tide: and since the space from
Nova Scotia to France and the British Isles, in which
the eastward tide moves, is very narrow compared
to that extending through the equatorial regions from
the Gulf of Guinea to the Gulf of Mexico—therefore,
since the tide in the east of the temperate zone must
counterbalance that in the west of the equatorial
regions, its rise and fall must be greater in propor-
tion with the lesser extent of ocean through which it
moves. So also with the tides in the west of the
temperate zone, which counterbalance those in the
east of the equatorial zone ; the rise and fall abaut
Nova Scotia is far greater than that in the Gulf of
Guinea, for the same reason that the rise and fall
about the British Isles is greater than that about the
West Indies. This counterbalancing movement of
the tides is still more strikingly indicated by the
contrast between the rise and fall in the temperate
zone of the North Atlantic Ocean, compared with
that in the temperate zone of the southern hemi-
sphere. In the latter case the tide, which moves
eastwards, has a more or less clear sweep from about
the Falkland Islands and the River Plate to the
156 THE OCEAN. [Boox VI.
shores uf Chili; and the rise and fall is less, in
proportion as the space through which it moves is
greater than that through which, in the equatorial
regions, the same tide moves westwards. Thus, in-
the temperate zones of the South Atlantic Ocean (in
the neighbourhood of the River Plate), the rise and
fall of the tides is less than in the equatorial regions,
because the space through which they move is greater
than that of the equatorial tides which they counter-
balance. In the South Pacific Ocean the tides,
which roll eastwards in the temperate zones, have a
considerable rise and fall against the shores of Pata-
gonia, in order to counterbalance those which roll
westwards, through the long extent of the equatorial
regions, to the East Indies. .
The action of the coast-lines in crowding the tide
in some parts of the ocean more than in others, is seen
on a smaller scale wherever parts of a tide are raised
higher than other parts of the same tide by the crowd-
ing action of the coast-lines of bays and estuaries.
PART III.
CONVERGENCE TOWARDS THE EQUATOR.
In an ocean completely enveloping the earth the
tide would, according to Chapter X., be an hour
earlier on the average for each fifteen degrees of lati-
tude as well as for each fifteen degrees of east longi-
Cuap. XIII. ] THE TIDES. 157
tude ; for the tide travels down each meridian from
the poles to the equator in about six hours. This
_ convergence should be most apparent in high latitudes,
in which the change in velocity of rotation is most
rapid. And, in fact, it seems to be indicated in the
North Atlantic by a southward course of the tide to
the North of Scotland and Labrador, coalescing with
the eastward course through the temperate zone ;
and in the South Atlantic by the northward course
along the coast of Patagonia of the tide which meets
that coming down the coast of Brazil from the equa-
torial regions.
In the eastern part of the Pacific this converging
action is sufficiently indicated by the extract on page
153 in which Admiral Fitzroy argues against the
course of the tide-wave being from south to north ;
for the preponderance of the eastward action in both
of the temperate zones seems simply to make the
convergence of the tides towards the equator more
rapid than it would otherwise be, due allowance being
made for the direction of the coast-line.
Throughout the Great Southern Ocean the motion
along the meridians towards the equator is clearly
indicated on Dr. Whewell’s chart of co-tidal lines ;
and though that chart professes to show a westward
motion in the Great Southern Ocean to be the source
of the North Atlantic tides, it gives evidence of the
opposing motions of the tides westwards in the equa-
torial regions and eastwards in higher latitudes.
158 THE OCEAN. fBoox VI.
CHAPTER XIV.
EVIDENCE OF THE TIDAL ACTION DESCRIBED IN
CHAPTER IX.
WE have seen, in the preceding chapter, that the
actual course of the tide-waves, in relation to the
surface of the earth, accords with the theory which
gives them a motion westwards in the equatorial
regions, and eastwards in the temperate zones: that
the relative rise and fall on different coasts accords
with the theory which requires that the tide which
rolls westwards in the equatorial regions must coun-
terbalance that which rolls eastwards in the tem-
perate zones, so as to preserve the equilibrium of the
ocean as a whole; and that the advanced position
of the tide in high latitudes is indicated by a con-
vergence from those latitudes towards the equator.
As regards the hours of the spring-tides raised by
the sun and moon in the positions given in Fig. 4,
Plate XIII., we cannot, in consequence of the contor-
tions of coast-lines, expect, without a very elaborate
analysis of the subject, to arrive at more than rough
approximation to the theory sketched in Chapter X.
Let us suppose that when the central part of the
Atlantic, midway between the coast of America on
the west, and that of Africa and Europe on the east,
Cuar. XIV. ] THE TIDES. 159
is at the hour of 9 a.m., the tidal action of the luni-
solar force is at its greatest point on the Atlantic, so
as to make the undulation or vibration then formed
the principal source of the tidal undulations vibrating
through the Atlantic until the next action of a tide-
raising force.
Now, when it is 9 A.M. in the central parts of the
ocean, it is about 12 (noon) about the western shores
of Europe. And as on the days of full and new
moon, the high tides reach those shores at about
4 pm and 4 a.m.’ the high tides two days after
(when the solar and lunar tides are in conjunction)
occur at about 6 A.M. and 6 p.M., low water occurring
at the intermediate hours, which are those of noon
and midnight: but when it is noon on the western
shores of Europe, it is 9 a.m. about the central parts
of the ocean. ‘Thus the time of low water occurs at
noon on the shores of Europe, because it is then
9 A.M. in the central part of the Atlantic, and the
meridian of 9 A.M. and 9 P.M. is, approximately, that
on which the combined action of the sun and moon
tends to raise the high spring-tides about two days
after full and new moon. When the lunar and solar
forces which raised the tide in the centre of the
ocean are withdrawn, it falls in the centre of the
ocean, and rises on the shores. And since the hours
of 9 A.M. and 9 p.m. are the times of high water in
the centre of the ocean, the intermediate hours
(which are those of 3 p.m. and 3 a.m.) are the hours
WP. 151.
160 THE OCEAN. [Book VI.
ot low water in the central parts of the ocean. But
when it is 3 A.M. in the central parts of the Atlantic
it is 6 A.M. on the western shores of Europe, which
is, approximately, the actual time of high water on
those shores two days after full and new moon.
We have also shown that when the action of the
sun and moon passes west of the position in which it
has raised a tide, it ceases to be a disturbing influence ;
but the water, being placed in that part of the ocean
by those or any other forces, is at once carried along
with the course of the oceanic circulation caused by
the action of vis-inertia. And by this action the tide
is consequently carried from the central parts of the
ocean eastwards in the temperate zones, and west-
wards in the equatorial regions, by the axial rotation
of the earth ; and by the same action, in consequence
of the onward motion of the earth southwards through
space, the tide is carried northwards through the
deep and central parts of the ocean, with a corre-
sponding tendency southwards along the shores.
That the course of the tides thus indicated by
theory is that which they actually follow, appears to
be shown by the fact of high water occurring at almost
the same time on the western shores of Europe and
on those of Africa south of the equator ; and also by
their having such a general tendency northwards, as
well as to synchronise on opposite sides of the ocean,
as to have led to the general acceptance of the theory
which supposes a great tide-wave to follow the course
of the sun and moon westwards through the Great
Cuar. XIV.] THE TIDES. 161
Southern Ocean, and to send off a branch northwards
through the Atlantic, making the tides of the North
Atlantic Ocean simply the effect of undulations caused
three tides earlier in the Great Southern Ocean—
the direct action of the sun or moon on the North
Atlantic Ocean, in their intervening passages of the
meridian, not being supposed to interfere with the
progress of the tide-wave previously raised in the
Great Southern Ocean. We need not here argue
against this theory, for its non-accordance with actual
facts has been sufficiently pointed out by Admiral
Fitzroy, even supposing the course of the tide-waves
through the great Southern Ocean to be westwards.
Admiral Fitzroy, though objecting to the idea of the
tides of the North Atlantic Ocean being simply deri-
vative from the Great Southern Ocean, does not
appear to have thought of the tide through the lone-
est expanse of water on the globe running eastwards
against the course of the sun and moon ; but he so far
accepted the prevailing theory as to suppose the tide-
waves to follow the course of the sun and moon west-
wards through that ocean ; whereas, according to the
theory suggested in this volume, though the pivot
of the tide maintains its position in relation to the
force which raises it (or, rather, would maintain that
position if the ocean surrounded the globe com-
pletely), the tide has, in relation to the surface of the
earth, a motion eastwards in the temperate zones, and
westwards in the equatorial regions.
162 THE OCEAN. [Boox VL.
Besides the foregoing, the theory in Chapter X.
accords with and explains the fact of the spring-tides
occurring a day or two after new and full moon, and
the neap-tides a day or two after the moon’s quarters.
For it is only some time (approximately stated as
two days) after the moon has been in conjunction or
opposition that the lunar and solar tides are in con-
junction ; and the same time after being in quadra-
ture, the lunar and solar tides are in complete oppo-
sition. It is because the apparent course of the
earth round the moon is in the opposite direction to
that of its course round the sun (the real course of
the moon round the earth being in the same direction
as that of the earth round the sun), that the conjunc-
tion of the tide raised by lunar gravitation with that
raised by solar gravitation occurs about the time
when those bodies are in opposition, and not when
those bodies are in conjunction. And it is because
the orbit described by the earth in its course round
the moon is smaller than that which it describes in its
orbit round the sun that the time at which the tides
are in conjunction does not coincide exactly with the
time at which the sun and moon are in opposition.
Note.—Independently of the configuration of the
oceans, the meeting of the equatorial tide with those
converging towards it from the polar regions, together
with the convergence of the meridians, may give the
tides a general tendency to a greater rise and fall in
the temperate zones than elsewhere.
BOOK VII.
REFUTATION OF OBJECTIONS TO THE FOREGOING VIEWS.
165
CHAPTER XY.
REFUTATION OF OBJECTIONS, ON A PRIORI GROUNDS,
AGAINST THE POSSIBILITY OF THE EXISTENCE OF
THE ACTION OF VIS-INERTIZ IN THE OCEAN OR
ATMOSPHERE.
Dr. CuarLes Hurron appears to have been among
those who rejected the idea of the winds being an
adequate cause to account for the currents known to
exist in the ocean; for he speaks of the ‘ natural
and general currents of the sea’ as ‘arising from the
diurnal rotation of the earth on its axis, or the
tides,’ &e. !
But, though appearing to regard the axial rota-
tion of the earth as the cause of oceanic currents, Dr.
Hutton discards its action in the atmosphere ; though
he gives no reason to show why, if the arguments
used to disprove the existence of the action of vis-
inertize in the atmosphere be valid, they are not to
be regarded as equally valid if applied to the ocean.
In speaking of the winds, Dr. Hutton mentions
that Descartes, Rohault, and others, considered the
diurnal rotation of the earth to be the cause of these
1 A Philosophical and Mathematical Dictionary. By Charles
Hutton, LL D. London, 1815. Article, CuRRENT.
166 THE OCEAN. (Boox VII.
aérial currents; and says that against this hypo-
thesis it is urged that—‘the air being kept close
to the earth by the principle of gravity, would in
time acquire the same degree of velocity that the
earth’s surface moves with, as well in respect of the
diurnal rotation as of the annual revolution about
the sun, which is about 60 times swifter.’ *
Now, in the first place, hypothetically, let every
word of this be unreservedly admitted,—and even
more—let it not only be said that the air would mm
time acquire the same degree of velocity that the
earth’s surface moves with, because it might then be
argued that the air has not yet had suficzent time to
acquire that degree of velocity, and that therefore
vis inertia, not being yet overcome by gravitation,
still causes movements of the air and water—there-
fore let it, I say, in the first place be asserted and
admitted that the air and water have, and must
have, the same degree of velocity that the earth’s
surface moves with, both in respect to the diurnal
rotation and orbital motion, and that the laws of
gravitation will not admit of its being otherwise.
If taken literally, even admitted in this more ab-
solute manner, that which is offered as an objection
to the possibility of currents being caused by the
motion of the earth, instead of being a real objection,
would, as far as the axial rotation of the earth is
1 4 Philosophical and Mathematical Dictionary. By Charles
Hutton, LL.D. London, 1815. Article, W1np.
CHar. XV.] REFUTATION OF OBJECTIONS. 167
concerned, absolutely necessitate the formation of
currents westwards, both in the ocean and the at-
mosphere—those of the atmosphere having the greater
velocity ; because, since the circles of rotation in the
ocean, and still more in the atmosphere, are greater
than those of the surface on which they rest, there-
fore, unless the velocity of the motion of the ocean
and the air be greater than that of the surface on
which they rest, they must lag behind, forming cur-
rents westwards ; therefore, if in the motion of axial
rotation the air has the same velocity that the earth’s
surface moves with, it must then have a relative
motion westwards over the surface of the earth.
And, as far as the orbital motion of the earth is
concerned, that which is offered as an objection is not
logically an objection at all; because, since in the
orbital motion of the earth all particles of the solid
surface of the earth move in equal ellipses with equal
velocities, therefore, the atmosphere, without chang-
ing the relative positions of its particles as regards
each other, might, by its particles moving in concen-
tric ellipses, keep pace with the earth, and at the same
time have a relative motion over the surface of the
earth in lines parallel with the plane of the ecliptic ;
and at a velocity amounting in the plane of the
ecliptic to more than sixty miles a day.
It thus appears that, if taken literally, that which
has been offered as an objection to the possibility of
any current-creating action resulting from the motions
168 THE OCEAN. [Boox VII.
of the earth—does, in fact, necessitate a current-
creating action in the plane of the equator as far as
the axial rotation of the earth is concerned : and that
it admits of a current-creating action in the plane of
the ecliptic, as far as the orbital motion of the earth
is concerned, at a velocity of more than sixty miles a
day.
I do not, however, by any means suppose that I
have replied completely to the sense in which the
objection is intended to be understood. The objection
appears to be twofold.
One of the objections intended appears to be, that
since the velocity of the earth’s orbital motion is
more than sixty times greater than that of its axial
rotation, therefore, if the atmospheric currents said
to be caused by axial rotation really were so, there
ought then to be far more manifest effects resulting
from orbital motion. But in reply to this I have .
shown, in Chapter III., that the current-creating
action of vis-inertie depends on the differences in
the force of its action in different parts of the ocean
(or atmosphere), and that, in consequence of this, the
current-creating action of axial rotation is far greater
than that of orbital motion.
And if, instead of the literal sense of the objections
above refuted, it be asserted that the ocean and
atmosphere are held in their positions, 7m relation to
that part of the surface of the earth on which they rest,
by gravitation, and that no action of vis-inertiw can
Cuap. XV.] REFUTATION OF OBJECTIONS. 169
even in the least degree modify or affect those posi-
tions,—let this, then, also be admitted : and even then,
supposing all the particles of which either the ocean
or the atmosphere is composed to be of the same
specific gravity, it is then clearly of no importance, as
far as the laws of gravitation are concerned, how those
particles arrange themselves in relation to each other
within the bounds in which gravitation tends to hold
them. The particles may indeed, as far as gravita-
tion is concerned, arrange themselves in any con-
ceivable manner: and if any causes whatever tend to
set the particles in motion, all that the laws of gravi-
tation can require is, that as particles vacate any
position they must immediately be replaced by other
particles. Itis of noimportance, as far as gravitation
is concerned, what the forces may be which cause the
particles to exchange positions. If anything cause
a difference in the relative specific gravity of the
particles, then gravitation will itself cause them to
exchange positions. Or, if any force whatever be
brought into play, acting with greater force in one
direction, or in one place, than in another, among
particles of equal specific gravity, then, since, as far
as gravitation is concerned, the particles may ex-
change positions in any conceivable manner, and
since a cause exists to move some of the particles, a
motion must be effected. When force, unopposed by
equal force, urges particles from any position, they
leave it, and, simultaneously with their motion from
170 THE OCEAN. + [Boox VIL.
the given position, gravitation draws other particles
into the position vacated.
According to the foregoing considerations—first,
as regards the orbital motion of the earth, or any
onward motion of the earth :—as the earth moves in
any given direction, then, wherever least obstruc-
tion exists to prevent the progress of the water in
the opposite direction, there vis-inertize acts more
freely than elsewhere : its existence as a cause neces-
sitates an effect, and, as any particles are set in
motion by vis-inertiz, gravitation draws other par-
ticles into the positions vacated, to be in their turn
expelled and replaced—and so on, as long as the
motion which causes the preponderating action of vis-
inertiz to occupy any given position lasts. And thus
a circulation of the ocean is effected by a current run-
ning through the deep and central parts of the ocean
in the opposite direction to that of the earth’s onward
motion, and returning to the source of action by
counter-currents along the shores ; and this without
the position of the ocean, as a whole, being in any
way affected, as it is carried along with the motion of
the earth, firmly held to the earth’s surface by the laws
of gravitation.
Then also, as regards the axial rotation of the earth
eastwards—in which, as already explained, there is not
only the current-creating action westwards through
the deep and central parts of the ocean, but also that
great inequality in the velocity of the motion in polar
Cuar. XV.] REFUTATION OF OBJECTIONS. 171
and equatorial regions, in consequence of which the
current-creating action resulting from axial rotation
preponderates over that resulting from any motion by
which all parts of the earth’s surface are moved with
the same velocity :—in this, as in the preceding case,
a circulation is effected by currents running with the
action of vis-inertiz in the regions of greatest force,
and counter-currents returning to the source of action
through the regions of lesser force: and this without
the position of the ocean, as a whole, being in any
manner affected, as it is carried along with the motion
of the earth, firmly held to the earth’s surface by the
laws of gravitation, which, as we have seen, simply
grasp the ocean as a whole, and do not tend to ob-
struct the action of any forces, of whatsoever nature
they may be, which may tend to cause a change in
the relative positions of particles of the same specific
oravity.
It has also been objected against the action of
_-vis-inertize that it must tend to retard, and therefore
in the course of time to annihilate, the motion of the
earth.
But, in the first place, without a knowledge of the
nature or mode of action of the forces which cause the
various movements of the earth, it is not possible for
us to know whether the action of vis-inertie would or
would not retard those motions. A cannon-ball is
retarded in its course because the retarding action of
172 THE OCEAN. [Boox VIL
the atmosphere is continuous, whereas the propelling ©
force is not: but a rocket is not retarded in its course
(as long as it lasts) because the propelling force, as
well as the retarding action, is continuous ; and the
velocity throughout is therefore proportioned to
the amount by which the propelling force exceeds
the retarding action. If the motion of the earth be
of the latter nature, then, even admitting the retard-
ing action of vis-inertie, the velocity of the motion,
being evenly proportioned to the resistance, would
be as lasting as the propelling force, the endurance —
of which need not necessarily be considered to be
limited, as in the case of the rocket. And even if
the nature of the forces which move the earth be
shown to be such that the action of vis-inertiz in the
ocean and atmosphere must necessarily retard and
gradually annihilate the earth’s motions: this would
not disprove the existence of the action of vis-inertizx,
unless it be also shown that the motion of the earth
will never be retarded.t The existence or non-exist-
ence of the action of vis-inertize in the ocean is a
question to be decided by practical investigation, and
not by theoretical opinion concerning its reaction on
the motions which produce it.
The question as to whether the action of vis-
1 A Paper on the Retardation of the Earth’s Rotation, read
before the Royal Astronomical Society by the late Professor
Adams, since the first publication of the above, has practically
annulled the objection.
a al i
Cuap. XV.] REFUTATION OF OBJECTIONS. 173
inertiz does or does not exist in the ocean is, there-
fore, not affected at all by such considerations as
those which have been urged against it. The real
questions at issue are: what is the nature of the
forces which move the earth, and what the manner
in which they act ? And, therefore, in the absence
of definite knowledge on these points, the question as
to whether vis-inertiz acts on the ocean and atmo-
sphere or not must be decided by observing what the
actual movements of those fluids are, and whether
movements in accordance with what may be shown to
be the natural action of vis-inertiz, and which cannot
be regarded as effects of any other reasonable cause,
do or do not exist in those fluids.
The displacement of the ocean from the poles
towards the equator, alluded to in the first book, suf-
ficiently indicates that vis-inertie does act on the
ocean ; and the arguments contained in the five sub-
sequent books show that it tends to cause a system of
circulation closely according with the most marked
and constant features of that which actually exists in
the ocean.'
1 Throughout Zhe New Principles of Natural Philosophy
further refutations of objections are given on points not discussed
in this volume.
174 THE OCEAN. [Boor VII.
CHAPTER XVI.
REFUTATION OF AN ARGUMENT SUGGESTING A SUS-
PENSION OF THE ACTION OF GRAVITATION.
I HAVE heard it asserted that the spinning of a top
shows that its motion causes the action of gravitation
on it to be suspended whilst that motion lasts. But
this is an unnecessary assumption. I say that the
direct action of gravitation tending to make it fall
is exactly the same as if it were at rest, and that
astral gravitation is the force which keeps the top
from falling. For as the relative number of the
orbital revolutions of the planets in a given time
increases as the square root of the sun’s revolving
force, it may, I think, be admitted that the resist-
ance of astral gravitation increases as the square of
the velocity of the motion which it resists. As far
as the present argument is concerned, it is, however,
immaterial whether the force of astral gravitation
increases as the square or as the cube of the velocity
or in any other ratio. Let us suppose it to increase
as the square.
Then let the falling motion be any amount, say
4; and the mean rotating motion of one half of the
top in any direction 8.
Cuap. XVI.] REFUTATION OF OBJECTIONS. 175
Then the actual motion of one half is 10, and
that of the other half 6 in the opposite direction.
Therefore, when not rotating, the force with
which the top resists the earth’s gravitation is 4
squared, and with the above motion of rotation it
becomes 10 squared less 6 squared ; so that that
rotation increases its resistance four times, and a
faster rotation would increase it still further.’
1 The above subject is further explained in Chapter VIII.
of The New Principles of Natural Philosophy. A complete
demonstration is also given in Chap. XXI., Proposition XXVLI.,
which has been added to the present edition of this work for the
purpose.
BOOK VIII.
REFUTATION OF ACCEPTED THEORIES BY WHICH
EXPLANATIONS OF THE MOVEMENTS OF THE OCEAN
AND ATMOSPHERE HAVE BEEN ATTEMPTED.
179
CHAPTER’ XVIE
ON THE RELATIVE ACTION OF THE TIDES, THE WINDS,
SPECIFIC GRAVITY, AND VIS-INERTLA.
Boox II. demonstrates theoretically the action of
vis-inertiz in the ocean, and Book V. shows that
movements according with those theoretical deduc-
tions are apparent. We will now proceed to consider
whether the currents which exist in the ocean may
not more naturally be ascribed to the action of vis-
inertie than to that of the winds, evaporation, or any
other current-creating forces.
The action of the winds in causing currents, by
driving the surface-water before them, has been de-
scribed by Major Rennell ; and that of evaporation,
which, by causing differences of specific gravity,
tends to create currents to restore the equilibrium of
the ocean, has been advocated by Captain Maury,
Major Rennell, in his work on the Currents of
the Atlantic, says :—‘ The tides do not occasion an
absolute removal of water from one place to another,
except very near the coasts ; and even that motion is
very circumscribed. ‘ The winds (with very few ex-
ceptions) are to be regarded as the prime movers of
N 2
180 THE OCEAN. [Boor VIII.
the currents of the ocean. . . . Operating incessantly
on the surface of the ocean,’ the wind ‘ causes, in the
first instance, a gentle, but general, motion of the
fluid to leeward (as is proved by ships being always
found to leeward of their reckonings in the Trade
Winds) ; and the water so put in motion forms, by
accumulation, streams of current.’ !
Here, without argument, the author quoted
assumes the very basis of the question at issue to
be proved. For, though the motion of the ships to
leeward when sailing in the Trade Winds be accepted
as a proof that the water in which they sail moves to
leeward, it is clearly no proof that the motion of the
water is caused by the winds: but as far as this
motion to leeward is concerned, the atmospheric and
the oceanic currents may both be effects resulting
from the action of the same cause, vis-inertiw ; the
pressure of the superincumbent atmosphere, in more
rapid motion than the water, tending only, to some
extent, to increase the natural motion of the latter
in those localities where, as is generally the case in
the region of the Trade Winds, the action of vis-
inertiz is westwards in both fluids. If all the
oceanic motion westwards under the Trade Winds
be proved to be caused by those winds, as Major
Rennell assumes it to be, we then certainly have
force sufficient to account for the ocean currents
which exist, without seeking for other causes ; but
1 In the work mentioned on p. 129.
ae ae
Cap, XVII.] THE WINDS AND EVAPORATION. 181
this, as I have above stated, is the very point at
issue.
Captain Maury, whose experience in this matter,
both practical and theoretical, is unrivalled, clearly
recognises that the winds indisputably do tend to
cause currents; but considers that, in respect to
other current-creating forces, their action is com-
paratively trivial, and altogether insufficient to
account for the currents which actually exist in the
ocean.
Sir John Herschel is surprised that Captain
Maury can see ‘any possible ground for doubting
that the Gulf Stream owes its origin entirely to the
Trade Winds’: and considers that ‘if there were no
atmosphere there would be no Gulf Stream, or any
other considerable oceanic current (as distinguished
from a mere surface drift) whatever.’* In reply to
this alleged supremacy of the winds among current-
creating forces, Captain Maury says :—‘ We know of
instances in which waters have been accumulated on
one side of a lake, or in one end of a canal, at the
expense of the other. The pressure of the Trade
Winds may assist to give the Gulf Stream its initial
velocity, but are they themselves adequate to such
an effect ? Examination shows that they are not.
With the view of ascertaining the average number
of days during the year that the NE. Trade Winds
1 Encyclopedia Britannica: Article, PuystcAL GEOGRAPHY,
sec. 57,
182 THE OCEAN. {Boox VILL.
of the Atlantic operate upon the currents between —
25° N. and the equator, log-books containing no less
than 380,284 observations on the force and direction
of the wind in that ocean were examined. The data
thus afforded were carefully compared and discussed.
The results show that within those latitudes, and on
the average, the wind from the NE. quadrant is in
excess of the winds from the SW. only 111 days
out of the 365. During the rest of the year the SW.
counteract the effect of the NE. winds upon the
currents. Now can the NE. trades, by blowing for
less than one-third of the time, cause the Gulf
Stream to run all the time, and without varying its
velocity, either to their force or their prevalence ?’ *
For these and many other reasons of the same
nature, given at length in his work on the Physical
Geography of the Sea, Captain Maury rejects the
theory which makes the wind the prime mover of the
oceanic currents, and considers that—‘ If we except
the tides, and the partial currents of the sea, such as
those that may be created by the wind, we may lay
it down as a rule that all the currents of the ocean
owe their origin to difference of specific gravity
between sea-water at one place and sea-water at
another ; for wherever there is such a difference,
1 Physical Geography of the Sea, by M. F. Maury, LL.D.
U.S.N. (New York, 1861), sec. 78. See also the extract from
Rennell given on page 129 of this volume, regarding the current
alluded to as assisting vessels in their progress northwards against
the North-East Trade Wind.
Cap. XVII.] THE WINDS AND EVAPORATION. 183
whether it be owing to difference of temperature or
to difference of saltness, &c., it is a difference that
disturbs equilibrium, and currents are the conse-
quence.’ !
Though Sir John Herschel argues that the Gulf
Stream is caused by the combined action of the NE.
and the SE. Trade Winds, and in the extract on the
opposite page Captain Maury argues that it is not
caused by the NE. Trade Wind, the latter argument
is, nevertheless, applicable against the theory which
makes (as Sir John Herschel does) the winds in
general the principal cause of ocean currents. A
general accordance of the movements of the atmo-
sphere and ocean—such as an average motion west-
wards in the equatorial regions and eastwards in the
temperate zones—would naturally result from their
being effects of the same cause, and must not be
regarded as a proof that they are related as cause
and effect. I cannot pretend to do justice to the
manner in which the theories of the winds and
specific gravity are enforced in the interesting works
in which they are respectively maintained. I quote,
however, once more from the same article by Sir
John Herschel, to show the nature of his objections
to the theory which makes differences of specific
gravity the principal cause of the currents which
exist in the ocean. Allowing that ‘Sea-water, by
evaporation, acquires additional saltness and density,
' Sec. 406 of the work just quoted.
184 THE OCEAN. {Boox VIII.
and by dilution with rain, the reverse qualities,’
he admits that ‘in this fact we have a vera causa,
though a very feeble one, for the production of
an indraught on both sides towards the lines of
maximum evaporation and minimum precipitation :’*
but argues that its action is insufficient to cause the
currents which exist, and, that it would not tend to
give them the direction which they actually have.
And, as regards the direct action of the sun’s rays,
Sir John Herschel says: ‘The surface of the ocean
becomes most heated, and the heated water will,
therefore, neither directly tend to ascend (which it
could not do without leaving the sea) nor to descend,
which it cannot do, being rendered buoyant, nor to
move laterally, no lateral impulse being given, and
which it could only do by reason of a general declivity
of surface—the diluted portion occupying a higher
level :’ and argues to show that this may be dismissed
“as a cause capable of creating only a very trifling
surface drift, and not worth considering, even were
it in the proper direction to form, by concentration, a
current from east to west ; which it would not be, but
the very reverse.’ ”
HIS: Ws) ;
2 Sec. 57. I do not profess to endorse all the details of
Herschel’s argument in the above quotations, but only the cor-
rectness of the opinion based upon them, which, since the text
above was published in 1868, has been corroborated in a very
decided manner by the extract from Sir Wyville Thompson given
on page 5 of this volume.
Cuar. XVII.] THE WINDS AND EVAPORATION. 185
This last remark refers to the fact of the water
in the west of the equatorial regions, in each ocean,
being warmer than in the east ; so that, if the expan-
sion of the water by heat caused an overflow, the
stream caused by that overflow would run from west
to east ; whereas the general course of the water in
the equatorial regions is from east to west. It may
here also be remarked, in connection with one of the
quotations above, that, the heating action of the
sun’s rays is, by Sir John Herschel himself, admitted
to tend to cause the surface-water of the ocean to
ascend (causing it to leave the sea in the form of
vapour) ; and, thus, to tend to cause an indraught
towards the places of maximum evaporation.’ The
effects resulting from this action are, in fact, discussed
in the preceding quotation made from Sir John
Herschel.?
1 The places of maximum evaporation being the equatorial
regions, the surface indraught would be to those regions ; and the
‘additional density acquired by evaporation,’ as stated in the first
of the above extracts from Herschel, would obviously, as indicated
in the text above, have a tendency to neutralise the buoyancy
suggested in the second extract, and therefore to cause the water
to sink in those regions. This action has been elaborately dis-
cussed by Mr. Croll. Climate and Time: by James Croll, London,
1875.
2 The conflicting action of the ‘additional density acquired by
evaporation’ and the ‘buoyancy acquired by being heated’ are
indicated in the text above, which stands as first published in
Chapter IV. of the Treatise on Vis-Inertic, and makes it evident
that I did not desire to endorse the details of the arguments used
by Sir John Herschel.
186 THE OCEAN. [Book VIII.
Besides the objections urged by Sir John Herschel
against the theory which makes differences in specific
gravity the prime cause of the currents of the ocean,
it must be observed that, if differences in specific
eravity, resulting from the difference of temperature
and other conditions in polar and equatorial regions,
were the principal cause of ocean currents—in conse-
quence of the tendency of the heated and cold water
to exchange positions in order to re-establish their
equilibrium in specific gravity—then, the heated
water flowing from the equator would be under that
influence of change of latitude which tends to carry
it eastwards, and the cold water from the polar regions
would be under that influence of change of latitude
which tends to carry it westwards ; so that, therefore,
the warm water would naturally flow from the
equator on the east side of the ocean, and the cold
water as naturally flow to the equator on the west
side of the ocean ; whereas in fact, with the existing
currents of the ocean, the very reverse is the case ;
the cold water is brought to the equator partly by
currents running towards the equator on the eastern
side of each ocean, and partly by under-currents
rising to the surface chiefly in the eastern parts of
the ocean ; then, it flows westwards through the equa-
torial regions, and flows from the equator on the west
of the ocean, as warm currents ; having been heated
during its course through the equatorial regions.
This actual course of the currents is in accordance
Caar. XVI.] THE WINDS AND EVAPORATION. 187
with the natural action of vis-inertiz as described in
Book II., according to which the water flows west in
the equatorial regions ; because, the westward pressure
in those regions is the greatest of all current-creating _
forces: also, the water carried west in the zone of
greatest force must return east through the zones
' of lesser force in higher latitudes; and, therefore,
flows from the equator on the west side of each
ocean, and returns to the equator on the east: and,
the under-currents which convey cold water to
the equator, tend to the eastern side of the ocean ;
because, their natural tendency westwards must yield
to the greater force of the westward tendency of the
upper strata wherever the latter can draw no supply
directly from the east. The current which flows
west in the equatorial regions draws its supply from
higher latitudes, because in those latitudes the force
of westward pressure is less; and it draws this
supply chiefly through under-currents, because the
westward pressure at the bottom of the ocean is less
than at the surface.
Doubtless, if no more powerful agencies were in
play, then, the disturbed equilibrium resulting from
differences of temperature and other conditions in
polar and equatorial regions, would cause an inter-
mixing of the waters of the ocean, by means of a
system of currents causing a constant interchange of
equatorial and polar waters. But, we have to con-
sider how the system of oceanic circulation which
188 THE OCEAN. [Book VIII.
actually exists is caused, rather than how a system of
circulation might be caused in the absence of any
more powerful cause. And, if the actual system of
oceanic circulation be in accordance with the theo-
retical action of vis-inertize, it must then be admitted
that this force is the great prime cause of the ocean
currents by which a constant interchange of equa-
torial and polar waters is effected ; so that, by its
action, all portions of the waters of the ocean are in
their turn alternately exposed to the heat of equa-
torial and the cold of polar regions without the
action of the agencies so interestingly described
by Captain Maury, tending to cause differences of
specific gravity, being brought into play. Regarding
the action of these agencies and that of the winds as
comparatively trivial forces, the theoretical action of
vis-inertie described in Book II. serves to discover
‘and to explain the actual course of the currents by
which the circulation of the ocean is effected.
Sir John Herschel is surprised how Captain
Maury can doubt that the winds are the great prime
cause of ocean currents; and, indeed, theoretically
considered, it appears plansible enough to assume
that the winds must tend, to some extent, to cause
a system of currents, by driving the surface-water
before them ; which, wherever it accumulates against
obstructions, must tend to run off in streams. But,
practically considered—that is to say, considering
Cuap. XVII.] THE WINDS AND EVAPORATION. 189
what are the actual winds which blow, and what
the actual currents of the ocean—it appears to me
incomprehensible how anyone who studies these
systems of aérial and oceanic circulation can reconcile
them as cause and effect. It appears to me surpris-
ing, how, considering the enormous volume and
weight of water borne along in the oceanic currents,
anyone can help doubting the power of the com-
paratively hght atmosphere to keep such a mass in
motion, even if it were shown that the cowrse of the
oceanic currents corresponded with that which would
naturally result from the action of the winds which
exist. But, when it is found that the winds tend to
a great extent to neutralise each other, and that,
even in the region of the Trade Winds, where the
- power of the winds is greatest, ocean-currents, even
on the surface of the ocean, run across and against
those winds, whilst in the lower strata immense
under-currents run their course regardless of the
winds which blow above ; it then seems surprising
how anyone can consider that the position and
direction of the ocean currents which exist are in
accordance with the current-creating action of the
winds, even if it be assumed that the latter are suffi-
ciently powerful to control the vast volume of water
which is carried along in those currents.
Major Rennell himself appears to have had less
confidence in the power of the winds to cause the
existing circulation of the ocean than some who
190 THE OCEAN. [Boox VIII.
advocate his theory at present. And many other
eminent authorities, besides Captain Maury, have
doubted the sufficiency of the winds as a cause for
the existing oceanic circulation. Mr. Findlay says :
‘Tt will be seen that throughout the breadth of this
ocean the set of the stream is not to SW. or NW., as
might be expected from the direction of the Trade
Winds, which may be taken as the prime mover
of these mighty drifts, but westward:’ and then
adds: ‘This fact would seem to indicate that the
rotation of the earth on its axis has more to do with
its motion than has usually been attributed to it.’ *
From this view, which has suggested itself to many
others practically acquainted with the actual move-
ments of the ocean and atmosphere, Sir Charles
Lyell differs ; and says, after mentioning ‘ the wind,
the tides, evaporation, the influx of rivers, and the —
expansion and contraction of water by heat and cold,’
as causes of currents—‘ But there is another cause,
the rotation of the earth on its axis, which can only
come into play when the waters have already been
set in motion by some one or all of the forces above
enumerated, and when the direction of the current so
raised happens to be from south to north, or from
north to south.’* Sir Charles Lyell does not say
why the action of the axial rotation of the earth can
1 P. 299 of the work mentioned on p. 129.
2 Principles of Geology, by Sir Charles Lyell, Bart., M.A., F.R.S.
(London, 1867), p. 500.
Cuap. XVII.] .THE WINDS AND EVAPORATION. 191
only come into play when the waters have already
been set in motion by other causes ;' and, indeed,
though the influence of the axial rotation of the
earth here referred to accelerates the motion of cur-
rents caused by other forces, and determines their
direction, or controls them in their course, it is not
itself, strictly speaking, a cause of ocean currents at
all. Apart, however, from the question as to whether
the term cause has been correctly applied in this
instance, it is surprising how anyone admitting the
action of this influence of the axial rotation of the
earth—which, indeed, cannot reasonably be denied,—
can, nevertheless, at the same time, continue to en-
force Major Rennell’s theories regarding the causes of
ocean currents. Major Rennell had no idea of the
existence in the ocean of this influence of the earth’s
axial rotation which Sir Charles Lyell admits. It has
only recently been pointed out by Captain Maury,
and is, in fact, incompatible with Major Rennell’s
theories ; for we have seen, a. few pages back, that,
if the waters of the ocean were set in motion from
the equator to the poles and from the poles to the
equator otherwise than by the action of vis-inertie,
then, that influence of the axial rotation of the earth
which Sir Charles Lyell admits would, as it tends
eastwards from the equator and westwards to the
' The reason for Sir Charles Lyell’s opinion is, however, that
which I have explained in Chapter I. of this volume, it being, of
course, a consequence of his acceptance of the ‘ Laws of Motion.’
192 THE OCEAN. [Boox VIII.
equator, carry the warm water from the equator on
the east side of each ocean, and the cold water to the
equator on the west side of each ocean, and conse-
quently eastwards through the equatorial regions ;
all three of which conditions are exactly the reverse
of what is known to be the actual circulation of the
ocean. The idea of the Trade Winds being consi-
dered a sufficient cause to account for this complete
reversal of the course which the currents would natu-
rally take under that influence of the axial rotation
of the earth which Sir Charles Lyell admits is one
which I do not suppose anyone will seriously main-
tain: and, indeed, I do not see how it can be ac-
counted for otherwise than by admitting the action
of vis-inertie ; in which case, change of latitude
being an attribute of the westward pressure which
results from axial rotation, and, that influence of ©
axial rotation admitted by Sir Charles Lyell being
an attribute of change of latitude,—then, the action
of the latter cannot annihilate that of the force of
which it is an attribute; but, a sufficiency of force
must be created by the direct action of westward
pressure, setting the water in motion westwards in
the regions of greatest force, to keep the currents in
motion in whatever course the attributes of westward
pressure may subsequently tend to give them.
Major Rennell, as quoted on page 179, says that—
‘The tides do not occasion an absolute removal of
water from one place to another, except very near
Car. XVII.] THE WINDS AND EVAPORATION. 193
the coasts ;’ but I think that the arguments in Book
IV. show that, though in an ocean completely cover-
ing the globe the tides would not cause any current,
nevertheless the breaking-up of them by the coast-
lines may necessitate the formation of currents follow-
ing the general course of the tide- waves, and, therefore,
revolving in each ocean, westwards in the equatorial
regions and eastwards in each of the temperate zones.
But the question whether the breaking-up of the
tides by the coast-lies does or does not lead to the
formation of currents through the central parts of the
ocean may perhaps be more easily determined by a
practical investigation, for the purpose of ascertaining
whether or not they are alternately accelerated and
retarded at intervals corresponding with the succes-
sive passages of the moon across any meridian, than
by theoretical disquisitions on the subject. A cur-
rent-creating action of the tides in the manner here
indicated may, it seems to me, be much more effective
than that of the winds, whose action, to some extent,
is certain, whereas that resulting from .differences of
specific gravity need not necessarily be brought into
play at all where more powerful and rapidly acting
forces cause a circulation.
BOOK IX.
THE MOVEMENTS AND CONFIGURATION OF THE
SURFACE OF THE EARTH.
CHAPTER XVIII.
PRELIMINARY.
In examining the outer crust of the earth, endeavour-
ing to discover signs of movement, and the nature
and causes of the movements which take place,
suppose that, after traversing the mountains and
plains of Europe, you at length set off to look at the
most extensive of all mountain ridges, which is that
which extends almost from pole to pole along the
western coasts of North and South America. You
traverse the pampas, where the land is, for the most
part, slightly undulated, so that in riding over it the
horizon is constantly changing, and the eye is ever
on the alert, as objects appear or vanish in the
distance. After passing San-Luiz you traverse a
series of undulations which give to the country the
appearance of a succession of huge ocean rollers
pressing forward in parallel lines towards the moun-
tains. You cannot fail to be struck with the peculi-
arity of the scene. They are a series of undulations
upon a much greater undulation, for the land falls
again before reaching the mountains. When yet
two hundred miles east of that mountain range, you
may catch sight of it as its snow-covered peaks fling
198 THE OCEAN. [Boox IX.
back the rays of the rising sun. You pass through
the ruins of the city of Mendoza, which, but five
years ago, was destroyed by a comparatively slight
movement of the outer crust of the earth. Atlength
you commence to mount the eastern slope of the
huge mountain ridge. You may glance eagerly from
mountain to mountain, from valley to valley ; districts
of gravel, districts of sand, districts of earth ; strati-
fied masses and unstratified masses : you may glance |
at all, vainly endeavouring by inductive steps to learn
the process of their formation. All appears crude
disorder and confusion. As the keen winds rush by,
perchance they laugh a derisive laugh ; and the vast
mountain ranges—rugged, stern, and inhospitable—
frown in silent, majestic disdain. Here man is
scorned. The rude mountains frown, and the angry
winds rage, as if threatening destruction to all
who dare to venture here. But man shall triumph
yet ; for, as you stand upon a narrow ridge which
rises like a wall fourteen thousand feet above the sea,
and on your right and left snow-covered peaks tower
upwards nine or ten thousand feet higher, there,
stung by the failure of your efforts by the paths of
induction, you boldly rush upon the dizzy heights
which are traversed by the dangerous paths of deduc-
tion. With a vigorous effort you fling imagination
back through time, and let it place you in an age
between which and the present countless ages have
intervened. You then find that not only the moun-
Car. XVIII.] THE SURFACE OF THE EARTH. 199
tains, but the whole continent has fallen away from
beneath you, and there now lies below you one vast
expanse of water. The water is deep; but below
there is a hard stratified ground, beneath which the
interior of the earth is in a state of liquid heat,
but gradually cooling ; and, as it cools, the hardened
surface is compelled to bend in graceful curves, in
order to suit the decreasing size of the globe. By
this bending, the water becomes of unequal depths,
deepening in parts as it becomes shallow in other
parts. At length, immediately below you, a ridge of
dry land appears—this, then, is the birth of the
South American continent—it continues gradually to
rise, throwing off the water to the east and west ;
there, then, lies the Pacific, and there the Atlantic
Ocean. The bending upwards and downwards, in
the same easy graceful curves, continues as long as
the surface remains sufficiently pliant ; but at length,
becoming more hard and brittle, as the strain still
continues, it cracks with a tremendous crash, the
rent extending north and south, almost from pole to
pole. Up to this moment the surface has yielded
gradually to the power of gravitation, offering great
resistance. But, once broken, this resistance is gone,
and gravitation, acting with unchecked power, crushes
and grinds the broken edges together with a force
scarcely conceivable by the mind of man. Enormous
masses of what had once been horizontal strata are
now perpendicular, or even reversed. The smashing
200 THE OCEAN. [Boox IX.
and grinding of the broken edges, by the overwhelm-
ing lateral pressure caused by gravitation, leaves
scarcely a trace of the former stratified order, but
leaves mass piled on mass in vast confusion, forming
this huge mountain range along the course of the
crack. And, more than this: the outer crust of the
earth had hitherto been in a great measure self-sup-
porting, its weight resting upon itself laterally im all
parts, so that the interior parts of the earth were in
the same measure relieved from the weight of its
inward pressure. ‘That is, inward pressure had been
changing to lateral pressure, in proportion as the
hardening surface of the earth offered increased
resistance to the power of gravitation. But when
the hardening surface of the earth, becoming more
brittle, had bent upwards as far as it could without
breaking, it at length breaks along the top of the
ridge, and, in proportion with the loss of lateral
support thus caused, the weight of the adjacent parts
of the surface press inwards ; and, the inner parts of
the earth being in a state of liquid heat, the increased
weight pressing upon the fluid part forces the fluid
matter upwards through the fissures in the crack ;
and thus, in some places, mountain ranges of un-
stratified rock are formed as the fluid hardens on the
surface ; but here the accumulation of broken masses
of stratified matter is so enormous that this part of
the range seems to consist of nothing else. The
stratified surface to the east of the crack has here
Cuar. XVIII.] THE SURFACE OF THE EARTH. 201
overlapped that to the west. So that on the west,
the Pacific Ocean rolls against the disjointed masses
that have been piled up about it ; whereas on the
east, the elevated strata slope away gradually to the
Atlantic Ocean. That slope is itself undulated by
pressure ; but those undulations are probably prece-
dent to the occurrence of the crack which led to the
piling up of the Andes; most, if not all, subsequent
readjustments of the surface having been arranged
by movements along the still unfirmly placed edges
of the crack. The sudden movements in this neigh-
bourhood even now cause at times a shock, or earth-
quake, sufficient to overwhelm cities. In these
movements, also, either by direct pressure of the
surface downwards, or oftener probably by water or
other matter being suddenly brought into contact
with intense heat, matter from below the stratified
surface is, in a state of liquid heat, forced upwards
through openings in the crack ; thus forming, as the
matter hardens on the surface, those high volcanic
peaks which are here so numerous. Or, in other
places, the same expansion not having sufficient
force to burst through the surface, simply raises it in
the form of an evenly rounded hill.
Now, if these observations be not erroneous, we
must conclude that granite, and most unstratified
rocks, are in general forced to the surface in the same
manner as is mud through the fissures between
paving-stones ; that is, not by the direct pressure of
202 ' THE OCEAN. [Book IX.
the granite upwards, but by the pressure of the
stratified surface downwards. As long as the strati-
fied surface remains unbroken, it is in a great
measure self-supporting, resisting the power of
gravitation, to which it gradually is compelled to
yield by bending, until at length it breaks. When
once the breakage occurs, the adjacent parts, no
longer offermg the previous resistance to gravita-
tion, are drawn inwards, pressing upon the liquid
granite below, and forcing it outwards through the
fissure. Now, if we suppose two great breakages
to have been caused by the force of lateral pres-
sure, the one corresponding with the course of the
Rocky Mountains, the other with that of the Sierra
Nevada of California, it is obvious that the inter-
vening portion of the earth’s surface, having up to
the time of the breakage been in a great measure
supported laterally, will, after its occurrence, exert
an increased pressure inwards proportionate to the
loss of lateral support; and this inward pressure,
acting upon matter in a fluid or semi-fluid state,
will, to a greater or lesser extent, force that fluid
matter upwards, through the breakages; so that
the unstratified rock would appear in ridges along
the course of each breakage. Looking at the Yo-
semite valley in the Sierra Nevada, a superficial
glance makes it appear probable that, after a granite
district having been formed here in the manner Just
suggested, the bending of the surface caused by
Cap. XVIII.] THE SURFACE OF THE EARTH. 203
lateral pressure has continued, whilst the granite
was becoming cool and hard on the surface, and
that as soon as its surface became too hard and
brittle to bend further, it cracked along the top of
a bending ridge, the upper edges parting asunder,
and leaving a deep wedge-shaped gorge. The débris
from the sides and part adjacent to the crack has
filled up the lower part of it, and formed the present
bottom of the valley.
There are some trees which, when young, are
covered with a smooth thin bark; but as the tree
grows the pressure from within bursts the first
layer, disclosmg through the crack a new layer,
proportioned to the increased growth of the tree.
Thus layer after layer forms and bursts; and, as
the old layers continue to adhere to the tree, ridges
are formed which as each successive layer is added
get higher, and the hollows between them wider and
deeper, until at length the bark of the old trees
presents that rough, uneven surface, which at first
sight looks so strange. Now, glance at the bark, or
outer crust of the earth—it also presents a rough,
uneven surface, rising and falling in mountains and
valleys. The cause of this unevenness in the sur- -
face of the earth, though diametrically opposite, is
no less simple, and no more wonderful than the cause
of the unevenness in the surface of the tree. The
latter is an expanding force—the former is a con-
tracting force. As contraction proceeds in the
204. THE OCEAN. [Boox IX.
interior of the earth, the outer shell, not being
sufficiently strong to resist the power of gravitation
and support itself, must either bend or break, so as
to accommodate itself to the reduced circumferente
which it has to enclose. A glance round the world
shows that it has bent all over, and in many places
broken. In some parts the bending is only sufficient
to form gentle, easy undulations ; in other places,
sufficient to form hills and valleys ; and where the
surface, after bending as much as its pliancy would
admit of, has at length broken, the broken edges,
crushing against each other, have piled up mountain
ranges of broken strata; or, in other places, the
inward pressure of the stratified surface has forced
the liquid matter from below upwards through the
crack, forming chains of unstratified mountains.
CHAPTER XIX.
THE ACTION OF VIS-INERTLEZ ON THE SURFACE OF
THE EARTH.
Ir is evident that, if from the oblate spheroidal form
of the earth, resulting from axial rotation, we can
infer an action of vis-inertiz in the ocean, such an
inference is equally applicable to the outer crust of
the earth. So that, according to this, the whole
surface of the earth, and all upon it, must tend to
lag, while some revolving force within is dragging it
round eastwards.
And can any natural phenomena be adduced in
refutation of this view? It may, with exquisite
logic, be shown to be at variance with assertions
which have for some generations been taught in
schools and colleges as laws of motion ; but it cannot,
I think, be shown to be at variance with absolute
fact ; and I will now briefly consider what movements
and configuration of the outer crust of the earth
should result from an action of vis-inertie on it
similar to that described as acting in the ocean, in
order to ascertain whether the actual configuration is
such as to admit of its having resulted from the
action of that force.
206 THE OCEAN. [Boox IX.
For the sake of illustration, let us suppose the
earth in the condition described in the foregoing
chapter—namely, with an outer covering of air ;
beneath that air an unbroken expanse of water ;
beneath the water a hardening, but still more or less
pliant, surface of land ; and beneath the land a fluid,
incandescent, and gradually contracting mass, homo-
geneous with the materials whose solidification has
formed the outer crust or land.
_ Under the sole action of its own force of gravita-
tion that globe would naturally tend to preserve its
form as a perfect sphere. But by the motion of
rotation round its axis a centrifugal force is created,
acting from the axis towards those parts of the
surface which, being most remote from the axis,
rotate with the greatest velocity. On the surface of
the globe this force acts from the poles of the axis
towards the equator. And, supposing the land or
outer crust of the globe to be sufficiently pliant, then
the liquid mass within it would bulge it out all round
the equator and draw it inwards at each of the poles ;
thereby causing its equatorial to be greater than its
axial diameter. The action of this force would not
tend to cause any difference between the hemispheres
lying on either side of the equator ; but, as far as its
action is concerned, those hemispheres would be
equal and their configuration similar.
The tendency to contraction, as described in the
foregoing chapter, induces lateral pressure through-
Cmar. XIX.] THE SURFACE OF THE EARTH. 207
out the outer crust of the earth ; and if that outer
crust have not sufficient strength to resist the action
of gravitation, it must, if sufficiently pliant, have a
tendency to undulate all over ; or, if not sufficiently
pliant to undulate, its tendency must then be to
shiver to fragments. Let us consider in what manner
this tendency to undulate or to fracture can be
affected by the action of vis-inertiz.
We have seen that the action of vis-inertix
resulting from axial rotation, and that resulting from
orbital motion, both act westwards in any given part
of the surface of the earth when that part of the surface
is turned from the sun, but as soon as that part of the
surface reaches the point of sunrise, then the conjoint
action of those forces ceases; the orbital force turns
eastwards, and acts in opposition to the force result-
ing from axial rotation. Thus, then, the alternate
conjunction and opposition of these two separate
actions of vis-inertiz would control the undulating |
action of lateral pressure, and cause those undula-
tions to take the form of a series of ocean waves
sweeping westwards; for the action westwards is
the strongest, and it receives a check during each
rotation of the earth. These, then, appear to be the
forces which have determined the peculiarities of
conformation, which have been so clearly pointed out
by the late Rear-Admiral Fitzroy in the following
passage, which I extract from the ‘ Weather Book.’
On page 121 of that work Admiral Fitzroy draws
208 THE OCEAN. [Boor IX.
attention ‘ to a very remarkable geologic conforma-
tion, common toa great part of our world approach-
able by sea, though not so much to the far interior of
extensive continents : namely, gradual slope up from
east towards west, and comparatively precipitous
steeps, from summits, westward. Norway, Europe
generally, Africa, with its outlying islands, both
Americas, the Galapagos, the (elevated) Polynesian
islands, the ranges of Australia, China, and Asiatic |
sea-coasts generally, when viewed extensively in
profile from south to north, have the wedge-like
outline that is familiar to Englishmen in the Bill
of Portland. To the physical philosopher and the
geologist we must turn for reasoning on this striking
peculiarity—one that the writer has often noticed
and considered with extreme interest. His attention
was first drawn to it by seeing the Galapagos group,
from a distance, appearing like several “ Bills of
Portland,” all exactly similar in their profile outlines
when many miles distant. Since that time (1836),
many opportunities have occurred for inquiries and
careful comparisons, of which the result is a belief
that (excepting those greater east and west ranges of
mountains embodied within continents, or continental
islands, such as Australia and Borneo), the general
average direction of ranges or chains of mountains
is nearly meridional, and their section approaches
that of a wedge (pointing eastward).
‘This wedge-like shape is common to every little
CHap. XIX.] THE SURFACE OF THE EARTH. 209
sand-ridge, every shifting shingle bank formed along
shore by wave or tidal action. It is also that of
sand-ridges on a plain, drifted by wind alone, and it
is the form of snow-drifts—the point of the wedge
being towards the source of action. Whether water,
or wind, or both, acting continuously, have been
agents in these conformations ; whether, in contract-
ing or expanding, the earth’s surface or crust has had
a tendency to scale-like fracturing, must be left to
the consideration of competent judges.’
These conformations, observed by Admiral Fitz-
roy, appear clearly to coincide with such as might
naturally be expected to result from the alternate
conjunction and opposition of the two actions of vis-
inertie in combination with the undulating tendency
of lateral pressure.
Besides the motions of axial rotation and orbital
revolution, whose effects we have just considered, let
us suppose the earth to have an onward motion
southwards, since the evidence deduced from the
course of the currents of the ocean has indicated a
motion of the earth in the direction of the South
Pole or thereabouts.
And since, according to the theory just sketched,
the motion of the earth results from attraction, it
seems natural to expect that the movements of the
magnetic-needle may be an effect of the action of the
force which is carrying the earth onwards in that
course. And, if so, we may then infer that the
P
210 THE OCEAN. [Boor IX.
~
tendency of magnetism is to turn the positive end—
that is, what is commonly called the north pole of
the needle—in the direction of the earth’s motion ;
that is to say, in the direction of the South Pole, or
thereabouts. And, as in the ocean, lines of lesser
force are overwhelmed by lines of greater force, so
that currents are caused to run along the lines of
lesser force in the opposite direction to that in which
the force which impels them acts ; so also must the
northward direction of the magnetic-needle result
from the overwhelming of lines of lesser magnetic
force by those of greater force; that is to say, the
lines of magnetic force must run through the central
parts of the earth from the north to the south mag-
netic pole, and then spread out over the surface of
the earth towards the equator, crossing which, they
must converge again towards the north magnetic
pole; so that the lines of greatest force, running
through the central parts of the earth, overwhelm
the lines of lesser force on the surface of the earth ;
thus causing the needle, when placed in.the lines of —
lesser force, to point in the opposite direction to that
in which magnetism acts ; and, at the north magnetic
pole, being in the line of greatest force, to point down
through the central parts of the earth to the South
Pole ; and, at the south magnetic pole, to point right
away into space, marking the point in space towards
which the earth may be moving.
Then, by the magnetic action which we have
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Cuap. XIX. | THE SURFACE OF THE EARTH. 211
described, the surface of the earth should be drawn
inwards about the North Pole, bulged outwards
about the South Pole, pressed downwards between
the South Pole and the equator, and piled upwards
between the equator and the North Pole; because
the force returning from the South to the North Pole
would, in the southern hemisphere, be pressing the
surface of the earth from latitudes of lesser into
latitudes of greater circumference ; whereas, in the
northern hemisphere, it would be pressing the sur-
face from latitudes of greater into latitudes of lesser
circumference.’
The independent action of each one of the forces
I have described is illustrated by the curve lines in
Plate XVI. : in which the sphere shows the action of
1 According to Mr. Croll’s work, Climate and Time, already
alluded to, the great Southern Ocean exists in consequence of the
southern ‘ice-cap’ having moved the earth’s centre of gravity
' southwards ; whereas, according to the argument above, that
ocean exists in consequence of the surface of the earth having
collapsed in the temperate regions of the southern, and bulged
out in those of the northern hemisphere under the influence of
the earth’s motion through space.
_ The latter action is corroborated by the existence of the
Arctic Ocean, almost encircled by the lands of the Northern
Hemisphere ; and by the Antarctic lands surrounded by the ocean
of the Southern Hemisphere ; whereas, the attraction of the water
to the Southern Hemisphere by the ‘ice-cap’ would have tended .
to leave the Arctic Regions all dry land, and to submerge the
Antarctic Regions as much as the South Temperate Zone. The
great height of the mountains in the Antarctic Regions, where in
corresponding latitudes in the Arctic Regions no land exists, seems
at variance with the idea of the ocean having been drawn south-
wards by the formation of the ‘ice-cap.’
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THE OCEAN [Boox IX.
gravitation ; the oblate spheroid the action of centri-
fugal force, resulting from axial rotation; and the
cardioid the action of magnetic force, resulting from
motion through space. And under the combined
action of these forces the configuration of the earth
would, therefore, be such, that if on the surface of
the earth there lay water sufficient to cover one half
of the earth’s surface—that water lying in each of the
depressions, and leaving the protuberances dry land—
then the surface of the earth would be divided into
the following alternate zones of land and water:
namely, land about the South Pole; a vast expanse
of water throughout the temperate regions of the
southern hemisphere; a zone of dry land in the
equatorial regions ; a narrow zone of water north
of the equator; a zone of dry land throughout the
temperate regions of the northern hemisphere ; and
a district of water about the North Pole.
The land in the temperate zone of the northern
hemisphere, and that about the South Pole, would
be raised by the action of the magnetic force con-
comitant with motion through space: and the land
in the equatorial zone would be raised by the action
of the centrifugal force concomitant with axial rota-
tion. The relative positions of land and water re-
sulting from the action of the forces just described
strikingly correspond with the actual relative positions
of land and water in each hemisphere, as is shown
by the illustration given in Plate XVI.; excepting
Crear. XIX.] THE SURFACE OF THE EARTH. 213
that the zones, instead of being continuous, are inter-
sected by undulations running north and south.
In the north there is the depression which contains
the Arctic Ocean, surrounded by the continents of
Europe, Asia, and America; then there is the de-
pression of which the Mediterranean and Caribbean
Seas, separating Europe and North America from
Africa and South America, form a part ; and thirdly,
there is the greatest hollow, which contains the
Southern Ocean, separating the continents just men-
tioned from the lands of the Antarctic regions.
Though the centrifugal force resulting from axial
rotation might be expected in some measure to neu-
tralise the undulating action of lateral pressure acting
north and south, so that the greatest apparent effects
of undulating force should result from the pressure
acting east and west ; this would not account for any
one of the meridional undulations being greater than
any other. But, as far as the forces thus far con-
sidered are concerned, all the meridional undula-
tions on our hypothetical globe would be equal and
similar. There are, however, on the surface of the
earth two meridional undulations immensely greater
than all others, the crests of which form respectively
the Old and New Worlds ; the depressions between
them containing respectively the Atlantic and Pacific
Oceans.
Such a meridional division of land and water
‘would naturally result from a change of the earth’s
214 THE OCEAN. [Boox IX.
axial rotation from any axis to a new axis at right
angles to the position of the old axis. And, in fact,
if in this sketch I have correctly described the action
of the forces brought into play, then it would appear
from the actual conformation of the outer crust of
the earth that such a change of the axis of rotation
as above mentioned has occurred, not once only, but
many times. In such case the wave-like conforma-
tions observed by Admiral Fitzroy must have been
formed since the occurrence of the last change of
axis : these comparatively modern undulations inter-
secting older similar undulations, and obliterating, to
a greater or lesser extent, the traces of their original
conformation.
Let us consider how such a change of axis as
that just mentioned would affect the configuration of
the globe which we have been describing. By such
a change the position of the poles of the new axis
would be in opposite points of the old equator: and
the new equator would intersect the old at points
ninety degrees from each of those poles. The equa-
torial diameter between those points would then be
oreater than that at right angles to it ; for this latter
would be the line of the former axis of rotation.
And centrifugal force, carrying the water to the
equatorial regions, would cause it to accumulate in
two great oceans whose central points would be over
the poles of the former axis: and those oceans would
be separated meridionally by a belt of land lying
Coar. XIX.] THE SURFACE OF THE EARTH. 215
along the line of the former equator. Then, sup-
posing the outer crust of the earth to be sufficiently
pliant, the configuration which the action of the
forces before described would tend to restore would be
modified by meridional undulations. For those un-
dulations which, before the change of axis, formed
the zones of land and water running parallel to the
old equator, would after that change of axis lie
meridionally, or at right angles to the new equator.
In this new position, under the action of the
forces which caused the former configuration, a
portion of the former equatorial regions would be
sustained to form the new Antarctic continent, and
the opposite part depressed to form the basin of the
Arctic Ocean. And also, from the central parts of
one of the great oceans, there would gradually be
upraised the crest of the undulation which had
formed the old Antarctic continent ; and about the
central parts of the other of the great oceans there
would gradually be upraised the crest of the undula-
tion which had encircled the former Arctic Ocean.
The undulating tendency of lateral pressure, acted
upon by the actions of vis-inertiz resulting from axial
rotation and orbital motion, would then tend to raise
a new series of meridional undulations intersecting,
at right angles, those previously raised by the action |
of those same forces.
If a portion of Brazil be supposed to have
formed at one time an Antarctic continent, then the
216 THE OCEAN. (Boox IX. _
actual configuration of land and water on the surface
of the earth presents a striking resemblance with
that which would naturally result from the action of
the forces just described.
The clear records of glacier action on an enor-
mous scale traced by Professor Agassiz over all parts
of Brazil which he visited give support to the idea of
the last change of the earth’s axis being as above
suggested! And it is also mteresting to observe
that the only part of the present continents which,
notwithstanding that change of axis, would have
preserved its position relatively with both the poles
and the equator, and would in those former times, as _
well as in the present, have enjoyed a temperate
climate, is the very spot which the accepted traditions
of the Caucasian race record as being that where our
ancestors escaped destruction during such a deluge
1 The striations and apparent remnants of glacier moraines
on the Tijuca Hills and the Organ Mountains near Rio de
Janeiro, which, at the time I published Zhe Hlements, and for
eight or nine years previously, I supposed to be traces of glacier
action similar to what I had seen among the glaciers of Norway
and Switzerland, I afterwards found to be effects of the sliding of
a stratum of broken rock over the solid rock of which the moun-
tains are formed. A stratum of very hard and brittle rock seems
to have been shivered to fragments, and, the parts adjacent to
each crack having decomposed, the whole mass has taken a
downward motion over the mountain sides, not only causing
striations exactly similar to those caused by glacier action, but
also leaving moraines which, though in general appearance
similar to glacier moraines, are formed in consequence of the
portion of the same stratum, which formerly surrounded them,
having moved away more rapidly on steeper declivities. This of
Car. XIX.] THE SURFACE OF THE EARTH. 217
as would naturally result from the suggested change
of the earth’s axis.’
Besides the above change of axis, some previous
changes would be requisite in order to account for
the absence of land in the central parts of the Pacific,
opposite the equatorial regions of Africa.
The investigation of this point offers a problem,
intricate and interesting, but unsuited to the purpose
of this chapter, which is simply to illustrate the
universality of the action of the forces which deter-
mine the position and movements of the ocean and
atmosphere. And, if the foregoing arguments be
not erroneous, then the actual configuration of the
earth’s crust shows the action of the forces in play in
course does not disprove the supposed glacial period, but merely
proves that the surface has undergone more important changes since
that period than I and, as it seems to me, Professor Agassiz at
one time thought apparent. I, at any rate, supposed the surface
of the ground in Brazil to be almost as left after the melting of a
heavy covering of ice, but I have found that to have been a mistake,
for there have been considerable changes since the existence of
any glacial epoch there. Or, at least, causes now in action could
very well have produced all the ‘striations’ and ‘ moraines’ that
I have seen there.
1 «Tn those days Noah saw that the earth became inclined.’—
The Book of Enoch, \xiv. 1.
‘The earth labours and is violently shaken,’—Jdem, 3.
‘The fountains of the great deep were broken up.’—Genesis,
wi, LI:
‘And the foundations of the earth became equalised, while
other depths were opened ; into which the water began to descend,
until the dry ground appeared. —TZhe Book of Enoch, \xxxviii.
9 and 10.
218 THE OCEAN. - [Boox IX.
the ocean and atmosphere and confirms that south-
ward motion of the earth in the first instance
deduced from the observed course of the ocean
currents.
1 A further development of the action of vis-inertiz on the
surface of the earth is given in The New Principles, as stated in
the footnote to Proposition X., Chapter X XI. of this volume.
BOOK X.
THE ACTION OF VIS-INERTIAZ IN THE HEAVENS.
bo
bo
—
CHAPTER XX.
PRELIMINARY.
In Book I. a single phenomenon was accepted as
sufficient to indicate that a force whose action is a
matter of commonplace knowledge, is in play in the
ocean in the same manner as that in which its action
can be observed in ordinary phenomena.
In Book II. it is shown that the action of that
force in the ocean tends to cause the elaborate circu- —
lation through the system of ocean currents there
described.
In Book III. it has been ascertained that the
force which causes the foregoing system of circulation
is intrinsically the same as that which causes the
well-known phenomena of the tides.
And it has been shown that that force must tend
to give both the moon and its tide a relative motion
over the surface of the earth by the same action as
that which circulates any particle of water in the
ocean. And a cursory consideration of the motions
of the moon and the planets has shown that they are
not at variance with the action of that force,
That analysis has shown that the vis-inertie of
922 THE OCEAN... [Boox X.
matter is the source of gravitation, through the action
of which the apparent motion of every star must
affect the ocean in the same manner as the corre-
sponding motions of the sun and moon.
Just as the lunar tide follows the apparent motion
of the moon, so also a similar action of the gravita-
tion of every star draws the water in the direction of
its apparent motion ; but as the stars are distributed
all round the earth, the combined action of their
innumerable tidal forces causes the equable system
of circulation on which the lunar and solar tides are
excrescences, on account of the irregularity of the
action of these latter bodies on different meridians not
being balanced by the action of bodies at the same
distance on other meridians.
Thus the ocean moves in concert with every
motion of every star, just as it moves with the move-
ments of the sun and moon, so that every movement
in the universe is, as it were, reflected by a corre-
sponding movement in the ocean.
The object of this Book will be to endeavour to
trace in the heavens the action of the force which
forms the connecting link between the ocean and
every part of those distant realms.
CHAPTER XXI.
THE MOVEMENTS OF THE PLANETS.
Tur System oF THE WORLD.
AN EXTENDED APPLICATION OF THE LAWS OF GRAVITATION DEMON-
STRATED BY NEWTON’S ‘PRINCIPIA’ AND ‘SYSTEM OF THE WORLD.’
TABLE OF CONTENTS.
PROP.
The gravitation of a body in motion in free space tends to
draw other bodies in the same direction.
II. A rotating sphere tends to revolve surrounding bodies.
III. The ratio of the revolving to the direct force is inversely as
the distance.
IV. The revolving force is inversely as the cube of the distance.
V. The velocities of motion are as the square roots of the ratio of
the revolving to the direct force.
VI. The velocities of revolution are as the square roots of the
revolving force.
VII. Vis-inertize being the cause of gravitation, the moon must have
both an orbital and an apparent motion.
VIII. The centrifugal force of astral gravitation increases as the
square of the velocity of revolution.
IX. The direct force of the Sun’s gravitation acts as a retarding force,
opposing its revolving force, along the orbits of the planets.
'X. The direct force of the Sun’s gravitation tends to retard the Sun’s
axial rotation more than the revolution of the planets round
the Sun.
XI. The retarding action indicated by the foregoing proposition is
apparent as regards the axial rotation of the Sun, and also as
regards the axial rotation of the Earth and of the planets
Saturn and Mars.
XII. The ratio which vis-inertiz bears to the Sun’s gravitation is as
the square of the distance from the Sun.
XIII. That which it bears to the revolving force is as the cube of the
distance.
XIV. The ratio which the vis-inertiz of the planets bears to the com-
bined action of the direct and revolving forces of the Sun’s
Prop.
XVI.
XVII.
XVIII.
XIX.
XX,
XXII.
XXII.
XXIII.
XXIV.
XXV.
XXVI.
THE OCEAN. [Boox X.
gravitation is as the fifth power of the distance from
the Sun.
The combined action of the direct force and the revolving
force of the Sun’s gravitation make its motive action
along the orbits of the planets inversely as the relative
distances.
The ratio which the motive force of gravitation, acting
along the orbits of the planets, bears to the vis-inertiz
of the planets is as the sixth power of the distance.
The velocities with which the Sun’s revolving force endea-
vours to move the planets along their respective orbits
are decreased as the square roots of the revolving forces
in the respective orbits decrease.
To determine the normal period in which the foree which
causes the Sun’s rotation endeavours to revolve the
planets, as indicated by the actual relative periods in
which they perform their orbital revolutions.
The revolving force of the Sun’s gravitation in the orbits of
the planets is directly as the ratio which the velocities
of the orbital and lagging motions bear to each other in
each orbit respectively.
The relative velocities of the lagging motions of the planets
are ag the square roots of the ratio which vis-inertiz
bears to the direct and revolving force of the Sun’s
gravitation in their respective orbits.
The relative velocities of absolute motion with which the
planets move along their orbits are to each other
directly as the square roots of the fractions of the Sun’s
force of gravitation which act as revolving forces in
each orbit respectively,
The ratio of the relative velocities of orbital and apparent
motions is as the square root of the ratio of the forces of
gravitation by which they are caused.
The orbital motions of the planets are caused by the revolv-
ing action of the Sun’s gravitation, and the apparent
motions by the retarding action of astral gravitation.
The revolving force of the Sun’s gravitation, decreasing in-
versely as the cube of the distance, makes the relative
velocities with which the planets perform their orbital
revolutions round the Sun to be as the cubes of the
velocities of the motion along the respective orbits in
which the revolutions are made.
The distances of the planets from the Sun are regulated by
the action of astral gravitation.
To apply Proposition XXV. to the motion of a spinning-
top.
i
Cnap. XXI.] CONTENTS OF CHAP. XXI.
PROP.
XX VII.
XXVIII.
XXIX,
XXX.
XXXII.
XXXII.
XXXII.
XXXIV,
XXXV.
XXXVI.
XXXVI.
XXXVITI.
bo
bo
ii
To apply Proposition XXV. to the upheaval of the ocean
round the equatorial regions, by the action of the Karth’s
rotation.
A planet continuously acted on by any motive force,
tending to carry it onwards in its orbit, excepting the
Sun’s revolving force, could not remain in the solar
system.
Objects free to move on the surface of a rotating sphere
will have a relative motion along the surface if the
direct be greater than the revolving force of the sphere.
If the revolving be greater than the direct force of the
sphere, nothing can rest loosely on its surface.
. Within the limits of the atmosphere, the normal force of
astral gravitation and the Earth’s revolving force are
together less than the direct force.
At some distance from the Earth its direct force must be
brought into equilibrium, as regards the normal and
centrifugal forces of astral gravitation.
An indefinite number of these lines of equilibrium may be
formed.
The effective action of the Earth’s revolving force depends
on the proximity and power of other centres of rotation.
To determine the motion of a body acted on by revolving
forces from different centres of rotation,
Src. 1—The action of two equal forces rotating in oppo-
site directions.
Src. 2.—The action of two equal forces rotating in the
same direction.
Src. 3.—Unequal forces rotating in opposite directions.
Sec. 4.—Action on the Moon of the revolving forces of
the Sun and Earth if rotating in the same plane.
Src. 5.—Effect of the inclination of the planes of rotation.
Sxc. 6.—Newton’s demonstrations of the laws of gravita-
tion harmonise necessarily with the theory of
vis-inertiz.
To apply Propositions XXXIV. and XXXV. to the dis-
turbing action of the Earth’s rotation as regards the
orbital motion of the Moon round the Sun.
To apply Propositions XXXIV. and XXXV. to the dis-
turbing action of Neptune on the orbital motion of its
satellites.
To determine the interaction of revolving forces.
226 THE OCEAN. [Boox X.
PROPOSITION I.!
Theorem.—If one of any two bodies in space be
moved in such a manner as to increase the dis-
tance between the two, the other tends to follow
with the same motion.
Because the force of gravitation tends to hold
them together, and, therefore, if one be moved by
an extraneous force, the other is drawn in the same
direction by the action of their gravitation towards
each other.
Corollary.—Y¥or the same reason the gravitation
towards other bodies will tend to keep the second
body in its position ; and, therefore, between the two
forces it can neither remain at rest nor move with
the full velocity of the first.
1 It must be borne in mind that the theory under demon-
stration in this Book is one arrived at by induction from the
investigation of the movements of the ocean, not invented for the
purpose of explaining the cause of the movements of the planets.
From the movements of the latter corroborative evidence of the
truth of what I consider already established as the cause of the
movements of the ocean is given in such a manner that the result
arrived at shows that the conflicting action of terrestrial and astral
gravitation is of necessity tending to cause the system of oceanic
circulation described in Book IT.
: , |
QQ (AL |
tangent
mtal circle
described from centre x.
torce,
\
mdary
Seco
to the hoerixo
London, Longmans & Co.
Cuar. XXI.] THE HEAVENS. ~ 255
on p. 88. In consequence of the increase of the re-
tarding force of astral gravitation the planet at a is
carried to c in the orbit ¢ d ¢, instead of moving from
a to } in its former orbit, a bf. The increased force
of astral gravitation thus lifts the planet into an orbit
farther from the sun at «.
Note.—The planet having been held in equilibrium
by vis-inertiz, the whole of that force, except the
force of astral gravitation created by the action of
the revolving force, tends to keep it at its normal
distance of equilibrium.
Corollary.—Therefore the action of a revolving
sphere on other bodies in positions of normal equi-
librium may be considered as exerting a centripetal
force decreasing as the square of the distance, and a
revolving force decreasing as the cube of the distance
and of necessity resisted by a retarding and centrifugal
force also decreasing in the latter proportion.
PROPOSITION XXVI.
Problem.—To apply Proposition X XY. to the motion
of a spinning-top.
Suppose the velocity of rotation be, say, 8 in the
direction abcd (Plate XVIII.) ; if the resisting
256 THE OCEAN. [Boox X.
force of astral gravitation is equal to the square of
velocity, then the resistance of astral gravitation is as
the square of 8 on each side ; but immediately the
top moves downwards from that position—say with
the velocity of 4 in a downward direction—then the
particles on the side d a b, with this motion added to
them, have their velocity increased ; and that velocity
of 4 added to the velocity of 8 makes the velocity of
12, whereas the velocity on the side b ¢ dis reduced
to 4; so that the resistance of astral gravitation on
one side is the square of 4, or say 16, whereas the
force on the other side is 144, say the square of 12;
so that the force of astral gravitation on the side
dab is 144 drawing upwards and 16 on the side
bc d drawing downwards. Thus there is a difference
of 128, representing an excess in the force of astral
gravitation drawing upwards; and, unless the earth’s
power of gravitation drawing it downwards is equal
to that difference of 128, the top cannot fall ; it is
then supported, and it is only when the top’s rotation
becomes so slow that the earth’s power of gravitation
dragging it down is greater than the difference be-
tween those two forces of astral gravitation, that the
top can fall.
The tangential action of the force at a, which
supports the top (constantly lifting that side whilst
the side c falls) carries the top round with the motion
of revolution in the direction ef g h.
A force of astral gravitation at the point 6 then
Cuoar. XXI.j THE HEAVENS. 257
resists this horizontal motion exactly as that at the
point a resists the downward motion ; and the tan-
gential action of the force at ) also supports the top ;
because it tends to carry the point ) farther than the
point d, from the centre x, just as the tangential
action at the point a makes the top revolve by tending
to carry the point a farther than the point ¢ from the
centre 2.
If the velocity of rotation be great, the force at d
will lift the top into an upright position in the same
manner as the force at a carries the top round in the
direction ef g h.
As soon as the velocity with which the top rotates
becomes so slow that it falls, under the influence of
the earth’s gravitation, the onward motion commu-
nicated to it by the action of astral gravitation is
immediately reversed, and it runs on the ground like
a Wheel.
PROPOSITION XXVII.
Problem.—To apply Proposition XXV. to the up-
heaval of the ocean round the equatorial regions
by the action of the earth’s rotation and to its
constant circulation in that position.
1, Let the circle n ws er (Fig. 22) be the
surface of the earth, N the north, and s the south
s
258 THE OCEAN. - [Book X.
pole. And let the circle abcd be the form which
the ocean would take with the earth at rest.
Then give the earth an axial rotation in the plane
of the equator, W E. 3
This rotation creates a centrifugal force which
gives the particles of water resting on each parallel
of latitude a tendency to rise from the circles in
which they are revolved.
Thus, under the action of the centrifugal force,
particles on the equator, w , tend to rise from &
towards g in the plane of the equator ; and particles
on the parallel z « tend to rise in the direction z ¢,
parallel to the equator. But the earth’s gravita-
tion, acting across the plane x ¢in the direction v 7,
draws the latter particles towards the equator.
Thus, as the centrifugal force tends to carry off
Cuar. XXI.] THE HEAVENS. 259
the particles in the plane of rotation, z w, the earth’s
gravitation inclines them out of that plane into the
next parallel of greater circumference, 0 y, where the
centrifugal force is augmented ; and pressing in this
manner through each parallel of latitude towards the
equator, they replace the particles at 5, whose centri-
fugal force, augmented by the pressure of the particles
from x, carries them towards 6 and g.
Thus the water sinks from a to n, glides along the
surface of the earth from Nn to £, and rises upwards
from E to g.
The centrifugal tendency imparted by the rotating
surface of the earth increases as any particle travels
from N to E; but as it rises from E to g it gradually
loses the centrifugal impetus which caused it to fly
off from the surface at & (for its motion is retarded,
as shown in Proposition X XV. of the planet moved
from the orbit a bf to the higher orbit ¢ d ein F int, 19:
p. 88), and as the particles raised up towards g
lose their centrifugal force, their gravitation to the
earth must tend to restore the equilibrium of the ocean,
making the pressure of the column E g at E equal to
the pressure of N f at N.
2. As the centrifugal force continues to act on the
particles resting on the surface of the earth tending to
carry them from N (Fig. 22) through « y to £ and 3,
they prevent the particles at g from falling to the
earth in a direct line; and therefore as the centri-
fugal force of the particles at « tends to cause them
$2
260 THE OCEAN. [Boox X.
to displace those at rn, and that of the particles at £
tends to cause them to displace those at g, the latter
are by the earth’s gravitation (being released from
the immediate action of the centrifugal force) drawn
back towards f, and thus supply the sinking motion
from / to N.
A constant circulation in the directon Eg /fNE
is thus established with the ocean in equilibrium.
3. Also, because, being less firmly held by the
earth’s gravitation, the particles in the line fw are
more free to flow towards the equator under the
action of the centrifugal force, than those in the line
ny; therefore, there is a tendency to.a circulation in
the direction y NfugE y.
But, as the excess of this horizontal force, tending
to cause a circulation with an upward motion about
the poles, is greatest in the polar regions, and
decreases gradually towards the equator, where it
ceases to act; and the excess of the vertical force
previously described as tending to cause a circulation
_ with an upward motion about the equator, is greatest
in the equatorial regions, and decreases gradually
towards the pole, where it ceases to act; therefore,
the sinking motion must be in an intermediate latitude
with a circulation in the direction uy Nf win the
polar regions, and in the direction wy Eg uin the
equatorial regions.
4, Also, because the retarding and centrifugal
force of astral gravitation, being as the square of the
Cap. XXI.] THE HEAVENS. 261
velocity of rotation, is greater along the equator W.E.
than along the parallel o y, the ratio which the
earth’s force, drawing downwards and eastwards, bears
_ to the astral force drawing upwards and westwards,
is greater along the parallel oy than along the
equator W.E. ; therefore there is a circulation across
the meridian a r eastwards, as well as downwards,
along* the parallel o y, and westwards, as well as
upwards, along the equator H.W.
And the eastward motion across the meridian is
in latitudes intermediate between the equatorial and
the polar regions, and not in the highest polar regions,
because in the vicinity of N. (Fig. 20 in Proposition X.)
the revolving forces acting from v and o neutralise
each other (as shown by Proposition X.) leaving the
retarding force little resisted by the direct action of
the revolving force; but farther from the pole, as
at ¢, Fig. 20, the normal eastward velocity is increased
by the excess of force acting from 0 and E over that
acting from vand W. Therefore, whilst the water
lags westwards in the equatorial and in the polar
regions under the retarding action of the astral force,
it is carried eastwards through the temperate zones
by the relative excess of the revolving action of the
terrestrial force.
5. Also, let tT, in Fig. 23, be a point on the 45th
parallel, and let 0, the source of the revolving
force, in the equatorial radius Cc E be so placed that
oTbe tooras12istol. The revolving force at
262 THE OCEAN. [Book X
Eis to the same at T as 1°72 is to 1 (being inversely
as the cube of the distance). And the resulting
velocities, being as the square roots of the respective —
forces, would be as 1°312 is to 1, making the velocity
at T°76 of the velocity at x. But the length of the
parallel at T is only ‘71 of the length of that at © on
the equator ; and therefore a revolving force acting
N
Cc 0) i
Ine, Da
from 0, sufficient to give the water at E the equatorial
velocity, would give to the water at T a greater
velocity than that of the surface of the earth at T.
6. Or, since the velocity of motion at the equator
is 1,000 miles an hour, and on the 45th parallel 710
miles an hour; and since the retarding action of
astral gravitation is as the sqnare of the velocity ;
therefore the relative retarding action is—
At the Equator . : - 1,000,000
On the 45th parallel : 504,100
But, as shown in the foregoing section, the relative
revolving force in the same positions is as 1°72 isto 1,
pip sete Ole
oo
Cuap. XXI.] THE HEAVENS. 26:
and therefore the revolving force being at the equator
1,000,000, it is on the 45th parallel 581,000.
There is therefore a relative excess of revolving
action on the 45th parallel ; for the normal amount
of retarding force on the 45th parallel is 504, and the
revolving force 581 of the same forces respectively
on the equator if the source of the revolving force be
as given in the foregoing section.
PROPOSITION XXVIII.
Theorem.—If any force inherent in a planet, or any
extraneous force continuously acting on it, tended
to give it a faster motion in its orbit than that
imparted by the revolving force of the sun’s
gravitation, that planet could not remain in the
solar system.
Data.—Proposition XXV.
Proof.-—Because, however slight the increase of
velocity, the equilibrium in the orbit is destroyed by
the centrifugal force increasing as the square of the
velocity : and as the planet, whilst increasing the
velocity of its onward motion, recedes from the
centre under the action of the opposing force, the
opposing forces become more and more unequal ; for
264 THE OCEAN. [Boox X,
the motive force, being independent of the sun, does
not decrease as the distance from it increases ; whereas
the power of the sun’s gravitation to retain the planet
does constantly decrease : therefore a planet acted on
by such a force could not be retained within the solar
system.
PROPOSITION XXIX.
Theorem.—Objects lying loosely on the surface of a
rotating sphere, of which the direct force of
eravitation is greater than the revolving force,
will rest upon it, but at the same time have
relative motions along the surface.
Because the objects would be held to the surface
by the direct force of gravitation ; but on the surface,
if free to move, vis-inertiz would determine their
positions between the ‘conflicting forces of astral
gravitation and the revolving force of gravitation
(Proposition VII.), and so give them a relative
motion along the surface.
Note.—Bricks, even loosely piled, are too firmly
held by the direct force of the earth’s gravitation to
be sufficiently free to move ; but the drops of water
superimposed on each other in the ocean are inces-
OL
Cuap. XXI.] THE HEAVENS. 26:
santly exchanging their positions as the ratio of the
conflicting forces varies at different depths or in
different parts of the ocean.
PROPOSITION XXX.
Theorem.—If the revolving force of a sphere be greater
than its direct force, nothing can rest loosely on
its surface.
Because the centrifugal force of astral gravita-
tion is equal to the revolving force (Proposition
WII:):;
Therefore objects placed on the surface are earried
from it by astral gravitation sufficiently far to bring
this into equilibrium with the direct force (Propo-
sition X XV.)
PROPOSITION XXXI.
Theorem.—The revolving force of the earth’s gravita-
tion, and the force of astral gravitation which
resists the direct force of the earth’s gravitation
in the absence of any revolving force, are together
less than the direct force of the earth’s gravitation
266 THE OCEAN. [Boox X.
at all points within a distance from the earth’s
surface at least as great as the limits of the atmo-
sphere.
Because objects within at least those limits are
drawn to the earth’s surface by the force of gravita-
tion ; therefore the force drawing towards the earth
is greater than that drawing from it:
But the force drawing from the earth is the
normal force which opposes the direct force of the
earth’s gravitation increased by that which opposes
the motion caused by the revolving force :
Therefore these two are together less than the
direct force.
But the force drawing from the earth in conse-
quence of the action of the revolving force is equal
to the revolving force :
Therefore the sun’s revolving force and the
normal force of astral gravitation are, within those
limits, less than the direct force of the earth’s gravi-
tation.
PROPOSITION XXXII.
Theorem.—At some certain distance from the earth
the direct force of its gravitation must be brought
into a state of equilibrium as regards the combined
Cnar. XXI.] THE ITEAVENS. 267
action of the forces of astral gravitation mentioned
in the foregoing Proposition.
’ Because vis-inertie is the gravitation of the
universe, of which the sun’s direct force of gravita-
tion is a part and astral gravitation the remainder ;
Therefore the decrease of the solar. force is the
increase of the astral force; and therefore at some
greater or lesser distance from the sun the opposing
forces are equal.’
1 We have said that, setting aside planetary influences, the
earth in its orbit round the sun is held between the opposing forces
of astral and solar gravitation. But, in fact, the astral gravitation
which at any given point of the earth’s orbit is acting in opposition
to the sun, isat the opposite point of the orbit acting in conjunction
with the sun, its force being there diminished in the inverse
proportion to that in which the square of the distance at which
it is acting is increased. Therefore, the astral gravitation acting
in opposition to solar gravitation, is at any point of the earth’s
orbit equal to the force of solar gravitation, together with the
force of astral gravitation which, by acting across the orbit of the
earth, acts in conjunction with the sun. From which it follows,
that the force of solar gravitation is equal to the amount by which
the force of astral gravitation is diminished by the increase of its
distance in acting across the orbit of the earth. Now, if we take
into consideration only the mean distance of that part of the
universe which the telescope has revealed to us—even taking that
distance as the mean distance from which astral gravitation acts
upon the solar system—even then, the difference in the force
acting in the same direction at two opposite points of the earth’s
orbit causes an inexpressibly slight difference in the relation of
those forces to each other: and since this difference is equal to
the power of solar gravitation, this latter is, therefore, when
compared with that of astral gravitation, insignificant beyond the
power of mathematical expression. The comparison is as that of
day with the entire duration of time, or as that of a mile with the
268 THE OCEAN. [Boox X.
The distance at which they are equal forms the
normal line of the equilibrium of vis-inertie.
This normal line of equilibrium is destroyed by
the force of astral gravitation which opposes the
sun’s revolving force (Proposition X XV.)
But as this force of astral gravitation decreases
inversely as the cube of the distance from the sun
(Proposition X XV.) ;
Whilst the direct force of the sun’s gravitation
decreases inversely as the square ;
Therefore the line of equilibrium will be reached
at some greater distance from the sun, as already
shown in Proposition X XV.
PROPOSITION XXXII.
Theorem.—An indefinite number of successive lines
of equilibrium separated by spaces, in which the
forces of gravitation drawing towards and from
the earth are unequal, might be formed in the
same manner as that shown in the preceding
Proposition.
Because bodies in the first line of equilibrium
entire extension of space. And yet to us these comparatively
infinitesimal portions of power, of time, and of space are equally
all-important.— The Elements: Longmans, Green & Co, London,
1866, vol. 1. p. 89.
Cuap. XXI.] THE HEAVENS. 269
would there form in the space beyond them a fresh
accession of gravitation acting towards the earth.
But by the decrease of this direct force and con-
comitant increase of the astral force, the opposing
forces must again at some greater distance be brought
into equilibrium.
The second normal line of equilibrium would be
disturbed in the same manner as the first by the
revolving force; and bodies in it would be carried
farther from the earth by the astral force, until by
the force drawing towards the earth decreasing as
the square, and the revolving force decreasing as the
cube of the distance increased (as shown in Propo-
sition XXXII. of the first line of equilibrium), the
equilibrium of the opposing forces would be restored.
Thus an indefinite number of successive lines of
equilibrium might be formed at different distances
from the earth.
PROPOSITION XXXIV.
Theorem.—The distance within which the revolving
force of the earth’s gravitation will be effective in
causing surrounding bodies in space to revolve
around the earth depends on the proximity and
relative power of other revolving forces.
Because it is evident that, in the absence of any
other revolving force, that of the earth would extend
270 THE OCEAN. [Boox X.
the successive lines of equilibrium (Proposition
XXYV.), and would revolve all surrounding bodies
with a force inversely as the cube of the distance from
the earth (Proposition IV.) ;
Therefore, unless overwhelmed by the action of
revolving forces acting from other centres of rotation,
that of the earth would revolve the universe with the
earth’s rotation.
Corollary.—Therefore the revolving force of the
earth’s gravitation is constantly endeavouring to re-
volve the sun in the opposite direction to that in
which the earth actually is revolved round the sun ;!
but because the sun’s revolving force is greater than
that of the earth, therefore the earth is revolved
round the sun. So also the sun revolves all the
planets, because there is no greater force sufficiently
near to overwhelm its action.
The solar system extends as far as its revolving
force is greater than that proceeding from any other
centre of rotation, and within which all bodies, being
under its dominion, are revolved with it as planets.
The planetary systems extend to the limits within
which any one of their revolving forces is greater
than that of any of the other planets. Within those
limits it revolves surrounding planets, whilst it and
they are together revolved by the greater force of
the sun’s rotation.
1 See the Chapter on the Secular Acceleration of the Moon's
Motion in The New Principles of Natural Philosophy.
Cuap. XXI.] THE HEAVENS. 271
PROPOSITION XXXvV.
Problem.—To determine the motion of a body in space
under the action of revolving forces proceeding
from different centres of rotation.
1. Ifa body in space be acted on equally by equal
forces proceeding from two different centres of rota-
tion, and tending to carry it in the same direction, it
is evident that as it proceeds, and the directions of
rotation diverge, it must take an intermediate course
between the two, and therefore be equally carried
away from both centres of rotation.
As it recedes it must, at some point equidistant
from both centres, be brought into equilibrium as
regards the centripetal and centrifugal forces: be-
cause it is carried off from both centres in conse-
quence of the force of astral gravitation acting from
them increasing as the square of the velocity (Propo-
sition VIII.) is increased by the combined action ot
the two revolving forces; but, whilst carried off
along a line forming a tangent to both of the orbits,
the centripetal forces decrease as the square of the
distance increases, whilst the centrifugal forces of
astral gravitation which carry it off along that tan-
gent (because in it they equally retard it from the
positions on each side to which the revolving forces
THE OCEAN. [Boox X.
bo
“I
bo
tend to carry it) decrease as the cube of the distance
increases (Proposition LV.) ; so that it must, sooner
or later, be brought to rest between the conflicting
forces.
But, if a third revolving force exist, the equi-
librium must be destroyed ; because, whilst receding
along the tangent, the body must be inclined by that
third force towards the direction of one or other of
the equal forces, and thus be caused to revolve with
one or other of those centres of rotation.
2. If the equal action of the equal forces alluded
to in Section 1 be in opposite directions, then the
body under their action can neither advance nor
recede, for the forces of astral gravitation, as well as
the direct forces, neutralise each other.
But the action of a third force must incline ae
body towards one or other of the two equal forces ;
and by that force it will then be revolved, increasing
unequally its distance from both centres as the
velocity of its motion is increased by the gradually
decreasing opposition of the revolving forces.
3. Let us now suppose the revolving forces of
Section 1 to be unequal, then the body lying between
the two centres of rotation tending to carry it in the
same direction is accelerated, and thus carried farther
from both centres, until, as it inclines more and more ~
in the direction of the primary force, the conjoint
action ceases and becomes opposing ; and then, as the
motion becomes retarded, it approaches its centre of |
Coar. XXL] THE HEAVENS. 273
rotation until checked by the acceleration resulting
from this approach.
4. And if the revolving forces of Section 2 be
unequal, then the body lying between the two tend-
ing to carry it in opposite directions is retarded.
But, as it is carried onwards with the course of the
rotation of its primary, the revolving forces are in
less and less direct opposition, and the motion be-
coming accelerated, the body recedes from both
centres until the normal velocity and normal distance
from both centres is arrived at, as one revolving force
acts directly across the other.
There a conjoint action of the forces commences,
causing acceleration, and consequently continued re-
cession from both centres until the forces act com-
pletely in conjunction.
As it advances from that point the direct conjunc-
tion of the forces ceases, and the motion becomes
gradually retarded, letting the body fall towards both
centres until the normal velocity and distance from
both centres is again attained, as the revolving forces
act at right angles to each other.
There the opposition of the forces recommences.
The retardation of the motion is increased, and the
body consequently continues to approach both centres
until the revolving forces are completely in opposition.
Then, as direct opposition gradually ceases, ac-
celeration and recession from both centres recom-
mence.
274 THE OCEAN. [Boor X.
Thus, since the sun and earth rotate in the same
direction, as also do the revolving forces under con-
sideration in this section, therefore, according to the
foregoing, if the planes of their rotation coincided,
the radius of the moon's orbit round the earth point-
ing towards the sun would be shortened, and that
pointing in the opposite direction lengthened, so that
the line of the apsides would always point through
the earth and sun ; because its position, lymg from
the point at which the revolving forces are in con-
junction to that in which they are in opposition,
would lead it through those bodies.
5. But, the planes of rotation being inclined, the
sun’s revolving force tends to throw the moon out of
the plane of the earth’s rotation, and, as it leaves
that plane, the earth’s revolving force decreases, allow-
ing the moon to fall towards the earth. This action
is reciprocal, and might attain its maximum in any
part of the orbit, bemg dependent on the changing
of the inclination.
Thus, instead of the moon’s apogee and aphelion
coinciding and occurring when the moon was at its
greatest distance outside the orbit of the earth, as
would be the case if the revolving forces acted in the
same plane, they become dependent on the changing
of the intersection of the planes of rotation. By the
disturbing action of the changing inclination of these
planes, the perigee and perihelion might both be
thrown outside the orbit of the earth ; or the perigee
Cuar. XXI1.] THE HEAVENS. 275
and aphelion might occur together outside ; or the
points of perigee and perihelion might be for ever
changing their relative positions.
6. Throughout these problems we have dealt
with the motions caused by the revolving forces and
controlled by the forces of astral gravitation brought
into action by the motions : but in those motions the
heavenly bodies are held in equilibrium between the
forces of astral gravitation and the direct forces
of the gravitation of the bodies round which they
are revolved ; therefore the study of gravitation, as
followed by Newton and subsequent astronomers,
must show its action to harmonise with the motions
caused by the revolving forces.
But as the laws of vis-inertiz have indicated the
cause of the motions which have been the objects of
study, it is evident that the science of astronomy
must be simplified and more easily extended by the
use of this new power of reasoning from cause to
effect than by the former process of demonstrating
the necessary connection of concomitant effects, pro-
ceeding from an unknown cause.'
But, as regards the revolution of the apsides, one
part of the force which determines it will probably
have to be ascertained, by analogy, from its effects.
! The paper on the Secular Acceleration of the Moon’s Motion
which forms Chapter XIII. of Zhe New Principles of Natural
Philosophy, is an extension of the argument of these Propositions,
and forms a practical corroboration of the above remarks.
m2
276 THE OCEAN. [Boox X.
Because the earth’s perihelion has a motion of
revolution similar to that of the moon’s perigee ; and
therefore the arguments of this Proposition indicate
the existence of a central force of rotation, bearing
the same relation to the sun and earth as the sun
does to the earth and moon.
The action of this force on the motion of the
moon’s perigee will be less than on that of the earth’s
perihelion, in proportion as the diameter of the moon’s
orbit about the earth is less than that of the earth
about the sun. For its effect depends on the differ-
ence in the force of its action in opposite parts of
the orbit.
PROPOSITION XXXVI.
Problen.—To apply Propositions XXXIV. and |
XXXYV. to the disturbing action of the earth _
on the moon’s orbital motion round the sun.
The earth’s revolving force accelerates the orbital.
motion of the moon round the sun when the moon is
outside the earth’s orbit ; the force of astral gravita-
tion, drawing it from its orbit, then increases as the
square of the increase of the velocity of the motion,
and carries it farther and farther from the sun, until
the decrease in the revolving force of the latter, and
Caar. XXI.] THE HEAVENS. 277
the changing of the conjoint action of the disturbing
force, reduce the velocity ; and then the reduction
of the astral force allows the moon to fall inwards
towards the sun: and this falling towards the sun
continues as the motion is retarded by the opposing
action of the earth’s force when the moon passes in-
side the earth’s orbit, until the increase of the sun’s
revolving force and the changing of the earth’s action
from direct to less and less complete opposition cause
a gradual acceleration of the motion, and a conse-
quent increase of the astral force, which again draws
it outwards from the sun.
Thus, in consequence of the action of an ex-
traneous force alternately accelerating and retarding
the moon’s motion in its orbit round the sun, the
alternate increase and decrease of the retarding force
of astral gravitation carries the moon alternately
inside and outside the normal line of its orbit.
PROPOSITION XXXVII.
Problem—To apply Propositions XXXIV. and
XXXV. to the motion of the satellites of Neptune
round the sun.
In respect to the sun’s rotation the satellites
of Neptune revolve in the opposite direction round
278 THE OCEAN. [Boox X,
Neptune to that in which the moon is revolved round
the earth, from which it is to be inferred that Neptune
rotates in that direction.
Therefore the acceleration caused by the disturb-
ing force occurs when the satellite is inside the
normal line of its orbit, and retardation when it is
outside, so that, though the path described backwards
and forwards across the normal line of the orbit will
be similar to that described by the moon, the relative
velocities of the motion at different distances from
the sun will be reversed.
And, besides this, the action of the retardation of
the moon’s motion tending to bring it nearer to both
of the centres of rotation, might be accomplished
without any increase in the inclination of the planes
of rotation.
But the acceleration of Neptune’s satellite causing
an increase of distance from both centres of rotation,
could not be accomplished, whilst Neptune remained
at the same distance from the sun, without throwing
the satellite out of the plane in which Neptune and
the sun rotate.
CnAr. XXI.] THE HEAVENS. 279
PROPOSITION XXXVIII.
Problem.—To determine the interaction of revolving
forces.
1. Two equal forces revolving in the same direc-
tion, in the same plane, will mutually revolve each
other ; so that they will both revolve in an orbit
whose diameter will be the radius of either of the
orbits in which one endeavours to revolve the other.
2. If two equal forces revolve in planes at right
angles to each other, the one whose axis lies in the
plane of the rotation of the other will be revolved hy
the latter.
3. If two equal forces revolve in opposite direc-
tions in the same plane they cannot revolve each
other, unless the equilibrium of their forces be dis-
turbed by the action of some extraneous force.
4, Let each of the foregoing couples be revolved
by the action of a greater central force of rotation.
And let this central force rotate in the same plane
and in the same direction as the bodies in Section I.
Then, when these latter are equidistant from the
central force, they are equally acted on by it, and
therefore remain at their normal distance from each
other.
But, as they advance in their orbital motions
round each other, the one approaches and the other
280 THE OCEAN. [Book X
recedes from the central force. And as the revolving
force of the inner one accelerates the motion of the
outer one round the central force, the centrifugal
force of astral gravitation, increasing as the square of
the velocity, carries the outer one farther from the
common centre ; whilst at the same time the revolving
force of the outer body retards the motion of the
inner one round the common centre, and the conse- .
quent decrease of the centrifugal force of astral
gravitation therefore lets it fall nearer to the common
centre.
Thus, as the two bodies revolve round the central
force, the revolution round each other is performed
in an elliptical, instead of the circular orbit which
their own undisturbed action would cause.
5. Then, as regards the action of this central
force on the bodies in Section 2. In this case the
body whose axis lies in the plane of rotation may
for the present be regarded as having no axial rota-
tion, as we consider the one which revolves it to
revolve in the same plane as the central body.
In this case the action would be the same as in
Section 4, except that, as there is no reciprocal revolv-
ing action between the two lesser bodies, the changing
of the form of the orbit is not the same when the
revolving body is inside as when it is outside the
greater orbit; and therefore the orbit of the non-
rotating body round its primary, instead of being a
true ellipse, is wider when the non-rotating body is
;
4
_
“4
4
;
a
Car. XXI.] THE HEAVENS. 281
farther than its primary from the central force: be-
cause there is then a conjoint action of the revolving
forces, as shown in Proposition XXXVL., Section 4,
concerning the revolving action of the sun and earth
upon the moon.
If the two motions of rotation were in opposite
directions, then the conjoint action on the non-rotat-
- ing body would occur when the latter was- nearer
than its primary to the central force, making the
distortion of the ellipse the reverse of that resulting
from the foregoing conditions.
6. As regards the action of the central force on
the bodies in Section 3, supposing it to revolve in
the same plane as they; then, if they be equidistant
from the centre they would simply be swept round
in the same orbit.
But, if the action of any extraneous force (such
as a force causing an ellipticity of their orbit) prevent
them from being equidistant, then, in their efforts at
mutual revolution, the one nearer the common centre
will be more retarded than the one more remote, and
therefore the latter will have a motion onwards in its
orbit round the former which will at the same time
have a faster motion than it round the common
centre.
Thus, whilst carried round the central force, they
would be revolved about each other by the alternate
preponderance of their revolving action.
a PRINTED B¥
‘ : SPOTTISWOODE AND CO., NEW-STREET SQUARE
; LONDON ras
WORKS BY THE SAME AUTHOR.
Published by Messrs. LONGMANS, GREEN, & CO.
————_+e————
Demy 8vo. cloth, illustrated, 21s.
Tae NEW PRINCIPLES: OF
NATURAL PHILOSOPHY.
A Defence and Extension of the Principles established by the Author’s
Treatise on Ocean Currents,
TABLH OF CONTENTS.
CHAPTER I.—Preliminary Remarks on How Little we Know and How we
Know it.
Abstract of an Address delivered on the opening of the Fifth Session of the
English Literary Society, April 26, 1880. Reprinted from the Report published
in the Buenos Ayres Herald.
CHAPTER II.—Remarks on the Recent Oceanic Explorations and the Current-
Creating Action of Vis-Inertize in the Ocean.
Published in 1877.
CHAPTER III.—The Winds and the Earth’s Rotation.
Published in 1877.
CHAPTER IV.—The Winds and the Earth’s Onward Motion.
Published in 1877.
CHAPTER V.—Replies to Critics of ‘The Ocean.’
Published in 1876.
CHAPTER VI.—The Winds, Ocean Currents, and Tides, and what they Tell of the
System of the World.
A Lecture delivered at Willis’s Rooms. King Street, St. James’s, November 3,
1877, as a Public Challenge to the Council of the Royal Society and the Scientific
Staff of the ‘ Challenger’ Expedition.
CHAPTER VII.—Second Challenge Lecture.
Delivered at Willis’s Rooms, December 20, 1877, in continuation of the above
subject.
CHAPTER VIII.—The Gyroscope.
Published with the First Edition of the ‘ Challenge Lectures,’ in 1877.
2 NATURAL PHILOSOPHY.
CHAPTER IX.—Huxley on the Laws of Motion—Present Position of the Question.
Published February 1, 1881, in the Buenos Ayres Herald.
CHAPTER X.—Oceanic Circulation—Present Position of the Question.
Published November 8, 1881, in the Buenos Ayres Herald.
CHAPTER XI.—Copernicus versus The Royal Astronomical Society—The Theory
of the Moon’s Motion.
Articles reprinted from the Buenos Ayres Heraid of September 4, 1880,and =
from the Buenos Ayres Standard of August 22 and November 19, 1880.
CHAPTER XII.—The Elements of Astronomy.
An Essay read before the English Literary Society on August 20, 1879, in
illustration of The Old and the New Definitions of Vis-Inertia.
CHAPTER XIII.—The Secular Acceleration of the Moon’s Motion.
Published in Buenos Ayres, April 1879, and Dedicated to William Spottis-
woode, Esq., President of the Royal Society, as a Challenge on behalf of the
New Elements of Natural Philosophy.
CHAPTER XIV.—The Theory of the Tides.
A Paper rejected by the Royal Society in February 1868.
CHAPTER XV.—The Circulating Action of Gravitation in the Ocean and the
Atmosphere.
A Paper rejected by the Royal Geographical Society in 1876.
CHAPTER XVI.—Defence of Vis-Inertiz.
And Answer to the President of the Argentine Scientific Society ; published
in Buenos Ayres, September 19, 1879.
CHAPTER XVII.—Dr. Siemens on Solar Heat—Present Position of the Question.
Published April 30 and May 11, 1882, in the Buenos Ayres Herald.
CHAPTER XVIII.—Scientific Honour.
Articles published in the Buenos Ayres Herald, December 10, 1880, and
January 8, 1881, and dedicated to the editor of the Hdinburgh Review.
CHAPTER XIX.—Is Force Inherent in Matter ?
Published in the Buenos Ayres Herald, September 22, 1881.
CHAPTER XX.—The Nebular Hypothesis, modified by the Discoveries of the
. Action of Astral Gravitation, and the Revolving Force of Gravitation.
Articles published in the Buenos Ayres Standard, on September 2, 15,
and 16, 1880.
CHAPTER X XJI.—Amenities of Science.
1. The Tone of Science.
Published in the Buenos Ayres Standard on December 7 and 13, 1878.
2. The Board of Trade on Oceanic Circulation.
Published in the Buenos Ayres Standard on December 28, 1878.
NATURAL PHILOSOPHY. 3
3. The Earth as the Cause of the Moon’s Motion.
Published in the Buenos Ayres Herald on January 1, 1882.
4, Vis-Inertiz and Geology.
Published in the Buenos Ayres Standard, June 26, 1880, and in the Buenos
Ayres Herald, October 15, 1881.
5. The Gravitation Theory of Heat.
Published in the Buenos Ayres Standard on August 17, 1880.
6. Replies to the ‘ Popular Science Review’ on Vis-Inertiz.
Published in the Bucnos Ayres Standard on September 29 and October 2, 1878.
7. Replies to an Anonymous Critic on the Old and New Theories of
Vis-Inertize.
Published in the Buenos Ayres Standard on January 8, 14, and 24, 1879.
CHAPTER XXII.—Further Astronomical Indications of the Action of the New
Theory—-
1. Comets.
Published in the Buenos Ayres Herald on February 12, 1880.
2. ‘The Sun’s Long Streamers.’
Published in Buenos Ayres, January 27, 1879.
3. Stellar Movements.
Published in Buenos Ayres, June 1880.
4, The Circulation of the Surface of J upiter.
Published in the Buenos Ayres Standard on June 29, 1879.
5. The New Planet.
Published in the Buenos Ayres Standard on December 18, 1879.
6. The Zodiacal Light.
Published in Buenos Ayres, February 1881.
7. Letter to the President of the Royal Society.
CHAPTER XXIII.—Remarks on the Admiralty Current Charts.
Published in Buenos Ayres, March 18, 1879.
CHAPTER XXIV.—Dr. Carpenter on Oceanic Circulation.
Published in Buenos Ayres, 1871.
The ‘ Moon’s Rotation’ and the ‘ Flat Earth.’
CHAPTER XXY.-—Former Theories of the Winds,
The greater part extracted from the ‘ Treatise on the Action of Vis-Inertiz,
published in 1868.
Crown 8vo, cloth, 2s.
TEE WIN D:s.
AN ESSAY
IN ILLUSTRATION OF THE NEW PRINCIPLES OF NATURAL
PHILOSOPHY.
(Forming Chapter III. of THE NEW PRINCIPLES OF NATURAL PHILOSOPHY.)
wn
no
oF WN
aD
ANALYSIS OF CONTENTS.
PART I.
THE ACTION OF SOLAR HRFAT.
. The circulation it tends to cause.
The Trade Winds accord with that action.
. The Anti-Trades do not.
PART II.
THE ACTION OF SOLAR AND LUNAR GRAVITATION.
. The circulation it tends to cause.
_ The Trades and Anti-Trades accord with that action.
. But that action is intermittent, and the Trades and Anti-Trades are too
constant to be dependent on it.
PART III.
THE MERIDIONAL ACTION OF THE EARTH'S ROTATION.
_ The circulation it tends to cause.
. This forms a constant and equable cause for the Trades and Anti-Trades.
PART IV.
IDENTICAL ACTION OF CENTRIFUGAL FORCE AND GRAVITATION,
. Solar and Lunar gravitation have the same current-creating action as the
centrifugal force resulting from the earth’s rotation. And their gravitation
is a part of the centrifugal force which causes the meridional circulation
thus far considered.
_ The action of Solar heat causes the Anti-Trades to be mure inconstant than
the Trades.
PART V.
THE ACTION OF THE EARTH’S ROTATION. THE NORMAL CIRCULATION.
. Effect of change of latitude.
. This does not explain all the existing latitudinal circulation.
. Nor the westward course of the Upper Trades diverging from the equator.
. The earth’s rotation tends to cause a latitudinal circulation.
. This explains the westerly winds of the temperate, and the easterly winds
of the equatorial regions.
. The three predominating circulating forces created by the earth’s rotation.
_ The combined action of these forces tends to cause what are known to be the,
main features of the existing circulation.
ae
AL
:
:
THR WINDS.
PART VI.
ASTRAL AND TERRESTRIAL GRAVITATION,
1. Conflicting action of terrestrial and extraneous forces of gravitation.
2. The centrifugal and westward forces are parts of the action of the force of
extraneous or astral gravitation.
3. The current-creating action of the gravitation of the sun and moon is an
intrinsic part of the force described as astral gravitation.
PART VII.
REVOLVING ACTION OF THE EARTH’S GRAVITATION.
The difference between the direct force of the earth’s gravitation and its
revolving action. The latter, and with it the centrifugal force, increases
or diminishes inversely as the cube of the distance from the earth.
PART VIII.
LAGGING OF THE TRADE WINDS AND THE MOON.
The actual velocity of the Lagging of the moon in its orbit accords with the
Lagging of the Trade Winds.
PART IX.
LAGGING OF THE PLANETS IN THEIR ORBITS.
The actual velocities of the orbital motions of the planets show the existence
of a similar revolving force about the sun.
PART X.
THE CONNECTION OF GRAVITATION AND SOLAR HEAT.
Observations on a suggested transmutation of terrestrial gravitation into heat on
the surface of the earth by the action of the sun’s rays.
Those rays of light are created by the conflicting action of the same forces of
gravitation which carry the planets along their orbits.
The action of Solar heat must tend to derange the circulation of the ocean and
atmosphere.
PART XI.
THE AIR AS A REVOLVING RING.
With an increased velocity of rotation the foregoing forces would hold the
atmosphere in equilibrium in the form of a belt above the equatorial regions.
And the conflicting action of those forces within the belt would continue to
cause the circulation which forms the Trade and Upper Trade Winds.
PART XII.
DESCENT OF THE OCEAN.
With a faster rotation, the ocean would form a similar belt with the same system
of circulation.
That system is deranged by the descent of the ocean and atmosphere to the earth.
The effect of the winds on the circulation of the ocean.
PART XIII.
A BELT OF BOULDERS.
Further suggestions as to the previous existence of revolving rings about the
earth’s equator.
Crown 8yo. cloth, 5s.
THE STANDARD OF VALUE
PART I. LORD LIVERPOOL’S OVERSIGHT AND ITS
CONSEQUENCES.
PART II. THE DOUBLE STANDARD AND THE NATIONAL DEBT.
PART III. THE POUND STERLING: irs HISTORY Anp
CHARACTER.
OPINIONS OF THE PRESS,
‘A lucid statement and clear case for bimetallists. —FINANCE CHRONICLE.
‘This is one of the cleverest and most intelligent expositions of the thesis of bimetallism _
which have appeared. Mr. Jordan is indeed a practised writer. This well-written book
can be read with pleasure and instruction by all.,—Monry.
‘A pleasant historical résumé, as well as afree statement of the case of the bimetallists.’
—ScHOOLMASTER.
‘A perusal of the work, which is written in an attractive and popular style, should
effectively dissipate the misty prejudices entertained on the question of bimetallism, which
has become the most important question of the present age.—LIVERPOOL DAILY COURIER.
‘Three timely papers on bimetallism.-—GRAPHIC.
‘ Ably and forcibly written. —Guascow HERALD.
‘We do not see how it is possible carefully to read the facts which Mr. Jordan sets out,
or candidly to consider the arguments which he grounds upon them, without coming to
the conclusion that Lord Liverpool’s “mistake” on the Currency Question was a very
disastrous one, and that Sir Robert Peel’s Act of 1816 is now bearing better fruit..—
British Matt.
‘Mr. Jordan shows a knowledge of the subject and its bearings which implies a familiar
acquaintance with questions of finance’—DaiLy Review, Edinburgh.
‘British taxpayers at large are interested more deeply in the disputed question of
bimetallism than they perhaps imagine. It is,in fact, a question in which every one is
interested, for we all pay taxes, either directly or indirectly. Those who wish to get an
insight into the bearings of the question, as presented by one having decided views,
cannot do better than read Mr. Jordan’s little book. It is written in a clear and interest-
ing style, and whether the reader carries his studies further or not, he will at all events
be enlightened upon one sufficiently curious aspect of the case.—GLascow News.
‘There is no denying that the question of “‘ The Standard of Value” is not only a
“living one,” but one that will sooner or later become a burning one. Those who desire to
be well informed on the subject ought to read Mr. William Leighton Jordan’s contribution
to the controversy.’—Soctery.
'* An interesting contribution to this much-vexed question.,—LLoyp’s WEEKLY.
‘Contains some very interesting remarks on the origin of the Funding System.’—
BANKER’S MAGAZINE.
‘The remarkably able essays of Mr. Leighton Jordan, which should certainly be read
by all interested in trade or commerce, have again roused attention to this all-important
question. MERCANTILE SHIPPING REGISTER AND CoMMERCIAL REVIEW.
‘This is an ably written answer to the question, What isa pound? We recommend
an actual perusal of this excellently written and valuable work. The reader may assure
himself that these pages are well worth a perusal, and the writer thinks for himself.’—
METROPOLITAN.
‘Those interested in the bimetallic controversy will peruse this well-written book
with much interest. EDINBURGH COURANT.
‘This third edition of Mr. Jordan’s views on an important public question deserves
calm and earnest consideration. We recommend a close perusal of the entire work.’—
CoLLreRY GUARDIAN.
‘The essay on the “ Pound Sterling” is extremely interesting. Although inspired
by enthusiasm, isis perfectly logical. —ScHooLMASTER.
‘Those who interest themselves in bimetallism will find the arguments in its fayour
ably stated by Mr. Jordan, and the lengthy preface to the third edition of this book brings
the controversy down to date.—Ecuo
‘Mr. Jordan has in such large development the faculty of making abstruse questions
clear that we do not wonder his little work has passed into a third edition. —SnurrigLp
DaAity TELEGRAPH.
‘Those who desire to acquaint themselves with the arguments of the bimetallists will _
find them clearly stated by Mr. Leighton Jordan..—WerstrmMinstER REVIEW.
A CATALOGUE: “OF
September 1885;
WORKS IN GENERAL LITERATURE & SCIENCE
PUBLISHED BY
MESSRS. LONGMANS, GREEN, & CO.
AAA ARO
PL NINA NI NS NINS NS
Classified Index.
AGRICULTURE, HORSES, DOGS,
and CATTLE.
Dog (The), by Stonehenge ............ 4
Dunster's How to Make the Land Pay
srateiejere Aree)
Fitzwygram's Horses and Stables ...........- to
Greyhound (The), by Stonehenge.............. 21
Horses and Roads, by Free-Lance ............ 12
Loudon's Encyclopedia of Agriculture ........ 14
Lloyd's The Science of Agriculture ............ 14
Miles’ (W. H.) Works on Horses and Stables ..
17
Wevite's Farms and Farming ...............008 18
forses'and: Radingss/s.. cv. ccss cececees 18
eee SPE ALIN =V ALGET T6220 cles sie tives cect cescieeeees 20
Stee?s Diseases of the Ox .
Taylor's An Agricultural Note-Book .......... 22
Vidle’s Artificial Manures
comaudind COC COONDOaS 23
BPEL LOWIENE OS™ (0:0 she's cise ca ce vclac ce valdeleees 24
emt LL OISC eieicldia'sicieloe cee ciieci esos nec _ 24
ANATOMY and PHYSIOLOGY.
Ashby's Notes on Physiology..........eseeseee 5
Buckton's Health in the House.......0....00. Bay
Cooke's Tablets of Anatomy and Physiology.... 8
Gray's Anatomy, Descriptive and Surgical .... 11
Macalister's Vertebrate Animals
Owen's Comparative Anatomy and Physiology.. 19
Quain's Elements of Anatomy ............006 - 20
Smith's Operative Surgery on the Dead Body.. 21
ASTRONOMY,
Bail’s Elements of Astronomy ..... Siolersim staves leet 22
Hlerschel’s Outlines of Astronomy........ Ejod0 Hey
exnowledge, Library (The) \...0...scceessses a es)
AIL OFS U3, Zc)! WOLKS sie oless/a\e\iere leie:d oi via c ove Se Bi)
Veison’s The Moon ....... slaitraiaiste Boot JoxoeTS
Schellen’s Spectrum Analysis 2
Webo’s Celestial Objects for Common Telescopes 23
BIOGRAPHY, REMINISCENCES,
LETTERS, &e.
Bacon's Uifeiand Works. ........0..e00ee. Fron as
Bagehot’s Biographical Studies .............. see 35
rey S PhASeSSOL OPINION cieccces cree csccnsce 7
Carlyle's (T.) Life, by James A. Froude ...... 7
—— (Mrs.) Letters and Memorials........ 7
Cates’ Dictionary of General Biography........ 7
Cox's Lives of Greek Statesmen .........0..4 8
D’' Eon de Beaumont's Life, by Telfer.......... 8
. fox(C. F.), Early History of, byG. O. Trevelyan 10
Grimston’s (Hon. R.) Life, by Gale............ II
Hamilton's (Sir W. R.) Life, by R. P. Graves... 11
Havelock’s Memoirs, by J. C. Marshman ...... 12
Macaulay's Life and Letters, byG. O. Trevelyan 15
Malmesbury’s Memoirs .....+ Reieeieteteers shelsia rae = 20
Maunder’s Biographical Treasury ............ 16
BEE EP ESSOMTES NACLECTS vols \viats 0,cis,s's:0.4:.0 o'vie 6.c'ale 0 4.6 17
Mill (¥ames), a Biography, by A. Bain........ 6
Mill (Fohn Stuart), a Criticism, by A. Bain.... 6
Mills (F. S.) Autobiography..........eesseees 17
Mozley’s Reminiscences of Oriel College, &c. .. 18
——— — Towns, Villages, &c. 18
Miller's (Maz) Biographical Essays .......... 18
BeeSHIPP IIE ST VLCINIOIN seiset crc s,cie cc oe 0.0 0.0 ele 0's oofe ae
Pasteur’s Life and Labours
sisfeleca.s'» 2,0 es.Gla eiarata - I9
Shakespeare's Life, by J. O. Halliwell-Phillipps 2r
Stephen's Ecclesiastical Biography .:........+- 2
Taylor's (Sir Henry) Autobiography .........-. 22
Wellington's Life, by G. R. Gleig ............ 23
BOTANY and GARDENING.
Allen's Flowers and their PedigreesS.......0.0008 4
De Caisne & Le Maout's Borany...ereesscesee 8
Lindley's Treasury of Botany .....seseeeeeees 14
BOTANY and GARDENING —continued.
Loudon s Encyclopedia of Gardening
Hateseyete oor:
— Encyclopedia of Plants........ : as
Rivers: Orchard=Hlousesaeeeeseseeten ness SBaod
Rose Amateur’s Guide ..........eseees 20
Thoné’s Botany ........ Parclanepiecsia hie alaia\bye (e100, 022
CHEMISTRY.
Armstrong's Organic Chemistry ..........s00e 22
Kolbe’s Inorganic Chemistry ........ses.eee0e a
Miller's Elements of Chemistry ............5- 17
Inorganic Chemistry.........ceeceeees 17
Thorpe & Muir's Qualitative Analysis ....666. 22
"s Quantitative Analysis ......cescsscecs 22
Tilden’s Chemical Philosophy .......... SOuGbe Gs
Watts’ Dictionary of Chemistry ...........06 + 23
CLASSICAL LANGUAGES,
LITERATURE, and ANTIQUITIES.
“Eschylus Eumenides, Edited and Translated
by Daviesis.ni occ siete aalacl delaidielaisiote sata Bae
Aristophanes’ The Acharnians, translated...... 5
Aristotle's Works .....2.2.00 Beieisheeistneretantarctes 5
Beckers Charicles) esac cetacean 6
GALE eae A ceite wesc on eee €
Cicero's Correspondence, by Tyrrell........ swee 7
Hlomer's Iliad, translated by Cayley .,...0.. 12
Greenl eanacssters wi Ee
fort's The New Pantheon
Mahaffy’s Classical Greek Literature .......... 16
Perry's Greek and Roman Sculpture
sete ww enee I
Rich's Dictionary of Antiquities ............5. oo
Stmcox’s History of Latin Literature ........ apy en
Sophocies* Works iw scence detect ee 2r
Virgils Enid, translated by Conington..... 4s 7
= ROCMS Hae. :Faceeeceteeeee we eee,
- Works, with Notes by Kennedy ...... 23
Wares: Niyfis of sitellas ” .. same eee cones 24
he Projan-War 2 s.. te nee eee 24
——— The Wanderings of Ulysses ............ 24
COOKERY, DOMESTIC
ECONOMY, &e.
Acton’s Modern Cookery mayer
Buckton’s Food and Home Cookery............ 7
Reeve's Cookery and Housekeeping
ENCYCLOPZADIAS, DICTIONARIES,
and BOOKS of REFERENCE.
Ayre’s Bible Treasury
Blackley’s German Dictionary ..... Sogpncesonk 6
Brande’s Dict. of Science, Literature, and Art.. 6
Cabinet Lawyer (The)!
J sicieie ejeiniejniaie'vieln ae DOOUCOU Li wy,
Cates’ Dictionary of Biography ........ aieid sinew om Ti
Contanseau’s French Dictionaries.............. 8
Gwilt’s Encyclopedia of Architecture.......... It
Fohnston’s General Dictionary of Geography .. 13
Latham’s English Dictionaries .........0eeee0
14
Liddell & Scott's Greek-English Lexicon...... 14
Lindley & Moore's Treasury of Botany........ 14
Longman's German Dictionary.......... eee 14
Loudon's Encyclopedia of Agriculture ........ 14
SSS (CAME se stn 14
— n+ — PlantSseettene ae 14
M'‘Culloch’s Dictionary of Commerce ...... 16
Maunder's Treasuries ........ sinfale! olny sum sivejcecin: 96
Quain’s Dictionary of Medicine.............- ee 20
Rich’s Dictionary of Antiquities ......... ae ZO
Roget's English Thesaurus.......ccsssessececs 20
Ure's Dictionary of Arts, Manufactures, &c..... 23
White's Latin Dictionaries .......0...s0000. ey 2a
Wiltich’s Popular Tables.........0.
Yonge's English-Greek Dictionary -+........+. 24
2 LONGMANS 3 co 2 List os Se oe SCIENTIFIC BOOKS
EN INEERING, MECHANICS,
MANUFACTURES, &e.
Anderson’ 's Strength of Materials...........0+-
Barry 's Railway Appliances
Bourne's Works on the Steam Engine...... cece
Cudlley’s Handbook of Practical Telegraphy «.
Edwards’ Our Seamarks.......0...seeeeeeeee :
Fairbairn’s Mills and Millwork.............+--
—— Useful Information for Engineers ..
Goodeve's Elements of Mechanism........-+.+++
—— Principles of Mechanics............+.
Gore's Electro-Metallurgy
Gwilt’s Encyclopedia of Architecture
FYackson's Aid to Engineering Solution .......-
Mitchells Practical Assaying........eeseeeeeee
Northcott’s Lathes and Turning
Piesse's Art of Perf UMELY ....-+eeeee conan oo
Preece & Sivewright’s Velegraphy .......-----
Sennett's Marine Steam Engine
Shelley's Workshop Appliances..,.-...--.+-++-
Swinton’s Electric Lighting
Unwin’ 's Machine Design
Ure's Dictionary of Atts, Manufactures, & Mi ines
ENGLISH LANGUAGE and
LITERATURE.
Arnolds English Poetry and Prose .
ee ne ae
Manual of English Literature . noacaas :
Lathanes English Dictionaries .............+ °
Handbook of English Language..... .
Roget's English Thesaurus ............22-0005 =
Whately’ Ss English DY MOMyAS elaeetctelcinictoeeel=te
5
14
14
20
23
HISTORY, POLITICS, HISTORICAL
MEMOIRS, and CRITICISM.
Amos Fifty Years 3 the English Constitution ..
Primer of the English | Constitution .....+ 5
Arnold's Lectures on Modern History ..sececs
Beaconsfiela’s Selected Speeches .....2...- e000
Boultbee’s History of the Church of England...
Bramston & Levoy's Historic Winchester.....»
Buckle’s History of Civilisation....... efeicletelareke 5
C hesney. 's Waterloo Lectures .....-..20--> 54000
Cox’s General History of Greece ..--.seees cece
Lives of Greek Statesmen ..........--++
Creighton’s History of the Papacy ...-. pietelateia :
De Tocqueville's Democracy in America ....-.
Doyle's The English in America ...
Epochs of Ancient History ........
Modern History ........--.- pocosaa0
Freeman's Historical Geography of Europe ....
Froude’s History of England......... Goougo0n6
=. Short Studies-.......-.... soceoasong
The English in Ireland ....... sopo0e 5
Gardiner’s History of England, 1603-42........
— Outline of English History ........
Grant's University of Edinburgh . cooapeodaoNee
Greville’s Journal ......+ceeeeseeeeeeee 00004
Hickson’s Ireland in the 17th Century naacannnes
Lecky’s History of England ....... sas cduengad
Ce EE European Morals ....... 500
Rationalism in Europe......
Leaders of Public Opinion in Ireland ..
Lewes’ History of Philosophy....... jagsodcn004
Longman’s (W.) Lectures on History of England
—_—_——— Life and Times of Edward iM ease
(F#. W.) Frederick the Great
Macaulay's Complete Works ..-.0.-+0sssee sees
——_—— Critical and Historical Essays
—- History of England
Speeches
Maunder’s Historical Treasury
Maxwell's Don John of Austria ....++....- 56
May’s Constitutional Hist. of Eng. rise ye ae
Democracy in Europe.......-.-
Merivale’s ¥ all of the Roman Republic . ppisielsieiele
—— General History of Rome ...+.....
Romans under the Empire.. 5
The Roman Triumvirates .....--- 5
we enee
i i ay
Noble’ s The Russian Revolt .........+0+-0s00
Rawilinson’s Seventh Great Oriental Monarchy..
Seebohm’s English Village Community ........
— The Oxford Reformers....++ ajeld sielainis
——-—— The Protestant Revolution ..........
Short’s History of the Church of England..
_ Svzith’s Handbook for Midwives .-
HISTORY, POLITICS, HISTORICAL
MEMOIRS and CRITICISM—cow.
Sith’s Carthage and the Carthaginians ......
Taylor's History of India ...,..,.... 4 apie
Walpole’ s History of England, 1815-4z ........
Wylte’s England under Henry DV ct dete Bisleeiate
ILLUSTRATED BOOKS anal
BOOKS on ART.
Dresser’s Japan’; its Architecture, &c. .....
Eastlake's Five Great Painters ......0+...se00
——— Hints on Household Taste..........
— Notes on Foreign Picture Galleries..
Fameson’s Mrs.) Works .. 02.000 se seecscevecve
Lang’s (A.) Princess Nobody, illus. by R. Doyle
Macaulay's (Lord) Lays, illustrated by Scharf .
illustrated by Weeuelin
Moore's Irish Melodies, illustrated by Maclise ..
— Lalla Rookh, illustrated by Tenniel....
New Testament (The), illustrated............. .
Perry's Greek and Roman Sculpture
MEDICINE and SURGERY.
Buil’s Hints to Mothers .... fale iefatele
Maternal Management ‘of Children pinot =
Coats’ Manual of Pathology Boastboos
Dickinson On Renal and Urinary Affections. :
Evichsen's Concussion of the Spine .
ee ee eersee
— Science and Art of Surgery........ ne
Garrod’s Materia Medica ......sccceccseuvecs
‘Treatise ‘on Gout: sc. smarts sae Rees
Hassall. s Inhalation Treatment of Disease .....
Hawara’s Orthopaedic Surgery
Hewitt’s Diseases of Women...... Btoooaccs
Mechanic. System of Uterine Pathology
Holmes’ System of Surgery..
Husband's Questions in Anatomy... cjateietettelinls ets
ee ee eres cesses
eeeeee
Fones’ The Health of the Senses ..-.2.0..-- oe
Little's In-Knee Distortion........ Sobosonsoos-
Liveing’s Works on Skin Diseases ........ Age:
Longmore’s Gunshot Injuries........ Ristelsieicterte .
Mackenzie's Use of the Laryngoscope..........
Macnamara’s Diseases of Himalayan Districts..
Morehead’s Disease in India ........-.0.+.--s
Murchison’s Continued Fevers of Great Britain, &
Diseases of the Liver..... Apocesoos
Paget’s Clinical Lectures and Essays ..........
Lectures on Surgical Pathology........
Pereira’s Materia Medica a
Quain’s Dictionary of Medicine............:.. :
Salter's Dental Pathology and Surgery «. Soha 1
Thontson’s Conspectus, by Birkett | noel
Watson’s Principles and Practice of Physic ...
West's Diseases of Infancy and Childhood.....
MENTAL and POLITICAL PHILO-
SOPHY, FINANCE, &e.
A bbott’s Elements of Logic ..........+... Agh48
Amos Science of Jurisprudence........++. clea!
A xistatle's WiOxkS 0 cis\e sinje +) slofeielein(s cists) -isl= ia .
Bacon's Essays, with Notes, by Abbott ...... aA
ee — by Bunter. eine
—— by Whately ..... .
—- Letters, Life, and Occasional Works....
— Promus of Formularies
Bagchot’s Economic Studies
Bain's (Prvof.) Philosophical Works .....
Crozier's Civilisation and Progress ...+.+++s-
seen eens
Davidson's The Logic of Definition...... wea nets
De Tocquevilte’s Democracy in America....+++
Dowells History of Taxes ..........-++eeeeee 5
Green’s (T. Hill) Works......-. aeieleraeho inten ste
Hume's Philosophical Works .......+-++++ee++s
Fustinian’s Institutes, by T. Sandars .......-- “
Kant's Critique of Practical Reasqn ....-+++- 4
Lang’s Custom and Myth ........++++-eeeees
List’s The National System of Political Economy
Lubbock’s Origin of Civilisation...... mieten, jnis/aele
Macleod's (H. 7D) ) Works” <2. cjrelsaicte steiner
Mills (¥ames) Phenomena of the Human iad
Mills (¥. S.) Logic, Killick’s Handbook to .
WOKS 02 oe cep ecenc ccc esinceeeee :
Miller's Social Economy......++++++ ciajaleofBvainietp
ODOWDMOAUMNUNUNNUNNMh
mr SINSN LON LIN LIN INS INI IN IN
MENTAL and POLITICAL PHILO-
SOPHY, FINANCE, one NO eid
Sully’s Outlines of Peycholosy auctor eiee aI
Szuznburne’s Picture Logic ..cccscepeccccccscce 22
Thompson's A System of Psychology ARID 0 cies om, 22
Thomson's Laws of Thought .....ceveccecevecs 22
Twiss on the Rights and Duties of Nations .... 22
MARCO LEN V Ell Of ISIS os ccienievcdeceqesccucs * 23
Whately's Elements of Logic ........ceeceecese 23
— Elements of Rhetoric ..........00 . 723
Wylie's Labour, Leisure, and Luxury ....... | a4
Zellers Works on Greek Philosophy ......... + 24
MISCELLANEOUS WORKS.
Aik. A. B., Essays and Contributions of...... | 4
Arnold's (D>. ) Miscellaneous Works .......... 5
Bagehot's Literary Studies ...........645 geste! tS
Beaconsfield Birthday Book (The) ............ 6
Beaconsfields Wit and Wisdom ...........4- 6
£vans Bronze Implements of Great Britain .... 10
Farrar's Language and Languages...........5 10
BencecPOrink I FNEIANd. <6. sc ccecceseeccece 10
salad Sbatentee’s Mantial.. ..cscccssccsvecs 13
RIAING VEAP AZINIC! sicicw cece sasecccecccasees 14
Macaulay's (Lord) Works, Selections from .... 15
BELEr SS OVIEE)WOEKS soso occ ecscccsicece ses Hinee aits!
Peels A Highland Gathering........ 19
Swith’s (Sydney) Wit and Wisdom .
Verney’s (Lady) Peasant Properties .......6.. 23
NATURAL HISTORY (POPULAR).
Dixon's Rural Bird Life ...... meeierenrap aemrecejeacn sO
mel artwig's (Dr. G.) WorkSeess sescdecessvvet wwe DE
Maunder's Treasury of Natural History ...... 16
_ Stanley's Familiar History of Birds..........0 21
Wood's (Rev. F. G.) Works ......ccsccees cdisietn 2A)
POETICAL WORKS.
Bailey's Festus .1.-saeeeeeveeeegee ee 5
Dante's Divine Comedy, ‘translated By Minchin 8
| Goethe's Faust, translated .........0... ataaierare aif aie
_ Homer's Mliad, translated by Cayley” Se Cacao 12
eee Ean slated) by Green cise. eicicc ie « - I2
iL; ngelow’ BPP OEHCAL WOLkSh (fia coos oh rads oe 13
_ Macaulay's (Lord) Lays of ‘Ancient Romessesse} 15
' Macdonald's A Book of Strife ........eeeees ._ 15
Penneld’s ‘ From Grave to Gay’.......... ceele ee LQ
_ Reader's Voices from Flower-Land ........... + 20
_ Shakespeare, Bowdler’s Family Edition...... Bet ZT
: Haunlet, by George Macdonald .. 15
. Southey’s Poetical Works. ..e.seecesee “2
_ Stevenson's Child’s Garden of Poems «22
_ Virgil’s neid, translated by Conington ...... 23
a Poems, translated by Conington Jeseseh 23
| SPORTS and PASTIMES.
, ee Shot (The), by Marksman ,......2.00.% “apes
yuekers Bookon Angling” ..20:.....ccccss ees <) 0
¥ BEES TREANDICEL) wichie wre Loe ware ac doce ce ale * I3
F Longman S Chess Openings. \...006.ceceseabete 14
, Pole's The Modern Game of Whist ......+-0+0 19
: Ronalds’ Fly-Fisher's Entomology ........+++. 20
_Verney’s Chess Eccentricities ......00-...005 23
Mi alhers The Correct Card ....acccsceecosees 23
i Ws tlcocks’ The Sea-Fisherman..........esse0 24
SCIENTIFIC WORKS (General).
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i Bauerman's Descriptive Mineralogy .. 22
Seca Systematic Mineralogy ..:..0.. 22
| ee s Dictionary of Science &c. we.. 6
: Buckton’s Our Dwellings &c. ...... : 7
(Gano?’s Natural Philosophy ..... mints feta vseuatel ZO
NEUES Godage once nn cended Ieee sinjsivieiiioln nO
( Grove’s Correlation of Physical Borces\. je \atee oh IL
| Haughton’s Lectures on Physical Geography .. 12
| Helitholtz Scientific Lectures ........0..e.08- me ie
—_— On the Sensation of Tone .......... 12
iHullah's History of Modern Music............ 12
Transition Period of Musical History., 12
Kert’s Treatise on Metallurgy .....3..... celia I
* Knowledge’ Library (The) .....cesesseeeeeess 20
Lloyd's Treatise on Magnetism Matte. a\e sista siataitl isa 14
F Macfarren’ 's Lectures on nik ad Chesabg ae | 5S
Mazunder’s Scientific Treasury .......0s2e+e2008 16
ms CGL7F- (ltt, A.) WOLKS io cinc.civ'aacicesicciee oevice 5 ie,
LONGMANS te CO. oe LIST OF GENERAL AND pCrENt TRIC BOOKS.
P-— LLIN LOL IOP OES
3
SCIENTIFIC WORKS (General) con
Schellen’s Spectrum Analysis....sseesseeseeees
Swith's Airand Rain ..coccscceccs Ce ve dates ooce
Dext-HOOKS OM SOIEUCEl sale ced veide oats te cilen sane
Tyndall's (Prof) Works weeeeeeescecees
Wilson’s Manual of Health Science...
THEOLOGY and RELIGION.
Arpaia S| CD 7a SeOMOUSi inaisisisie sie cccagevaceces ’
Ayre’s Treasury of Bible Knowledge ......... F
BLoultbee’s Commentary on the 39 Articles ..... F
Browne's Exposition of the 39 Articles nisaisigsyne
Calvert's Wife’s Manual ........s¢eceesues bide
Colenso’s Pentateuch and Book of Joshua | tee
Conder’s Handbook to the Bible
Conybeare and Howson’s St. Paul
Davidson's Introduction to the New Testament
Dewes Life and Letters of St. Paul............
LEdersheim’s Jesus the Messiah ..........200006
———-—— Warburton Lectures..............
£lticot¢’s Commentary on St. Paul’s Epistles ..
— Lectures on the Life of Our Lord ....
Ewald’s Antiquities of Israel ..........+seeceee
———_ ——_—_ HIStory, OL ISEACH: re crest sievel aisles teat etaciate
LTobart’s Medical Language of St. Luke ......
Hlopkins’ Christ the Consoler ....00..-+e+eeeee-
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