Henry F. A Pratt.

Astronomical investigations; the cosmical relations of the revolution of the lunar apsides. Oceanic tides online

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UNIVERSITY OF CALIFORNIA

ANDREW

SMITH

HALLIDIE:



1868 1901




ASTKONOMICAL INVESTIGATIONS.



30tronomtai Jfabesttgattons,



THE COSMICAL RELATIONS



REVOLUTION OF THE LUNAK APSIDES,



OCEANIC TIDES.



BY

HENRY F. A. PRATT, M.D.




LONDON:
JOHN CHURCHILL AND SONS, NEW BURLINGTON STREET.

MDCCCLXV.




LONDON :

BENJAMIN PARDON, PRINTER,
PATERNOSTER ROW.



PREFACE.



WHEN Pilate asked the question, What is truth? the
apocryphal gospel of Nicodemus affirms that he was told
in reply, that Truth is from heaven : but that it is on
earth, among those who, when they have the power of
judgment, are governed by truth, and form right judg-
ment.

Three conditions are thus declared to be necessary to the
enunciation of the truth in all cases: the power of judg-
ing, the acceptance of true evidence, and the formation of
a right judgment.

In Astronomical Science the combination of these con-
ditions is very rare, for the power, when unconsciously
severed from the will, fails to recognise the value of the
evidence; or else, comprehending its force, permits it to
remain unverified, as though valueless; the sense of the
imperative duty of forming the right judgment, when the
true evidence is presented, being only too often wanting,
here as elsewhere, in those who have the power of judging,
but not the courage to face the consequences of their judg-
ment : for, perhaps unfortunately, those with whom, by an
almost universal sufferance, if not necessarily, the power
of judging is permitted to rest in this science, are parties
in any issue that may be raised in which accepted theories
are controverted, and thus are virtually made the judges



105138



VI PREFACE.

in their own cause; for the unlearned public admits its
incompetence to decide in such cases ; but, as a consequence
of this special interest, they almost unavoidably read all
evidence that may be submitted to them through the dis-
torting lens of their own preconceived opinions.

In the judgment of facts, however, on which observation
can be brought to bear, and where prejudice must yield
to the determining and determined results of a rigid
scrutiny, they will, themselves, become truthful witnesses
when their attention is sufficiently roused to the bearings
of any given fact to the verification of which they are
invited. The Author, therefore, now appeals to them, the
practical astronomers, who are also through the force of cir-
cumstances the judges in his cause, to test the value of his
views as to the true cosmical relations of the revolution
of the lunar apsides, and the teachings that can be drawn
from tidal phenomena considered in their oceanic origin ;
confident that if they can be once led to see the importance,
not to say the necessity, of reconsidering accepted theories
on these points, through a new and possibly true bearing
of the actually observed facts, the true evidence on which
their judgment ought to be based, the right judgment will
come, and these Astronomical Investigations not have been
written in vain.



THE COSMIOAL RELATIONS



REVOLUTION OF THE LUNAR APSIDES.




INTRODUCTION.



THE following paper on "The Cosmical Relations of the
Revolution of the Lunar Apsides" was written at the
suggestion of a friend, who considered the author's astro-
nomical opinions of sufficient importance to deserve a
formal discussion, and therefore kindly offered to commu-
nicate them to the Royal Society. It was accordingly
placed in the hands of one of the secretaries of that
Society, but returned by him as not suitable for the con-
sideration of its members.

Perhaps it was declined because an attempt has been
made in it to free an abstruse and difficult subject from
the technicalities and obscurities in which it is commonly
involved, by reducing the principles through which some
of the phenomena resulting from revolving motion, combined
with a gravitating attraction in a complex system, ought
to be interpreted, to simple geometrical demonstrations,
stripped of algebraic formulae and symbolic calculations :
though it may have been because the views advanced in
it do not agree with the opinions of the day.

However this may be, the author regrets that an oppor-
tunity for discussion has been denied to him, for he
conceives the whole subject to be of sufficient importance
to deserve examination, notwithstanding any seeming un-
scientific method in the manner in which it is approached ;
while, if learned societies decline to discuss unaccepted

B



2 INTRODUCTION.

opinions, either because they are opposed to those held by
the greater part of their members, or else fear that they
may compromise themselves as a body, by seeming for a
time to endorse views which may turn out to be incorrect,
but can only be tested by such a searching inquiry as it is
in their power to institute, it becomes evident that they
have fallen away from the end proposed in their institution,
and, instead of aiding, render themselves real impediments
to the advance of science.

The author still desires that his opinions may be ex-
amined, in order, if they are incorrect, that their fallacy may
be established: he therefore now publishes them, but in
the form in which it was proposed to submit them to the
Royal Society, in order that his readers may have exactly
the same opportunity of judging their merits.

The progress of science is unfortunately beset by two
classes of difficulties, each of them presenting peculiar
impediments to the onward movement. The first of these
accompanies the observation and determination of pheno-
mena and facts, and is sometimes so impenetrable that a
series of successive patient observers has been necessary in
order to establish a single relation.* The second lurks in
the path of the interpreter of observed and determined
phenomena and facts, and often leads him to give a false
value to the results of observation, f

As the intrinsic worth of facts is measured, not only by
the difficulty with which the knowledge of them has been
gained, but also by the importance of the lesson which
they appear to teach, there is always a tendency in the

* Until the time of Copernicus, the earth was supposed to be stationary.
"What a long period and series of observers passed away before its actual
motion was determined ! That is, under the present order of science.

f As hi the case of Bradley, who discovering the apparent, interpreted it
as an actual nutation of the earth's polar axis, and attributed it to the in-
fluence of attraction acting upon the assumed preponderating equatorial
mass of the earth.



INTRODUCTION. 3

mind of the successful observer to estimate his facts (or
supposed facts), by the labour which their attainment has
cost him, and to interpret them more or Jess through his
own preconceived opinions hence there is always a pos-
sibility, nay, perhaps even a strong probability, that every
newly ascertained fact will be at first misinterpreted.*

Even in those cases in which facts have not been over-
estimated, an importance is often given to the opinion of
their discoverer in proportion to their actual value, so that
he is raised into an authority on the subject, and his inter-
pretation considered as certain as the fact which he inter-
prets all other methods of interpretation being most pro-
bably overlooked ; so that it is possible that simultaneously
with the knowledge of fresh facts a false method of inter-
pretation may arise and be perpetuated for an indefinite
time, the authority of a name being thus rendered an
obstacle to the discovery of the truth. f

The science of Astronomy has been in all ages peculiarly
exposed to this influence. Its facts are always learnt by
slow processes and with very great difficulty, while they
are, at the same time, so important, that every discoverer
becomes an authoritative exponent of opinion ; and yet,
unfortunately, in order to become a discoverer a peculiar
training is necessary, which perforce involves the adoption
of preconceived opinions, so that, a given theory having once

* This was done by Galileo, who, when he discovered that balls of diffe- <*
rent weights appeared to take the same time in falling from the same height
to the earth, rashly generalized that gravity acted equally upon all masses
of matter at the same distance, forgetting that his experiments were on so
small a scale, as compared with the mass of the earth, that differences could
not be made perceptible to the senses of man, which nevertheless reason and
philosophy show must exist. See On Eccentric and Centric Force, Part I.,
sec. 1, and Part III., sec. 10.

f This is strikingly seen in the case of Sir Isaac Newton, who, recognis-
ing the cosmical influence of gravity as a source of attraction, rashly gene-
ralized the principle that it was the saarc^_pjjth^jnotions of the heavenly ' '
bodies, instead of a tendency in their constituent matter to draw them }
together,~~and bring them to a state of union and rest.

B 2



4 INTRODUCTION.

been accepted, every succeeding phenomenon will be of
necessity read and interpreted through that theory.*

In this science, from the earliest ages, but certainly from
the time of Copernicus downwards, the almost constant
obstacle to onward progress has been the misinterpretation of
observed phenomena. Every fact added to the general stock,
when once it has been established, is an actual gain. The
whole group of recognised facts forms the common store
from which all interpreters must draw the bases of their
inductions ; but, though the facts are (perhaps) admitted by
all, and even beyond the reach of question, any method of
interpretation may be far from being so. And therefore,
and as long as a possibility of error exists, every new system
of interpretation is entitled to a hearing, and those who with-
hold this right expose themselves to the risk of opposing
the advance of that truth which every inquirer is in reality
labouring to define and put within the reach of all.f

The writer of these pages, after a patient and careful
examination of the whole subject, has come to the conclusion,

* The predicted existence and subsequent discovery of the planet Neptune,
through the perturbations caused by its mass, is given as a triumphant proof
of the truth of the theory of universal gravitation. In reality it only shows
that an attraction is seated in matter which acts at immense distances, and,
when acting excentrically, alternately accelerates and retards the motion of
those bodies on which it is acting, and causes relatively slight deviations
from their true paths. It gives no further proof of the truth of the New-
tonian interpretation or theory of universal gravitation than does the calcu-
lation and prediction of eclipses, which is quite independent of that theory.

t The theory of universal gravitation was constructed on a basis of mis-
interpreted facts, and then became a groundwork of preconceived opinions
through which a misinterpretation of subsequently discovered facts was
provided for and perpetuated. Thus, Sir Isaac Newton read, in the
apparent, an actual variability in the moon's motion, and attributed this
assumed variability to the attraction of the earth ; and then, observing the
effects of attraction in planetary perturbations and the tides, promulgated
a scheme which, when once it was accepted, became the source of all sub-
sequent interpretations ; so that already recognised phenomena, as recession .
and precession, as well as every fresh discovery, such as the apparent
nutations of the earth's polar axis, were interpreted by and read as further
proofs of its accuracy.



INTRODUCTION. 5

that by studying the mutual relations of the whole series of
observed phenomena from a new point of .view, in which
they are combined into groups, each of which is referred
to certain distinct causes, principles can be developed more
philosophic in themselves, and at the same time more
easily subjective to examination and verification, and more
facile of comprehension, and results elicited from these
principles, under which far greater scope is given to the
present limited range of astronomical theory.

The present range of astronomical vision, as far as the
system of which the earth is a component part is concerned,
is centred in the sun, to which motion has at length been
attributed, and even the direction of that motion conjectured ;
so that the picture presented to the mind's eye is that of the
solar system hurrying through space, and possibly revolving
in an extensive orbit, the relations, range, and period of
which are not even attempted to be surmised.

Grand as this ideal picture may be, and perfect, as far as
it goes, it is yet a very limited one, when contrasted with
the results which can be drawn from a more careful examina-
tion of the mutual relations of the observed phenomena ; for,
under such an examination, it can be shown that the solar
system, vast and complicated though it be, is but a single
member of a wonderful compound system, the general scheme
and relations of which can be depicted : thus, the solar system
is hurrying round an as yet unrecognised body or central
sun* which is itself again hurrying round an also unrecog-
nised body or centric sunf each of these bodies lying on
what may for convenience be termed the plane of the
zodiac, though in reality the actual planes of the orbits of
motion are inclined to each other. J

* See On Orbital Motion, by the author. (London : John Churchill and
Sons.) Par. 12.

f This body is not mentioned in Orbital Motion. The author has only
demonstrated its existence since the publication of that work.

J See Orbital Motion, Notes 96 and 117.



6 INTRODUCTION.

Moreover, the actual measures of the respective periods of
these several bodies exist ; for the lunar cycle (of recession)
is the measure of the time occupied by the sun in revolving
in its orbit, while the terrestrial cycle (of precession) is the
measure of the period occupied by the central sun in its
revolution.*

But the manner in which the phenomena can be made to
speak does not end here ; on the contrary, it can be shown
that the centric sun is itself in motion nay, more than this,
although so far its period cannot be determined, the direction
in which it is moving can be ascertained, when singularly
enough it is found that the observed motion at present attri-
buted to the sun is that of the centric sun, which, instead of
revolving on the plane of the zodiac, like the component
members of its system, is passing through (or across) that
plane, f

In order to understand these several relations, it is necessary
to regard the whole compound system as spheroidal in cha-
racter ; and to consider all these motions as taking place on
the surface of the assumed spheroid but with this difference,
that the orbit of the centric sun is a great circle of the
spheroid, while the other bodies are revolving on its surface ;
so that, while the plane of motion of the centric sun is through
the centre of the spheroid, the general direction of the planes
of the orbits of the other bodies is parallel to a segment of
its surface ; in consequence of which the plane of the orbit
of the centric sun may be said in general terms to be at right

* See Orbital Motion, Notes 25 and 81.

f See Fig. 1. See also Orbital Motion, Fig. 1, where the path of the
central sun should be treated as that of the centric sun. The evidence of
the motion of the centric sun is drawn from the difference in period between
the revolution of the terrestrial apsides and equinoctial points. The great
difference between the periods of these two simultaneous revolutions in
opposite directions, is owing to the path of the centric sun being across
the zodiac.



INTRODUCTION. 7

angles to the common plane of motion of the members of its
system.*

The centric sun is in reality revolving round a point or
body situated within, and probably (relatively) in the neigh-
bourhood of the centre of the spheroidal system but still
excentric in the path of the centric sun.f

This focal body of the orbit of the centric sun has pecu-
liar relations to all of the bodies forming the entire system.
It lies upon and is the common focus of the axes of their
poles in the North Celestial Pole, and thus can be very pro-
perly termed the Celestial Polar Centre. It is an attracting
body. It has drawn the bulk of the solid matter of the earth
into the northern hemisphere. It is the source of attraction
of the magnetic needle ; and by its attraction maintains the
stability of the polar axis of the earth and of the other mem-
bers of the system. Its attraction varies with the distance
through which it acts ; and it is this varying attraction,
acting upon the earth by slow degrees, through long periods
of time or cycles, that has produced a large proportion of the
physical changes in the constitution of the earth ; and besides
this, it is probably the primary source of the electrical and
magnetic currents which pervade the whole system, and
become, from time to time, visibly sensible in the Northern
Lights. $

Three simple but well- recognised principles, acting through
the relations determined by the spheroidal system just
described, when rightly and carefully applied to the inter-
pretation of the observed phenomena, at once throw a fresh

* The simplest way of studying these relations is to view the centric sun
as moving in a direction parallel to the mean polar axis, or from north to
south, while the other bodies are passing respectively from west to east.

f This excentricity will have a double aspect ; for though it may not be
great with reference to the volume of the imaginary spheroid, it would
yet, relatively to the volume and mass of the earth, cause immense differ-
ences in its actual distance in the different and ever- varying positions of
the entire system and its relative parts.

See Orbital Motion, Note 95.



8 INTRODUCTION.

flood of light upon the physical history of the earth. These
principles are

First. The mutual attraction which the several bodies have
for each other, and especially the increase which takes place
in this attraction inversely as the distance diminishes, and
vice versd*

Second. The inclination of the planes of the several orbits
to each other and to the equators of their proper bodies ; f
and,

Third. The excentricity of the several focal bodies.:}:

The source of the first of these principles is, probably,
an inherent tendency in all matter to combination, union,

* This attraction is twofold in its character : between a primary and its
satellites, when it acts concentrically, resisting the force which maintains
the persistent motions of the satellites round it, and tending to draw them
into itself, thus becoming a true centric force, as in the case of Jupiter and
its moons, a due balance between this attraction and the active motive force
maintaining the systemic relations ; and between any two (or more) other
bodies, as between Jupiter and the earth, when it acts eccentrically, tending
to disturb the systemic relations, and produce what are termed perturbations.
The Newtonian theory has failed to discern the force of this distinction.

f This inclination is the cause of one form of variation in the degree of
attraction that acting through the polar axis, since it causes a regular
alternate variation in the distance between the revolving body and the
celestial polar centre.

There are three ways in which orbital inclination might originate :

1. Through the eccentric attraction of a remote concentric body, as
explained in Orbital Motion, Note 117, and Fig. 13.

2. Through alternate systemic concentration and expansion, also indi-
cated in Orbital Motion.

3. During the progressive motion of the centric sun across the zodiac,
the inclination of the zodiacal plane would diminish as its centre was
approached, and increase again after it was passed.

The two former appear to be both of them in operation, the one acting
on the plane of the moon's orbit, the other on that of the earth.

J This provides for another form of variation in the degree of attraction.

The probable cause of excentricity has been discussed in Eccentric and
Centric Force and Orbital Motion. There is another way of accounting for
jt : by regarding each revolution as an act of projection, under which
circumstances the law of projection given by the author in the works just
referred to would be followed, and the revolving body increase its velocity
of motion as it increased its distance from the focal body of its orbit.



INTRODUCTION. 9

rest;* while the second and third appear to depend upon
the varied modifications and modifying action of the first,
when resolved into the several forces drawn from the mutually
re-acting bodies, and their antagonistic relations to the active
force through which the persistent motions of the universe
are maintained. f However this may be, it is sufficient to
regard them here as principles drawn from the actual and
observed phenomena, when, read in and through them, a
wonderful provision is at once found for all the changing
relations of the whole system.

Thus, to apply them to the earth considered as a spheroid
of revolution in equilibrium .J The bulk of the land is in

Perhaps both forms are in actual cosmical operation, the excentricity of the
celestial polar centre depending upon the motion of the centric sun follow-
ing the laws of projection ; while the secondary and tertiary, or more remote
forms, result from the simultaneous motion of both primary and secondary
alternately towards and from each other. Two causes seem to be in opera-
tion, determining variations in the planes of orbit that re-acting upon the
moon's path (Orbital Motion, Note 117), and that acting upon the ecliptic
(Orbital Motion, Note 119) ; it is, therefore, not unlikely that two causes,
resulting in two forms of excentricity, primary and subordinate, are simul-
taneously acting and producing the combined result.

* See Eccentric and Centric Force, Part I., sec. 3, and Part III.,
sec. 10 ; and Orbital Motion, Chap. III., par. 112 and 113.

f See Eccentric and Centric Force, Part IV., sec. 7 ; and Orbital
Motion, par. 165.

In a spheroid of revolution of equal density, the centre of gravity is on
and at the centre of the axis of revolution ; so that radii drawn from the
same latitude to its centre of gravity, or any point of its polar axis, will be
of equal length. In a spheroid of revolution of unequal density, the centre
of gravity will still be on the axis of revolution ; but radii drawn to it from
the same latitude will be longer in the less dense than the more dense por-
tions, equilibrium being preserved in the parallel planes of revolution by an
increase in volume on the one side compensating for an increase in density
on the other.

It must be remembered, that in a spheroid of revolution, there will be
a physical tendency to elongate the polar axis at one set of velocities,
just as there may be a physical tendency to shorten it at another. Thus,
if a body like the earth is revolving with a low velocity of revolution
with regard to its axis of motion, determined by the number of revo-
lutions accomplished in a given time, but with a high velocity of transition,
as between its equatorial surface and space, its equatorial fluid particles



10 INTRODUCTION.

the northern hemisphere ; and of the water in the southern.
The land, as a whole, has a greater specific gravity than the
water : hence the centre of gravity of the earth will be north
of the equator ; and, as it is in revolution, on its polar axis.
But since the earth is necessarily in equilibrium, a plane
parallel to its equator, and drawn through its centre of
gravity, would divide it into two portions of equal weight,
but unequal volume ; for the polar axis is divided by it into
two unequal parts, the shortest of which is in the northern
hemisphere, the centre of figure being in the southern or
larger portion ; so that the greatest volume of matter lies
south of the plane drawn through the centre of gravitj\ On
the other hand, the equatorial plane may be considered to
pass through the centre of figure, and so give an approximate
equality in volume to the two hemispheres. But now a pre-
ponderance of weight is found in the northern hemisphere,
it is heavier than the southern : hence the centre of figure
becomes a true centre of suspension the polar axis the line
of suspension, the celestial polar centre the centre of attrac-
tion towards which the suspension is directed. The relations


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