SEEN BY
PRESERVATION
SERVICES
FOR USE IN
LIBRARY ONLY
POPULAR LECTURES
AND
ADDRESSES
VOL. III.
NATURE SERIES
POPULAR LECTURES
AND
ADDRESSES
BY
SIR WILLIAM THOMSON, LL.D., F.R.S., F.R.S.E., &c.
PROFESSOR OF NATURAL PHILOSOPHY JN THE UNIVERSITY OF GLASGOW, AND
FELLOW OF ST. PETER*S COLLEGE, CAMBRIDGE
[ Lord
IX THREE VOLUMES
VOL. III.
NAVIGATIONAL AFFAIRS
WITH ILLUSTRATIONS
H o n to o n
MACMILLAN AND CO.
AND NEW YORK
1891
The A' /!>/// of Translation and Reproduction is Reserved
Q
ni
v.3
RICHARD CLAY AND SONS, LIMITED,
LONDON AND BUNGAY.
PREFACE
A LARGE part of this volume was already in
print when it was decided, and promised in the
Preface to Vol. I., that the second volume should
include subjects connected with Geology, and the
third should be chiefly concerned with Maritime
affairs. Accordingly, two hundred pages on
navigational subjects were marked " Vol. III."
and struck off before any progress was made
with Vol. II. Hence Vol. III. now appears
before Vol. II., the publishers having advised me
that they would not be professionally shocked
by such an irregularity. The present volume
ends with an article kindly contributed by Capt.
PREFACE.
Creak, R.N., on a subject of great navigational
importance, disturbance of ships' compasses by
proximity of magnetic rocks under water at
depths below the ship's bottom more than
amply safe for the deepest ships.
WILLIAM THOMSON.
THE UNIVERSITY, GLASGOW,
April 28, 1891.
CONTENTS
PAGE
NAVIGATION i
A Lecture delivered in the City Hal!, Glasgow, on
Thursday, November II, 1875, under the Auspices
of the Glasgow Science Lectures Association.
THE TIDES 139
Evening Lecture to the British Association at the
Southampton Meeting, Friday, August 2$, 1882.
APPENDIX A 191
Extracts from a Lecture on " The Tides" given to
the Glasgou1 Science Lectures Association, not
hitherto published, and now included as explaining
in greater detail certain paragraphs of the preced-
ing Lecture.
APPENDIX B. — INFLUENCE OF THE STRAITS OF
DOVER ON THE TIDES OF THE BRITISH CHANNEL
AND THE NORTH SEA 201
Abstract of a paper read at the />«/>/*// (1878) meeting
of the British Association.
CONTENTS.
APPENDIX C.— ON THE TIDES OF THE SOUTHERN
HEMISPHERE AND OF THE MEDITERRANEAN . . . 204
Abstract of paper by Captain Evans, R.N., F.K.S.,
and Sir William Thomson, LL.D., F.R.S., read
in Section E of the Dublin (1878) meeting of the
British Association.
APPENDIX D.— SKETCH OF PROPOSED PLAN OF PRO-
CEDURE IN TIDAL OBSERVATION AND ANALYSIS . 209
Circular issued by Sir William Thomson in Decem-
ber, 1867, to the members of the Committee, ap-
pointed, on his suggestion, by the British Association
in 1867 "For the Purpose of Promoting the Ex-
tension, Improvement, and Harmonic Analysis of
rfidal Observations"
APPENDIX E. — EQUILIBRIUM THEORY OF THE TIDES 224
Thomson and Taif s " Natural Philosophy," §§ 804—
870.
TERRESTRIAL MAGNETISM AND THE MARINER'S
COMPASS 228
Taken from " Good Words ; " and United Service
Institution Lectures, 1878 and 1880.
APPENDIX A.— AN ADJUSTABLE DEFLECTOR BY
MEANS OF WHICH THE COMPASS ERROR CAN BE
COMPLETELY CORRECTED WHEN SIGHTS OF
HEAVENLY BODIES OR COMPASS MARKS ON SHORE
ARK NOT AVAILABLE 3:
Being extract from United Service Institution Lecture,
1878.
CONTENTS.
PAGE
APPENDIX B.— ON A NEW FORM OF AZIMUTH
MIRROR 329
Being extract from United Service Institution Lecture,
1878 ; with, additions of date 1890.
APPENDIX C. — REMARKABLE LOCAL MAGNETIC DIS-
TURBANCE NEAR COSSACK (PORT WALCOTT),
NORTH-WEST AUSTRALIA 501
Being an account by Captain Creak, R.N., F. /v. S. ,
of observations made subsequently to those described
on pp. 255 — 266.
ON DEEP-SEA SOUNDING BY PIANOFORTE
WIRE 337
Paper communicated to the Society of Telegraph
Engineers, Apr^l 22, 1874
APPENDIX A. — ON FLYING SOUNDINGS 369
APPENDIX B. — DESCRIPTION OF THE SOUNDING
MACHINE 372
APPENDIX C.— THE DEPTH-RECORDER 375
APPENDIX D 377
Extracts from paper read, and illustrated by apparatus
exhibited, before United Service Institution,
February 4, 1878.
ON LIGHTHOUSE CHARACTERISTICS 389
• Paper read at the Naval and Marine Exhibition,
Glasgow, Febrttary n, 1881.
CONTENTS.
PAGE
ON THE FORCES CONCERNED IN THE LAYING
AND LIFTING OF DEEP-SEA CABLES .... 422
Address delivered before the Royal Society of Edin-
burgh, December 18, 1865.
APPENDIX I. — DESCRIPTIONS OF THE ATLANTIC
CABLES OF 1858 AND 1865 413
APPENDIX II 445
ON SHIP WAVES . 450
Lecture delivered at tJie Conversazione of the Institu-
tion of Mechanical Engineers in the Science and
Art Muscnin, Edinburgh, on Wednesday evening,
yd August, 1887.
INDEX 507
POPULAR LECTURES
AND
ADDRESSES
popular ^cdurcs anb
NAVIGATION.
[A Lecture delivered in the City Hall, Glasgow, on 77mrsday,
November nth, 1875 ; under the Auspices of the Glasgow
Science Lect tires Association.]
I. NAVIGATION, in the technical sense of the
word, means the art of finding a ship's place at
sea, and of directing her course for the purpose
of reaching any desired place. The art of keeping
a ship afloat, and managing her so as to follow
the course traced out for her, belongs rather to
what is technicaly called Seamanship than to
Navigation ; still the two great branches of the
sailor's art must always go hand in hand : all the
great navigators have been admirable for their
seamanship ; and every true seaman tries, as far as
VOL. III. B
2 POPULAR LECTURES AND ADDRESSES.
his circumstances permit, to be a navigator also.
I have often admired the zeal with which even
untaught sailors con over a chart when they get
access to one, and the aptitude which they display
for the scientific use of it. It is a common saying
that sailors are stupid ; but I thoroughly and
heartily repudiate it, not from any sentimental
fancy, but from practical experience. No other
class of artizans is more intelligent ; and, more-
over, sailors' wits are kept sharp by the ever
nearness of difficulties and dangers to be met by
ready and quick action. The technical division
between navigation and seamanship, if pushed so
far as to leave one class of officers chiefly or wholly
responsible for navigation and another for seaman-
ship, would not tend to excellence or ski! fulness
in either department. The subject of the present
lecture is, however, Navigation in its technically
restricted sense.
2. To find a ship's place at sea is a practical
application of Pure Geometry and Astronomy. It
is on this piece of practical mathematics that I am
now to speak to you.
NA V1GA TION.
Four modes are used, separately or jointly, for
finding the place of a ship at sea.
I. PILOTAGE. — Navigation in the neighbourhood
of land. The means of finding the ship's place in
pilotage are chiefly by sight of terrestrial objects,
as headlands, lighthouses, landmarks, or hills, and
other objects of known appearance, and by feeling
the bottom by " hand-lead soundings."
II. ASTRONOMICAL NAVIGATION. — Sights of
celestial objects — sun, moon, planets, stars.
III. "DEAD RECKONING" or "ACCOUNT." —
Distance and direction travelled from a previously
known position.
IV. DEEP-SEA SOUNDINGS. — Depth of water and
character of bottom.
3. The instruments and other aids used are : —
For tJie first mode. — The sextant, the azimuth
compass, station pointer, and other mathematical
drawing instruments, charts, books of sailing
directions.
For the second. — The sextant, the chronometer,
the Nautical Almanac, a book of mathematical
tables, and mathematical drawing instruments.
B 2
4 POPULAR LECTURES AND ADDRESSES.
For the third. — A Massey's log (or instead of
Massey's log, the old log-ship and glasses), the
ordinary mariner's compass, a traverse table,
mathematical drawing instruments, and a common
clock or watch.
For the fourth. — The lead [with improvements
described in § 37 below], the instruments used for
the third mode, arid a chart.
I shall first briefly describe the instruments,
beginning with the sextant.
4. THE SEXTANT. — The sextant is an admirably
devised instrument, invented by Sir Isaac Newton
(and first made by Hadley), for measuring, on
board ship, the angle between any two visible
objects. The general principle of the instrument
is this : — One object, A, is looked at directly, the
other, B, by two reflections — first, from a silvered
mirror, and next from a piece of unsilvered plate-
glass, in the manner illustrated in the drawing
before you. The second of these mirrors is fixed
on the framework. The first mirror, which is
movable round an axis, is turned by the observer
until the doubly reflected image of B is seen, like
NAVIGATION.
Pepper's ghost, in the transparent plate-glass
coincidently with A seen through the same. From
the law of reflection, that the incident and reflected
rays make equal angles with the mirror, it is clear
that when the silvered mirror is turned through
FIG. i. — Sextant.
any angle, the ray reflected from it turns through
twice as large an angle, and after its second re-
flection (as the second mirror is fixed) it turns
through still the same angle, that is to say,
through twice the angle turned by the silvered
mirror. The angles through which the silvered
6 POPULAR LECTURES AND ADDRESSES.
mirror is turned in the use of the sextant are
measured by very fine divisions on an arc forming
a sixth of the circumference of a circle, whence
the instrument derives its name of sextant.
5. Imagine now that I am standing on the
ship and looking directly at the horizon. What
do you mean by the horizon at sea ? It is the
bounding line of sea and sky. It is a real
line on the sea. When you look from the deck
of a ship at the sea, you are looking down.
Look as far as you can along the sea, and you
are still looking somewhat downwards. The angle
at which you must look down from the true level
to see the line of the horizon is called the dip
of the horizon. Looking then at the horizon, and
turning the silvered mirror about with my left
hand, I bring the ghostly image of the sun down
till its lower edge touches the sea-horizon. I then
look at the divided circle of the instrument, read
off the number, and I have the angle through
which I have had to turn the silvered mirror to
bring down the image of the sun from the direction
in which I had to look to see the sun directly, to
NAVIGATION.
the direction in which I must look to see the sea-
horizon. This gives me what is called the apparent
altitude of the sun.
The framework of the instrument used in old
times to be made of ebony, and the divided arc
of ivory inlaid in it, as in one of the instruments
before you. In the best modern sextants the
framework is a light structure of brass, and the
graduated arc is of silver, or of platinum, or of
gold, inlaid in it. It is of silver in this other instru-
ment before you (one of Troughton and Simms').
6. Now as to the divisions of the circular scale,
I must tell you that, for the purpose of the
measurement of angles, the complete circumference
of a circle is divided into three hundred and
sixty equal parts called degrees, so that a quarter
round is measured by ninety degrees. The sixtieth
part of a degree is called a minute of arc or of
angle, and the sixtieth part of a minute is called
a second of arc or of angle. The ambiguity of
the names minute and second, sometimes used for
angles, and more often, as you well know, for the
reckoning of time, is perniciously troublesome in
8 POPULAR LECTURES AND ADDRESSES.
practice, and sometimes, though rarely, leads
to temporary error through inadvertence on the
part even of a careful and skilled navigator. It
will torment us repeatedly in the course of the
present lecture.
7. As the sextant is used for the measurement
of angles, the doubles of those turned through
by the movable arm, its arc of sixty degrees is
divided into 120 equal parts, and each of these
parts is divided into three equal subdivisions.
Thus, the subdivision which is actually 10' of arc
measures 20' turned through by the reflected ray.
The main divisions are numbered by fives from
o to 1 20, and, being actually half degrees of arc,
measure whole degrees turned through by the ray.
When the minutest accuracy is aimed at the scale
is read by aid of a vernier attached to the movable
arm ; but in cases which frequently occur, where an
error of four or five minutes of angle is of no moment,
the reading is more easily taken directly by a single
division marked on the movable arm. This single
division is the zero line of the vernier, as illustrated
by the drawing before you. The fractions of a sub-
NA VIGA TION.
division are read off on the scale of the vernier, when
they cannot be estimated directly with sufficient
accuracy and readiness. A small magnifying lens is
generally used in reading the scale with or without
the vernier.
8. Take now the instrument in your hand, and
look at a distant object, A, through the unsilvered
plate-glass, and turn the silvered mirror till the
ghost of the same object A, seen by the double
reflection, coincides precisely with the object itself
seen directly. Then read, on the graduated scale,
the number corresponding to the position of the
marker carried by the turning arm. Suppose the
reading to be 5'^. This is what is called the index
error of the instrument. Now take the instrument
in your hand again, and turn the arm carrying the
silvered mirror round till the ghost of one object, B,
seems coincident with the substance of another,
A, seen through the unsilvered glass. Look at the
scale again and take the reading, say 117° 8':
subtract the index error from this and you find
1 17° 2'f, which is the angle between A and B as
seen from your actual position.
io POPULAR LECTURES AND ADDRESSES.
9. A small telescope attached to the framework
is generally used for magnifying the object and
the ghost, which are both seen through it simul-
taneously. It is removable, and it is often more
convenient to do without it when the most minute
accuracy is not required. It is not shown in the
drawing before you. The only other optical adjuncts,
besides the telescope and the magnifying lens for
reading the scale, are two sets of coloured glasses,
which may be placed in the way of rays coming
from the silvered mirror to be reflected at the
unsilvered glass, and of rays coming direct through
the unsilvered glass. They are not shown in the
drawing, but they are essential for observation of
the sun. In moderately clear weather, and when
the sun is at any considerable height above the
horizon, even his ghostly image, by the second
reflection at the unsilvered glass, is of dazzling
brilliance, unless abated by one or more of the
coloured glasses ; and when the sun is bright, but
not very high above the horizon, the sea itself at
the boundary between sea and sky under the sun
is often too dazzling to be looked at in its un-
NA VI G A TION. 1 1
diminished brilliance ; then the coloured glasses in
front of the unsilvered mirror must be put in
requisition. Lastly, I must not omit to tell you
that a portion of the glass which I have been
speaking of as the unsilvered glass, or unsilvered
mirror, is actually silvered ; but this portion is
advantageously put out of the way (by means
of a sliding piece and screw) in almost all
ordinary uses of the instrument. It is useful for
star observations when the ghostly image in the
unsilvered part of the glass is too faint.
10. THE AZIMUTH COMPASS. — Before describ-
ing the azimuth compass, I must tell you what an
azimuth is. It is simply a horizontal angle. The
azimuth of one object relatively to another, as
you see the two from any particular place, is the
angle between the two horizontal lines verti-
cally under the directions in which you see the two
objects. In navigation, azimuths, or " bearings," as
they are commonly called by sailors, are generally
measured from the true north, or from the magnetic
north, point of the horizon.
11. The true north is found, whether at sea or on
12 POPULAR LECTURES AND ADDRESSES.
shore, by observation of the heavenly bodies. Look
at the stars, hour after hour, on a clear night, you
will see them all seeming to turn round one point
in the sky. That pivot point of the sky is called
the north celestial pole. You understand that you
are in the northern hemisphere. Any one south of
the equator observing the stars similarly, would
perceive in the southern sky another point, the
south celestial pole, round which the stars there
would seem to turn.
12. The north and south terrestrial poles are
those points on the earth's surface where the north
celestial pole and the south celestial pole are exactly
overhead, that is to say, they are the two points
of the earth's surface whose verticals are precisely
parallel to the axis of the earth's rotation. It is by
finding the pivot point of the stars vertically over
his head, that Captain Nares will recognise the
north pole when he comes to it.
13. There is no distinctly visible star exactly at
the north celestial pole ; but there is one star of the
second magnitude which nowadays is at a dis-
tance of i° 2 1' from it. This star is therefore now
NA VI G A TION.
called Polaris, or the pole star, and it will probably,
if there is continuity of men and books upon the
earth, still have the same name twelve thousand
years hence, when it will be 47°-| from the north
celestial pole.
SCYGNI
FIG. 2. — Illustrating Precession.
In the dawn of human history the earth's axis
pointed to a star not enduringly named till nearly
2000 years later, when the pole had moved about
10° or 1 1° from it, and it was called by the Greeks
a Draconis.
14. The diagram before you, Fig. 2, shows how
1 4 POPULAR LECTURES AND ADDRESSES.
the north celestial pole has moved among the stars
for thousands of years, and may be expected to
move for hundreds of thousands of years to come.
It represents a small circle among the stars on which
the earth's celestial pole travels at the rate of once
round in 25,868 years, or at the rate of i° of great
circle per 180 years. The diameter of this circle
is about 47° (more nearly 46°55'), and its centre
is in the direction perpendicular to the plane of
the earth's orbit round the sun.1 To understand
this motion, and its effect on the line of the
equinoxes, as the line of intersection of the
earth's equator and the ecliptic is called, look at
the model before you which shows the rotation
of the earth round an axis constantly changing
position in space. The line of the equinoxes
travels once completely round the ecliptic in
25,868 years, or at the rate of i° per 71-85 years
in the direction contrary to the earth's rotation.
This motion is called the precession of the
1 Or is what is called the " pole of the ecliptic," the ecliptic being
a name given by the Greeks to the plane of the earth's orbit, because
the moon must be nearly, if not exactly, in this plane to produce or
experience an eclipse.
NAVIGATION.
equinoxes. If the earth revolved under guidance
of a mechanism such as this model, the circum-
ference of its rolling pivot-shaft would be 5! feet
and that of the fixed ring or hoop on which it
rolls, 52,000,000 feet.
FIG. 3. — Precessional Model.
15. Our astronomical knowledge of the pre-
cession of the equinoxes has given a most
interesting and marvellous assistance to historians
in estimating the date of the pyramid-building
of Egypt. In six of the pyramids of Gizeh and
1 6 POPULAR LECTURES AND ADDRESSES.
two of the pyramids of Abooseer are found
tunnels pointing in a certain direction towards
the heavens. The directions of these tunnels are
from 26° to 28° above the horizon, and in true
north azimuth. They are from 4° to 2° under
the north celestial pole (the latitude of the place
being 30°). It has been conjectured, with con-
siderable probability, that they were designedly
made in such directions as to let the then' pole
star be seen through them at its lower transit.
There was then no star so near the pole as our
present Polaris. The nearest was a Draconis,
which, from 3564 B.C. to 2124 B.C., had the pole
within 4° of it, at distances varying as shown in
the annexed table : —
Date.
Distance of j
u Draconis
Date.
B C.
from pole.
B.C.
3564
4°
2124
3474
3h
2214
3384
3
2304
3294
2i
2394
3204
2
2484
3"4
I*
2574
3024
I '02
2664
2934
'54
2754
2844
'2
2844
NAVIGATION. 17
The building of the pyramids might therefore
have been at any time from 2480 B.C. to 2120 B.C.,
or at any time from 3560 B.C. to 3200 B.C., to
suit the astronomical hypothesis. It was supposed
to be about 2100 B.C. when Sir John Herschel
first took up the question at the request of Col.
Howard Vyse. Now, from independent historical
evidence,1 the date 3200 is the most probable.
The astronomical hypothesis cannot decide be-
tween these two dates, but if it were granted, it
would show that either of them is more probable
than any date between 3200 B.C. and 2480 B.C.
1 6. The point on the horizon under the north
celestial pole is called the true North ; the true
1 I am informed by my late colleague, Professor Lushington, that
"the whole chronology of early Egyptian times is perplexingly ob-
scure ; probably a dozen different systems have been built on equally
stable foundations. The latest attempt known to me to establish a
real basis is given in a little treatise by Diimichen, which is, I
believe, in the University Library ; it rests upon a comparison of the
fixed and vague year, found coupled with the name of a king which
is read as Bicheris, the sixth name in Manetho's list of the fourth
dynasty (the great pyramid dynasty). It would bring his time to
about 3000 B.C., and the pyramids from 100 to 200 years earlier.
It is found on the back of a huge papyrus just published at Leipzig
by G. Ebers in facsimile, a most important work, being the largest
and clearest written papyrus known, the contents chiefly medical.'*
VOL. III. C
1 8 POPULAR LECTURES AND ADDRESSES.
East and West, and the true South, are the
points in the directions at right angles to it, and
in the direction opposite to it, each on the horizon.
The four right angles between these four cardinal
points, as they are called, are, in nautical usage,
divided each into eight equal parts, and the
successive points of division, from N. by E. round
to N. again, are called N. by E., N.N.E., N.E. by
N., N.E., N.E. by E., E.N.E., E. by N, E. ; E.
by S., and so on. A part of the early training
of the young navigator used to be to rattle over
these designations as fast as his youthful tongue
could utter them ; and this exercise was some-
what comically called "boxing the compass."
The successive angular spaces from point to
point of the compass are generally divided into
four equal parts, and the corresponding divisions
are read off by quarters, halves, and three-
quarters ; for example, thus N.JE., N.|E., N.f E.,
and so on.
17. The term "point" is habitually used without
any inconvenient ambiguity, sometimes to denote
one of the thirty-two directions corresponding to
NAVIGATION. 19
the points of division, and sometimes any angular
space that is equal to the space from one of the
thirty-two points to the next on either side of
FIG. 4. — Compass Card.
it. The terms quarter-point and half-point are
sometimes applied to the subdividing marks, but
more often to designate the angular spaces between
them. From what I have told you already, you
C 2
20 POPULAR LECTURES AND ADDRESSES.
now see that the angle from point to point of
the compass is the eighth part of 90°, that is to
say, i i°J. This is just two per cent, less than
one-fifth of the radian.1 Hence nearly enough
for most practical purposes, you may reckon that
an error of one point in steering will lead you
wrong one mile in five. More precisely reckoned,
an error of a quarter-point will lead you wrong
one mile in twenty and a half.
1 8. The magnetic north and south points are
the points of the horizon marked by the direction
in which a thin straight magnetised steel needle
rests when balanced on a point, or hung by a
fine fibre, so as to be very free to turn round
horizontally. A magnet of any shape or kind,
for example, a bar or horse-shoe of magnetised
steel, or a lump of loadstone, or even an electro-
magnet, if somehow supported by its centre of
gravity, but free to turn round it, will not rest
indifferently in all positions, but balances only
when a certain line of it, which is called its
1 The " radian " is an angle whose arc is equal to the radius
it is 57'3°, or thereabouts.
NAVIGATION. 21
magnetic axis, is in a particular direction de-
pending on the particular locality in which the
experiment is made. This direction is actually
shown by the " dipping needle." The ordinary
horizontal needle tends to dip into the same
direction, but is prevented by a counterpoise
adjusted to keep it horizontal. The dipping
needle is vertical at the two magnetic poles, and
there the horizontal needle shows no direction.
Early Arctic navigators imagined the magnetic
virtue to be impaired by cold, when they found
their compasses becoming sluggish as they ap-
proached the north magnetic pole ; but the
dipping needle disproves this idea by vibrating
actually with greater energy, rather than with less,
in polar regions. The charts (Figs. 5 and 6) before
you explain sufficiently how the magnetic north
and south line lies in any part of the world.
19. The lines on these diagrams show what
Faraday would have called the lines of horizontal
magnetic force. They are sometimes called
magnetic meridians. All these curved magnetic
north and south lines pass through two points
22 POPULAR LECTURES AND ADDRESSES.
— a north magnetic pole and a south magnetic
pole. The north magnetic direction in any one
of them is that which leads you to the north
magnetic pole. You see that in the northern
180
I-'IG. 5.— Magnetic Chart: Northern Hemisphere.
polar region, between the true north pole and
the magnetic north pole, the north magnetic
direction leads obliquely, or directly, southward ;
and, again, in the region between the true south
NAVIGATION.
pole and the magnetic south pole, the south
magnetic direction leads obliquely, or directly,
northward. In all places of the world, except
these Arctic and Antarctic regions between the
FIG. 6.— Magnetic Chart : Southern Hemisphere.
magnetic and the true poles, the magnetic north
and magnetic south directions are northward and
southward ; but agree exactly with the true
north and south directions only on certain lines
24 POPULAR LECTURES AND ADDRESSES.
of the earth's surface, as the reader will readily
see and understand by looking at the annexed
magnetic charts, Figs. 5 and 6 (pp. 22 and 23).
Observation shows that nowadays the lines of
horizontal magnetic force are as represented on
the diagrams before you. But a comparison with
observations made within the last 300 years shows
us that the magnetic poles and lines of force are
changing. Three hundred years ago (1576), in
London, the compass pointed to the east of
north. Two hundred and seventeen years ago
O^SQ)) the compass pointed due north there.
After that, for 164 years, it showed an increasing
westerly direction, till in 1823 it pointed 24' 30'
to the west of north, and began to come back
towards the north. Now its deviation in London
is only 20° 30' west, and it is decreasing about
6' annually. Here, at Glasgow, the deviation is
at present about 24° west.
20, The dip at London is now about 67° 40',
at Glasgow 71°, and for the British Islands it is
at present decreasing at about 2*69' annually. It
is ascertained to have been decreasing during
NA VI G A TION.
the last 20 years, and no doubt it has been
decreasing during the 217 years which have
elapsed since the needle pointed due north.
21. The fact brought out is, that the whole
system of terrestrial magnetism, with its poles
and lines of force, is travelling round the earth's
axis at the rate of once round, relatively to the
earth, in 960 years, backwards or the way of
the sun ; or, which amounts to the same, the
system of terrestrial magnetism lags behind the
earth's rotation at the rate of one turn less per
960 years. The north magnetic pole is about
20° from the true north pole. In 1659, the north
magnetic pole was between London and the true
north pole, and since that time it has travelled
82° westwards in a circle round the true pole, so
that it is now in about 82° of west longitude,
and still 20° from the true north pole.
In the year 2139, it may be expected to be
again due north of London, but on the far side of
the true north pole in longitude 180°, and so on.
22. ORDINARY MARINER'S COMPASS, AND
AZIMUTH COMPASS. — The mariner's compass is
26 POPULAR LECTURES AND ADDRESSES.
an instrument adapted for showing, in a manner
most convenient to the mariner, the azimuth of
the ship's length relatively to the magnetic north
and south line. It consists of a circle of card-
board, or of mica coated with paper, marked on
its upper side with the points of the compass, or
degrees, or both points and degrees, and carrying
two or four parallel bars of magnetised steel
attached to it below, and an inverted cup of
sapphire or ruby, or other hard material, attached
to it over a hole in its centre. It is supported
by the crown of the cup resting on a hard metal
point standing up from the bottom of a hollow
case called the compass bowl. The compass bowl
is covered with glass to protect the card against
wind and weather, and the bowl is hung on
gimbals in a binnacle attached to the deck, and
bearing convenient appliances for placing lamps
to illuminate the card by night. The cheapest
and roughest instrument made according to this
description — provided the bearing cup is of hard
enough material and properly shaped, and provided
the bearing point is kept sufficiently fine by
NA VIGA TION. 27
occasional regrinding, or by the substitution of a
fresh point for one worn blunt by sea use — is
accurate enough for the most refined navigation,
and is perfectly convenient for use at sea, on
board of any ordinary wooden sailing ship, large
or small, in all ordinary circumstances of waves
and weather.
23. If it were my lot to speak to you for a
whole evening on the subject of the mariner's
compass, I would have to tell you of the qualities
which the instrument must possess to render it
suitable for use in all ships, and all seas, and all
weathers, and of the correctors which must be
applied to it if it is to point correctly in iron
ships. To-night, I cannot for want of time.
[See articles on the compass below.] The azimuth
compass, for use at sea, is an ordinary mariner's
compass, with the addition of a simple appliance for
measuring the azimuths of celestial or terrestrial
objects on its card with great accuracy.
24. GLOBES AND CHARTS. — A celestial and ter-
restrial globe ought both to be found in every
school of every class. In navigation schools, much
28 POPULAR LECTURES AND ADDRESSES.
of the difficulty in understanding the methods of
spherical astronomy taught there for subsequent
daily use at sea, would be smoothed down by aid of
either the celestial or the terrestrial globe or both.
The mystery of great circle sailing is done away
with by merely looking at a terrestrial globe ; and
in actual practice at sea, a terrestrial globe would
be exceedingly useful in laying out great circle
courses, and planning the courses to be actually
sailed over, and for approximate measurements of
great distances on the earth's surface, instead of
laboriously (and sometimes with useless exactness)
working out these questions by a blind use of
logarithms. The celestial globe would be exceed-
ingly useful at sea for facilitating the identification
of stars to be used for finding the ship's position by
altitudes, or correcting the compass by azimuths.
A blackened globe, upon which circles can be
drawn in chalk, is also useful at sea for approxi-
mate solutions of some problems which occasionally
occur, and is indispensable in a navigation school
whether on shore or on board ship, for the in-
struction of young officers. Still the main work
NA VIGA TION. 29
of navigation must be laid down on charts.
Though useful auxiliary drawings may be done on
the round surface of a blackened globe, you cannot
draw a straight line on a globe, and for accurate
drawing with existing mathematical instruments, a
flat surface is necessary.
25. The various kinds of projections to be found
in different maps and atlases would take too long
to describe, but except for polar regions, the only
one of them used in navigation is that very
celebrated one called Mercator's projection, and I
shall therefore limit myself to describing it to you
this evening. It has the great advantage, that it
shows every island, every cape, every bay, every
coast line, if not too large, sensibly in true shape.
Every course, every direction, at any point of the
earth's surface, is shown precisely in its true
direction on Mercator's projection. Imagine a skin
of paper to coat this globe before you as the skin
of an orange coats an orange. Imagine a hole
made at the north pole, and another at the south
pole, and the skin to be stretched out without
altering the length from equator to either pole. Or
30 POPULAR LECTURES AND ADDRESSES.
suppose you were to cut the skin into countless
liths, and then cutting it open across one point of
the equator, lay it flat and fill up the spaces
between the liths : then you have a plane drawing
or chart of the earth's surface such as the ac-
companying diagram, Fig. 7, shows. You have
so
20
60
40
20 0 20
FIG. 7.— Plane Chart.
stretched the polar regions in longitude without
altering them in the north and south direction.
Stretch them now polewards north and south to
the same proportionate extent as you have already
stretched them in longitude. By doing so you
put the north and south pole away to an infinite
distance and lose the polar regions, but you thus
NA VI G A TION.
get a very convenient chart for the middle and
tropical regions, which is called Mercator's pro-
jection. It is illustrated in the annexed diagram,
Fig. 8. Contrast the shapes of Greenland as
shown on these two charts, Figs. 7 and 8, with
50
40 20 0 20 40 60
FlG. 8. — Chart on Mercator's Projection.
one another, and with that shown on the magnetic
chart of the northern hemisphere, Fig. 5 (p. 22\
which is more nearly the true shape than either.
A " great circle " of the earth's surface is a circle
whose plane passes through the earth's centre.
Any diameter of the great circle measured along
32 POPULAR LECTURES AND ADDRESSES.
the surface is 180°; and the shortest line on the
surface from any one point to any other, must
clearly lie along a great circle. Look at your
terrestrial globe to illustrate this. The Mercator
chart before you, extending from latitude 40° to
latitude 80°, shows what great circles look like on
Mercator's projection. One of the lines is a great
circle from Cape Farewell to a point in longitude
70° E., latitude 50° N. The other is a great circle
from Valentia to Trinity Bay, Newfoundland, along
which the original Atlantic cables were laid.
The oval curves on the Mercator's projection of
§ 56, Fig. 14 below, represent what are in reality two
circles on the earth's surface, drawn for the purpose
of illustrating Sumner's method, to be explained
later. They are what are technically called " small
circles," their diameters being respectively 100° and
80°, and their centres inlat. 10° N.
26. STATION POINTER. — The station pointer
consists of three rulers turning in one plane round
a common centre, with their edges so set as to
radiate from this centre, and with a graduated arc
showing the inclinations of the edges one to
NA VIGA TION. 33
another. The common hinge or joint is open in
its centre ; the actual central point from which the
three edges of the three rulers radiate is marked
by a pointer attached to one of the three limbs.
27. THE CHRONOMETER. — For the second mode
of navigation, the chronometer is the only other
instrument I have to mention. The object of the
chronometer is to show Greenwich time all over the
world. It is merely a watch adapted to go with
the greatest possible accuracy. The main feature
of the chronometer, besides very fine finish in all its
parts, and an escapement movement of peculiar
excellence, is that the vibrating balance-wheel is
" compensated " for variation of temperature. An
ordinary balance-wheel, with continuous rim of
one metal, vibrates more slowly at high than at
low temperatures, because the hair-spring has less
of elastic stiffness, and because the balance-wheel
is larger, at higher temperatures ; but a small part
only of the whole difference in time-keeping de-
pends on the last-mentioned cause. About twelve-
thirteenths of it is due to the diminished elastic
stiffness of the hair-spring. In the compensated
VOL. III. D
34 POPULAR LECTURES AND ADDRESSES,
balance-wheel, the rim is composed of two metals,
the outer part brass, the inner part steel, and it
is cut into two halves, which are nearly semi-
circular, and are supported by one end attached
to one end of a stout diameter of the wheel, Fig. 9.
Weights are attached to the two semicircles in
FIG. 9.— Chronometer Balance Wheel.
proper positions, to produce, as nearly as possible^
the desired equality of period of vibration for
different temperatures, according to the following
principle : — When the temperature is augmented,
the two halves of the rim, supported as they are on
two ends of one diameter, curve inwards from their
outer parts being brass (more expansible), and the
NAVIGATION. 35
inner parts steel (less expansible), and thus carry
the attached weights inwards. The whole vibrating
mass, composed of axle, diameter, rims, and at-
tached weights, has thus less moment of inertia,
and so, with the less elastic stiffness of the hair-
spring, the balance-wheel vibrates with the same
quickness.
This mode of compensating for temperature was
invented about one hundred years ago by Thomas
Earnshaw, to whom is also due the excellent form
of escapement now universally used in the marine
chronometer.
28. The first chronometer used for determining
the longitude was invented by John Harrison, and
completed by him in a life-work of fifty years.
The origin of this first marine chronometer pre-
sents a most interesting chapter in the history of
inventions. Sir Isaac Newton pointed out the
great importance of an accurate chronometer at
sea, for determining the longitude. On the I ith of
June, 1714, the House of Commons appointed a
Committee, of whom he was one, to consider the
question of encouragement for the invention cf
D 2
36 POPULAR LECTURES AND ADDRESSES.
means for finding the longitude. This Committee
gave in a report explaining different means by
which the longitude could be found, and recom-
mending encouragement for the construction of
chronometers as likely to lead to a better solution
of this important problem of navigation than any
other that had been or could be devised. In
consequence of this report, an Act of Parliament
was passed offering prizes of i,ooo/., I5,ooo/., and
2O,ooo/., for the discovery of a method for deter-
mining the longitude within 60, 40, and 30 miles
respectively : " one moiety or half part of such
" reward or sum shall be due and paid when
" the said commissioners, or the major part of
" them, do agree that any such method extends to
11 the security of ships within 80 geographical
" miles of the shores which are places of the
" greatest danger, and the other moiety or half
" part when a ship, by the appointment of the said
" commissioners, or the major part of them, shall
" thereby sail over the ocean from Great Britain to
" any such part in the West Indies as those com-
" missioners, or the major part of them, shall choose
NAVIGATION. 37
" or nominate for the experiment, without losing
" their longitude beyond the limits before
" mentioned." l
After first completing a chronometer in 1736,
Harrison offered a chronometer to the commis-
sioners for this prize, which, tried " in a voyage to
Jamaica in 1761-62, was found to determine the
longitude within 18 miles ; he therefore claimed
the reward of 2O,ooo/., which, after a delay caused
by another voyage to Jamaica, and further trials,
was awarded to him in 1765 — io,ooo/. to be paid
on Harrison's explaining the principle of con-
struction of his chronometer, and io,ooo/. whenever
it was ascertained that the instrument could be
made by others. The success of Harrison's
chronometer is owing to his application of the
compensation curb to the balance-wheel, and on the
same principle he invented the gridiron pendulum^
for clocks. These, along with his other inventions,
the going fusee, and the remontoir escapement,
were considered to be the most remarkable im-
provements in the manufacture of watches of the
1 Extract from Act of Parliament passed in 1714.
38 POPULAR LECTURES AND ADDRESSES.
last century. Harrison died in Red Lion Square,
London, in I/76."1
Harrison's compensation curb, here referred to,
was a contrivance in which the bending of a com-
pound bar of brass and steel soldered together was
applied to shorten the vibrating portion of the
hair-spring of the watch when the temperature
rises, and elongate it again when the temperature
falls. The very different method of compensation
subsequently invented by Earnshaw was no doubt
much superior, but Harrison's curb must always be
interesting as the first successful method for com-
pensating the temperature error of a watch, and
the first usefully applied to determine the longitude
at sea.
29. The most important improvement in marine
chronometry since the time of Earnshaw has been
made by Mr. Hartnup, Astronomer to the Marine
Committee of the Mersey Docks and Harbour
Board of Liverpool. It had been long known that
the simple compensation balance, whether of
Harrison or Earnshaw, however perfectly executed
1 Chambcrs's Encyclopaedia, Art. "Harrison."
NA VI G A TION. 39
in workmanship, and however carefully adjusted
by trial, does not give equable time-keeping at all
temperatures through wide natural ranges. It had
been sought to remedy this defect by the appli-
cation of secondary compensation on various
ingenious plans, but with no practical success.
Thus the best chronometers of the best makers
in modern times are practically perfect only
within a range of 5° or 10° Fahrenheit on each
side of a certain temperature, infinitely near to
which the compensation is perfect in the individual
chronometer.
The temperature for which the compensation is
perfect, and the amount of deviation from per-
fection at temperatures differing from it are
different in different chronometers. Mr. Hartnup
finds that at the temperature for which the com-
pensation is perfect, the chronometer goes faster
than at any other temperature, and that the rate
at any other temperature is calculated with
marvellous accuracy (if the chronometer be a good
one) by subtracting from the rate at that critical
temperature the number obtained by multiplying
40 POPULAR LECTURES AND ADDRESSES.
the square of the difference of temperature by
a certain constant co-efficient This constant co-
efficient and the temperature of maximum rate
remain the same for the same chronometer until
it is cleaned or repaired, or until it requires to be
cleaned or repaired. Thus, for example, a certain
chronometer, " J. Bassnett & Son, No. 713," after
being rated by Mr. Hartnup, was put on board the
ship Tenasserim, in Liverpool, December, 1873, for
a voyage to Calcutta. The result of Mr. Hartnup's
rating and the application of his method showed
that this chronometer had its maximum rate at
temperature 70° Fahrenheit, and that the difference
of rates at any other temperature, reckoned in
seconds or fractions of a second per day, was to
be calculated by multiplying the square of the
difference of temperature from 70° into '0034 sec.
Thus at 80° or 60°, the chronometer would go
slower than at 70° by "34 of a second per
day ; at 90° or at 50° it would go slower than
at 70° by 1*36 seconds per day ; and so on for
other temperatures.
The ship sailed from Liverpool on the 2ist of
NAVIGATION. 41
January, 1874, and on her voyage to Calcutta the
chronometer was subjected to variations of temper-
ature ranging from 50° to 90°. The chronometer
was tested by the Calcutta time-gun on the 26th of
May. The time reckoned by it, with correction
for temperature on Hartnup's plan, was found
wrong by 8J seconds. Another chronometer,
similarly corrected by Mr. Hartnup's method, and
from his rating, gave an error of only 3^ seconds.
The difference between the reckonings of the two
chronometers was thus only 5 seconds, and the
error in reckoning by taking the mean between
them only 6 seconds. This corresponds to an
error of only a mile and a half in estimating the
ship's place in tropical regions. The reckonings of
Greenwich time from the two chronometers,
according to the ordinary method, differed actually
by 4 minutes 35 seconds, corresponding to 68 J
geographical miles of error for the ship's place.
From Mr. Hartnup's investigations, it is
obvious that one important point for a good
chronometer is, that the temperature of maximum
rate should be as nearly as may be the mean
42 POPULAR LECTURES AND ADDRESSES.
temperature at which it is to be used ; but the
main quality required for good work is constancy
in temperature of maximum rate, and in co-
efficient for calculating rates at other temperatures.
To facilitate the application of Hartnup's
method at sea, a small thermometer, to be placed
in the chronometer case, with a scale graduated
not to degrees but to squares of numbers of
degrees of difference from the temperature of
maximum rate, would be a valuable adjunct to be
supplied to every chronometer. The navigator in
winding his chronometer daily, would look at this
thermometer, and enter two or three figures in a
properly prepared chronometer rate-and-reckoning-
book. All that he would have to do, thus, to take
full advantage of Hartnup's method, need not
occupy more time than about as much as it takes
him to wind his chronometer.
30. INSTRUMENTS FOR MEASURING SPEED
AND DISTANCE RUN. — The name log was origin-
ally applied to a floating piece of wood, by the
aid of which the speed of a ship through the
water was determined. What is commonly called
NAVIGATION. 43
at sea the " Dutchman's log " is a very primitive
method of measuring speed, in which a bottle is
thrown overboard from the bow, and its times of
passing two fixed marks, at a measured distance
apart on the ship, are observed. But primitive
as it is, it is more accurate than any other method
which has ever been practised for low speeds
and large ships. Suppose, for example, the marks
to be 250 feet apart, and the times of the floater
passing them to be
ih. 1 7m. I2s.
and ih. I7m. 48^5.
The interval, therefore, was 36^ seconds. Hence
the ship went 250 feet in 36 J seconds, and therefore
was going at the rate of 1000 feet in 146 seconds.
To find the rate in miles per hour, multiply the
number of feet per second by 3600 and divide by
6080. The result is 4-05. Therefore the ship was
going at the rate of 4*05 miles per hour. This
process would of course, be too troublesome for
ordinary use, requiring as it does two accurate
observers with watches having seconds hands,
and an assistant. It would be found, however,
44 POPULAR LECTURES AND ADDRESSES.
exceedingly useful in some circumstances for
speeds below six or seven knots.
31. The following description of the LOG AND
GLASSES in ordinary use is taken from Lieutenant
Raper's excellent book on navigation.1
" THE LOG. — The log consists of the log-ship
and line. The log-ship is a thin wooden quadrant,
of about five inches radius ; the circular edge is
loaded with lead, to make it float upright, and
at each end is a hole. The inner end of the
log-line is fastened to a reel, the other is rove
through the log-ship and knotted ; and a piece
of about eight inches of the same line is spliced
into it at this distance from the log-ship, having
at the other end a peg of wood, or bone, which,
when the log is hove, is pressed firmly into the
unoccupied hole.
"At 10 or 12 fathoms from the log-ship a bit
of bunting rag is placed to mark off a sufficiency
of line, called stray-line, to let the log go clear of
the ship before the time is counted.
1 The Practice of Navigation and Nautical Astronomy, by Lieut.
Henry Raper, R.N. (tenth edition, 1870; original edition, 1840).
NAVIGATION. 45
" The log-line is divided into equal portions
called knots, at each of which a bit of string, with
the number of knots upon it, is put through the
strands.
" The length of a knot depends on the number
of seconds which the glasses measure, and is thus
determined : —
" No. of ft. in I knot : No. of ft. I m. : : No. of sees, of the glass :
3600 (No. of seconds in an hour).
" The nautical mile being about 6080 feet, we
have, for the glass of 30 seconds, the knot
= (6080 x 3o)/36oo = 507 feet, or 50 feet 8
inches ; for the glass of 28 seconds, the knot
= (6080 X 28)/36oo = 47*3 inches, or 47 feet
4 inches, and so for any other glass.
"The log-line should be repeatedly examined,
by comparing each knot with the distance between
the nails, which are (or should be) placed on the
deck for this purpose at the proper distance. The
line should be wet whenever it is required thus
to remeasure it, or to verify the marks.
"As the manner of heaving the log must be
learned at sea, it is only necessary to remark, for
46 POPULAR LECTURES AND ADDRESSES.
reference, that the line is to be faked in the
hand, not coiled ; that the log-ship is to be thrown
out well to leeward to clear the eddies near the
wake, and in such a manner that it may enter the
water perpendicularly, and not fall flat upon it ;
and that before a heavy sea the line should be paid
out rapidly when the stern is rising, not when the
stern is falling ; as this motion slacks the line, the
reel should be retarded.
32. " Massey's Log. — This instrument shows the
distance actually gone by the ship through the
water, by means of the revolutions of a fly, towed
astern, which are registered on a dial plate.
This log is highly approved in practice ; and
it is much to be desired that the patentee could
manufacture, at a moderate price, an instrument
which affords a method, at once so simple and
so accurate, of measuring a ship's way, and
which could not fail to come into extensive, if
not genera1, use.
33. " The Ground Log. — When the water is
shoal, and the set of the tides or current much
affected by the irregularity of the channel, or
NA VI G A TION. 47
other causes ; and when, at the same time, either
the ship is altogether out of sight of land, or
the shore presents no distinct objects by which
to fix her position, recourse may be had to the
ground log. This is a small lead, with a line
divided like the log-line, the lead remaining
fixed at the bottom ; the line exhibits the effect
of the combined motion of the ship through the
water, and that of the water itself, or the current ;
and therefore the course (by compass), and distance
made good are obtained at once.
34. "THE GLASSES.— The long glass runs out
in 3OS or in 28s ; the short glass runs out in
half the time of the long one.
" When the ship goes more than five knots, the
short glass is used, and the number of knots shown
is doubled.
"The sand-glasses should frequently be ex-
amined by a seconds watch, as in damp weather
they are often retarded,1 and sometimes hang
altogether. One end is stopped with a cork, which
1 Why is the glass not hermetically sealed so that the sand put
in dry may remain dry for ever ? — (W. T.)
48 POPULAR LECTURES AND ADDRESSES.
is taken out to dry the sand, or to change its
quantity."
Lieutenant Raper's anticipation, published first
in 1840, that the Massey log would come into
extensive, if not general, use, has been amply
verified. It is now to be found, I believe, on
board of almost every British ship, not running
at too great a speed for its use. It is the instru-
ment chiefly trusted for finding distances run at sea,
failing sights of sun or of stars ; and the old log-ship
and glass, though capable of doing very good work
in careful hands, has fallen, or is falling, into
general disuse. The Massey log is kept con-
tinually in tow when the ship is out of sight of
land, except for a few minutes occasionally, when
it is taken on board and its dial read off. Its
reckoning of the distance run in different con-
ditions of the sea and wind, in clear weather is
checked by the ordinary astronomical observations.
Then judging from the results, the navigator cor-
rects its indications, if necessary, before using them
to estimate the distance run in cloudy weather.
All the different kinds of logs, which I have now
NAVIGATION, 49
explained, depend, you will perceive, upon a
measurement of the distance actually run, in
some particular interval of time, long or short.
35. THE DEEP-SEA LEAD. — The deep-sea lead
is about 56 Ibs. in weight, with a hollow in its lower
end, armed with stiff wax or tallow to bring up
specimens of the bottom, and is attached to a
rope of I \ in. circumference, and from 100 to
200 fathoms in length. If the depth is to be
found simply by the quantity of rope carried out
by the lead before it reaches the bottom, the ship's
way through the water must be as nearly as
possible stopped if the depth is anything more
than twenty fathoms. But by the introduction of
a " Massey Sounding Fly " l a few feet above the
lead, and in line between it and the rope, the
distance travelled by the lead through the water
may be measured with considerable accuracy, and
thus soundings may be taken from a steamer going
at full speed, even when the depth is as much as
1 In the tenth edition of Raper's Navigation (1870) I find an
amusing statement given on the authority of the "Survey of the
River St. Lawrence," by Capt. Bayfiald, that "In depths exceeding
100 fathoms, the fly is liable to be crushed."
VOL. III. K
50 POPULAR LECTURES AND ADDRESSES.
fifty or sixty fathoms. Suppose the ship is going
at 12 knots, and it is important not to lose time
by heaving to, or even by reducing speed ; the lead,
with Massey fly and rope attached, is carried
•forward as far towards the bow as possible. Two or
three coils of the rope are carried outside of the rig-
ging, and several men, at different places along the
ship's side, stand by, each with a coil or two of it
in his hands. The foremost man casts the lead ;
when the next man feels 'the rope beginning to pull
he lets go, and so on. By the time the ship's stern
has passed, the lead may have reached the bottom,
or it may not have reached the bottom until a con-
siderable distance astern of the ship. It is very
hard work pulling in 1 50 or 200 fathoms of the thick
deep-sea sounding rope, with 56 Ibs. at the end of
it, when the ship is going at any such speed as
12 knots through the water, even with twenty or
thirty men employed to do it ; but a careful and
judicious navigator will not spare his ship's com-
pany. He will keep them sounding every hour or
every half hour rather than run any unnecessary
risk, and (if to lose no time is important) he will
NAVIGATION. 51
only reduce speed when he cannot, at full speed,
take the soundings required for safety.
36. I have shown elsewhere l that the labour of
taking deep-sea soundings, whether for surveys of
the ocean's bed, or for guidance in cable laying,
or for ordinary navigation, may be immensely
diminished, and the quickness, sureness, and
accuracy of the operation much increased by the
use of steel pianoforte-wire instead of hemp rope.
You see before you a first rough attempt at an
instrument for ordinary navigational sounding by
pianoforte wire. I have tested its efficiency off
the Island of Madeira, and off Cape Finisterre, and
Cape Villano, at the south-west corner of the Bay
of Biscay, and found it to work perfectly well.
Even without the Massey fly, it gives a fairly
approximate sounding in as great a depth as 1 50
fathoms, when the ship is running at any speed not
exceeding five or six knots, a result quite unattain-
able by the ordinary deep-sea lead. There is no
difficulty whatever in using it with a Massey fly
1 See papers on "Deep- Sea Sounding" included in present
volume ; also § 37 below.
E 2
52 POPULAR LECTURES AND ADDRESSES.
attached, although I have not yet tested it with
this adjunct. With or without the Massey fly it
can be hauled in quite easily by two men, though
the ship is going at a speed of twelve knots. The
whole watch in a large steamer is habitually em-
ployed in hauling in the ordinary deep-sea lead,
when soundings are taken with the ship going at
full speed.
[37. ADDITION OF AUGUST 4, 1887. — The
machine referred to in the preceding paragraph
has, since this lecture was delivered, been developed
and become a practical and useful aid to naviga-
tion. The diagram (Fig. 10) shows the machine
in the position for taking a cast. The steel wire
is coiled on a V'sriaPed ring, A. This ring A can
revolve independently of the spindle, or it may be
clamped to the spindle by means of the plate BB.
When the ring A is undamped from the spindle
the sinker descends and the wire runs out. As
soon as the sinker touches the bottom the wire
slacks. The ring is then clamped to the spindle,
which prevents any more wire running out, and
winding in commences. The sinker is a hollow
NA VI G A TION.
FIG. 10. — Navigational Sounding Machine.
54 POPULAR LECTURES AND ADDRESSES.
tube, inside of which is placed
the depth-recorder represented at
Fig. n, for showing the depth to
which the sinker goes. As the
sinker descends the increased pres-
sure forces the piston D up into an
air-vessel, while the spiral spring
pulls the piston back. The amount
that the piston is forced up
against the action of the spiral
spring depends on the depth. The
marker C is used for recording
the depth. As the sinker goes
down, the 'marker is pushed along
the piston-rod. When the recorder
is brought to the surface of the
water, the piston comes back to
its original position, but the marker
remains at the place on the piston-
rod to which it was pushed. The
depth is read off by the position of
FlG> '0613111 the cross wire °f tlie mai~ker on the
scale of the piston-rod.]
NAVIGATION. 55
I. PILOTAGE OR NAVIGATION IN THE NEIGH-
BOURHOOD OF LAND.
38. Sure and ready knowledge of the general
appearance of the places visible from the ship's
course is the first requisite in a pilot. It was
probably the only kind of navigational skill, except
taking soundings, possessed by the ancient Medi-
terranean navigators, or by European navigators
generally, until nine hundred years ago, when the
mariner's compass first became known in Europe.
When there are outlying dangers (as shoals and
sunken rocks are technically called in navigation),
the pilot must know familiarly their positions, with
reference to visible objects on the shore, or on
islands and rocks standing out above the water.
Mere acquaintance with the general appearance of
the visible objects no longer suffices, and the pilot,
however unscholarly may have been his training,
becomes of necessity a practical mathematician.
The principle of clearing marks for dangers is of
the purest geometry. A certain line is described
56 POPULAR LECTURES AND ADDRESSES.
or specified by aid of two objects seen in line
or nearly so, or one over the other. The danger
lies altogether on one side of this line ; or, it may
be, a line so specified is a safe course between two
dangers.
An outlying danger is completely circumscribed
by three lines, each specified according to the same
principle, and the navigator who knows the three
clearing lines, but nothing more for certain, takes
care to keep outside their triangle ; but with more
minute knowledge he may, when there is occasion,
cut off a corner of the triangle by guess or by
feeling his way by the lead. Generally, if the
danger be of large extent, four or five, or more,
clearing lines, forming a quadrilateral or polygon
circumscribing it complelely, are specified, still all
on the same principle.
39. There are three serious limitations to the
complete usefulness and sufficiency of clearing
marks for pilotage : —
(i.) However well a pilot may know them, still
he must see two objects for each clearing line,
one of them generally at a considerable distance.
NAVIGATION. 57
It often happens that, through rain or haze, the
more distant of the two objects is invisible alto-
gether, although the nearer may be well seen,
and thus the clearing specification is absolutely
lost.
(2.) A stranger, however well prepared by
reading his book of sailing directions, must have
superhuman quickness of perception to always,
when running at a high speed, recognise with
sufficient readiness the successive pairs of objects
constituting the clearing marks for dangers which
he must skirt along or pass between in his
course.
(3.) Often while there are good single objects
to serve as near landmarks visible from the ship's
course, it may be impossible to find, beyond
them, any distinct marks, or any marks at all ;
as when there is too uniform a background of
hills, or when there is no background at all, the
land being flat, with no buildings or trees dis-
tinctly visible in the distance. For one or other,
or all, of these reasons, the azimuth compass is
continually in requisition for pilotage. Thus the
58 POPULAR LECTURES AND ADDRESSES,
sailing directions always add to the descriptions
of the two objects which are to be seen in line
for a clearing mark, a statement of their compass
bearings when so seen ; also information regard-
ing soundings when needed, or when available
as an aid.
40. I cannot better illustrate the subject, and
particularly the kind of difficulties which the
stranger must grapple with, if, aided only by
sailing directions, he acts as his own pilot, than by
reading to you from the Admiralty Book of
Sailing Directions for the West Coasts of France,
Spain, and Portugal, some extracts regarding the
entrance to the Tagus over the bar of Lisbon.
I must premise that " turning through a channel "
is a technical expression for sailing through the
channel by a zig-zag course against the wind.
Directions for turning through a channel neces-
sarily specify, by proper landmarks, the extreme
limit to which a ship may safely go on either
side, from mid-channel, before turning to windward
for her next tack.
" Opposite Lisbon, on the south shore, is
NA VIGA TION. 59
Cassilhas Point, being the eastern point of what
may be termed the port of Lisbon, and from
whence the wide expanse already alluded to
opens out ; here the river is a long mile wide,
but it narrows to about three-quarters of a mile
at Belem, when it becomes considerably wider,
and at its entrance it is if miles across.
*****
" CACHOPO OR CACHOP SHOALS. — Off both
points of the entrance to the Tagus there are
dangerous sandy shoals extending in a westerly
direction, and having between them a deep
channel, which is nowhere less — between the
five fathom lines of soundings — than nine-tenths
of a mile in breadth. The shoals are called
the North and South Cachopo.
" From the depth of 4! fathoms, at the west
end of the North Cachopo, Fort San Julian bears
about E. by N.JN., distant about 3^ miles.
" Thence the shoal, with from 2\ to I fathom
water on it, extends in the direction of the fort,
leaving at its east end a narrow passage into
the Tagus, called the North Channel.
60 POPULAR LECTURES AND ADDRESSES.
" From the south-east point of entrance to the
Tagus, the South Cachopo extends to the W.
and W.S.W. for 2j miles. From the depth of
4| fathoms, at the west end of the shoal, Bugio
Fort bears E.N.E. easterly distant if miles.
The larger portion of this shoal has little more
than i fathom water on it, and around Bugio
Fort the sand is dry at low water.
" The bar between the western extremes of
the Cachopos, has 6 and 7 fathoms over it at
low water springs ; the channel within it soon
deepens to 9 fathoms, increasing to 19 fathoms,
abreast Bugio Fort. Notwithstanding the depth
upon the bar, and the distance between the
extremes of the Cachopos, the sea in S.W. gales
rolls over it with great force, frequently forming
one tremendous roller that breaks with irresistible
violence the whole distance across ; at such times
the bar is impracticable, and in winter, or wrhen
the freshes are strong and accompanied with
westerly gales, continues so for several days
together.
NAVIGATION. 61
" Pilots are usually to be found some distance
from the entrance of the Tagus ; their boats are
to be distinguished from others by a blue flag
hoisted at the yard-arm of their lateen sails.
" LEADING MARKS. — Santa Martha Fort, to
the southward of Cascaes, is white, and of a
triangular form to the eastward, with a low
battery extending to the northward ; Guia light-
house in one with the bastion of this fort,
N.W.iW., leads through the North Channel.
*****
" Fort San Julian is an extensive fortification,
erected on a high steep point on the north-west
side of the entrance to the Tagus. A ledge of
rocks, with 3^ fathoms, extends a short distance
to the south-eastward of the fort.
" Bugio Fort stands upon the highest part of
the South Cachopo, about two-thirds of a mile
from Medao Point, the south-east point of the
mouth of the Tagus ; the fort is of a circular
form, and the sand round it is dry at low water.
" The Paps are very difficult to be distinguished,
particularly on the bearing used for the South
62 POPULAR LECTURES AND ADDRESSES.
Channel, from whence they appear over some
flat ground, which scarcely shows above the
land to the south-west of it ; they lie to the
eastward of a ridge of hills with several wind-
mills, five of which are close together, then two,
and just to the eastward of the latter the Paps
will be found. ' When seen to the northward
of San Julian, or to the southward of the Bugio,
they show like two small hummocks, but when
in a line with either of the turning marks, or
with the leading mark, they appear as a single
hummock with a flat top.'
" The Mirante or Turret of Caxias, is a small
white building formed of two octagonal turrets,
with red cupolas, on a hill nearly 3 miles E. by
N. of San Julian Fort, and is used as the northern
turning mark for the South Channel when in
one with the Paps, bearing about E. by N.JN.
" Jacob's Ladder is a range of black masonry
or stone wall that supports the cliff, and is not
easily distinguished, but there is a stone wall
resembling an aqueduct to the eastward of it,
and another to the westward. Jacob's Ladder is
NA VI G A TION. 63
used as the centre leading mark for the South
Channel when brought in one with the Paps,
bearing about E. by N.f N. A large conspicuous
cypress tree stands a third of a mile to the
eastward of Jacob's Ladder, and when in line
with the Paps, bearing about E.N.E., is used as
the southern turning mark for the South Channel.
*****
" The dome of Estrella is an excellent mark,
and readily distinguished by its great size, being
the largest dome in Lisbon, and towering above
all other buildings in the city ; when in one
with Bugio Fort it bears E.JN.
*****
" The South Channel is the principal passage
into the river. On entering it with a fair wind,
and rounding the southern extremity of the
North Cachopo, keep the Peninha (or western
part of the mountains of Cintra), bearing N.|E.,
and open westward of Cascaes Fort, until Bugio
Fort comes in one with the Estrella dome E.JN.
Then steer towards Bugio, keeping it in one with
the Estrella dome, in which line the bar con-
64 POPULAR LECTURES AND ADDRESSES.
necting the North and South Cachopos will be
crossed in the deepest water, and in not less
than 6\ fathoms ; and when the Paps are in one
with Jacob's Ladder, E. by N.fN., a vessel will
be inside the bar, and the depth of water will
have increased. Now run up with the Paps in
one with Jacob's Ladder, or if the wind hangs
to the northward, borrow as far as the northern
turning mark (the Paps in one with Caxias, E.
by N4N.).
" On the contrary, if the wind be from the
S.E., borrow towards the southern turning mark,
with the Paps in line with the cypress tree,
bearing about E.N.E., but avoid going too near
Bugio, as the tides there are strong and irregular,
and the South Cachopo steep-to.
" Having passed between Bugio and San Julian,
keep to the northward, so as to clear the sandy
flat inside Bugio, till Belem Castle is in a line
with the south part of the city of Lisbon,
bearing E.f S. Pass Belem Castle at the distance
of two or three cables, and then proceed to the
anchorage, keeping the whole of Fort San Julian
NA VIGA TIOX. 65
and all its outworks open to the southward of
the parapet of Belem Castle, which will clear
the shoals of Alcantara, until the vessel arrives
off the Packet Stairs, where there is anchorage
in from 10 to 14 fathoms water, or farther up
in 12 or 1 6 fathoms, mud.
"TURNING THROUGH THE SOUTH CHANNEL.
— A vessel from the north-west standing towards
the west tail of the North Cachopo, should keep
Peninha peak, bearing N.JE., open westward of
Cascaes Fort, and in not less than ' 1 2 fathoms
water, until the south part of the city of Lisbon
is in line with Bugio Fort, E.JS. ; then haul to
the wind.
" The turning mark for the north side of the
channel is the Paps, in line with the Mirante or
Turret of Caxias, E. by NAN. ; and the turning
mark for the south side of the channel is the
Paps, in line with the cypress tree (which stands
a third of a mile eastward of Jacob's Ladder)
E.N.E.
" The northern turning mark is a safe and
prudent one, as a vessel will not approach any
VOL. in. F
66 POPULAR LECTURES AND ADDRESSES.
part of the North Cachopo nearer than a quarter
of a mile ; but the southern turning mark carries
a vessel within ij half cables of the South Cachopo
and as the tides here are uncertain, the shoal
should be approached with caution. It is by no
means desirable to have a tree for a clearing mark,
which may be down at any moment ; but the
mariner in this case, in standing towards the latter
bank need go but little beyond the line of the
central leading mark. In places, both the North
and South Cachopo are steep-to."
41. The process of "taking angles" by the
sextant is found useful for finding the ship's place
when in sight of land. It consists of measuring
by the sextant, held horizontally, the differences of
azimuth as seen from the ship (s) of three known
objects or landmarks (A, B, c). Open the three
rulers of the station pointer to the measured
angles ASB, BSC, and then lay it down on your
working chart, and slip it about till the edges
of the three rulers pass through the positions
of A, B, C, as shown on the chart. The centre, or
pointer of the instrument then shows the place
NA VIGA TION. 67
of the ship. On account of the great exactness
attainable by it, this process is valuable when
greater accuracy is desired than can be obtained
by the use of the azimuth compass, and when three
objects or landmarks are available. It is also of
great value as a means for determining the error
of the compass. It is continually used in nautical
surveys ; also frequently in ordinary navigation.
The sextant is also used for finding the distance of
the ship from some object of known magnitude, as
for example a lighthouse tower, or another ship.
Suppose, for example, the height of the tower from
its base, or a conspicuous mark near its base, to its
top to be known to be 100 feet. This at a dis-
tance of a nautical mile (6086 feet), will subtend an
angle a little less than 1/60 of the radian. Taking
the radian as 57°'3, dividing this by 6086, and
multiplying by 60, to reduce to minutes, we get
5 6'* 5 as the angle, subtended by 100 feet, seen
at a distance of a nautical mile. Hence we have
the rule : Multiply the magnitude of the object in
feet by '565, and divide by the angle which it
subtends ; the result will be the distance in miles.
F 2
68 POPULAR LECTURES AND ADDRESSES.
This method is much used by naval officers to
measure the distance at any moment from the
admiral's ship, or some other ship, when sailing in
squadron, as an aid to keeping in station.
II. ASTRONOMICAL NAVIGATION.
42. Before attempting to explain Astronomical
Navigation, I must tell you something of the earth
as a whole.
When you look at the hills you see that the
earth is not exactly globular ; but if I could show
you an exact model of the size of this large globe be-
fore you (of two feet diameter), with every mountain
chain, and hill, and valley, and tree, and building
constructed exactly to scale, and with the whole sea
solidified in the form ruffled by waves, precisely as
it is at any instant, you could not perceive without
minute and careful examination, that it was any-
thing different from an exact sphere. The
Himalayas and Andes would be barely perceptible
roughnesses, the highest of them being about I 60
of an inch. The greatest buildings of the world,
NA VI G A TION. 69
St. Peter's Church at Rome and the Great
Pyramids, would be utterly imperceptible to touch,
but would be seen by aid of a powerful microscope.
The great chimney at St. Rollox would be an
exceedingly fine thorn of one hundred-thousandth
of an inch long, and therefore imperceptible to
touch. The sea would seem a perfectly unruffled
and brilliant mirror. The figure, however, would
not be exactly spherical, even though the
mountains were smoothed off. It would be found
that the diameter from pole to pole is less by
about a three-hundredth part than diameters
through the equator. Thus on the model an
accurate circular gauge, just fitting over the ends
of any diameter through the equator, and passing
round the poles, would show a depression of about
a three-hundredth of a foot (or 1/25 of an inch) at
each pole, gradually diminishing to nothing at the
equator.
Were it not for this flattening of the solid at the
poles and protuberance at the equator, the sea
would not be distributed as it is, partly in polar
and partly in equatorial regions, but in virtue of
70 POPULAR LECTURES AND ADDRESSES.
centrifugal force would lie almost entirely in a belt
round the equator, leaving a great island of dry
land round each pole.
43. In elementary books on geography, as-
tronomy, and navigation, terrestrial latitudes and
longitudes, and meridians, and horizontal planes,
and verticals and altitudes, are commonly de-
fined on the supposition that the earth is an exact
sphere. I prefer definitions of a more practical
kind, which, be the figure of the earth what it may,
shall designate in each case the thing found when
the element in question is determined in practice
by actual observation.
(i.) A vertical in any place is the direction of
the plumb line there, when the plummet hangs at
rest. The zenith is the point of sky vertically
overhead, or the point in which the vertical
produced upwards, cuts the sky.
(2.) Any plane through a vertical is called a
vertical plane. The prime vertical is a vertical
plane perpendicular to the meridian, that is to say,
it is an east and west vertical plane.
(3.) The vertical plane in any place passing
NAVIGATION. 71
through the point of the sky defined as the
celestial pole (§ 1 1 above) is the meridian of
that place.
(4.) A horizontal plane is a plane perpendicular
to the plumb-line or vertical ; or it may be defined
as a plane surface of mercury, or water, or other
liquid, in a basin large enough to give a middle
portion of liquid surface, not sensibly disturbed
by the capillaVy action which curves the liquid
near the sides of the vessel ; yet not so large as to
show any sensible influence from the curvature of
the earth. Either a plummet or a basin of liquid
is practically used for finding horizontal planes or
horizontal lines.
(5.) The altitude of any object, terrestrial or
celestial, as seen from any point of view, is the
angle between a line drawn to the object and
a horizontal line in the same vertical plane with
it ; or it is the angle between the line going
to the object and the nearest horizontal line ;
or, as it is sometimes put, it is the inclination to
the horizontal plane of a line directed to the
object.
72 POPULAR LECTURES AND ADDRESSES.
(6.) The latitude of a place is the altitude there
of the celestial pole.
(7.) The longitude of a place is the angle between
its meridian and that of Greenwich.
(8.) In the preceding definitions the term sky is
used so as strictly to mean a spherical surface of
infinitely large radius, having its centre at the centre
of the earth, or at the eye of an observer situated
anywhere at the surface of the earth. The great-
ness of the radius makes it a matter of no moment
whether the centre be at the earth's centre or at
the eye of the observer.
44. (9.) Horizon, derived from a Greek word,
which signifies bounding, is the boundary between
sky and earth, or sky and sea, as seen by any
observer. The term is not usually applied where
the sky is cut off by high hills or mountains, but
it is usually and properly enough applied to the
boundary between earth and sky, as seen by an
observer looking over a wide extent of level
country from any elevation, great or small. The
most common application of the term is to the
sea horizon, as described in § 5 above. Some-
NAVIGATION. 73
times "horizon" is used to designate the actual
line of earth or sea which is seen in line with the
sky, that is to say, the boundary of the visible
portion of the surface of earth or sea ; sometimes,
again, " the horizon " means the boundary line of
the ideal celestial sphere, separating the visible
part of it from the part eclipsed by the earth or
sea. This little ambiguity does no harm. When
we speak of the distance of the horizon, an ex-
pression frequently used in navigation, horizon has
its terrestrial signification. When we speak of
the distance of a star from the horizon, it is the
heavenly horizon that we mean.
45. (10.) A nautical or geographical mile is
the length of one minute of longitude at the
equator, and contains 6086 feet or 1014 fathoms.
This is very nearly the average length of a minute
of latitude, as the approximately elliptic quadrant
from the equator to either pole is very nearly
equal in length to the quadrant of the equator.
At the equator the length of a minute of latitude
is less by 1/150, and at the pole it is greater by
i 150 than the minute of longitude at the equator.
74 POPULAR LECTURES AND ADDRESSES.
Thus the actual length of a minute of latitude
at the equator is '993 of the geographical mile,
at the pole it is 1*007 geographical miles. Ac-
cording to the foundation of the French metrical
system, the length of any meridional quadrant of
the earth or of a quadrant of the earth's equator
is very approximately, nearly enough for all
practical purposes of geography and navigation,
equal to 10,000,000 metres or 10,000 kilometres.
Thus 10,000 kilometres are equal to 5,400 nautical
miles, and as one kilometre is equal to '54 of a
geographical mile, a geographical mile is equal
to I '85 kilometres. The existence of the British
statute mile (5280 feet!) is an evil of not incon-
siderable moment to the British nation. I shall
never use the unqualified expression umile" in
this lecture, nor, indeed, I hope on any other
occasion, as meaning anything else than the
geographical or nautical mile. The mean equa-
torial diameter of the earth is 6,876 miles, the
diameter from pole to pole is 6,853 miles. There are
60 times 360 or 21,600 minutes in the circumference
of a circle, hence the earth's circumference, which
NAVIGATION.
75
is very approximately the same round a meridian
or round any geodetic line,1 as round the equator,
is 21,600 miles.
The accompanying diagram represents any
section through the earth's centre. HH' are two
points of the terrestrial or sea horizon, as seen
from a point P, at a height of 1/81 of the earth's
diameter, that is to say, a height of nearly 85 miles.
PH, the distance of the horizon, is 1/9 of the earth's
diameter or 762*6 miles. The angle LPH is the
1 If a line on a given surface be such that a part of it, on each side
of any point of it whatever, is the shortest distance on the surface
between the two ends of this part, then it is a geodetic line.
76 POPULAR LECTURES AND ADDRESSES.
dip of the horizon. Let HC be the vertical through
H, meeting the vertical through P in C, then the
lines CP and CH being perpendicular to LP and
HP respectively, LP and HP must have the
angle between them, HCP equal to the angle
LPH. Considering the earth as approximately
spherical and gravitation approximately always
towards its centre, we thus see that the dip of the
horizon is the angle subtended at the centre by
the distance of the horizon from the point of
view. In the case represented in the drawing, PH
is 2/9 of the radius HC, and therefore obviously
the angle HCP is very approximately 2/9 of the
radian, or (2 x S7'3)/9 = I2°7> which therefore is
the dip of the horizon for a point of view 85 miles
above the sea.
To find the distance of the horizon generally,
multiply the height of the point of view by the
sum of the height and the earth's diameter, and
take the square root of the product. This rule is
applicable to any height however great. When
the height is not more than a few miles, it is not
worth while to add it to the earth's diameter.
NA VIGA TION. 77
Thus, the square root of the number of miles in
the earth's diameter being 8 2 '8, we have very
approximately the distance of the horizon in
miles, equal to 82'8 times the square root of the
height in miles, or ro6 times the square root of
the height in feet. To find the distance of the
horizon in feet, multiply the square root of the
height in feet by the square root of the diameter
in miles, and divide the result by 78.
To find the dip in decimal of the radian, divide
the distance of the horizon by the earth's radius ;
or (as we see by using the preceding rules for
distance), divide the square root of the height by
the square root of half the radius. Thus the dip
in radians is equal to the square root of the height
in miles, divided by 41*4, or is equal to the square
root of the height in feet divided by 3230. The
amount of the dip must be subtracted from the
observed altitude to find what it would have been
if the observation had been made from a true
horizontal plane instead of from the dipping
visual cone, along which the observer looks to his
horizon.
78 POPULAR LECTURES AND ADDRESSES.
46. (11) The refraction, of light is the change
of direction which a ray is found to experience
in passing from one transparent medium as
luminiferous ether,1 or air or water, to another
transparent medium, as air or water or glass.
Light entering the earth's atmosphere from
the sun or moon or stars, in any other direc-
tion than the vertical experiences refraction, by
which its inclination to the vertical is diminished
as it passes through denser and denser strata of
the atmosphere down to the surface. Hence every
observed altitude must be corrected for refraction,
in order that the true altitude of the straight line
from the object to the observer may be determined.
The correction is clearly greater the farther the
object is from the zenith. The amount of the
correction is 33' when the line of vision is
horizontal. In this case the object is actually
below the horizon by this amount, so that a ray
1 Luminiferous ether is a name given to the substance, ether or
aether, occupying space outside some indefinite limit, perhaps 20,
perhaps 50, perhaps 100 miles high, within which the earth's
sensible atmosphere is contained.
NA VIGA TION. 79
entering from the luminiferous ether in a straight
line which, if continued, would pass over the
observer's head is bent so as to reach his eye
horizontally, and to make the object seem on the
horizon. The denser the air is, the greater is the
refraction ; and therefore, when, as in " lunars "
(§56 below), extreme accuracy in the allowance for
refraction is required, the height of the barometer
and thermometer must be noted at the time of the
observation. The higher the barometer and the
lower the thermometer, the greater is the amount
of refraction. Books on navigation give the
amount of refraction for different altitudes, for
mean temperature and mean height of the
barometer, and auxiliary tables for correction
according to the actual heights of the baro-
meter and thermometer at the time of observa-
tion.
47. If the earth were perfectly symmetrical
round its axis of rotation, like a body turned in a
lathe, the lines of equal latitude would be exact
circles in parallel planes perpendicular to the earth's
axis. They are not exactly so in reality, because
So POPULAR LECTURES AND ADDRESSES.
of the disturbance in the directions of verticals at
different parts of the earth's surface, produced by
the attraction of mountains and continents, and
the defect of attraction of great depths of the sea,
and by unknown variations of density in the solid
earth below the bottom of the sea, and below the
visible surface of dry land. But they are nearly
enough so for all the purposes of practical
navigation ; and therefore lines of equal latitude on
the earth's surface are habitually called circles of
latitude, or parallels of latitude.
According to the same supposition of symmetry
round an axis, the meridian plane of any locality
would pass through the earth's axis of rotation,
and it would be the meridian also of every other
place on the line in which it cuts the earth's
surface. This result of the imagined symmetry is
nearly enough true in reality for navigation, and ac-
cordingly in navigation it is allowable and usual to
regard lines, in which the earth's surface is cut by
planes through its axis, as lines of equal longitude ;
and farther, these lines are often called meridians,
or terrestrial meridians, there being a habitual
NAVIGATION. 81
ambiguity in the use of the word meridian,
according to which it is sometimes used for a line
on the earth's surface, and sometimes for the north
and south vertical plane denned above — an am-
biguity not very inconvenient when we are on our
guard against any mistake which could arise from
it. It is exceedingly interesting, in respect to the
theory of gravitation and of the earth's figure,
though of no moment in respect to navigation,
to remark that, in reality, lines of equal longitude
are not precisely meridional lines, or true north
and south lines ; ?nd that lines of equal latitude
are not exactly circles, but slightly sinuous curves.
48. Just two kinds of observation are used in
astronomical navigation which are shortly desig-
nated as " altitudes " and " lunars" I shall say
nothing of lunars at present, except that they are
but rarely used in modern navigation, as their ob-
ject is to determine Greenwich time, and this object,
except in rare cases, is nowadays more correctly
attained by the use of chronometers than it can
be by the astronomical method.
The astronomical observation, which is practised
VOL. in. G
82 POPULAR LECTURES AND ADDRESSES.
regularly by day and frequently also at night in
practical navigation, consists simply in measuring
by the sextant the apparent altitude of the sun or
star above the horizon (§ 5 above) and noting
accurately the hour, minute, and second by the
ship's chronometer, at which the observation is
taken. The immediate results of the observation
are corrected according to explanations I have
already given you in respect to the following
several particulars — index-error, dip of the horizon,
and refraction ; also for the sun's semi-diameter,
when it is the sun, not a star, that is observed.
49. LATITUDE. — With these definitions and
explanations premised, we are prepared to under-
stand readily how latitude and longitude are
determined by actual observation of stars or sun.
If there were a bright enough star exactly at the
celestial pole of whichever hemisphere we are in,
we should only have to observe its altitude above
the horizon, and that would be the latitude. In
the northern hemisphere, Polaris, as I have told
you, is seen describing daily a small circle of i° 21'
distance from the true north celestial pole ; and
NAVIGATION. 83
therefore, if you are satisfied with knowing your
latitude within i° 21', the simple altitude of Polaris
gives it. But if you know the sidereal time of
your observation, even very roughly, say within
five or ten minutes of time, you can calculate the
correction required to give the true latitude from
the observed altitude of Polaris accurately enough
for practical purposes.1. This method is practised
very frequently at sea in the northern hemisphere.
The meridian altitude of any known star, or of the
sun, gives the latitude, for the Nautical Almanac
tellsv you the distance2 of the observed body from
1 The greatest error in the deduced latitude due to error in your
reckoning of time is, of course, to be met if the observation is made
when the star is rising or sinking with the greatest rapidity — that is
to say, when it has made a quarter of its revolution from the lowest
or highest points of its diurnal circuit. At such times there is an
error of 2' latitude for six minutes' error in your reckoning of time.
2 The Nautical Almanac gives what is called the declinations of
stars and sun, that is, the angular distance north or south from the
celestial equator, this being a plane through the observer's eye perpen-
dicular to the axis of the earth's rotation. The north polar distance
is found by subtracting the declination from, or adding it to, 90°,
according as it is north or south declination. Thus the declination
of Arcturus is 19° 50' N. ; its north polar distance, therefore, is
70° 10' N. Again, the declination of the sun to-day (Nov. u, 1875)
is 17° 24' S ; his north polar distance, therefore, is 107° 24'.
G 2
84 POPULAR LECTURES AND ADDRESSES.
the celestial pole at the time of your observation.
From the observed altitude, then, of the stars or
sun, you can deduce the altitude of the pole
thus :—
1. If the star crosses the meridian under the
pole, add the polar distance to the observed
altitude.
2. If the star crosses the meridian above the
pole, but north of your zenith, subtract its polar
distance from the observed altitude.
3. If star or sun cross the meridian south of
your zenith, add its polar distance to the observed
altitude and subtract the sum from 180°.
So, in any one of the three cases the latitude
is calculated from your observation.
In meridian observations for the latitude the
aid of the chronometer is not needed : the
observer keeps watching the altitude by aid of
a sextant till he finds it cease to diminish and
begin to increase (in case No. i), or till he finds
it cease to increase, and begin to diminish (in
case 2 or case 3). He thus finds, as nearly as
he can in each case, the least altitude or the
NA VI G A TION.
greatest altitude, as the case may be. Practically,
he does help himself by finding by the aid of
his Nautical Almanac the time on his watch
within a few minutes of the precise instant when
the least or greatest altitude is to be observed ;
but then, though the altitude changes but very
little within five or ten minutes, before and after
this instant, the observer generally satisfies himself
that he has got the true minimum or the true
maximum by waiting till he finds the change
from sinking to rising, or rising to sinking.
50. LONGITUDE. — To determine the longitude
by astronomical observation, two things must be
done. The local time must be found from sun
or stars, and Greenwich time taken at the same
instant from your chronometer, or, failing the
chronometer, by lunars. The difference of the
times thus found reduced to angle at the rate
of 15° to the hour, 15' of angle to one minute
of time, 15" of angle to one second of time, is
your longitude east or west of Greenwich, ac-
cording as your local time is before or behind
Greenwich time. On shore local time is most
86 POPULAR LECTURES AND ADDRESSES.
accurately found by observing the instant when
the sun or a star crosses the meridian. But on
board ship this method cannot be practised, and
instead an altitude, whether of sun or star, is
observed when the body is anywhere out of the
meridian. Now remember that a star (or, neg-
lecting a very slight error due to change of
declination, the sun) is at its greatest altitude
when it is crossing the meridian, and you will
understand that, when the observed altitude is
anything less than the greatest altitude, you can
calculate how long time before or after its
meridian passage, must have been the instant of
your observation. The calculation requires a
knowledge of the declination of the observed
body, and of the latitude of the ship's place at
the time of the observation ; but if you have
chosen a star in the prime vertical, or very
nearly in the prime vertical, a very rough ap-
proximation to your latitude suffices. The
method most commonly practised at sea is to
estimate the latitude as accurately as possible by
dead reckoning from previously determined
NAVIGATION. 87
positions, to use this latitude in determining
local time from an observation of altitude, and
thence by chronometer to determine the longitude.
But, except any case in which the observed body is
on the prime vertical at the instant of observation
(and for every such case, the old ordinary method
is virtually equivalent to Sumner's method), that
method is not, and Sumner's method (to be ex-
plained later) is, the simple and direct interpretation
of what you learn as to the ship's place from an
observation of altitude (see Art. 5 above).
51. SUMNER'S METHOD OF INTERPRETING
AN OBSERVATION OF ALTITUDE.— The Greenwich
time of the instant of observation is to be cal-
culated according to the known error of the
chronometer or the mean of the errors of several
chronometers, wrhen there are several on board.
Now, what is the inference to be made from the
fact that the altitude of the sun's centre above a
true horizontal plane through the ship was so and
so — say 40° — at such and such a time, say on the
2;th of August 1874, at IH. 2IM. 23$. P.M. mean
Greenwich time ? It is simply this, that the
88 POPULAR LECTURES AND ADDRESSES.
ship at the time of observation was somewhere
on a certain circle of the earth at every point of
which the sun's altitude was the same. To draw
this circle on a drawing globe, such as the black
globe before you, you must find first at what
point of the earth the sun was overhead at the
instant of observation. This you do immediately
by aid of the Nautical Almanac, which gives you
the instant of the sun's being due south at Green-
wich every day of the year. Thus on the 27th of
August 1874 the sun "southed" at Greenwich at
I2H. IM. 238. P.M.; therefore in a place in west
longitude 20°, he was due south at the instant
of observation. His declination was 10° N., hence
he was overhead in lat. 10° N., Ion. 20° W. Put
one point of the compasses at the corresponding
point of your drawing globe, and draw by aid
of the compasses a circle running at 40° of the
earth's surface from this point. The ship was
somewhere on this circle at the instant of the
observation. The chart before you shows this
circle drawn on Mercator's projection — not a true
circle as you see, because circles on the earth's
NA VI G A TION.
89
surface are not shown as circles on Mercator's
projection.
Suppose now that 2H. 4OM. later the altitude of
the sun is again taken and found to be 50°. At
the moment of this second observation, the ship
was on this other circle which you see on the
I2O IOO 80 60 40 2O O 2O 40 60
FIG. 14. — Mercator chart, showing Sumner circles.
chart. What we learn from the two observations
then is, that at the time of the first observation
the ship was somewhere on that first circle, and
that at the time of the second observation she
was somewhere on that second circle. These
90 POPULAR LECTURES AND ADDRESSES.
circles are called by Sumner circles of equal
altitude. The portions of them shown on your
working chart are conveniently called Sumner
lines. Now simply by dead reckoning estimate
the course and distance made by the ship in the
interval between the two observations. Take a
length equal to this distance, and by aid of a
parallel ruler place it in proper direction, with one
end of it on one of the Sumner lines, and the other
on the other. The two ends of the line show the
places of the ship at the instants of the two
observations.
The process of drawing on a globe which I put
before you is, you must understand, merely put
by way of illustration of the principle. It would
be practically impossible, or at all events so
difficult as to be impracticable, to carry out the
construction at sea by means of compasses on
a globe, or by ruler and compasses on a plane
chart, with sufficient exactness to give the ship's
place as accurately as it can be determined from
the observations. Calculations by what is called
spherical trigonometry, therefore, must take the
NAVIGATION 91
place of drawing by ruler and compasses ; and it
is by calculation that the ship's place is found every
day at sea from the observations of altitude. The
ordinary mode of calculation is given in full in
every book on navigation and need not be repeated
to you by me.
52. The clear and obvious mode of interpreting
the information derivable from a single altitude of
the sun or stars which I have put before you,
is due to Captain Thomas B. Sumner of Boston,
Massachusetts. It is not only valuable as giving
us a clear view of the geometrical process under-
lying the piece of calculation by logarithmic tables
which is performed morning and evening by the
practical navigator at sea, but it actually gives
him a much more useful practical way of working
out the results of his observations than that which
is ordinarily taught in schools and books of
navigation, and ordinarily practised on board ship.
It is too usual to wait for the noon observation
before working out the result of the morning
altitude. Instead of this, the Sumner line ought to
be calculated for each observation independently,
92 POPULAR LECTURES AND ADDRESSES.
and drawn on the ordinary working chart. Then
the navigator knows that the ship is somewhere on
that line, even though he may not know his
latitude within twenty or thirty miles.
I have known a case of a ship bound from South
America to England, intending to call at Fayal,
Azores, for provisions, and being saved from passing
out of sight of the island before noon by the
Sumner line, calculated from observation at seven
in the morning. This observation proved the ship
to be about eleven miles further west than estimated
from the afternoon observation of the previous day ;
and a timely change of the course, three points
to the eastward at eight o'clock, brought the heights
of Fayal in view ahead about half-past ten. If
the ordinary course had been held on till noon,
the ship would then have been eleven miles
to the west of the west end of Fayal, and the
island still unseen as the weather was somewhat
cloudy ; and the ship must have been turned
round at right angles to her course to look for
the island.
53. Having been much impressed with the value
NA VIGA TION. 93
of Sumner's method, from seeing the valuable
results of the skilful use made of it by Captain
Moriarty, R.N., in the Atlantic cable expeditions
of 1858, 1865, and 1866, and particularly in finding
the places for the successive grapplings by which
the lost 1865 cable was recovered and completed
in 1866, I have long felt convinced that it ought
to be the rule and not the exception to use
Sumner's method for ordinary navigation at sea.
I have therefore prepared tables, copies of which
I hold in my hand, for facilitating the practice
of Sumner's method at sea, and have had them
printed and "stereotyped for publication. The pub-
lication only waits the preparation and printing of
the pamphlet of rules and illustrations to explain
how they are to be used.1
The practice of Sumner's method for star ob-
servations is even more valuable than for the
altitudes of the sun taken by day. By taking
the altitudes of two stars at the same time, or
1 The pamphlet of rules and illustrations is now (April, 1876) in
type, and nearly ready for press. It will, with the stereotyped tables,
be published in the course of a few weeks by Messrs. Taylor and
Francis, London.
94 POPULAR LECTURES AND ADDRESSES.
within so short a time one after the other that the
ship has not travelled far in the interval, we
get two Sumner lines on our chart, and know
that, at the time of the observations, the ship
was actually on the point in which the two lines
met.
Thus on a clear night we can at any time find
the ship's actual place, as we can always choose
two good stars in good positions for the purpose ;
while by day, all we can tell, as we have only one
sun and no other visible body (except sometimes
the moon, which is not very convenient for such
observations), is that the ship is on a certain
line, viz., the Sumner line for the moment of
observation. If, then, we could observe the al-
titudes of stars with the same accuracy as the sun,
we could know the ship's place better by night
than by day ; but, alas, the observation of the star
altitude is rarely to be made with all the desired
accuracy, even by the most skilful observer, because
it is so difficult at night to see precisely where
the sea-horizon is.
54. LATITUDE BY SUMMER'S METHOD. — One
NAVIGATION. 95
word about latitude before leaving Sumner's
method, the beauty of which, according to Captain
Croudace of Dundee, a very intelligent advocate
of it,1 " consists in its glorious disregard of the true
latitude." You see that, in describing it, I have
never once used the word latitude ; but now what
I have to say is this : If the altitude is taken
when the sun is exactly in the meridian, the
Sumner circle touches the circle of latitude in
which the ship is at the time, and therefore the
information which in this case we derive from
Sumner's method, is simply the ship's latitude.
Thus we see that the old well known and universal
way of finding a ship's latitude is only a particular
application of Sumner's method. But there is
this peculiarity of the noon observation : you do
not need to take time from a chronometer
when making it ; all you have to do is to find
the greatest altitude attained by the sun just
before he begins to dip. Should he be clouded
over at the critical moment when he is highest
1 Star Fontm/at y for Finding Latitude and Longitude by Sumner's
Method, p. 4, Preface. By W. S. Croudace.
96 POPULAR LECTURES AND ADDRESSES.
above the horizon, the meridian altitude is lost,
and Sumner's method, or something equivalent to
it, must be put in requisition. When the meridian
observation is lost, but instead of it the altitude
within half an hour before or after the sun crosses
the meridian is observed, it is usual to employ a
a table, which is given in the books on Navigation,
for computing what is called " reduction to the
meridian," that is to say, the addition which must
be made to the observed altitude to find the true
meridian or highest altitude ; but in practice it
is really much better to draw the Sumner line of
the actual observation on the chart, and judge from
it what the observation has really told you as to
the ship's position.
55. The chart before you (Fig. 15) illustrates
Sumner's method by an actual case of its use in
ordinary navigation, in a voyage from Falmouth to
Madeira, made by the sailing yacht Lalla Rookh,
from the 3rd to the Qth of May, 1874. The times
marked on the several Sumner's lines are the
Greenwich mean times of the observations. Look
carefully at the positions of the Sumner day-lines,
NAVIGATION.
97
as shown on the chart, and by considering the
12
20
50
42
38
16
FIG. 15 — Chart showing Suinner lines on a voyage— Falmouth to Madeira,
longitudes at the several places, the Greenwich
mean times marked, and the equation of time which
VOL. III. H
98 POPULAR LECTURES AND ADDRESSES.
was from three to four minutes " sun behind time,"
you will understand exactly how each line lies
as you see it on the chart, being, as I have told you
before, always in a direction perpendicular to the
line from the ship, to the point on the horizon
under the sun.
Look again at the lines determined by altitudes
of Polaris and Arcturus, observed on the night
before reaching Cape Finisterre. You see how
they intersect exactly in the place where the
vessel was at the time, and can understand how
important the full information thus given was in
the case of approaching land. Porto Santo was
sighted at noon on the pth of May, and Madeira
two hours later. No more astronomical obser-
vations were needed.
56. LUNARS. — I have spoken to you of the
marvellous accuracy of the marine chronometer, but
till Harrison's invention of the first useful artificial
marine chronometer, fulfilling Sir Isaac Newton's
anticipation, was given to the world, in 1765,
through the well-judged beneficence of the British
Government, the only chronometer generally avail-
NAVIGATION. 99
able for finding longitude at sea was that great
natural chronometer presented by the moon in
her orbital motion round the earth.
Imagine a line joining the centres of inertia
of the earth and moon to be, as it were, the
hand of a great clock, revolving round the
common centre of inertia of the two bodies,
and showing time on the background of stars
for dial. If the centres of inertia of the moon
and earth moved uniformly in circles round the
common centre of inertia of the two, the moon,
as seen from the earth, would travel through equal
angles of a great circle among the stars in equal
times ; and thus our great lunar astronomical
clock would be a perfectly uniform timekeeper.
This supposition is only a rough approximation
to the truth ; and the moon is, in fact, a very
irregular chronometer. But thanks to the mathe-
maticians, who, from the time of Newton, have
given to what is called the Lunar Theory in
Physical Astronomy the perfection which it now
possesses, we can tell, for years in advance,
where the moon will be relatively to the stars, at
H 2
ioo POPULAR LECTURES AND ADDRESSES.
any moment of Greenwich time, more accurately
than it can be observed at sea, and almost as
accurately as it can be observed in a fixed ob-
servatory on shore. Hence the error of the clock
is known more exactly than we can read its
indications at sea, and the accuracy with which
we can find the Greenwich time by it, is practically
limited by the accuracy with which we can ob-
serve the moon's place relatively to the sun,
planet, or star. This, unhappily, is very rough
in comparison with what is wanted for navigation.
The moon performs her orbital revolution in
27-321 days, and, therefore, moves at an average
rate of o°'55 Per hour, or '55 of a minute of angle
per minute of time. Hence to get the Greenwich
time correctly to one minute of time, or longitude
within 15 minutes of angle, it is necessary to
observe the moon's position accurately to half
a minute of angle. This can be done, but it is
about the most that can be done in the way of
accuracy at sea. It is done, of course, by measur-
ing, by the sextant, the angular distance of the
moon from a star, as nearly as may be in the
NAVIGATION. 101
great circle of the moon's orbital motion. Thus
supposing the ship to be navigating in tropical
seas, where a minute of longitude is equal to a
mile of distance, a careful navigator, with a good
sextant, whose errors he has carefully determined,
can, by one observation of the lunar distance,
find the ship's place within fifteen miles of east
and west distance. If he has extraordinary skill,
and has bestowed extraordinary care on the de-
termination of the errors of his instrument, he
may, by repeated observations, attain an accuracy
equivalent to the determination of a single lunar
distance within a quarter of a minute of angle,
and so may find the ship's place within seven
miles of east and west distance ; but, practically
we cannot expect that a ship's place will be found
within less than twenty miles, by the method of
lunars in tropical seas, or within ten miles in
latitude 60° ; and to be able to do even so much
as this is an accomplishment which not even a
good modern navigator, now that the habit of
taking lunars is so much lost by the use of
chronometers, can be expected to possess.
102 POPULAR LECTURES AND ADDRESSES.
57. The details of the method of lunars, the
practical mastery of which used to be the great
test of a good navigator before the time of
chronometers, are beyond the scope of the present
lecture. I must limit myself to telling you that
from rough observations of the altitudes of the
two bodies, moon, and sun or planet or star, and
observations of the barometer and thermometer,
the effects of atmospheric refraction in altering
the apparent distance between the two bodies
must be calculated. By an approximate know-
ledge of the ship's position, the difference between
the observed distance and that which would have
been observed if the place of observation had been
the earth's centre, must be determined.
The application of these corrections for refrac-
tion and parallax, so as to find, from the observed
distance, the actual angle between the line going
from the earth's centre to the moon's centre,
and the line from the earth's centre to the other
body, is what is technically called " clearing the
distance."
58. The books on navigation used at sea
NAVIGATION. 103
(Inman, Norrie, and Raper) contain carefully
elaborated rules and sets of tables for the pur-
pose of making the practical problem of clearing
the distance as easy as possible. The conclusion
of the process of finding Greenwich time by a
lunar observation at sea I can best explain to you
by reading from the Nautical Almanac for 1876,
page 511, premising that six pages of the Nautical
Almanac are devoted to data for finding the longi-
tude at sea by the method of lunars.
"Pages XIII. to XVIII. of each month, Lunar
" Distances, — These pages contain, for every third
" hour of Greenwich mean time, the angular
" distances available for the determination of the
" longitude of the apparent centre of the moon
" from the sun, the larger planets, and certain
" stars, as they would appear from the centre of
" the earth. When a lunar distance has been
" observed on the surface of the earth, and re-
" duced to the centre by clearing it of the effects
" of parallax and re/raction, the numbers in these
" pages enable us to ascertain the exact Greenwich
" mean time at which the objects would have
104 POPULAR LECTURES AND ADDRESSES.
" the same distance. They are arranged from
" west to east, commencing- each day with the
" object which is at the greatest distance west-
" ward of the moon, in the precise order in
" which they appear in the heavens ; W. indicating
" that the object is west, and E. east of the moon.
" The columns headed * P. L. of cliff.' contain
" the proportional logarithms of the differences
" of the distances at intervals of three hours,
" which are used in rinding the Greenwich time,
" corresponding to a given distance, according to
" the following rule, viz. : — For the given day,
" seek in the Ephemeris for the nearest distance
"preceding, in order of time, the given distance,
" and take the difference between it and the
" given distance ; from the proportional logarithm
" of this difference, subtract the proportional
" logarithm in the Ephemeris ; the remainder will
" be the proportional logarithm of a portion of
" time to be added to the hour answering to the
" nearest preceding distance, to obtain the ap-
" proximate Greenwich mean time corresponding
" to the given distance.
NAVIGATION. 105
" If the distance between the moon and a star
" increased or decreased uniformly, the Greenwich
" times corresponding to a given distance, as
" found by the above rule, would be strictly
" correct ; but an inspection of the columns of
" the proportional logarithms in the Ephemeris
" will show that this is not the case ; a correction
" must therefore be applied to the time so found
" for the variation of the difference of the
" distances. This correction may be obtained
u by means of the table at page 490 of the
" present volume, in the following manner."
[Here follow details of the method of inter-
polation to be used with examples of its
application.]
III. DEAD RECKONING.
59. I have now explained to you briefly, and
very imperfectly, navigation in clear weather. I
must next speak to you on a more sombre part
of our subject, navigation under clouds or through
fog. When no landmarks can be seen, and when
io6 POPULAR LECTURES AND ADDRESSES.
the water is too deep for soundings, if the sky
is cloudy so that neither sun nor stars can be
seen, the navigator, however clear the horizon
may be, has no other way of knowing where he
is than the dead reckoning, and no other guide
for steering than the compass.
We often hear stories of the marvellous exact-
ness with which the dead reckoning has been
verified by the result. A man has steamed or
sailed across the Atlantic without having got a
glimpse of sun or stars the whole way, and has
made land within five miles of the place aimed
at. This may be done once, and may be done
again, but must not be trusted to on any one
occasion as probably to be done again this time.
Undue trust in the dead reckoning has produced
more disastrous shipwrecks of seaworthy ships, I
believe, than all other causes put together. All
over the surface of the sea there are currents of
unknown strength and direction. Regarding these
currents, much most valuable information has
been collected by our Board of Trade and
Admiralty, and published by the Admiralty in
NAVIGATION. 107
its "Atlas of Wind and Current Charts." These
charts show, in scarcely any part of the ocean,
less than ten miles of surface current per twenty-
four hours, and they show as much as forty or
fifty miles in many places. Unless these currents
are taken into account then, the place of a ship,
by dead reckoning, may be wrong by from ten
to fifty miles per twenty-four hours ; and the
most accurate information which we yet have
regarding them is, at the best, only approximate.
There are, in fact, uncertain currents, of ten miles
and upwards per day, due to wind (it may
be wind in a distant part of the ocean) which
the navigator cannot possibly know at the time
he is affected by them. I believe it would be
unsafe to say that, even if the steerage and the
speed through the water were reckoned with
absolute accuracy in the "account," the ship's
place could in general be reasonably trusted to
within fifteen or twenty miles per twenty-four
hours of dead reckoning. And, besides, neither
the speed through the water, nor the steerage,
can be safely reckoned without allowing a con-
loS POPULAR LECTURES AND ADDRESSES.
siderable margin for error. In the recent court-
martial regarding the loss of the Vanguard, the
speed of the Iron Duke was estimated by one
of the witnesses at ten and a half knots according
to his mode of reckoning from revolutions of
the screw and the slip of the screw through the
water, while other witnesses, for reasons which
they stated, estimated it at only 8*2 knots. It
was stated in evidence, however, that the only
experiments available for estimating the ship's
speed in smooth water from the number of
revolutions of the screw, had been made before
she left Plymouth. If the old log-ship and glasses
had been used, there could have been no such
great range of doubt : or the Massey log, which
may be held to do its work fairly well if it
gives the whole distance run by the ship in
any interval within five per cent, of the truth.
60. Consider further the steerage. In a wooden
ship a good ordinary compass, with proper pre-
cautions to keep iron from its neighbourhood,
may be safely trusted to within a half-quarter
point ; but, reckoning the errors of even very
NAVIGATION. 109
careful steering by compass, we cannot trust to
making a course which will be certainly within
a quarter of a point of that desired. Now you
know an error of a quarter of . a point in your
course, would put you wrong by one mile to
right or left of your desired course for every
twenty miles of distance run. Thus in the most
favourable circumstances you are liable, through
mere error of steerage by compass, to be ten
miles out of your course in a run of two hundred.
In an iron ship, if the ordinary compass has been
thoroughly well attended to as long as the weather
permitted sights of sun or stars, a very careful
navigator may be sure of his course by it, within a
quarter of a point, when cloudy weather comes
on ; but by the time he has run three or four
hundred miles he can no longer reckon on the
same degree of accuracy in his interpretation of its
indications, and may be uncertain as to his course
to an extent of half a point or more until he
again gets an azimuth of sun or star. No doubt
an exceedingly skilful navigator may entirely, or
almost entirely, overcome this last source of
no POPULAR LECTURES AND ADDRESSES.
uncertainty when he runs over the same course
month after month and year after year in the
same ship ; but it is not overcome by any skill
hitherto applied to the compass at sea when a
first voyage to a fresh destination, whether in a
new ship or in an old one, is attempted.
All things considered, a thoroughly skilled and
careful navigator may reckon that, in the most
favourable circumstances, he has a fair chance
of being within five miles of his estimated place,
after a two hundred miles' run on dead reckon-
ing ; but with all his skill and with all his care,
he may be twenty miles off it ; and he will no
more think of imperilling his ship and the lives
committed to his charge on such an estimate,
than a skilled rifle-shot would think of staking
a human life on his hitting the bull's-eye at five
hundred yards. What, then, do practical navi-
gators do in approaching land after a few days'
run on dead reckoning ? Too many, through
bad logic and imperfect scientific intelligence,
rather than through conscious negligence, run
on, trusting to their dead reckoning. In the
NA VIGA TION. 1 1 1
course of eight or ten or fifteen years of navi-
gation on this principle, a captain of a mail
steamer has made land just at the desired place
a dozen times, after runs of strictly dead reckon-
ing- of from three or four hours to two or three
£3
days. Perhaps of all these times there has only
once been a strictly dead reckoning of over thirty
hours with satisfactory result. Still, the man
remembers a time or two when he has hit the
mark marvellously well by absolutely dead
reckoning ; he actually forgets his own prudence
on many of the occasions when he has corrected
his dead reckoning by the lead, and imagines
that he has been served by the dead reckoning
with a degree of accuracy, with which it is im-
possible, in the nature of things, it can serve
any man. Meantime, he has earned the character
of being a most skilful navigator, and has been
unremitting in every part of his duty, according
to the very best of his intelligence and know-
ledge. He has, moreover, found favour with his
owners, through making excellent passages in all
weathers, rough or smooth, bright or cloudy, clear
ii2 POPULAR LECTURES AND ADDRESSES.
or foggy. At last the fatal time comes, he has
trusted to his dead reckoning once too often, he
has made a "centre," not a "bull's-eye," and his
ship is on the rocks.
IV. DEEP-SEA SOUNDINGS.
61. What then, on approaching land in cloudy
weather, does the navigator do who is not only
careful but prudent, not only bold and able but
also intelligent and well taught, not only devoted
to the interests of his employers but devoted with
a knowledge which they can scarcely be expected
to appreciate ? He simply feels his way by the
lead, from the time he comes within soundings,
till he makes the land and makes sure by light-
house and landmark of where he really is.
Neither annoyance to the ship's company
through the extra labour which it entails, nor
consideration of the detention which it may
require, prevents him from using the deep sea
lead at least once an hour, unless he has satis-
factory grounds for confidence in proceeding with
NAVIGATION. 113
less frequent soundings. An admirable method
of navigation by the lead was recently explained
to me by Sir James Anderson, who told me he
was constantly in the habit of using it in his
transatlantic voyages, and that he found it had
been independently used by Captain Moriarty,
R.N. It seems not to be described in any of
the books on navigation, but it is so simple and
effective that I think you will be interested if I
explain it to you. Take a long slip of card, or
of stiff paper, and mark along one edge of it
points at successive distances from one another,
equal, according to the scale of your chart, to
the actual distance estimated as having been run
by the ship in the intervals between successive
soundings. If the ship has run a straight course,
the edge of the card must oe straight, but if
there has been any change of direction in the
course, the card must be cut with a corresponding
deviation from one straight direction. Beside
each of the points thus marked on the edge,
write on the card the depth and character of
bottom found by the lead. Then place the card
VOL. III. I
ii4 POPULAR LECTURES AND ADDRESSES.
on the chart, and slip it about till you find an
agreement between the soundings marked on the
chart and the series marked on your card. The
slight ups and downs of the bottom, even if they
be no more than to produce differences of five or
six fathoms in depths of, say, from five-and-thirty
to fifty fathoms, interpreted with aid from the
character of the bottom brought up, give, when
this method is practised with sufficient assiduity,
an admirably satisfactory certainty as to the
course over which the ship has passed. Sir James
Anderson tells me that he has run from the
Banks of Newfoundland for two days through
a thick fog at twelve knots, never reducing speed
for soundings, but sounding every hour by the
deep sea lead and Massey fly, has brought up
his last sounding black mud opposite to the mouth
of Halifax Harbour, and has gone in without
ever once having got a sight of sun or stars all
the way from England, or of headland before
turning to go into harbour.
[Addition of August 4th, 1887. — The taking
of soundings with the ordinary deep sea rope
NAVIGATION. 115
when the ship is going at a speed of twelve
knots, involves so much labour and requires so
many men to haul in the rope that it would not
be practicable to take casts more frequently than
once ever>' hour. The method of navigation with
the lead, described in the preceding paragraph, was
only used in very exceptional circumstances. But
with the wire sounding machine (already referred
to> § 37 above : see on this subject, articles " On
Deep-Sea Sounding," &c, in present volume),
this laborious operation is no longer necessary
The wire offers so very little resistance when
going through the water that two men can easily
take a cast in any depth up to 100 fathoms with
the ship going at any speed up to sixteen knots.
The whole operation does not take more than
from two to six minutes, according to the depth,
so that a sounding can be regularly taken every
ten minutes.]
In moderate weather, with her engines in work-
ing order, and coal enough on board to keep up
steam, no steamer making land from the ocean,
in a well explored sea, need ever, however thick
I 2
n6 POPULAR LECTURES AND ADDRESSES.
the fog, be lost by running on the rocks. Nothing
but neglect of the oldest of sailors' maxims, " lead
log, and look-out," can possibly ever, in such
circumstances, lead to such a disaster.
62. But there is a danger affecting navigation
in all weathers, though with greatest intensity
in fogs, which no degree of human skill and
conscientiousness can reduce to absolute zero,
and ttfat is collision.
The " Regulations for Preventing Collisions at
Sea," l which I hold in my hand, embody as in-
ternational law everything that human wisdom
has been able to devise up to the present time
for diminishing the chances of collision. A vast
majority of the collisions which have taken place,
have been produced by breach of these rules by one
ship or the other, or both.
REGULATIONS FOR PREVENTING COLLISION
AT SEA. — Here are some of them: — "Art. 10.
Whenever there is fog, whether by day or by
1 Issued in pursuance of the Merchant Shipping Act Amend-
ment Act, 1862, and of an Order in Council, dated Qth January
1863, and adopted by twenty-nine maritime nations by various
orders, dating from 1st May 1863 to 3Oth Aug. 1864.
NAVIGATION. 117
night, the fog signals, described below, shall be
carried and used, and shall be sounded at least
every five minutes, viz. : —
" (a) Steam ships under way shall use a steam
whistle placed before the funnel not less than eight
feet from the deck.
" (b) Sailing ships under way shall use a fog-
horn.
"(c) Steam ships and sailing ships when not
under way shall use a bell.
"Art 15. If two ships, one of which is a sail-
ing ship, and the other a steam ship, are proceed-
ing in such directions as to involve risk of collision,
the steam ship shall keep out of the way of the
sailing ship.
"Art. 1 6. Every steam ship when approaching
another ship so as to involve risk of collision shall
slacken her speed, or if necessary stop and reverse ;
and every ship shall, when in a fog, go at a
moderate speed.
"Art. 17. Every vessel overtaking any other
vessel shall keep out of the way of the said last-
mentioned vessel.
ii8 POPULAR LECTURES AND ADDRESSES.
"Art. 1 8. Where by the above rules one of
two ships is to keep out of the way, the other
shall keep her course, subject to the qualifications
contained in the following Article.
" Art. 19. In obeying and construing these
rules, due regard must be had to all dangers of
navigation ; and due regard must also be had to
any special circumstances, which may exist in
any particular case, rendering a departure from
the above rules necessary in order to avoid
immediate danger.
"Art. 20. Nothing in these rules shall ex-
onerate any ship, or the owner, or master, or
crew thereof, from the consequences of any
neglect to keep a proper look-out, or of the
neglect of any precaution which may be required
by the ordinary practice of seamen or by the
special circumstances of the case."
Art. 15 makes the duty of the steamer, in the
case referred to, unmistakable. It is to steer
in such a way that a collision cannot take place,
whatever the sailing ship may do. The steamer
has no right to reckon that the sailing ship will
NAVIGATION. 119
continue exactly on an unaltered course, or that
she will make some seemingly probable alteration
in her course (as in " turning to windward ") ; in
short, the steamer must, if possible^ steer in such
a manner that no action of the sailing vessel
can bring about a collision. So, of Art. 17, with
reference to one vessel overtaking another,
63. Under Arts. 18 and 19, the sailing vessel
of Art. 15, or the overtaken vessel of Art. 16 may
commit a fault. It happens often that the sailing
vessel or the overtaken vessel sees the steamer or
the overtaking vessel coming dangerously near.
It is generally impossible to tell whether this is
done wilfully with the intention of making "a
close shave," or wilfully with the intention of
unlawfully compelling the other to give way, or
unintentionally through total or partial want of
look-out. If the master of the threatened vessel
could tell for certain that there was no look-out
in the other vessel, and that the look-out ivould not
suddenly wake up, then he could ensure safety by
a variation of his own course, which then in virtue
of Art. 19 would not violate Art. 18. But he can
120 POPULAR LECTURES AND ADDRESSES.
have no such knowledge. The other vessel may
suddenly alter her course, whether through the
look-out wakening up, or through the master per-
ceiving he has failed in his attempt to unlawfully
compel the sailing vessel or the overtaken vessel
to get out of his way, or through a too late
resolution to do what he ought to have done
earlier — alter his own course. The master of the
threatened vessel feels he must " do something."
It seems impossible that he can escape if he holds
on his course : he alters his course, but does not
escape collision. He may be blamed under Art. 18,
or justified under Art. 19, but whether he be
blamed or whether he be justified, the other is
certainly culpable for breach of Art. 15 or Art. 17,
as the case may be.
It is not an exceedingly rare incident for two
steamers on the wide ocean, in clear and moderate
weather, to be on such courses that they cannot
in the nature of things, escape collision otherwise
than by the fulfilment of Art. 16. How can a
man walking towards a mirror escape collision
with his own image ? Only by slowing and
NAVIGATION. 121
stopping. Or two men meeting on a broad path,
with plenty of room to pass one another, how often
does it not happen that they can only escape
collision by one or both stopping ?
The rule of the road 1 at sea seems to me good in
almost every particular as it stands in the interna-
tional regulations, some of which I have just now
read to you ; and certainly among all the comments
upon the lav/ relating to them, I have scarcely
heard any proposal for its improvement except
national and international provisions for punish-
ment for breaches of them, even when not leading
to disaster. The most perfect steering rules cannot
but leave a margin of doubt in the limit between
the two cases in which a ship ought to alter its
course and ought not to do so, or again between the
two cases in which a ship ought to alter its course
in one direction, and ought to alter its course in
the contrary direction. This doubt essentially
1 By "rule of the road," I did not mean to include the rules con-
cerning lights to be carried by ships or boats at sea which form part
of the whole set of " Regulations for Preventing Collisions at Sea."
These rules too are generally approved of, but in some important
details various amendments have been urged on very good grounds.
122 POPULAR LECTURES AND ADDRESSES.
involves risk of collision, which can only be
obviated by fulfilment of the first clause of
Art. 1 6. "Every steam ship, when approaching
another ship so as to involve risk of collision,
shall slacken her speed, or, if necessary, stop and
reverse." It is not too much to say that no
collision between two steamers, or between a
steamer and a sailing ship, ever occurred in
daylight, and in clear and moderate weather,
which could not have been avoided by the timely
observance of this rule by at least one of the two
vessels.
64. Art. 10 of the Regulations which I have read
to you leads me to speak of the fog-horn, of which,
through the kindness of Mr. N. Holmes, I am able
to show you some very excellent specimens this
evening. You hear how loud even the smallest
of them is.
The question how far a sound can be heard at
sea is a very difficult one, and involves some
exceedingly subtle principles regarding the pro-
perties of matter and problems of abstract
dynamics. In a paper by Professor Henry in
NAVIGATION. 123
the 1874 Report of the United States Lighthouse
Board, in official papers printed by the House
of Commons in 1874 and 1875, and in the recent
edition of Tyndall's Lectures on Sound, very
interesting and important results of observations
are described, showing that in certain states of
the atmosphere (which seem to depend on a
streaky distribution of density, due to the com-
mingling of warmer and colder air, or as suggested
by Professor Osborne Reynolds, on an upward
curvature of the lines of propagation of sound
due to colder air above than below, or on both
causes combined) sound ceases to be heard at
extraordinarily small distances. One thing
brought out by these investigations is, that a
fog, however dense, is by no means unfavourable
to the transmission of sound, and that it is often
in clear bright days that sound travels worst.
65. In respect to navigation, it is satisfactory to
know that in the densest fog, with moderate weather
(and dense fogs generally occur only in moderate
weather), a sailing ship or steamer, sufficiently and
judiciously using a fog-horn, such as the most
124 POPULAR LECTURES AND ADDRESSES.
powerful of those you have now seen and heard,
or a good steam whistle, can, if not going at a
speed of more than four or five knots, give ample
warning of her approach, and sufficient indication
of her position, to allow any other vessel to give
similar information in return, in good time for the
two, if both acting judiciously, to surely avoid
collision by daylight. It is almost a pleasure to
be in the British or Irish Channel by daylight in
a dense fog, and to perceive so vividly through
your ears that you imagine you see a steamer
sounding her steam whistle and crossing your bow
at a safe distance, or a sailing vessel coming down
free on your starboard quarter, when you are
creeping to windward on the starboard tack. The
pleasure, such as it is, is no doubt greatly marred
by the thought that there may be near you some
lubber, or as I should prefer to say, felon, whether
under steam or canvas, sounding neither steam
whistle nor fog-horn.
I am informed by Mr. Thomas Gray, of the
Board of Trade, that probably soon a great im-
provement is to be made in the system of fog
NAVIGATION. 125
signals, by providing that every vessel shall not
merely sound her steam whistle or fog-horn, but
shall do so according to a carefully arranged code
of signals, so as to give certain definite useful in-
formation as to any change of course she (if a
steamer) may be making or be on the point of
making, and (if a sailing ship) so as to show the
tack on which she is sailing.
66. This brings me, almost in conclusion, to
speak of the communication of information, or
orders from ship to ship, by signals. The methods
chiefly used are : —
(1) Signalling by flags. This, when worked by
very skilful signalmen, as in the Royal Navy, is the
most effective method at present in use for signal-
ling by day from ship to ship in clear weather.
(2) For signalling in clear weather by night,
Captain Colomb's method by short and long flashes
has been successfully used in the British Navy for,
I believe, nearly twenty years. It has also been
largely used on land by our army, as in the
Abyssinian war. It is curious to find in military
operations of the nineteenth century a return to a
126 POPULAR LECTURES AND ADDRESSES.
kind of telegraph due, it seems, originally to
Aeneas, a Greek writer on tactics, and improved
by Polybius.1 The essential characteristic of
Captain Colomb's method, on which its great
success has depended, consists in the adoption of
the Morse system of telegraphing by rapid suc-
cession of shorts and longs, " dots " and " dashes "
as they are called ; and, I believe, its success would
have been still greater, certainly its practice would
have been by the present time much more familiar
to every officer and man in the service than it is
now, had not only the general principle of the Morse
system but the actual Morse alphabet for letters
and numerals been adopted by Captain Colomb.
A modification of Captain Colomb's system, which
many practical trials has convinced me is a great
improvement, consists in the substitution of short
and long eclipses for short and long flashes, except
when his magnesium lamp is to be used, as it is
when, whether from the greatness of the distance
to which the signals are to be sent, or from
1 Polybius, X. 44. Or see Rollin's Ancient History, Book
XVIII., Sec. 6.
NAVIGATION. 127
the state of the atmosphere, the light of a power-
ful oil lamp is insufficient. In the system of short
and long eclipses, the signal lamp is allowed
to show its light uninterruptedly until the signal
commences. Then groups of long and short
eclipses — the short eclipses of about half a second's
duration, the long eclipses three half seconds, the
interval or intervals of brightness between the
eclipses of a group half a second ; such groups, I
say, of long and short eclipses are produced by a
movable screen, worked by the sender of the
message, and read off as letters, numerals, or code
signals by the receiver or receivers. Experience
shows that a person, familiar with the flash method,
can, without further practice, read off the eclipses
with equal ease, and vice versa ; and, when it is ad-
visable to use the magnesium lamp, both sender and
receivers will be equally quick and sure in their use
of it if they ordinarily use the eclipse method instead
of, as now in the navy, the method of long and short
flashes. Whenever the light of a lamp suffices,
the eclipse method is decidedly surer, particularly
at quick speeds of working, than the flash method,
128 POPULAR LECTURES AND ADDRESSES.
and it has besides the great advantage of showing
the receivers exactly where to look for the signals
when they come, by keeping the signal lamp
always in view in the intervals between signals,
instead of keeping it eclipsed in the intervals as in
Colomb's method.
(3) Colomb's method of shorts and longs has
also been practised, with great success, in fogs by
day and by night, with long and short blasts of
the steam whistle or fog-horn, instead of long
and short flashes of light.
67. But here again a very great improvement is
to be made. Use instead of the distinction between
short and long the distinction between sounds of
two different pitches, the higher for the " dot," the
lower for the "dash." Whether in the steam
whistle or the fog-horn a very sharp limitation
of the duration of the signal is scarcely attain-
able. There is, in fact, an indecision in the
beginning and end of the sound, which renders
quick and sure Morse signalling by longs and
shorts impracticable, and entails a painful slow-
ness, and a want of perfect sureness, especially
NAVIGATION. 129
when the sound is barely audible. Two fog-horns
or two steam whistles, tuned to two different notes,
or when the distance is not too great, two notes
of a bugle or cornet may be used to telegraph
words and sentences with admirable smartness and
sureness. Five words a minute are easily attain-
able. Let any reader take the trouble to commit
to memory the annexed Morse alphabet. He will
know it all by heart in a day, and then writh a little
practice, he wrill soon be able to speak by two
notes of a pianoforte, or -two notes of his voice
or by whistling two notes with his lips, at the rate
of eight or ten wrords per minute. This method
has the great advantage that, if the sounds can be
heard at all, the distinction between the higher
and the lower, or as we may say for brevity,
" acute " and " grave," is unmistakable : whereas
the distinction between long and short blasts is
lost, or becomes uncertain, long before the sound is
inaudible.
VOL. III. K -
130 POPULAR LECTURES AND ADDRESSES.
GENERALIZED MORSE ALPHABET.
I. Short and long electric marks, or short and
long eclipses of a lamp, or short and long flashes
of light, or short and long blasts of sound.
II. Movements of one or other of two objects
(as left and right hand).
Movements to left and right,
Or movements upwards and downwards.
III. Two sounds of different musical notes —
acute and grave.
Short. f Long.
Left. J Right.
Upward movement. j Downward movement.
Acute sound. ( Grave.
Understand ABCDEFGH
IJKLMNOPQ RS
T U V W X Y Z Understand.
7890 Understand.
NAVIGATION. 131
68. An old instrument called the siren, in-
vented by Cagniard de la Tour, for the purpose
of illustrating the science of sound, has been
recently taken up by the United States Light-
house Board with great success, as a sub-
stitute for the fog horns previously used at
lighthouses in foggy weather. The siren, in
its original form, is an instrument in which a
hole or holes in a flat side or top of an air
vessel, are alternately obstructed and opened by
the revolution of a disc of metal, perforated
with a number of equidistant holes in a circle
round its axis. Air blown constantly into the
vessel escapes alternately in abundance, and
but slightly, as the holes are alternately opened
and obstructed by the revolution of the disc ; and
thus a musical note is produced, with a pitch
precisely determined by the number of openings
and closings per second of time. Instead of a
little instrument, suitable for a lecture-room table,
both turned and having its blast supplied by a
small acoustic wind-chest and bellows, the
Americans have made a powerful instrument with
K 2
132 POPULAR LECTURES AND ADDRESSES.
large disc, driven at a uniform l rate by wheelwork,
and the blast supplied from a steam boiler, or from
a large vessel of compressed air, sustained by
powerful condensing pumps. I am informed that
recently an improvement has been made in this
country by substituting a rotating cylinder for the
rotating disc.
69. Professor's Henry's experiment made for
the United States Lighthouse Board, of which
he is chairman, showed that the siren was much
superior to the powerful fog-horns and steam
1 It seems that improvement in respect to this quality is needed
in the instruments hitherto made. In some of the reports of the
experiments, I see it stated that the pitch of the sound gradually
fell when the siren was kept sounding continuously for some time ;
because the steam pressure in the boiler diminished, and so the
rotating disc ran slower. The rotating disc ought to be kept running
with almost chronometric uniformity. There is not the slightest
difficulty in doing this by having it driven either by a constant
weight, or by aid of a proper slip gear adapted to drive with con-
stant force. With this and a proper centrifugal governor, there is
no difficulty whatever in securing so nearly perfect uniformity that
the rate shall never alter by as much as I per cent. This would
produce not more than 1/4 of a semitone of difference in the pitch of
the note. The power required to turn the disc is so very moderate
that there is absolutely no difficulty in realising the improvement I
have now suggested. Possibly the best plan will be to drive it by
manual power. One man amply suffices for the purpose.
NAVIGATION. 133
whistles which had previously been in use at
their lighthouses ; and in a series of investigations
on the transmission of sound, under the auspices
of the English Trinity House, with a siren lent
for the purpose by the United States Lighthouse
Board, Professor Tyndall arrived at the same
conclusion, and found that often, and especially
in the more difficult circumstances, the siren
surpasses a signal gun in audibility at a distance.
There being, at all events, no doubt of its constant
superiority over fog-horns and steam whistles, it
seems that it ought immediately to be substituted
for them in our navy as means for communicating
intelligence, and giving orders from ship to ship
in a fog. Introduced for use in fogs, it will pro-
bably soon, in clear weather, supplant flags by
day and lamps by night, for much of the ordinary
telegraphic work between ships of war when at
sea. One thing stands out most clear from
the evidence produced at the recent court-martial
regarding the loss of the Vanguard, and that is
that great improvement in this respect is urgently
needed. Short and long blasts of the siren
134 POPULAR LECTURES AND ADDRESSES.
might be advantageously substituted for short
and long blasts of the steam whistle, but much
more advantageously short blasts of two sirens on
the same shaft, or on two shafts geared together,
sounding different notes, acute note for the short,
grave note for the long.
70. HOLMES' RESCUE LIGHT. — I shall conclude
by bringing before you (Fig. 16) an invention of a
most beneficent character. It is a light for life-
buoys, invented by Mr. Nathaniel Holmes, and
FIG. 16.
depending on the well-known property of phos-
phuretted hydrogen, to take fire when it bubbles
up from water. It is, I believe, contemplated by
NAVIGATION. 135
the Board of Trade to make a rule requiring that
every British ship going to sea shall be provided
with this adjunct to the life buoys, a most proper
requirement as seems to me. Even in the best
found and best disciplined ships the accident
does sometimes happen of a man overboard.
The life-buoy is thrown, but in the dark the man
may not see it, or if he does see it and reach
it, and keep himself afloat by it, the people in
the ship, as she runs on, lose sight of him before
she can be brought to and a boat lowered. Till
now, I believe, it may be said that not once in
a hundred times is a man rescued who falls over-
board in a dark night from a large ship sailing
or steaming rapidly through the water.
71. But if a life-buoy is thrown, with one of
these rescue lights attached to it, as I now throw
it, you see what happens. You see this metal
vessel full of phosphuret of calcium.1 It is lashed
1 I am indebted to Mr. Nathaniel Holmes for the following de-
scription of the construction of his patent Rescue Light : — " I take
" lumps of common chalk broken in pieces about the size of lump-
" sugar, these are placed in a crucible with certain proportions of
" prepared phosphorus, and the whole is placed in a furnace, and
136 POPULAR LECTURES AND ADDRESSES.
strongly to the life-buoy so that neither can be
thrown into the water without the other. I must
not forget to pluck away these soft solder stoppers
from the conical end below, and the top of the
projecting tube above. Having done so, I now
throw both the life-buoy and rescue light over-
board. All this is done within ten seconds of
time, after I hear the alarm " a man overboard."
You see now the moment the metal vessel plunges
into the water, it begins to smoke vehemently, and
almost instantly flames rise (Fig. 17). The man in
the water sees the light, swims towards it, catches
the life-bouy, and supports himself securely by
it. No danger now of him sinking or being
' * heated to a certain degree over cherry red. The phosphorus, by
' ' the heat, is converted into vapour, and the red-hot chalk takes up
" this vapour to saturation." "When cooled, the contents, phos-
" phuret of calcium and phosphate of calcium " (the former the
active ingredient), "are placed in the tin cases and soldered down.
"Upon using the signal, the water is admitted, and " acting on the
phosphuret of calcium, produces " phosphuretted hydrogen, which
" issuing out of the upper orifice, catches fire spontaneously, and
bursts into flame."
1 " The process of manufacture shows that the rescue signals
" are free from danger, are not affected by either heat, friction, or
" percussion, water alone can ignite them."
NA VI G A TION.
137
drowned by the water washing over him, or by
his getting his head under water. It is solely a
FIG. 17.
question of the water's temperature, and of his
own vigour, how long he may live. Already the
ship, dashing along at fourteen knots, is a quarter
138 POPULAR LECTURES AND ADDRESSES.
of a mile off, and before a boat can be manned
and cast off from her, she must be at least half
a mile from the life-buoy with its living burden.
But look at the light — the more the water washes
over it, the more brightly it burns. It will burn
for three-quarters of an hour, and can be seen
at a distance of five or six miles. It disappears
for a few seconds perhaps behind a wave, or
for the want of continuity which you see in the
flame, and then you see it blaze up again with
increased brilliance, and so on for three-quarters of
an hour. It goes on disappearing and blazing
up again visibly out of the horizon when at least
five or six miles off, as I have myself seen in the
river Para. The boat, now manned and rowing
away from the ship, has no difficulty in knowing
where to steer for. Guided by the light, they
will pull away through a heavy sea, and in
a quarter of an hour they have their comrade
in the boat with them. By this time the ship,
also guided by the light, has steamed or sailed
close up to them, and in a few minutes they
are all on board.
THE TIDES.
[Evening Lecture to the British Association at the South-
ampton Meeting, Friday ', August 25, 1882.]
THE subject on which I have to speak this evening
is the Tides, and at the outset I feel in a curiously
difficult position. If I were asked to tell what
I mean by the Tides I should feel it exceedingly
difficult to answer the question. The tides have
something to do with motion of the sea. Rise
and fall of the sea is sometimes called a tide ; but
I see, in the Admiralty Chart of the Firth of
Clyde, the whole space between Ailsa Craig and
the Ayrshire coast marked "very little tide here."
Now, we find there a good ten feet rise and fall,
and yet we are authoritatively told there is very
little tide. The truth is, the word " tide " as used
140 POPULAR LECTURES AND ADDRESSES.
by sailors at sea means horizontal motion of the
water ; but when used by landsmen or sailors in
port, it means vertical motion of the water. I hope
my friend Sir Frederick Evans will allow me to
say that we must take the designation in the chart,
to which I have referred, as limited to the instruc-
tion of sailors navigating that part of the sea, and
to say that there is a very considerable landsman's
tide there — a rise and fall of the surface of the
water relatively to the land — though there is
exceedingly little current.
One of the most interesting points of tidal theory
is the determination of the currents by which the
rise and fall is produced, and so far the sailor's idea
of what is most noteworthy as to tidal motion is
correct : because before there can be a rise and fall
of the water anywhere it must come from some
other place, and the water cannot pass from place
to place without moving horizontally, or nearly
horizontally, through a great distance. Thus the
primary phenomenon of the tides is after all the
tidal current ; and it is the tidal currents that are
referred to on charts where we have arrow-heads
THE TIDES. 141
marked with the statement that we have " very
little tide here," or that we have " strong tides "
there.
One instance of great interest is near Portland.
\Ye hear of the " race of Portland " which is pro-
duced by an exceedingly strong tidal current ; but
in Portland harbour there is exceedingly little rise
and fall, and that little is much confused, as if the
water did not know which way it was going to
move. Sometimes the water rises, sinks, seems to
think a little while about it, and then rises again.
The rise of the tide at Portland is interesting to
the inhabitants of Southampton in this, that
whereas here, at Southampton, there is a double
high water, there, at Portland, there is a double
low water. The double high water seems to
extend across the Channel. At Havre, and on
the bar off the entrance to Havre, there is a
double high water very useful to navigation ; but
Southampton I believe is pre-eminent above all
the ports in the British Islands with respect to
this convenience. There is here (at Southampton)
a good three hours of high water ; — a little dip
H2 POPULAR LECTURES AND ADDRESSES.
after the first high water, and then the water
rises again a very little more for an hour and a
half or two hours, before it begins to fall to low
water.
I shall endeavour to refer to this subject again.
It is not merely the Isle of Wight that gives rise
to the phenomenon. The influence extends to
the east as far as Christchurch, and is reversed at
Portland, and we have the double or the prolonged
high water also over at Havre ; therefore, it is
clearly not, as it has been supposed to be, due to
the Isle of Wight.
But now I must come back to the question
What are the " Tides " ? Is a " tidal wave " a
tide ? What is called in the newspapers a " tidal
wave " rises sometimes in a few minutes, does great
destruction, and goes down again, somewhat less
rapidly. There are frequent instances in all parts
of the world of the occurrence of that phenomenon.
Such motions of the water, however, are not tides ;
they are usually caused by earthquakes. But \ve
are apt to call any not very short-time rise and
fall of the water a tide, as when standing on the
THE TIDES. 143
coast of a slanting shore where there are long
ocean waves, we see the gradual sinkings and
risings produced by them, and say that it is a
wave we see, not a tide, till one comes which is ex-
ceptionally slow, and then we say " that is liker a
tide than a wave." The fact is, there is something
perfectly continuous in the species of motion called
wave, from the smallest ripple in a musical glass,
whose period may be a thousandth of a second
to a " lop of water " in the Solent, whose period is
one or two seconds, and thence on to the great
ocean wave with a period of from fifteen to twenty
seconds, where ends the phenomenon which we
commonly call waves (Fig. 18, p. 144), and not tides.
But any rise and fall which is manifestly of longer
period, or slower in its rise from lowest to highest,
than a wind wave, wre are apt to call a tide ; and
some of the phenomena that are analysed for, and
worked out in this very tidal analysis that I am
going to explain, are in point of fact more
properly wind waves than true tides.
Leaving these complicated questions, however,
I will make a short cut, and assuming the cause
144 POPULAR LECTURES AND ADDRESSES.
without proving it, define the thing by the cause.
I shall therefore define tides thus : Tides are
motions of water on the earth, due to the attrac-
tions of the sun and of the moon. I cannot say
tides are motions due to the actions of the sun and
of the moon ; for so I would include, under the
designation of tide, every ripple that stirs a puddle
or a millpond, and waves in the Solent or in the
FIG. 1 8. — Wave forms.
English Channel, and the long Atlantic wind
waves, and the great swell of the ocean from one
hemisphere to the other and back again (under
the name which I find in the harmonic reduction
of tidal observations), proved to take place once a
year, and which I can only explain as the result
of the sun's heat.
But while the action of the sun's heat by means
THE TIDES. 145
of the wind produces ripples and waves of every
size, it also produces a heaping-up of the water
as illustrated by this diagram (Fig. 19). Suppose
we have wind blowing across one side of a sheet
of water, the wind ruffles the surface, the waves
break if the wind is strong, and the result is a
strong tangential force exerted by the wind on
the surface water. If a ship is sailing over the
FIG. 19. — Showing the heaping-up of water produced by wind.
water there is strong tangential force ; thus the
water is found going fast to leeward for a long
distance astern of a great ship sailing with a side
wind : and, just as the sails of a ship standing
high above the sea give a large area for the wind
to act upon, every wave standing up gives a
surface, and we have horizontal tangential force
over the whole surface of a troubled sea. The
VOL. ill. L
146 POPULAR LECTURES AND ADDRESSES.
result is that water is dragged along the surface
from one side of the ocean to the other — from
one side of the Atlantic to the other — and is
heaped up on the side towards which the wind is
blowing. To understand the dynamics of this
phenomenon, think of a long straight canal with
the wind blowing lengthwise along it. In virtue
of the tangential force exerted on the surface of
the water by the wind, and which increases with
the speed of the wind, the water will become
heaped up at one end of the canal, as shown in
the diagram (Fig. 19), while the surface water
throughout the whole length will be observed
moving in the direction of the wind — say in the
direction of the two arrows near to the surface of
the water above and below it. But to re-establish
the disturbed hydrostatic equilibrium, the water
so heaped up will tend to flow back to the end
from which it has been displaced, and as the wind
prevents this taking place by a surface current,
there will be set up a return current along the
bottom of the canal, in a direction opposite to
that of the wind, as indicated by the lowermost
THE TIDES. 147
arrow in the diagram (Fig. 19). The return current
in the ocean, however, is not always an under
current, such as I have indicated in the diagram,
but may sometimes be a lateral current. Thus a
gale of wind blowing over ten degrees of latitude
will cause a drag of water at the surface, but the
return current may be not an under current but a
current on one side or the other of the area affected
by the wind. Suppose, for instance, in the
Mediterranean there is a strong east wind blowing
along the African coast, the result will be a current
from east to wesf along that coast, and a return
current along the northern coasts of the
Mediterranean.
The rise and fall of the water due to these
motions are almost inextricably mixed up with
the true tidal rise and fall.
There is another rise and fall, also connected
with the heating effect of the sun, that I do not
call a true tide, and that is a rise and fall due to
change of atmospheric pressure. When the
barometer is high over a large area of ocean, then,
there and in neighbouring places, the tendency to
L 2
148 POPULAR LECTURES AND ADDRESSES.
hydrostatic equilibrium causes the surface of the
water to be lower, where it is pushed down by the
greater weight of air, and to be higher where there
is less weight over it. It does not follow that in
every case it is lower, because there may not be
time to produce the effect, but there is this tendency.
It is very well known that two or three days of low
barometer make higher tides on our coast. In
Scotland and England and Ireland, two or three
days of low barometer generally produce all round
the shore higher water than when the barometer is
high ; and this effect is chiefly noticed at the time
of tidal high water, because people take less
notice of low water — as at Portland where they
think nothing of the double low water. Hence
we hear continually of very high tides — very
high water noticed at the time of high tides
—when the barometer is low. We have not
always, however, in this effect of barometric
pressure really great tidal rise and fall. On the
contrary we have the curious phenomenon that
sometimes when the barometer is very low, and
there are gales in the neighbourhood, there is very
THE TIDES. 149
little rise and fa!!, as the water is kept heaped up
and does not sink by anything like its usual amount
from the extra high level that it has at high water.
But I fear I have got into questions which are
leading me away from my subject, and as I
cannot get through them I must just turn back.
Now think of the definition which I gave of the
"tides," and think of the sun alone. The action of
the sun cannot be defined as the cause of the solar
tides. Solar tides are due to action of the sun, but
all risings and fallings of the water due to the action
of the sun are net tides. We want the quantifica-
tion of the predicate here very badly. We have a
true tide depending on the sun, the mean solar
diurnal tide, having for its period twenty-four solar
hours, which is inextricably mixed up with those
meteorological tides that I have just been speaking
of— tides depending on the sun's heat, and on the
variation of the direction of the wind, and on the
variation of barometric pressure according to the
time of day. The consequence is that in tidal
analysis, when we come to the solar tides, we can-
not know how much of the analysed result is due
ISO POPULAR LECTURES AND ADDRESSES.
to attraction, and how much to heating effect
directly or indirectly, whether on water, or on air,
or on water as affected by air. As to the lunar
tides we are quite sure of them ; — they are gravita-
tional, and nothing but gravitational ; but I hope
to speak later of the supposed relation of the moon
to the weather, and the relation that has to the
tides.
I have defined the tides as motions of water on
the earth due to the attractions of the sun and of
the moon. How are we to find out whether an
observed motion of the water is a tide or is not a
tide as thus defined ? Only by the combination of
theory and observation : if these afford sufficient
reason for believing that the motion is due to
attraction of the sun or of the moon, or of both,
then we must call it a tide.
It is curious to look back on the knowledge of
the tides possessed in ancient times, and to find as
early as two hundred years before the Christian era
a very clear account given of the tides at Cadiz.
But the Romans generally, knowing only the
Mediterranean, had not much clear knowledge of
THE TIDES. 151
the tides. At a much later time than that, we hear
from the ancient Greek writers and explorers —
Posidonius, Strabo, and others — that in certain
remote parts of the world, in Thule, in Britain, in
Gaul, and on the distant coasts of Spain, there
were motions of the sea — a rising and falling of the
water — which depended in some way on the moon.
Julius Caesar came to know something about it ; but
it is certain the Roman Admiralty did not supply
Julius Caesar's captains with tide tables when he
sailed from the Mediterranean with his expedition-
ary force, destined to put down anarchy in Britain.
He says, referring to the fourth day after his first
landing in Britain — " That night it happened to be
full moon, which time is accustomed to give the
greatest risings of water in the ocean, though our
people did not know it." It has been supposed
however that some of his people did know it — some
of his quartermasters had been in England before
and did know — but that the discipline in the
Roman navy was so good that they had no right
to obtrude their knowledge ; and so, although a
storm was raging at the time, he was not told that
152 POPULAR LECTURES AND ADDRESSES.
the water would rise in the night higher than usual,
and nothing was done to make his transports
secure higher up on the shore while he was
fighting the Britons. After the accident Csesar
was no doubt told — " Oh, we knew that before,
but it might have been ill taken if we had
said so."
Strabo says — "Soon after moonrise the sea
begins to swell up and flow over the earth till the
moon reaches mid heaven. As she descends thence
the sea recedes till about moonset, when the water
is lowest. It then rises again as the moon, below
the horizon, sinks to mid heaven under the earth."
It is interesting here to find the tides described
simply with reference to the moon. But there is
something more in this ancient account of Strabo ;
he says, quoting Posidonius — " This is the daily
circuit of the sea. Moreover, there is a regular
monthly course, according to which the greatest
rise and fall takes place about new moon, then
diminishing rise and fall till half moon, and again
increasing till full moon." And lastly he refers to
a hearsay report of the Gaditani (Cadizians) regard-
THE TIDES. 153
ing an annual period in the amount of the daily
rise and fall of the sea, which seems to be not
altogether right, and is confessedly in part con-
jectural. He gave no theory, of course, and he
avoided the complication of referring to the sun.
But the mere mention of an annual period is
interesting in the history of tidal theory, as sug-
gesting that the rises and falls are due not to the
moon alone but to the sun also. The account
given by Posidonius is fairly descriptive of what
occurs at the present day at Cadiz. Exactly the
opposite would be true at many places ; but at
Cadiz the time of high water at new and full moon
is nearly twelve o'clock. Still, I say we have only
definition to keep us clear of ambiguities and
errors ; and yet, to say that those motions of the
sea which we call tides depend on the moon, was
considered, even by Galileo, to be a lamentable
piece of mysticism which he read with regret
in the writings of so renowned an author as
Kepler.
It is indeed impossible to avoid theorising. The
first who gave a theory was Newton ; and I shall
154 POPULAR LECTURES AND ADDRESSES.
now attempt to speak of it sufficiently to allow us
to have it as a foundation for estimating the forces
with which we are concerned, in dealing with some
of the very perplexing questions which tidal
phenomena present.
We are to imagine the moon as attracting the
earth, subject to the forces that the different bodies
exert upon each other. We are not to take Hegel's
theory — that the Earth and the Planets do not
move like stones, but move along like blessed gods,
each an independent being. If Hegel had any
grain of philosophy in his ideas of the solar system,
Newton is all wrong in his theory of the tides.
Newton considered the attraction of the sun upon
the earth and the moon, of the earth upon the
moon, and the mutual attractions of different parts
of the earth ; and left it for Cavendish to complete
the discovery of gravitation, by exhibiting the
mutual attraction of two pieces of lead in his
balance. Tidal theory is one strong link in the
grand philosophic chain of the Newtonian theory
of gravitation. In explaining the tide-generating
force we are brought face to face with some of the
THE TIDES. 155
subtleties, and with some of the mere elements, of
physical astronomy. I will not enter into details,
as it would be useless for those who already
understand the tidal theory, and unintelligible to
those who do not.
I may just say that the moon attracts a piece of
matter, for example a pound-weight, here on the
earth, with a force which we compare with the
earth's attraction thus. Her mass is 1/80 of the
earth's, and she is sixty times as far away from the
earth's centre as we are here. Newton's theory
of gravitation shows, that when you get outside
the mass of the earth the resultant attraction of
the earth on the pound weight, is the same as if
the whole mass of the earth were collected at
the centre, and that it varies inversely as the
square of the distance from the centre. The same
law is inferred regarding the moon's attraction
from the general theory. The moon's attraction
i
on this pound weight is therefore • £ 8° , or
60x60
288000 °^ ^e atti"action °f tne earth on the
same mass. But that is not the tide-generating
156 POPULAR LECTURES AND ADDRESSES.
force. The moon attracts any mass at the nearest
parts of the earth's surface with greater force than
an equal mass near the centre ; and attracts a mass
belonging to the remoter parts with less force.
Imagine a point where the moon is overhead, and
imagine another point on the surface of the earth
at the other end of a diameter passing through the
first point and the centre of the earth (illustrated
by B and A of Fig. 20, p. 161). The moon attracts
the nearest point (B) with a force which is greater
than that with which it attracts the farther point (A)
in the ratio of the square of 59 to the square of 61.
Hence the moon's attraction on equal masses at the
nearest and farthest points differs by one fifteenth
part of her attraction on an equal mass at the
earth's centre, or about a 4,32O,oooth, or, roughly, a
four-millionth, of the earth's attraction on an equal
mass at its surface. Consequently the water tends
to protrude towards the moon and from the moon.
If the moon and earth were held together by a rigid
bar the water would be drawn to the side nearest
to the moon — drawn to a prodigious height of
several hundred feet. But the earth and moon are
THE TIDES. 157
not so connected. We may imagine the earth as
falling towards the moon, and the moon as falling
towards the earth, but never coming nearer ; the
bodies, in reality, revolving round their common
centre of gravity. A point nearest to the moon is as
it were dragged away from the earth, and thus the
result is that apparent gravity differs by about one
four-millionth at the points nearest to and farthest
from the moon. At the intermediate points of
the circle C, D (Fig. 20, p. 161), there is a somewhat
complicated action according to which gravitation
is increased by about one I /-millionth, and its
direction altered by about one I /-millionth, so that
a pendulum 17,000 feet long, a plummet rather
longer than from the top of Mont Blanc to sea level,
would, if showing truly the lunar disturbing force,
be deflected through a space of one thousandth of
a foot. It seems quite hopeless by a plummet to
exhibit the lunar disturbance of gravity. A spring
balance to show the alteration of magnitude, and
a plummet to show the change of direction are
conceivable ; but we can scarcely believe that
either can ever be produced, with sufficient deli-
158 POPULAR LECTURES AND ADDRESSES.
cacy and consistency and accuracy to indicate
these results.
A most earnest and persevering effort has been
made by Mr. George Darwin and Mr. Horace
Darwin to detect variations in gravity due to lunar
disturbance, and they have made apparatus which
notwithstanding the prodigious smallness of the
effect to be observed, is in point of delicacy and
consistency capable of showing it ; but when they
had got their delicate pendulum — their delicate
plummet about the length of an ordinary seconds'
pendulum— and their delicate multiplying gear to
multiply the motion of its lower end by about a
million times, and to show the result on a scale
by the reflection of a ray of light, they found
the little image incessantly moving backward and
forward on the scale with no consistency or regu-
larity ; and they have come to the conclusion
that there are continual local variations of ap-
parent gravity taking place for which we know
no rule, and which are considerably greater than
the lunar disturbance for which they were seeking.
That which they found— continual motions of the
THE TIDES. 159
surface of the earth, and which was not the
primary object of their investigation — is in some
respects more interesting than what they sought
and did not find. The delicate investigation thus
opened up promises a rich harvest of knowledge.
These disturbances are connected with earthquakes
such as have been observed in a very scientific
and accurate manner by Milne, Thomas Gray,
and Ewing in Japan, and in Italy by many
accurate observers. All such observations agree
in showing continual tremor and palpitation of
the earth in every pnrt.
One other phenomenon that I may just refer
to now as coming out from tide-guage observa-
tions, is a phenomenon called seiches by Forel,
and described by him as having been observed
in the lakes of Geneva and Constance. He
attributes them to differences of barometric
pressure at the ends of the lake, and it is pro-
bable that part of the phenomenon is due to
such differences. I think it is certain, however,
that the whole is not due to such differences.
The Portland tide curve and those of many other
160 POPULAR LECTURES AND ADDRESSES.
places, notably the tide curve for Malta, taken
about ten years ago by Sir Cooper Key, and
observations on the Atlantic coasts and in many
other parts of the world, show something of
these phenomena ; a ripple or roughness on the
curve traced by the tide gauge, which, when
carefully looked to, indicates a variation not
regular but in some such period as twenty or
twenty-five minutes. It has been suggested that
they are caused by electric action ! Whenever
the cause of a thing is not known it is immediately
put down as electrical !
. I would like to explain to you the equilibrium
theory, and the kinetic theory, of the tides, but
I am afraid I must merely say there are such
things ; and that Laplace in his great work, his
Mecanique Celeste, first showed that the equi-
librium theory was utterly insufficient to account
for the phenomena, and gave the true principles
of the dynamic action on which they depend.
The resultant effect of the tide-generating force
is to cause the water to tend to become protube-
rant towards the moon and the sun and from
THE TIDES.
161
them, when they are in the same straight line,
and to take a regular spheroidal form, in which
the difference between the greatest and the least
semi-diameter is about 2 feet for lunar action alone,
and i foot for the action of the sun alone — that
FIG. 20. — Spring Tides.
FIG. 21. — Spring Tides.
is a tide which amounts to 3 feet when the sun and
moon act together (Figs. 20 and 21), and to I foot
only when they act at cross purposes (Figs. 22
and 23), so as to produce opposite effects. These
diagrams, Figs. 20 to 23, illustrate spring and neap
tides : the dark shading around the globe, E, repre-
VOL. III. M
162 POPULAR LECTURES AND ADDRESSES.
FIG. 22.— Neap Tides.
FIG. 23.— Neap Tides.
THE TIDES. 163
senting a water envelope surrounding- the earth.
There has been much discussion on the origin
of the word neap. It seems to be an Anglo-Saxon
word meaning scanty. Spring seems to be the
same as when we speak of plants springing up.
I well remember at the meeting of the British
Association at Edinburgh a French member who,
meaning spring tides, spoke of the grandes marees
die printemps. Now you laugh at this ; and yet,
though he did not mean it, he was quite right,
for the spring tides in the spring time are greater
on the whole than those at other times, and we
have the greatest spring tides in the spring of
the year. But there the analogy ceases, for we
have also very high spring tides in autumn. Still
the meaning of the two words is the same etymo-
logically. Neap tides are scanty tides, and spring
tides are tides which spring up to remarkably
great heights.
The equilibrium theory of the tides is a way
of putting tidal phenomena. We say the tides
would be so and so if the water took the figure
of equilibrium. Now the water does not cover
M 2
1 64 POPULAR LECTURES AND ADDRESSES.
the whole earth, as we have assumed in the dia-
grams (Figs. 48 to 5 1 ), but the surface of the water
may be imagined as taking the same figure, so
far as there is water, that it would take if there
were water over the whole surface of the earth.
But here a difficult question comes in — namely,
the attraction of the water for parts of itself.
If we consider the water flowing over the whole
earth this attraction must be taken into account.
If we imagine the water of exceedingly small
density so that its attraction on itself is insensible
compared with that of the earth, we have thus
to think of the equilibrium theory. But, on the
other hand, if the water had the same density
as the earth, the result would be that the solid
nucleus would be almost ready to float ; and
now imagine that the water is denser than the
earth, and we put the tides out of consideration
altogether. Think of the earth covered over with
mercury instead of water — a layer of mercury a
foot deep. The solid earth would tend to float,
and would float, and the result would be that
the denser liquid would run to, and cover one
THE TIDES. 165
side up to a certain depth, and the earth would
be as it were floating out of the sea. That ex-
plains one curious result that Laplace seems to
have been much struck with : the stability of
the ocean requires that the density of the water
should be less than that of the solid earth. But
take the sea as having the specific gravity of
water, the mean density of the earth is only
5 "6 times that of water, and this is not enough
to prevent the attraction of water for water from
being sensible. Owing therefore to the attraction
of the water for parts of itself the tidal pheno-
mena are somewhat larger than they would be
without it, but neglecting this, and neglecting
the deformation of the solid earth, we have the
ordinary equilibrium theory.
Why does the water not follow the equilibrium
theory ? Why have we tides of 20 feet or 30
feet or 40 feet in some places, arid only of 2 or
3 feet in others ? Because the water has not
time in the course of 12 hours to take the equi-
librium figure, and because after tending towards
it, the water runs beyond it.
1 66 POPULAR LECTURES AND ADDRESSES.
I ask you to think of the oscillations of water
in a trough. Look at this diagram (Fig. 24), which
will help you to understand how the tidal effect
is prodigiously magnified by a dynamical action
due to the inertia of the water. The tendency
of water in motion to keep its motion prevents
it from taking the figure of equilibrium. [A
FIG. 24.— Oscillations of Water in a Trough.
chart showing the tides of the English Channel
was exhibited, from which it was seen that while
at Dover there were tides of 21 feet, there was
at Portland very little rise and fall.] Imagine a
canal instead of the English Channel, a canal
stopped at the Straits of Dover and at the
THE TIDES. 167
opposite end at Land's End, and imagine some-
how a disturbing force causing the water to be
heaped up at one end. There would be a swing
of water from one end to the other, and if the
period of the disturbing force approximately
agreed with the period of free oscillation, the
effect would be that the rise and fall would go
vastly above and below the range due to equi-
librium action. Hence it is we have the 21 feet
rise and fall at Dover. The very little rise and
fall at Portland is also illustrated in the upper-
most figure of this diagram (Fig. 24). Thus high
water at Dover is low water at Land's End, and
the water seesaws as it were about a line going
across from Portland to Havre (represented by
N in the figure) ; not a line going directly across »
however, for on the other side of the Channel
there is a curious complication.
At the time of high water at Dover there is
hardly any current in the Channel. As soon as
the water begins to fall at Dover the current
begins to flow west through the whole of the
Channel. When it is mid-tide at Dover the tide
168 POPULAR LECTURES AND ADDRESSES.
is flowing fastest in the Channel. This was first
brought to light by Admiral Beechey.
I wish I had time to show the similar theory
as to the tides in the Irish Channel. The water
runs up the English Channel to Dover, and up
the Irish Channel to fill up the basin round the
Isle of Man. Take the northern mouth of the
Irish Channel between the Mull of Cantire and
the north-east coast of Ireland. The water rushes
in through the straits between Cantire and Rathlin
Island, to fill up the Bay of Liverpool and the
great area of water round the Isle of Man. This
tidal wave entering from the north, running south-
ward through the Channel, meets in the Liverpool
basin with the tidal stream coming from the
south entrance, and causes the time of high
water at Liverpool to be within half-an-hour of
the time of no currents in the northern and
southern parts of the Channel.
I would like to read you the late Astronomer-
Royal's appreciation of Laplace's splendid work
on the tides.
Airy says of Laplace : " If now, putting from
THE TIDES. 169
our thoughts the details of the investigation, we
consider its general plan and objects, we must
allow it to be one of the most splendid works of
the greatest mathematician of the past age. To
appreciate this, the reader must consider, first,
the boldness of the writer, who, having a clear
understanding of the gross imperfections in the
methods of his predecessors, had also the cour-
age deliberately to take up the problem on
grounds fundamentally correct (however it might
be limited by suppositions afterwards introduced) ;
secondly, the general difficulty of treating the
motion of fluids ; thirdly, the peculiar difficulty
of treating the motions when the fluids cover an
area which is not plane but convex ; and fourthly,
the sagacity of perceiving that it was necessary
to consider the earth as a revolving body, and
the skill of correctly introducing this considera-
tion. This last point alone, in our opinion, gives
a greater claim for reputation than the boasted
explanation of the long inequality of Jupiter and
Saturn."
Tidal theory must be carried on along with tidal
170 POPULAR LECTURES AND ADDRESSES.
FIG. 25.— Tide Gauge.
observations. Instruments for measuring and re-
cording the height of the water at any time give
THE TIDES. 171
us results of observations.1 Here is such an
instrument — a tide gauge (Fig. 25). The floater
is made of thin sheet copper, and is suspended by
a fine platinum wire. The vertical motion of the
floater, as the water rises and falls, is transmitted,
in a reduced proportion by a single pinion and
wheel, to this frame or marker, which carries a
small marking pencil. The paper on which the
pencil marks the recording curve, is stretched on
this cylinder, which, by means of the clockwork,
is caused to make one revolution every twenty-
four hours. The leaning-tower-of-Pisa arrange-
ment of the paper-cylinder, and the extreme
simplicity of the connection between marker
and floater, constitute the chief novelty. This
tide-gauge is similar to one now in actual use,
recording the rise and fall of the water in the
River Clyde, at the entrance to the Queen's
Dock, Glasgow. A sheet bearing the curves
1 The various instruments and tide-curves referred to in this lecture
are fully described and illustrated in a paper on " The Tide Gauge,
Tidal Harmonic Analyser, and Tide Predicter " read before the In-
stitution of Civil Engineers, on 1st March, 1881, and published in
their Proceedings for that date.
i;2 POPULAR LECTURES AND ADDRESSES.
THE TIDES. 173
(Fig. 26) traced by that machine during a week
is exhibited.
After the observations have been taken, the next
thing is to make use of them. Hitherto this has
been done by laborious arithmetical calculation. I
hold in my hand the Reports of the late Tidal
Committee of the British Association with the
results of the harmonic analysis — about eight years'
work carried on with great labour, and by aid of
successive grants from the British Association.
The Indian Government has continued the har-
monic analysis for the seaports of India. The
Tide Tables for Indian Ports for tJie Year 1882,
issued under the authority of the Indian Govern-
ment, show this analysis as in progress for the
following ports, viz. : Aden, Kurrachee, Okha
Point and Beyt Harbour at the entrance to
the Gulf of Cutch, Bombay, Karwar, Beypore,
Paumben Pass, Madras, Vizagapatam, Diamond
Harbour, Fort Gloster and Kidderpore on the
River Hooghly, Rangoon, Moulmein, and Port
Blair. Mr. Roberts, who was first employed as
calculator by the Committee of the British Asso-
174 POPULAR LECTURES AND ADDRESSES.
elation, has been asked to carry on the work
for the Indian Government, and latterly, in
India, native calculators under Major Baird, have
worked by the methods and forms by which Mr.
Roberts had worked in England for the British
Association.1 The object is to find the values of
the different tidal constituents. We want to
separate out from the whole rise and fall of the
ocean the part due to the sun, the part due to
the moon, the part due to one portion of the
moon's effect, and the part due to another. There
are complications depending on the moon's position
— declinational tides according as the moon is or
is not in the plane of the earth's equator — and
also on that of the sun. Thus we have the diurnal
declinational tides. When the moon is in the north
declination (Fig. 27) we have (in the equilibrium
theory) higher water at lunar noon than at lunar
midnight. That difference in the height of high-
1 Note of September 17, 1887. On the subject of Tidal Har-
monic Analysis see " Manual of Instructions for Tidal Observa-
tion," by Major Baird, published by Messrs. Taylor and Francis,
London, 1886 ; also the Reports of the British Association Com-
mittee "On Harmonic Analysis of Tidal Observations." — W. T.
THE TIDES. 175
water, and the corresponding solar noon tides and
solar midnight tides, due to the sun not being
in the earth's equator, constitute the lunar and
solar diurnal declinational tides. In summer
the noon high water might be expected to be
higher than the midnight high water, because
FIG. 27.— Declinational Tide.
the sun is nearer overhead to us than to our
Antipodes.
By kind permission of Sir Frederick Evans, I am
able to place before you these diagrams of curves
drawn by Captain Harris, R.N., of the Hydrographic
Department of the Admiralty, exhibiting the rise
and fall of tides in Princess Royal Harbour, King
George Sound, Western Australia, from January
i;6 POPULAR LECTURES AND ADDRESSES.
ist to December 3ist, 1877, and in Broad Sound,
Queensland, Australia, from July I5th, 1877, to
July 23rd, 1878. Look at this one of these
diagrams/a diagram of the tides at the north-east
corner of Australia. For several days high water
always at noon. When the tides are noticeable at
all we have high water at noon, and when the tides
are not at noon they are so small that they are not
taken notice of at all. It thus appears as if the
tides were irrespective of the moon, but they are
not really so. When we look more closely, it is
a full moon if we have a great tide at noon ; or
else it is new moon. It is at half moon that we
have the small tides, and when they are smallest
we have high water at six. There is also a great
difference between day and night high water ; the
difference between them is called the diurnal tide.
A similar phenomenon is shown on a smaller
scale in this curve, drawn by the first tide-pre-
dicting machine. At a certain time the two
high waters become equalised, and the two low
waters very unequal (see p. 172 for real examples).
The object of the harmonic analysis is to analyse
THE TIDES. 177
out from the complicated curve traced by the tide-
gauge the simplest harmonic elements. A simple
harmonic motion may be imagined as that of a
body which moves simply up and down in a
straight line, keeping level with the end of a clock
hand, moving uniformly round. The exceedingly
complicated motion that we have in the tides is
analysed into a scries of simple harmonic motions
in different periods and with different amplitudes
or ranges ; and these simple harmonic constituents
added together give the complicated tides.
All the work hitherto done has been accom-
plished by sheer calculation ; but calculation of
so methodical a kind that a machine ought to
be found to do it. The Tidal Harmonic Analyser
consists of an application of Professor James
Thomson's disk-globe-and-cylinder integrator to
the evaluation of the integrals required for the
harmonic analysis. The principle of the machine
and the essential details are fully described and
explained in papers communicated by Professor
James Thomson and the author to the Royal
Society, in 1876 and 1878, and published in the
VOL. in. N
178 POPULAR LECTURES AND ADDRESSES.
Proceedings for those
years ; l also reprinted, with
a postscript dated April
1879, in Thomson and
Tait's Natural Philosophy,
Second Edition, Appendix
B. It remains now to
describe and explain the
actual machine referred to
in the last of these com-
munications, which is the
only tidal harmonic an-
alyser hitherto made. It
may be mentioned, how-
ever, in passing, that a
similar instrument, with
the simpler construction
wanted for the simpler har-
monic analysis of ordinary
meteorological phenomena,
has been constructed for the
1 Vide vol. xxiv. p. 262, and vol.
xxvii. p. 371.
THE TIDES. 179
Meteorological Committee, and is now regularly
at work at their office, harmonically analysing
the results of meteorological observations, under
the superintendence of Mr. R. H. Scott.
Fig. 28 represents the tidal harmonic analyser,
constructed under the author's direction, with the
assistance of a grant from the Government Grant
Fund of the Royal Society. The eleven cranks
of this instrument are allotted as follows : —
Cranks.
Object.
Dis-
tinguishing
Letter.
Speed.
i and 2
To find the mean lunar semi-diurnal tide . . .
M
2(y-a)
3 » 4
,, mean solar ,, ,, . . .
S
2 (r-*)
5 „ 6
,, luni-solar declinational diurnal tide
KI
y
7 „ 8
,, slower lunar ,, ,,
0
(y-2*)
9 » 10
,, slower solar ,, ,,
,, mean water level
p
Aff
(r-«*)
The general arrangement of the several parts
may be seen from Fig. 28. The large circle at
the back, near the centre, is merely a counter to
count the days, months, and years for four years,
being the leap year period. It is driven by a
N 2
i8o POPULAR LECTURES AND ADDRESSES.
worm carried on an intermediate shaft, with a
toothed wheel geared on another on the solar
shaft. In front of the centre is the paper drum,
which is on the solar shaft, and goes round in the
period corresponding to twelve mean solar hours.
On the extreme left, the first pair of disks, with
globes and cylinders, and crank shafts with cranks
at right angles between them, driving their two
cross-heads, corresponds to the Kv or luni-solar
diurnal tide. The next pair of disk-globe-and-
cylinders corresponds to M, or the mean lunar
semi-diurnal tide, the chief of all the tides. The
next pair lie on the two sides of the main shaft
carrying the paper drum, and correspond to S,
the mean solar semi-diurnal tide. The first pair
on the right correspond to O, or the lunar diurnal
tide. The second pair on the right correspond to
P, the solar diurnal tide. The last disk on the
extreme right is simply Professor James Thom-
son's disk-globe-and-cylinder integrator, applied to
measure the area of the curve as it passes through
the machine.
The idle shafts for the M and the O tides are
THE TIDES. 181
seen in front respectively on the left and right of
the centre. The two other longer idle shafts for
the K and the P tides are behind, and therefore
not seen. That for the P tide serves also for the
simple integrator on the extreme right.
The large hollow square brass bar, stretching
from end to end along the top of the instrument,
and carrying the eleven forks rigidly attached to
it, projecting downwards, is moved to and fro
through the requisite range by a rack and pinion,
worked by a handle and crank in front above the
paper cylinder, a little to the right of its centre.
Each of these eleven forks moves one of the
eleven globes of the eleven disk-globe-and-cylinder
integrators of which the machine is composed.
The other handle and crank in front, lower down
and a little to the left of the centre, drives by a
worm, at a conveniently slow speed, the solar
shaft, and through it, and the four idle shafts, the
four other tidal shafts.
To work the machine the operator turns with
his left hand the driving crank, and with his right
hand the tracing crank, by which the fork-bar is
182 POPULAR LECTURES AND ADDRESSES.
moved. His left hand he turns always in one
direction, and at as nearly constant a speed as is
convenient to allow his right hand, alternately in
contrary directions, to trace exactly with the steel
pointer the tidal curve on the paper, which is
carried across the line of to-and-fro motion of the
pointer by the revolution of the paper drum, of
which the speed is in simple proportion to the
speed of the operator's left hand.
The eleven little counters of the cylinders in
front of the disks are to be set each at zero at the
commencement of an operation, and to be read off
from time to time during the operation, so as to
give the value of the eleven integrals for as many
particular values of the time as it is desired to have
them.
A first working model harmonic analyser, which
served for model and for the meteorological analyser,
now at work in the Meteorological Office, is here
before you. It has five disk-globe-and-cylinders,
and shafting geared for the ratio I : 2. Thus it
serves to determine, from the deviation curve, the
celebrated "ABCDE"of the Admiralty Com-
THE TIDES. 183
pass Manual, this is to say, the coefficients in the
harmonic expression
A + B sin e + C cos 9 + D sin 2 6 + E cos 2 Q,
for the deviation of the compass in an iron ship.
The first instrument which I designed and
constructed for use as a Tide Predicter was
described in the Catalogue of the Loan Collec-
tion of Scientific Apparatus at South Kensington
in 1876; and the instrument itself was presented
by the British Association to the South Kens-
ington Museum, where it now is. The second in-
strument constructed on the same principle is in
London, and is being worked under the direction of
Mr. Roberts, analysing the tides for the Indian ports.
The result of this work is these books (Tide Tables
for Indian Ports) in which we have, for the first
time, tables of the times and heights of high water
and low water for fourteen of the Indian ports.
To predict the tides for the India and China
Seas and Australia we have a much more difficult
thing to do than for the British ports. The
Admiralty Tide Tables give all that is necessary
for the British ports, practically speaking ; but for
1 84 POPULAR LECTURES AND ADDRESSES.
other parts of the world generally the diurnal tide
comes so much into play that we have exceedingly
complicated action. The most complete thing
FIG. 29.— Tide Predictor.
would be a table showing the height of the water
every hour of the twenty-four. No one has yet
ventured to do that generally for all parts of the
world ; but for the comparatively complicated tides
THE TIDES. 185
of the India Seas, the curves traced by the Tide-
Predicter from which is obtained the information
given in these Indian tide tables, do actually tell
the height of the water for every instant of the
twenty-four hours.
The mechanical method which I have utilised
in this machine is primarily due to the Rev. F.
Bashforth who, in 1845, when he was a Bachelor
of Arts and Fellow of St. John's College,
Cambridge, described it to Section A of the 1845
(Cambridge) meeting of the British Association
in a communication entitled " A Description of a
Machine for finding the Numerical Roots of
Equations and tracing a Variety of Useful Curves,"
of which a short notice appears in the British
Association Report for that year. The same
subject was taken up by Mr. Russell in a com-
munication to the Royal Society in 1869, "On
the Mechanical Description of Curves," l which
contains a drawing showing mechanism sub-
stantially the same as that of the Tide Predictor.
Here is the principle as embodied in No. 3 Tide
1 Prof. Royal Society, June 17, 1869; (vol. xviii. p. 72).
1 86 POPULAR LECTURES AND ADDRESSES.
Predictor (represented in Fig. 29, p. 184), now
actually before you: —
A long cord of which one end is held fixed
passes over one pulley, under another, and so on.
These eleven pulleys are all moved up and down
by cranks, and each pulley takes in or lets out
cord according to the direction in which it moves.
These cranks are all moved by trains of wheels
gearing into the eleven wheels fixed on this driving
shaft. The greatest number of teeth on any wheel
is 802 engaging with another of 423. All the
other wheels have comparatively small numbers of
teeth. The machine is finished now, except a
cast-iron sole and cast-iron back. A fly-wheel of
great inertia enables me to turn the machine fast,
without jerking the pulleys, and so to run off a
year's curve in about twenty-five minutes. This
machine is arranged for fifteen constituents in all
and besides that there is an arrangement for
analysing out the long period tides.
The following table shows how close an
approximation to astronomical accuracy is given
by the numbers chosen for the teeth of the several
THE TIDES.
187
wheels. These numbers I have found by the
ordinary arithmetical progress of converging
fractions.
Tidal
Con-
stituents
Speed in Degrees per Mean Solar Hour.
Losses of Angle in
Machine.
Accurate.
As given by Machine.
Per Mean
Solar Hour.
Per
Half
Year.
MI
28° 9841042
15 X — = 28°'984o630
-f- 0°'00004I2
o°'i8o
Kl
,5.,4,o6S6
366
15 X 365 = 15 '0410959
— o° '0000267
o-n7
0
I3' "94 30356
343
15 X 369 = I3 '943°894
- o° 0000538
o°-237
P
•4-95S93.4
364
+ o° '0000242
o"'n9
N
*"<*»*
802
+ o°*ooooi33
o-o»
L
29?'5284783 • 15 X ~g = 2^-5283018
+ o-^,77
o° 78
V
,8-5,25830
•sxgf = =8-5,=3966
+ o°'ocoi864
o° 82
M S
58-.984,o42
230 271
15 X —- X — = 58 '9836600
+ 0-000444
i°'95
M
27° '9682084
468
15 X 251 - 270'963i27S
+ o°'oooo8o9
**
,\
29°'4556254
487
15 X 2^48 = 29°'455645i
- o° '0000197
0-08,
Q
13*3986609
15 X ^ = 13° 3986928
- o°'oooo3i8
o°-i4
To-day (Aug. 25, 1882), a committee, consisting
of only two members, Mr. George Darwin and
1 88 POPULAR LECTURES AND ADDRESSES.
Professor Adams of Cambridge, have been ap-
pointed, and one of their chief objects will be to
examine the long period tides [see note to p. 203].
There is one very interesting point I said I
would endeavour to speak of if I had time ; I
have not time, but still I must speak of it — the
influence of the moon on the weather. "We
almost laugh when we hear of the influence of
the moon on the weather," Sir F. Evans said
to me, "but there is an influence." Gales of
wind are remarkably prevalent in Torres Straits
and the neighbourhood about the time of new
and full moon. This was noticed by Dr. Rattray,
a surgeon in the navy, in connection with obser-
vations made by the surveying ship, Ffy, during
the three years 1841-44. Dr. Rattray noticed
that at those times there was a large area of coral
reef uncovered at the very low water of the
spring tides, extending out some sixty or seventy
miles from land. This large area becomes highly
heated, and the great heating of that large portion
of land gives rise to a tendency to gales at the
full and change, that is at the new and full moon.
THE TIDES. 189
This indirect effect of the moon upon the weather
through the tides is exceedingly interesting ; but
it does not at all invalidate the scientific con-
clusion that there is no direct influence, and the
general effect of the moon on the weather — the
changes in the moon and the changes in the
weather, and their supposed connection — remains
a mere chimsera.
The subject of elastic tides in which the yielding
of the solid earth is taken into account is to be
one of the primary objects of Mr. G. Darwin's com-
mittee. The tide-generating force which tends to
pull the water to and from the moon, tends to
pull the earth also. Imagine the earth made of
india-rubber and pulled out to and from the moon.
It will be made prolate (Fig. 30). If the earth were
of india-rubber the tides would be nothing, the
rise and fall of the water relatively to the solid
would be practically nil. If the earth (as has
long been a favourite hypothesis of geologists)
had a thin shell 20 or 30 miles thick with liquid
inside, there would be no such thing as tides of
water rising and falling relatively to land, or sea-
190 POPULAR LECTURES AND ADDRESSES.
bottom. The earth's crust would yield to and
from the moon, and the water would not move at
all relatively to the crust. If the earth were even
as rigid as glass all through, calculation shows that
the solid would yield so much that the tides could
only be about one third of what they would be if
the earth were perfectly rigid. Again, if the earth
were two or three times as rigid as glass, about as
rigid as a solid globe of steel, it would still, con-
FIG. 30.— Elastic Tides.
sidering its great dimensions, yield two or three feet
to that great force, which elastic yielding would
be enough to make the tides only twc thirds of
what they would be if the earth were perfectly
rigid. Mr. G. Darwin has made the investigation
by means of the lunar fortnightly tides, and the
general conclusion, subject to verification, is that the
earth does seem to yield somewhat, and may have
something like the rigidity of a solid globe of steel.
THE TIDES, (APP. A.] 191
APPENDIX A.
[Extracts from a Lecture on " The Tides" given to the
Glasgow Science Lectures Association, not hitherto pub-
lished, and now included as explaining in greater detail
certain paragraphs of the preceding Lecture.]
(i) Gravitation. — The great theory of gravitation
put before us by Newton asserts that every portion
of matter in the universe attracts every other por-
tion ; and that the force depends on the masses of
the two portions considered, and on the distance be-
tween them. Now, the first great point of Newton's
theory is, that bodies which have equal masses are
equally attracted by any other body, a body of
double mass experiencing double force. This may
seem only what is to be expected. It would take
more time than we have to spare were I to point
out all that is included in this statement ; but let
me first explain to you how the motions of dif-
ferent kinds of matter depend on a property called
inertia. I might show you a mass of iron as here.
Consider that if I apply force to it, it gets into a
state of motion ; greater force applied to it, during
192 POPULAR LECTURES AND ADDRESSES.
the same time, gives it increased velocity, and so
on. Now, instead of a mass of iron, I might hang
up a mass of lead, or a mass of wood, to test the
equality of the mass by the equality of the motion
which is produced in the same time by the action
of the same force, or in equal times by the action
of equal forces. Thus, quite irrespectively of the
kind of matter concerned, we have a test of the
quantity of matter. You might weigh a pound of
tea against a pound of brass without ever putting
them into the balance at all. You might hang up
one body by a proper suspension, and you might,
by a spring, measure the force applied, first to the
one body, and then to the other. If the one body
is found to acquire equal velocity under the in-
fluence of equal force for equal times as compared
with the other body, then the mass of the one is
said to be equal to the mass of the other.
I have spoken of mutual forces between any
two masses. Let us consider the weight or heavi-
ness of a body on the earth's surface. Newton
explained that the attraction of the whole earth
upon a body — for example, this 56 pounds mass
of iron — causes its heaviness or weight. Well,
now, take 56 pounds of iron here, and take a
mass of lead, which, when put in the balance,
is found to be of equal weight. You see we
have quite a new idea here. You weigh this
mass of iron against a mass of lead, or to
weigh out a commodity for sale ; as, for instance,
THE TIDES. (APP. A.} 193
to weigh out pounds of tea, to weigh them with
brass weights is to compare their gravitations
towards the earth — to compare the heavinesses of
the different bodies. But the first subject that
I asked you to think of had nothing to do with
heaviness. The first subject was the mass of the
different bodies as tested by their resistance to
force tending to set them in motion. I may just
say that the property of resistance against being
set into motion, and again against resistance to
being stopped when in motion, is the property of
matter called inertia.
The first great point in Newton's discovery
shows, then, that if the property of inertia is
possessed to an equal degree by two different
substances, they have equal heaviness. One of
his proofs was founded on the celebrated guinea
and feather experiment, showing that the guinea
and feather fall at the same rate when the resist-
ance of the air is removed. Another was founded
upon making pendulums of different substances —
lead, iron, and wood — to vibrate, and observing
their times of vibration. Newton thus dis-
covered that bodies which have equal heaviness
have equal inertia.
The other point of the law of gravitation is, that
the force between any two bodies diminishes as
the distance increases, according to the law of the
inverse square of the distance. That law expresses
that, with double distance, the force is reduced one
VOL. in. O
194 POPULAR LECTURES AND ADDRESSES.
quarter, at treble distance the force is reduced to
one-ninth part. Suppose we compare forces at the
distance of one million miles, then again at the
distance of two and a half million miles, we have
to square the one number then square the other,
and find the proportion of the square of the one
number to the square of the other. The forces are
inversely as the squares of the distance, that is the
most commonly quoted part of the law of gravita-
tion ; but the law is incomplete without the first
part, which establishes the relation between two
apparently different properties of matter. Newton
founded this law upon a great variety of different
natural phenomena. The motion of the planets
round the sun, and the moon round the earth,
proved that for each planet the force varies
inversely as the square of its distance from the
sun ; and that from planet to planet the forces on
equal portions of their masses are inversely as the
squares of their distances. The last link in the
great chain of this theory is the tides.
(2) Tide-Generating Force. — And now we are
nearly ready to complete the theory of tide-
generating force. The first rough view of the case,
which is not always incorrect, is that the moon
attracts the waters of the earth towards herself and
heaps them up, therefore, on one side of the earth.
It is not so. It would be so if the earth and moon
were at rest and prevented from falling together
by a rigid bar or column. If the earth and
THE TIDES. (APP. A.} 195
moon were stuck on the two ends of a strong
bar, and put at rest in space, then the attrac-
tion of the moon would draw the waters of the
earth to the side of the earth next to the moon.
But in reality things are very different from that
supposition. There is no rigid bar connecting the
moon and the earth. Why then does not the moon
fall towards the earth ? According to Newton's
theory, the moon is always falling towards the earth.
Newton compared the fall of the moon, in his
celebrated statement, with the fall of a stone at the
earth's surface, as he recounted, after the fall of an
apple from the tree, which he perceived when sit-
ting in his garden musing on his great theory.
The moon is falling towards the earth, and falls in
an hour as far as a stone falls in a second. It
chances that the number 60 is nearly enough, as I
have said before, a numerical expression for the dis-
tance of the moon from the earth in terms of the
earth's radius. It is only by that chance that the
comparison between the second and hour can be here
introduced. Since there are 60 times 60 seconds
in an hour, and about 60 radii of the earth in
the distance from the moon, we are led to the
comparison now indicated, but I am inverting the
direction of Newton's comparison. He found by
observation that the moon falls as far in an hour as
a stone falls in a second, and hence inferred that
the force on the moon is a 6oth of the 6oth of the
force per equal mass on the earth's surface. Then
O 2
196 POPULAR LECTURES AND ADDRESSES.
r
he learned from accurate observations, and from the
earth's dimensions, what I have mentioned as the
moon's distance, and perceived the law of variation
between the weight of a body at the earth's surface
and the force that keeps the moon in her orbit.
The moon in Newton's theory was always falling
towards the earth. Why does it not come down ?
Can it be always falling and never come down ?
That seems impossible. It is always falling, but it
has also a motion perpendicular to the direction in
which it is falling, and the result of that continual
falling is simply a change of direction of this
motion.
It would occupy too much of our time to go into
this theory. It is simply the dynamical theory of
centrifugal force. There is a continual falling
away from the line of motion, as illustrated in a
stone thrown from the hand describing an ordinary
curve. You know that if a stone is thrown hori-
zontally it describes a parabola — the stone falling
away from the line in which it was thrown. The
moon is continually falling away from the line in
which it moves at any instant, falling away towards
the point of the earth's centre, and falling away
towards that point in the varying direction from
itself. You can see it may be always falling, no\v
from the present direction, now from the altered
direction, now from the farther altered direction in
a further altered line ; and so it may be always
falling and never coming down. The parts of the
THE TIDES. (APP. A.} 197
moon nearest to the earth tend to fall most rapidly,
the parts furthest from the earth, least rapidly ; in
its own circle, each is falling away and the result is
as if we had the moon falling directly.
But while the moon is always falling towards the
earth, the earth is always falling towards the moon ;
and each preserves a constant distance, or very
nearly a constant distance from the common centre
of gravity of the two. The parts of the earth
nearest to the moon are drawn towards the
moon with more force than an equal mass at
the average distance ; the most distant parts are
drawn towards the moon with less force than
corresponds to the average distance. The solid
mass of the earth, as a whole, experiences y
according to its mass, a force depending on the
average distance ; while each portion of the water
on the surface of the earth experiences an attractive
force due to its own distance from the moon. The
result clearly is, then, a tendency to protuberance
towards the moon and from the moon ; and thus,
in a necessarily most imperfect manner, I have
explained to you how it is that the waters are not
heaped up on the side next the moon, but are
drawn up towards the moon and left away from
the moon so as to tend to form an oval figure.
The diagram (Fig. 21, p. 161) shows the pro-
tuberance of water towards and from the moon.
It shows also the sun on the far side, I need
scarcely say, with an enormous distortion of
198 POPULAR LECTURES AND ADDRESSES.
proportions, because without that it would be
impossible in a diagram to show the three
bodies. This illustrates the tendency of the
tide-generating forces.
(3) Elastic Tides. — But another question arises.
This great force of gravity operating in different
directions, pulling at one place, pressing in at
another, will it not squeeze the earth out of
shape ? I perceive signs of incredulity ; you think
it impossible it can produce any sensible effect.
Well, I will just tell you that instead of being im-
possible, instead of it not producing any such
effect, we have to suppose the earth to be of
exceedingly rigid material, in order that the effect
of these distorting influences on it may not mask
the phenomenon of the tides altogether.
There is a very favourite geological hypothesis
which I have no doubt many here present have
heard, which perhaps till this moment many here
present have believed, but which I hope no one
wrill go out of this room believing, and that is that
the earth is a mere crust, a solid shell thirty, or
forty, or fifty miles thick at the most, and that it is
filled with molten liquid lava. This is not a sup-
position to be dismissed as absurd, as ludicrous, as
absolutely unfounded and unreasonable. It is a
theory based on hypothesis which requires most
careful weighing. But it has been carefully weighed
and found wanting in conformity to the truth. On
a great many different essential points it has been
THE TIDES. (A PP. A.) 199
found at variance with the truth. One of these
points is, that unless the material of this supposed
shell were preternaturally rigid, were scores of
times more rigid than steel, the shell would yield so
freely to the tide-generating forces that it would
take the figure of equilibrium, and there would be
no rise and fall of the water, relatively to the solid
land, left to show us the phenomena of the tides.
Imagine that this (Fig. 30, p. 190) represents a
solid shell with water outside, you can understand if
the solid shell yields with sufficiently great freedom,
there will be exceedingly little tidal yielding left
for the water to show. It may seem strange when
I say that hard steel would yield so freely. But
consider the great hardness of steel and the smaller
hardness of india-rubber. Consider the greatness
of the earth, and think of a little hollow india-
rubber ball, how freely it yields to the pressure of
the hand, or even to its own weight when laid on a
table. Now, take a great body like the earth : the
greater the mass the more it is disposed to yield to
the attraction of distorting forces when these forces
increase with the whole mass. I cannot just
now fully demonstrate to you this conclusion ;
but I say that a careful calculation of the
forces shows that in virtue of the greatness of
the mass it would require an enormously in-
creased rigidity in order to keep in shape. So
that if we take the actual dimensions of the
earth at forty-two million feet diameter, and the
200 POPULAR LECTURES AND ADDRESSES.
crust at fifty miles thick, or two hundred and
fifty thousand feet, and with these proportions
make the calculation, we find that something scores
of times more rigid than steel would be required to
keep the shape so well as to leave any appreci-
able degree of difference from the shape of hydro-
static equilibrium, and allow the water to indicate,
by relative displacement, its tendency to take the
figure of equilibrium ; that is to say, to give us
the phenomena of tides. The geological inference
from this conclusion is, that not only must we
deny the fluidity of the earth and the assertion
that it is encased by a thin shell, but we must
say that the earth has, on the whole, a rigidity
greater than that of a solid globe of glass of the
same dimensions ; and perhaps greater than that
of a globe of steel of the same dimensions. But
that it cannot be less rigid than a globe of glass,
we are assured. It is not to be denied that there
may be a very large space occupied by liquid. We
know there are large spaces occupied by lava ; but
we do not know how large they may be, although
we can certainly say that there are no such spaces,
as can in volume be compared with the supposed
hollow shell, occupied by liquid constituting the
interior of the earth. The earth as a whole
must be rigid, and perhaps exceedingly rigid,
probably rendered more rigid than it is at the
surface strata by the greater pressure in the
greater depths.
THE TIDES. (APP. B.) 201
The phenomena of underground temperature,
which led geologists to that supposition, are
explained otherwise than by their assumption of a
thin shell full of liquid ; and further, every view
we can take of underground temperature, in the
past history of the earth, confirms the statement
that we have no right to assume interior fluidity.
APPENDIX B.
INFLUENCE OF THE STRAITS OF DOVER ON THE
TIDES OF THE BRITISH CHANNEL AND THE
NORTH SEA.
[Abstract of a paper read at the Dublin (1878) meeting
of the British Association.'}
THE conclusions are : —
I. The rise and fall of the water-surface and
the tidal streams throughout the North Sea, north
of the parallel of 53° (through Cromer, in Norfolk),
and on the north coasts of Holland and Hanover,
are not sensibly different from what they would be
if the passage through the Straits of Dover were
stopped by a barrier.
2. The main features of the tides (rise and fall
202 POPULAR LECTURES AND ADDRESSES.
and tidal streams) throughout the British Channel
west of Beachy Head and St. Valery-en-Caux, do
not differ much from what they would be if the pas-
sage through the Straits were stopped by a barrier
between Dover and Cape Grisnez (Calais).
3. A partial effect of the actual current through
the Straits is to make the tides throughout the
Channel, west of a line through Hastings to the
mouth of the Somme, more nearly agree with what
they would be were there a barrier along this line,
than what they would be if there were a barrier
between Dover and Cape Grisnez.
4. The chief obviously noticeable effect of the
openness of the Straits of Dover on tides west of
Beachy Head is that the rise and fall on the
coast between Christchurch and Portland is not
much smaller than it is.
5. The fact that the tidal currents commence
flowing westward generally an hour or two before
Dover high-water, and eastward an hour or two
before Dover low-water, instead of exactly at the
times of Dover high and low-water, is also partially
due to the openness of the Straits of Dover.
6. The facts referred to in Nos. 4 and 5 are
no doubt partially due also to fluid friction (in
eddies along the bottom and in tide-races), and
want of absolute simultaneity in the time of high-
water across the mouth of the Channel from Land's
End to Ushant. Without farther investigation it
would be in vain to attempt to estimate the
THE TIDES. (APP. B) 203
proportionate contributions of the three causes to
the whole effect.
7. According to Fourier's elementary principles
of harmonic analysis all deviations from regular
simple harmonic rise and fall of the tide within
twelve hours are to be represented by the super-
position of simple harmonic oscillations in six-
hours period, and four-hours period, and three-hours
period, and so on— like the " overtones " which give
the peculiar characters to different musical sounds
of the same pitch. The six-hourly oscillation
which gives the double low-water at Portland and
the protracted duration of the high-water at Havre *
is probably in part due to the complex-harmonic
character of the current through the Straits of
Dover ; that is to say, definitely, to a six-hourly
periodic term in the Fourier-series representing the
quantity of water passing through the Straits
per unit of time, at any instant of the twelve
hours.
8. The double high-water experienced at South-
ampton, and in the Solent, and at Christchurch
and Poole, and still further west, generally attributed
to the doubleness of the influence experienced
from the tidal streams on the two sides of the Isle
1 At Havre, on the French coast, the high- water remains station-
ary for one hour, with a rise and fall of three or four inches for
another hour, and only rises and falls thirteen inches for the space of
three hours ; this long period of nearly slack water is very valuable to
the traffic of the port, and allows from fifteen to sixteen vessels to
enter or leave the docks on the same tide.
204 POPULAR LECTURES AND ADDRESSES.
of Wight, seems to have a continuity of cause with
the double low-water at Portland, which is certainly
allied to the protracted high-water of Havre — a
phenomenon quite beyond reach of the Solent's
influence. It is probable, therefore, that the
double high-water in the Solent and at Christ-
church and Poole is influenced sensibly by the
current through the Straits of Dover, even though
the common explanation attributing them to the
Isle of Wight may be in the main correct.
APPENDIX C.
ON THE TIDES OF THE SOUTHERN HEMISPHERE
AND OF THE MEDITERRANEAN.
[Abstract of paper by Captain Evans, R.N., F.R.S., and Sir
William Thomson, LL.D., F.R.S., read in Section E of
the Dubli?i (1878) meeting of t]ie British Association^
ON the coasts of the British Islands and
generally on the European coasts of the North
Atlantic and throughout the North Sea, the tides
present in their main features an exceptional
simplicity, two almost equally high high- waters and
two almost equally low low-waters in the twenty-
four hours, with the regular fortnightly inequality of
THE TIDES. (APP. C) 205
spring tides and neap tides due to the alternately
conspiring and opposing actions of the moon and
sun, and with large irregular variations produced
by wind. Careful observation detects a small
" diurnal " inequality (so called because it is due
to tidal constituents having periods approximately
equal to twenty-four hours lunar or solar), of which
the most obvious manifestation is a difference at
certain times of the month and of the year
between the heights of the two high-waters of the
twenty-four hours, and at intermediate times a
difference between the heights of the two low-
waters.
In the western part of the North Atlantic and in
the North Sea, this diurnal inequality is so small in
comparison with the familiar twelve-hourly or
"semi-diurnal" tide that it is practically disre-
garded, and its very existence is scarcely a part of
practical knowledge of the subject ; but it is not so
in other seas. There is probably no other great
area of sea throughout which the diurnal tides are
practically imperceptible and the semi-diurnal tides
alone practically perceptible. In some places in
the Pacific and in the China Sea it has long been
remarked that there is but one high water in the
twenty-four hours at certain times of the month,
and in the Pacific, the China Sea, the Indian Ocean,
the West Indies, and very generally wherever tides
are known at all practically, except on the ocean
coasts of Europe, they are known to be not
206 POPULAR LECTURES AND ADDRESSES.
" regular " according to the simple European rule,
but to be complicated by large differences between
the heights of consecutive high-waters and of con-
secutive low-waters, and by marked inequalities of
the successive intervals of time between high-water
and low-water.
On the coasts of the Mediterranean generally the
tides are so small as to be not perceptible to
ordinary observation, and nothing therefore has
been hitherto generally known regarding their
character. But a first case of application of the
harmonic analysis to the accurate continuous
register of a self-recording tide-gauge (published
in the 1876 Report of the B.A. Tidal Committee)
has shown for Toulon a diurnal tide amounting on
an average of ordinary midsummer and mid-winter
full and new moons to nearly 4/5 of the semi-
diurnal tides ; and the present communication con-
tains the results of analysis showing a similar result
for Marseilles ; but on the other hand for Malta, a
diurnal tide (similarly reckoned), amounting to
only 2/9 of the semi-diurnal tide. The semi-
diurnal tide is nearly the same amount in the three
places, being at full and new moon, about seven
inches rise and fall.
The present investigation commenced in the
Tidal Department of the Hydrographic Office,
under the charge of Staff-Commander Harris, R.N.,
with an examination and careful practical analysis
of a case greatly complicated by the diurnal in-
THE TIDES. (APP. C) 207
equality presented by tidal observations which had
been made at Freemantle, Western Australia, in
1873-74, chiefly by Staff-Commander Archdeacon,
R.N., the officer in charge of the Admiralty Survey
of that Colony. The results disclosed very re-
markable complications, the diurnal tides pre-
dominating over the semi-diurnal tides at some
seasons of month and year, and at others almost
disappearing and leaving only a small semi-diurnal
tide of less than a foot rise and fall. These
observations were also very interesting in respect to
the great differences of mean level which they
showed for different times of year, so great that
the low-waters in March and April were generally
higher than the high-waters in September and
October. The observations were afterwards, under
the direction of Captain Evans and Sir William
Thomson, submitted to a complete harmonic
analysis worked out by Mr. E. Roberts. Not only
on account of the interesting features presented by
this first case of analysis of tides of the southern
hemisphere, but because the south circumpolar
ocean has been looked to on theoretical grounds as
the origin of the tides, or of a large part of the
tides, of the rest of the world, it seemed desirable
to extend the investigation to other places of the
southern hemisphere for which there are available
data. Accordingly the records in the Hydrographic
Office of tidal observations from all parts of the
world were searched, but besides those of Free-
2o8 POPULAR LECTURES AND ADDRESSES.
mantle, nothing from the southern hemisphere was
found sufficiently complete for the harmonic
analysis except a year's observations of a self-re-
gistering tide-gauge at Port Louis, Mauritius, and
personal observations made at regular hourly, and
sometimes half-hourly, intervals for about six
months (May to December) of 1842, at Port Louis,
Berkeley Sound, East Falkland, under the direction
of Sir James Clark Ross. These have been sub-
jected to complete analysis.
So also have twelve months' observations by a
self-registering tide-gauge during 1871-2 at Malta,
contributed by Admiral Sir A. Cooper Key, K.C.B.,
F.R.S.
Tide-curves for two more years of Toulon (1847
and 1848) in addition to the one (1853) previously
analysed, and for Marseilles for a twelvemonth
of 1850-51, supplied by the French Hydrographic
Office, have also been subjected to the harmonic
analysis.
[The numerical results obtained will be found in
Nature, October 24, 1878 (vol. xviii. p. 670).]
THE TIDES. (APP. D.} 209
APPENDIX D.
SKETCH OF PROPOSED PLAN OF PROCEDURE IN
TIDAL OBSERVATION AND ANALYSIS.
{Circular issued by Sir William Thomson in December, 1867,
to the members of the Committee, appoi?ited, on his sug-
gestion, by the British Association in 1867 u For the
Purpose of Promoting the Extension, Improvement, and
Harmonic Analysis, of Tidal Observations."}
[Brit is k Association Report, Norwich, 1868, p. 490.]
i. The chief, it may be almost said the only,
practical conclusion deducible from, or at least
hitherto deduced from, the dynamical theory is,
that the height of the water at any place may be
expressed as the sum of a certain number of simple
harmonic functions 1 of the time, of which the
periods are known, being the periods of certain
components of the sun's and moon's motions.2
Any such harmonic term will be called a tidal con-
stituent, or sometimes, for brevity, a tide. The
expression for it in ordinary analytical notation is
A cos nt + B sin nt ; or R cos (nt — e), if A = R
1 See Thomson's and Tail's Natural Philosophy > §§ 53, 54.
2 See Laplace, Mecanique Celeste, liv. iv. § 16. Airy's Tides and
Waves, § 585.
VOL. III. P
210 POPULAR LECTURES AND ADDRESSES.
cos e, and B = R sin e ; where t denotes time
measured in any unit from any era, n the corre-
sponding angular velocity (a quantity such that -
is the period of the function), R and e the ampli-
tude and the epoch, and A and B coefficients
immediately determined from observation by the
proper harmonic analysis (which consists virtually
in the method of least squares applied to deduce
the most probable values of these coefficients from
the observations).
2. The chief tidal constituents in most localities,
indeed in all localities where the tides are compara-
tively well known, are those whose periods are
twelve mean lunar hours, and twelve mean solar
hours respectively. Those which probably stand
next in importance are the tides whose periods
are approximately twenty-four hours. The former
are called the lunar semidiurnal tide, and solar
semidiurnal tide : the latter, the lunar diurnal tide
and the solar diurnal tide.1 There are, besides, the
lunar fortnightly tide and the solar semiannual
tide.2 The diurnal and the semidiurnal tides have
inequalities depending on the excentricity of the
moon's orbit round the earth, and of the earth's
round the sun, and the semidiurnal have inequali-
1 See Airy's Tides and Waves, § § 46, 49 ; or Thomson and Tail's
Natural Philosophy, § 808.
2 See Airy's Tides and Waves, § 45 ; or Thomson and Tail's
Natural Philosophy, § 880.
THE TIDES. (A PP. D.} 211
ties depending on the varying declinations of the
two bodies. Each such inequality of any one of
the chief tides may be regarded as a smaller super-
imposed tide of period approximately equal ; pro-
ducing, with the chief tide, a compound effect
which corresponds precisely to the discord of two
simple harmonic notes in music approximately in
unison with one another. These constituents may
be called for brevity elliptic and declinational tides.
But two of the solar elliptic diurnal tides thus
indicated have the same period, being twenty-four
mean solar hours. Thus we have in all twenty-
three tidal constituents : —
Coefficients of / in arguments.
Lunar. Solar.
The lunar monthly ana solar \
annual (elliptic) . . . . / :
The lunar fortnightly and ")
solar semiannual (decli- > 2 20- 2/7
national) ....... J
The lunar and solar diurnal \
(declinational) J
The lunar and solar semi-
diurnal
The lunar and solar elliptic "I
diurnal J
The lunar and solar elliptic 1 / 27— o--5> (27— T?
semidiurnal J '" (27— 3o--}-£> (27 — 3/1
The lunar and solar decli- )
national semidiurnal . . j 2 2y 2^
3. Here 7 denotes the angular velocity of the
earth's rotation, and a, rj, & those of the moon's
P 2
212 POPULAR LECTURES AND ADDRESSES.
revolution round the earth, of the earth's round the
sun, and of the progression of the moon's perigee.
The motion of the first point of Aries, and of the
earth's perihelion, are neglected. It is almost
certain that the slow variation of the lunar
declinational tides due to the retrogression of the
nodes of the moon's orbit, may be dealt with with
sufficient accuracy according to the equilibrium
method ; and the inequalities produced by the
perturbations of the moon's motion are probably
insensible. But each one of the twenty-three tides
enumerated above is certainly sensible on our
coasts. And there are besides, as Laplace has
shown, very sensible tides depending on the fourth
power of the moon's parallax,1 the investigation of
which must be included in the complete analysis
now suggested, although for simplicity they have
been left out of the preceding schedule. The
amplitude and the epoch of each tidal constituent
for any part of the sea is to be determined by
observation, and cannot be determined except by
observation. But it is to be remarked that the
period of one of the lunar diurnal tides agrees with
that of one of the solar diurnal tides, being
twenty-four sidereal hours ; and that the period of
one of the semidiurnal lunar declinational tides
agrees with that of one of the semidiurnal solar de-
clinational tides, being twelve sidereal hours. Also
1 The chief effect of this at any one station is a ter-diurnal lunar
tide, or one whose period is eight lunar hours.
THE TIDES. (APP. /?.) 213
that the angular velocities 7 —