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CORNELL UNIVERSITY LIBRARY

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Plate X

The Tide-predicting Machine of the Coast and Geodetic Survey. (Frontispiece}

NAUTICAL SCIENCE

m ITS RELATION TO PRACTICAL NAVIGATIONTOGETKKR WITH A STUDY OF THE

TIDES AND TIDAL CURRENTS

BY

CHARLES LANE POORl>nfutor of Aitronomy in Cotumbu UniTetetv; Author of "The

Solar System," etc.

ILLUSTRATED

G. P. PXJTN \M'S SONSNEW YORK AND LONDONSbe 1Knt hert^ocher press

1910

M Cornell UniversityM Library

The original of tliis book is intlie Cornell University Library.

There are no known copyright restrictions inthe United States on the use of the text.

http://www.archive.org/details/cu31924107202206

NAUTICAL SCIENCE

IN ITS RELATION TO PRACTICAL NAVIGATIONTOGETHER WITH A STUDY OF THE

TIDES AND TIDAL CURRENTS

BY

CHARLES LANE POORProfessor of Astronomy in Columbia Universityj Author of "The

Solar.System," etc.

ILLUSTRATED

G. P. PUTNAM'S SONSNEW YORK AND LONDONtCbe Iknicfierbocliec pcees

1910

COPYKIGHT, iglO

BY

CHARLES LANE POOR

/B.

Ube icntefenbocftet l>regs, Vtcw IBork

ry^,.% Jy^ p^y. ,^ (^, 2.% ^ 9'-^

PREFACE

THIS work is intended for the general readeras well as for the practical navigator. It is

an attempt to explain in non-technical languageand without the use of complicated mathematicalformulas the fundamental facts and principlesthat form the basis of all navigational methods.Navigation is founded upon Astronomy, but itis not essential for the navigator, in order to findhis way from port to port, to know the methodsby which the size, the shape, and the motions ofthe earth are determined, and to be familiarwith the physical characteristics of the stm andstars. A knowledge of these astronomical factsis, however, necessary to those who wish to bethoroughly posted in the science of navigation.Every navigator knows how to use the data foundin the Nautical Almanac, but few have theslightest idea how these data are collected andmade available for the immediate needs of thepractical sailor.

The Sumner method of finding one's positionat sea is fundamental and, when combined withmodern methods of reduction, is most simpleand readily applied to all navigational problems.

IV Preface

The time-honoured noon sight for latitude and themorning or afternoon sight for longitude are butspecial cases of this most powerful method. Thetheory of the Sumner lines of position is so easyto understand, and at the same time it is so widelyapplicable, that it is made the basis upon whichthe whole theory of practical navigation depends.At the end of each chapter is to be found a sortof appendix containing notes, formulas, andpractical examples. This portion of the bookforms a condensed treatise on modem methodsof navigation.

A considerable portion of the book is devotedto an explanation of the tides and tidal currents;their peculiarities and their causes. That thetides are caused by the attraction of the sunand moon is well known, but just how thisattraction causes the radically different tides indifferent portions of the earth is not fully realised.Until very recently the ablest investigators con-sidered the tides as world phenomena, the tidesin each bay and ocean as a part of one great tidalwave which sweeps around the entire world.To-day the able researches of Dr. Harris haveshown us that the tides and tidal currents areessentially local phenomena, that the tides of eachocean basin are practically independent of thoseof the rest of the world.Without the hearty co-operation and assistance

of the Coast and Geodetic Survey this portionof the book could never have been put into

Preface v

its present shape. Mr. Otto H. Tittmann, theSuperintendent, kindly placed the facilities ofthe Survey at the author's disposal and fur-nished maps, charts, and data, which have beenfreely used for illustration. Dr. RoUin A. Harris,whose tidal theories the author has attemptedto explain in non-technical language, kindly readand revised the manuscript. To him are duemany valuable suggestions as to text and toillustrations.

The thanks of the author are also due to Pro-fessor Geo. E. Hale, Director of the CarnegieSolar Observatory, to Professor Edwin B. Frost,Director of the Yerkes Observatory, to Mr. JohnBishop Putnam, and to others, for kindness infurnishing original photographs and drawingsused to illustrate the text; to Dr. M. F. Weinrich,who read and corrected the proof sheets andcompiled the index.

C. L. P.

October, 1909.

CONTENTSCHAPTER PARE

I. The Earth as an Astronomical Body iII. The Motions of the Earth . . 30

III. The Sun 48IV. The Stars and Planets ... 69V. The Making of an Almanac . 91VI. Time and its Determination

. "SVII. Finding One's Position at Sea . 150

VIII. Latitude...... 188

IX. Longitude . . .213X. Tides: Their Cause and Character-

istics . . . . . -233XI. The Representation and Prediction

OF THE Tides .... 268

XII. Tides and Tidal Currents of theAtlantic Coast . .

-293TABLES

TABLE

I. Length of a Degree (60') of Longi-tude in Different Latitudes . 315

II. Dip and Distance of Horizon forAverage State of Atmosphere . 316

viii Contents

TABLES

Continued.TABLE PAGB

III. Corrections to Dip for AbnormalRefraction . . . -317

IV. Corrections for Refraction, Paral-lax, AND Semi-Diameter, and Cor-rection for Refraction to beApplied to the Observed Altitudesof the Sun's Lower Limb, or of aStar . . . . -318

V. Corrections for the Variations inthe Sun's Semi-Diameter . .318

VI. Principal Dimensions and Elementsof the Solar System . . . 319

VII. Magnitude, Distance, and IntensityOF the Nearest Stars . . .321

VIII. Forty Useful Navigational Stars,with Approximate Mean Times ofMeridian Passage . . .322

ILLUSTRATIONS IN THE TEXTFIGURE PAGB

I. Weighing the Earth. .

. .1019

37

43

107

2. Dip of the Horizon ....

3. The Wanderings of the Earth's PoleDURING the Years i 900-1 908

4. The Orbit op the Earth

5. The Problem op Three Bodies6. The Orbits op the Earth and Jupiter 1097. The Equation of Time . . . 1218. Antique Form of Clepsydra . . 125

9. Old Italian Sun-Dial . . .13110. Time by a Single Altitude . .

-13711. A Circle OP Position . . . .15712. Finding the Circle of Position . .16013. New Navigation..... 16714. Astronomical Cross-Bearings . . 171

15. Lines op Position . . . .17316. Determining the Intersection op Sum-

ner Lines ..... 175

17. Latitude by Pole-Star Observations . 204ix

X Illustrations

FIGURE PAGB

1 8. Error in Longitude due to ErroneousAltitude...... 225

19. Error in Longitude due to ErroneousLatitude...... 227

20. Shelter Island Tide Curves forAugust, 1906 . . . . -237

21. Tide Curves for Port Townsend, St.Michael, and Havre . . .240

22. Tide-Generating Forces. . . 243

23. The Diurnal Variation . . . 24824. The Forced Vibrations op a Pendulum 25425. The Oscillatory Areas op the North

Atlantic.....

26. Non-Harmonic Tidal Constants.

27. Composition of Harmonic Motions28. Tide-Predicting Machine

29. Types of Bay Tides

30. Co-TiDAL Lines op the New EnglandCoast ......

31. Co-Current Lines op the New EnglandCoast 310

263

277

281

289

297

302

PLATESPAGE

The Tide-Predicting Machine of the CoastAND Geodetic Survey (Plate lo)

Frontispiece

1. Measuring A Base-Line WITH "iced-bar"Apparatus ..... 6

2. Distortion of the Sun's Disc by Re-fraction . . . .16

3. Foucault's Pendulum at ColumbiaUniversity ..... 32

4. Solar Cyclones, Photographed at theCarnegie Solar Observatory

. . 54

5. Prominences on the Sun, Aug. 14, 1907,Photographed at the Yerkes Ob-servatory ..... 66

6. Drawing of Mars by E. E. Barnard,Made with the 36-iN. Lick Telescope 76

7. Greenwich Observatory in Flamsteed'sTime ...... 96

8. Nevil Maskelyne, the Founder of theNautical Almanac .... 98

9. High and Low Tides on the PetitcodiacRiver ...... 234

II. Cotidal Lines of the World, as Drawnby Dr. Rollin A. Harris op the U. S.Coast and Geodetic Survey

. . 264

Nautical Science

CHAPTER I

THE EARTH AS AN ASTRONOMICAL BODY

TWO thousand years ago were the words writ-ten, "If at sea we sail towards mountains

or other high objects, we see these objects risefrom the sea, where they have been concealedhitherto by the ciirvature of the surface ofthe water." Other and even better proofs of thespherical shape of the earth were given bythe astronomers of old. They knew that theearth and moon are opaque bodies, that themoon shines by the reflected light of the sun,and that a lunar eclipse is caused by the moonpassing into the shadow cast by the earth. Nowthey noticed that the outline of the earth's shadow,thus cast upon, the moon, was always a smoothcurve, the arc of a circle; and they knew that asphere is the only body that always casts a cir-cular shadow. A fiat disc, a hemisphere, or an

2 Nautical Science

irregularly shaped body may, when placed insome special position, cast a circular shadow : butlet another side of such a body be turned towardthe light and the shadow will show straight linesand sharp, irregular edges.Thus from prehistoric times it was well known

that the earth is a globe. The popular idea thatColumbus discovered this fact, and that it was thisdiscovery which led to his voyage to America, isutterly wrong. At the time of Columbus it wasonly the unlearned and the intentionally igno-rant who did not know that the earth is spherical.In fact the earth was measured some seventeencenturies before Columbus was born. Eratos-thenes, about the year 200 B.C., measured thecircumference of the earth and found it to beabout 250,000 stadia, or some 30,000 Englishmiles. This is some twenty per cent, too great,for according to the latest measures, the equatorialcircumference of the earth is slightly less than25,000 miles.

In making such a determination of the earth'ssize, it is only necessary actually to measure asmall portion of the circumference. One degreeis one three hundred and sixtieth part of a circum-ference, and if the distance in feet and miles be-tween two points just one degree apart be found,then will the entire circumference* of the earth bejust three hundred and sixty times the distancebetween these two points. It is not essentialthat the two points be just one degree apart;

The Earth as an Astronomical Body 3

they may be at any convenient angular distance,the greater the better. Thus the actual problemof measuring the earth consists of two distinctoperations; namely:

1. The measurement of the angular distancein degrees, minutes, and seconds between twopoints on the earth's surface : this angular distanceis usually the difference in latitude between thetwo chosen places.

2. The meastirement of the actual distancealong the surface of the earth in miles, feet, andinches between the same two places.

There is no great difficulty in the first of theseoperations. Astronomical instruments and meth-ods are now so acciarate that the latitude of aplace can readily be determined to within onetenth of a second of arc, or to within i2,9m,(m P^^of the circumference. To obtain this degree ofaccuracy, carefully built and mounted instrumentsare necessary, but the astronomical methods bywhich the latitude is determined do not differessentially from those used at sea. And thesemethods are fully outlined and explained inChapter VIII.Far different, however, is the second part of

the problem, the accvirate measurement of thedistance between the two stations selected as theends of the arc. From the time of Eratosthenesthis portion of the problem has presented great-difficulties. The surface of the earth is roughand is traversed by valleys, by hills, and by rivers.

4 Nautical Science

Over such an uneven surface the determi-

nation, in feet and inches, of the distanceapart of two marks, separated by even a fewmiles, becomes extremely laborious and con-sumes much time and patience f the actualphysical measurement of great distances be-

comes impossible. Such distances are now de-termined by means of an elaborate survey andtriangulation.

The two points, whose distance apart is required,are connected by a series of triangles, the comersof which are marked by elaborate posts or signals.At each station, thus marked, the angles of thevarious triangles meeting at that point are care-fully measured. Thus are found the three anglesof each and every triangle of the series. Now, ifthe angles of a triangle and one side are known,the lengths of the other two sides can be foimd bysimple calculations. Hence if but one side of thefirst triangle be measured, the lengths of the othertwo sides can be found from this and the measuredangles. One of these two sides is also a side of thesecond triangle, and from this known length andthe angles the lengths of the other sides canreadily be found. Similarly for the third triangle,one of its sides is also a side of the second, and isthus known from calculation. From the measuredlength of one side of the first triangle are thuscalculated the lengths of the sides of all the tri-angles and finally the required distance betweenthe two places. The side which is actually

The Earth as an Astronomical Body 5

measured is usually comparatively short and isthe so-called "base-line."

For measuring the base-line metal rods or barsof known lengths are used. These are placed endto end and the length of the base-line measured offjust exactly as one would measure the length ofa room with two yardsticks, always picking upthe back one and laying it down in front of andjust touching the forward end of the other. Greatcare must be exercised in having the rods exactlylevel and pointing in a straight line. For thisreason the path along which the measurement ismade is carefully prepared and levelled before-hand. The difficulty of the operation is consid-erably increased by the fact that the rods changetheir lengths with the varying temperatures towhich they are of necessity exposed, when takeninto the open fields. Many devices have been usedto overcome this temperature difficulty, one ofthe simplest and best being the Woodward "ice-bar apparatus." In this the metal measuringbar is supported in a trough and completelypacked in ice and thus maintained at a uniformtemperature of 32 F.Arcs of the meridian have been measured in

various parts of the earth, and the results of thesevarious measures do not agree. In the northernparts of Europe a degree of latitude is nearly69.4 miles long, whilst near the equator onedegree is but 68.7 miles. These show that theearth is not an exact sphere, that it approaches

6 Nautical Science

more nearly to the figure of an ellipsoid. Thatis, the equator and all the parallels of latitudeare almost exact circles, while the meridians,

which run from pole to pole, are of a distinctelliptic form. Again the equatorial diameter, asmeasured from the Atlantic to the Pacific, is sometwenty-seven miles longer than the diameter along

the axis from pole to pole. This flattening at thepoles and bulging out at the equator was probablycaused many millions of years ago when the earthwas a hot, plastic mass. In fact it can be shownmathematically that a rotating fluid or viscousmass will always become ellipsoidal in shape. Thiscan also be shown experimentally in a number ofways, the simplest of which, perhaps, is by meansof a light metal ring, so movmted that it can berotated with great rapidity about a vertical di-ameter. When the ring is at rest it is circular inshape, but when it is rotated, it becomes flattenedalong the axis, bulging out at what we may callthe equator. The faster the ring is rotated, thegreater and greater becomes its departure fromcircular shape.

The earth, however, is not an exact ellipsoid.The latest measures indicate that the equator isnot a perfect circle and that there are manyplaces where local and continental irregularitiescause the actual surface to depart greatly fromany known geometrical figure. The equatorialdiameter which passes through Ceylon and theGalapagos Islands off the coast of Ecuador is

a.a.

= uncorrected dip in minutes.to = temperature of the water in degrees

Fahrenheit.t =temperature of the air at height of the eye.

26

Notes and Practical Applications 27

Hence

:

When the air is cooler than the water, the cor-rection is positive ( + ) and the dip increased.

When the air is warmer than the water, thecorrection is negative (-) and the dip isdecreased.

(c) Including the mean refraction (average stateof the atmosphere) the dip is given by:Dip (in minutes) = o'.gS Vh (in feet)

.

Distance (in miles) = 1.16 V^ (in feet).(d) The parallax in altitude, p, of any body isgiven by:^=7r cos h,

where:h = the observed altitude.7r = the horizontal parallax as given in the

Nautical Almanac.

3. Practical examples.The examples in this and following chapters were

taken from actual practice at sea. They show themethods of using the tables and correcting the ob-served altitudes. The dates of the various problems,however, have all been brought up to 1908, so that asingle almanac will furnish the data for any one whowishes to check the figures. The Tables for dip, re-fraction, etc., will be found in the appendix.

(a) Altitude of the Sun:

At sea Nov. 26th, in D. R. latitude 40 30' N. themeasured altitude of the sun's lower limb was 28 32';index correction, + i' 30"; height of eye, 30 feet.Required the sun's true altitude.

28 Nautical Science

Observed altitude O =

Notes and Practical Applications 29

(b) Altitude of Star or Planet:

On June 19th, the observed altitude of Vega was41 4s' 20"; no index correction: height of eye 15 feet.Required the true altitude.

Observed altitude = 41" 45' 20"Dip (Table II) 3' 49"Refraction (Table IV) i' 5*

*'s true altitude = 41 40' 26"

On Sept. 9th, the altitude of Saturn was measuredas 23" 45' 00"; no index correction: height of eye 15feet. Required the true altitude.

Observed altitude = 23 45' 00"Dip (Table II) - 3' 49"Refraction (Table IV) 2' 13"

*'s true altitude = 23 38' 58"

The parallax is so small that it can be neglected.Only in exceptional cases need the parallax of aplanet be taken into account. When Mars is inopposition the parallax might amount to 10" or more.

CHAPTER II

the motions of the earth

The Rotation of the Earth

DURING the ages of Greek supremacy inthought and for many centuries thereafter,

the earth was considered as immovably fixed atthe centre of the universe. Philolaus, a Greek phi-losopher, however, who lived in the fifth centurybefore the Christian Era, regarded the earth, aswell as the sun, moon, and planets, as revolvingabout a great central fire, the earth turning aboutan axis as it revolved, so that this central fire

should ever remain concealed from the inhabitants.From this time on many of the ancient writersseem to have favourably considered the idea of arotating earth, but no one grasped the essentialfacts. The regular alternation of day and nightwas thought to be caused by an actual dailymotion of the sun around the earth ; the fact thatthe change from daylight to darkness and fromdarkness to daylight is caused by a simple rota-tion of the earth was not clearly recognised anddid not become an accepted scientific belief until

30

The Motions of the Earth 3

1

some fifty years before Columbus discoveredAmerica.To-day there are numerous ways in which the

rotation of the earth can be demonstrated. Forexample, if a number of bodies be dropped from avery great height there is found to be a tendencyfor them to fall to the eastward. Small and per-fectly round balls have been dropped with greatcare into deep mines, and careful measurementsshow that they strike the bottom a small fractionof a foot to the eastward of the point verticallyunder the starting-point. The top of the mine isfarther from the centre of the earth than the bot-tom and is therefore moving faster toward theeast, and a body dropped from the upper partretains its eastward motion as it falls and strikes tothe east when it reaches the bottom. Similarly aball thrown from a moving train partakes of themotion of the train and reaches the ground manyfeet in advance of the object at which it is aimed.As a result of many trials with bodies having afree fall of 520 feet, an eastward deviation of1. 1 2 inches was observed. According to theorythis deviation should have been a trifle less, oronly 1.08 inches.But the best and most striking experimental

proof of the rotation of the earth is that devised

in 1851 by Foucault, who in that year swung hisfamotts pendulum from the dome of the Pantheon.This pendulum consisted merely of a heavy ironball supported by a thin flexible wire, which was

32 Nautical Science

securely fastened to the dome in such a mannerthat the bob could swing freely in any direction.Now if such a pendulum be started swinging, it

will, unless disturbed, continue to swing in thesame plane. If hung directly over the north poleand started swinging in such a manner that thebob moves in a line directly to and from the sun,it will continue so to swing and the bob will alwaysmove in a line directed towards the sun. But theearth rotates from west to east and the sunapparently moves toward the west, and, as thebob of the pendulvim keeps pace with the sun, thedirection of its swing would apparently shiftarotind toward the west. In other words, theearth would turn around under the pendulum,and complete a revolution every twenty-fourhours.

When such a pendulum is set up in any placeother than the north or south poles, the effect willbe similar but not identical. In the northernhemisphere the pendulum would appear to deviateslowly towards the right, in the southern hemi-sphere toward the left, and the amount of thedeviation depends upon the latitude of the placein which the pendulum is supported. The reasonfor this deviation will be made clear by a moment'sconsideration. A point of the earth's surface atthe equator moves eastward at the rate of onethousand miles an hour; from the equator thisspeed gradually diminishes from a thousand milesper hour to nothing at the poles, for at the poles

Plate III

Foucault's Pendulum at Columbia University


themselves the surface is stationary. In thelatitude of New York this eastward motion of therotating earth is somewhat greater than sevenhundred and fifty miles per hour. When hangingat rest all parts of the pendulum partake of thiseastward motion, and starting the ball swingingin a north and south plane will not destroy or alterthis motion. When, however, the ball reachesthe north end of its swing, it will be farther fromthe equator than when at rest, and it will then betravelling to the east a little faster than the pointof the earth then directly underneath it. Hence inswinging to the north the ball will apparentlydeviate a little to the east of a north and southline. When the ball is at the south end of itsswing, it will be moving a trifle slower than theearth tmdemeath, and it will be left behind ordeviate to the west of the south direction . At eachswing of the pendulum, it will deviate more andmore from a north and south line, and this appar-ent turning to the right will continue so long as thependulum can be kept vibrating. In New Yorkthis shift is a little less than ten degrees per hour,an angle through which the hour hand of a watchmoves in about nineteen minutes. This is suffi-ciently rapid for ordinary observation and thussuch a pendulum makes the rotation of the earthclearly visible.

To the rotation of the earth combined withits ellipsoidal shape is due a phenomenon whichhas been known for over twenty centuries. The

34 Nautical Science

"vernal equinox," the Greenwich of the heavens,is the point of intersection of the celestial equator

and the ecliptic, the apparent yearly path of thesun through the heavens. Now, one hundredand twenty years before the Christian Era, Hip-parchus found that this point is moving slowlyto the westward along the ecliptic, advancing tomeet the sun as each year it returns to the equator.Hipparchus called this motion the "precession ofthe equinoxes."

This slipping of the equinox backwards alongthe ecliptic is caused by a motion of the northcelestial pole, which travels aroimd and around acircular path among the stars. At present thismotion is carrying the north pole towards theNorth Star, so that to future generations the NorthStar will be a more accurate guide than it is at thepresent moment. Very slowly, indeed, does thepole travel along this path: in the span of anordinary lifetime it moves over a portion of the skysomewhat less than half the diameter of the fullmoon; it requires nearly 26,000 years for the poleto make one complete circuit of the heavens. Noris this motion exactly \miform, at times the polemoves at a greater speed, and at times more slowlythan the average, and it also wabbles a little toone side or the other of its prescribed path. Theaverage motion of the pole is technically the" precession, " while all the variations in this aver-age motion, all the wabblings, are technically called"nutations "


Precession and nutation may be illustratedwith a spinning top. When the axis about whichthe top spins is exactly vertical, the top apparentlyremains at rest or "sleeps," the axis pointingdirectly towards the zenith. When, however, theaxis of the top is tilted, then the top itself beginsto wabble; the iron point remains at rest on thefloor, but the upper part of the top swings roundand round in a circle which gradually increasesin size as the top slows down. As soon as thespinning ceases the top falls over on its side.Thus the circular motion of what might be calledthe north pole of the top is caused by a combina-tion of the rapid spinning of the top about its axisand of the force of gravitation which tends tomake it fall over on its side.

In the case of the spinning earth the attractionof the Sim and moon upon the protuberant matternear the equator replaces the force of gravitationwhich causes the top to fall over. If the earthwere spherical or if the sun and moon were alwaysin the plane of the equator, then there would benone of this tilting effect and the axis of the earthwould, like the axis of a "sleeping" top, remainfor ever pointing in the same direction.This motion of the pole and the consequent

precession of the equinoxes introduces compli-cations into astronomical measurements. Thepositions of all the stars are apparently changing,for these positions are all referred to the vernalequinox, and the vernal equinox is itself in

36 Nautical Science

motion. As this motion is accurately known,however, the apparent shift in position of any

star can be calculated. These shifts have beencalculated for the principal stars, and their posi-tions at various dates are tabulated in the Nauti-

cal Almanac.A second pecioliar and at first sight startling

effect of the rotation of the earth has been dis-covered within the last few years. The latitudeof a place is not constant : the distance from theequator to any other point on the earth's surfaceis changing from day to day and from year toyear. This variation of latitude was first de-finitely shown to exist by Chandler in 1891. Itarises from the fact that the axis about which theearth rotates is not fixed in the earth; the northpole, or point where this axis cuts the surface,wanders aroimd in an irregular curve, coveringin its wanderings an area equal to nearly twocity lots. As the equator is an imaginary circleeverywhere 90 distant from the poles, it mustoscillate back and forth over the surface, keepingpace with the movement of the pole, and thuschanging the latitude of every spot on the earth'ssurface.

This variation of latitude is rather minute, theextreme shift being some o".6, which correspondsto an actual motion of 60 feet. That is, at onetime each building in New York City is 60 feetnearer the equator than at other times. Duringthe years 1893-1900 an extensive series of latitude


observations was made at Columbia University.The latitude was the smallest on September 15,1895, and greatest on August 22, 1897, the total

-0.'20

0^

-aio

aoo

+oio

+0'80

-030

fOTBO -t-oao 0.00 - o;io -0.80

Fig. 3. The Wanderings of the Earth's Pole during the Yearsigoo-igoS

variation between these extremes being o".696, orvery nearly 70 feet.

Motion about the Sun

Besides the rotation about its axis, the earth

38 Nautical Science

has an actual motion through space: it is travel-ling about the sun in an immense elliptic path, ororbit, as it is called. To us on the flying earth,however, it is the sun, not the earth, which ap-pears to move, just as when we are on a smoothlyrunning train the trees and hills appear to rush bythe windows. In fact, for many centuries thisapparent motion of the sun was considered as anactual motion of that body around the earth, andit was not until the time of Copernicus and Gal-ileo that the motion of the earth was distinctlyrecognised.

This apparent motion of the sun through theheavens can be detected by the simplest obser-vations. In general it rises each day in the eastand sets in the west ; but only on two days a year,March 21st and September 21st, does it rise exactlyin the east and set exactly in the west. Duringthe summer months the sun rises to the north ofeast and sets far to the north of west: in winterit rises to the south of east and sets to the southof west. Further, in summer it rises far higherthan it does in winter ; at noon in the latter part ofJune at New York the sun is nearly 70 above ourhorizon, in December it rises but a scant 25above the southern horizon. The sun thus ap-pears to oscillate back and forth, in summer be-ing far to the north and in winter far to thesouth of the celestial equator.

If the stars were visible in the daytime it wouldbe seen that the sun also moves slowly and steadily


to the eastward. While the stars cannot be seenin the day and the motion of the sun among themactually observed, yet the effect of this motion canbe easily noted by watching the constellations atnight. At midnight that portion of the heavenswhich is directly opposite the sun will be on themeridian. At twelve o'clock on a clear Decembernight, the beautiful constellation of Orion will befotmd on the meridian about half-way between thesouthern horizon and the zenith. Each succeedingnight Orion will reach the meridian about fourminutes earlier, and after a week has elapsed itwill be found on the meridian at half-past eleveninstead of at twelve. By the middle of FebruaryOrion culminates in the early evening and byspring it is visible in the western sky for a fewminutes after sunset. The constellation thus ap-pears to move westward towards the sun, and aseach and every other constellation partakes ofthis westward motion, it is clear that this apparentwestward motion of the stars is in reality the effectof the eastward motion of the sun.By combining this eastward motion of the sun

among the stars with its north and south oscil-lation it is easily seen that the actual path of thestm around the heavens is in a path inclined 23^to the equator. This path is called the eclipticand in it the sun makes one complete circuit of theheavens in a year. It must always be remem-bered, however, that this apparent motion of thesun is due to an actual motion of the earth in the

40 Nautical Science

opposite direction ; the apparent eastward motionof the sun indicating a real motion of the earth tothe westward.Now, while it is customary to speak of the period

in which the earth travels about the sun as a year,yet a little consideration will show that the termyear is not definite, tmless certain careful dis-tinctions are drawn. In fact there are severaldifferent kinds of years, depending upon the pointin the orbit from which the period is reckoned.A " sidereal year," for example, is the interval be-tween two successive returns of the sun to thesame position among the stars; a " tropical year,"the interval between two successive returns ofthe sun to the vernal equinox. This latteryear is that upon which the seasons depend andis the year of ordinary, every-day conversation.These two years, the sidereal and the tropical,are not of the same length, for, as we have seen,the vernal equinox is in motion, is moving alongthe ecliptic in the opposite direction to thatin which the sun appears to move. In factit was this difference in the lengths of theyears which led Hipparchus to the discovery ofprecession.

The sidereal year measures the actual time thatit takes the earth to make one complete revolutionabout the sun. It is 365.25634 days, or 365" 6"9"" and 9^.4 long. The tropical year is a trifleshorter, its length being 365" 5" 48"" and 47'.5.Further the actual tropical year is not of constant


length, for the vernal equinox does not moveforward uniformly. When the equinox is movingfaster than usual the year will be a few secondsshorter, when the equinox moves more slowly, theyear will be longer. But as this variation in themotion of the equinox, or nutation, as it is called,is very small, the actual difference in the lengthsof various tropical years will be very slight. Theaverage value is that given above.Now the great orbit or path in which the earth

moves about the sun is some 185,000,000 milesin diameter. This path, however, is not circular

;

it is a sort of oval curve, a curve known to mathe-maticians as an ellipse. And ftirther the sun isnot at the centre of the curve, but slightly nearerone end, at a point called the focus. Differentparts of the curve are thus at different distancesfrom the sun, and as the earth travels around andaround its orbit each year, it will be at continuallyvarying distances from the sun. In January theearth is nearest the sun, or is at perihelion, andat this time it is some 3,000,000 miles nearer thanin midsummer. The apparent size of a bodyvaries inversely with its distance; the fartheraway a body is, the smaller it appears. The sun,therefore, should appear larger in January than inJuly, and careful measurements show this to be so.On January 3d the apparent semi-diameter of thesun is some 32" greater than on July 4th.

Further, the earth does not move at a constantspeed in this orbit; when it is nearer the sun it

42 Nautical Science

moves faster than when at a greater distance. Onthe average the earth moves forward at a rate ofabout nineteen miles per second, about fifty timesas fast as the bullet from a modem rifle. Atperihelion this speed is increased to 19.3 miles persecond, while at aphelion it drops down to only18.7 miles. A direct statement of the speed atwhich the earth moves at various distances fromthe sun involves complicated mathematical formu-las, but there is an indirect relation betweenspeed and distance, which was discovered byKepler nearly three hundred years ago. Thisindirect statement is involved in what is knownas Kepler's second law of planetary motion. Hisfirst two laws which apply to the earth and all theother planets of the Solar System are so import-ant and so easily understood that they are herereproduced. They are:

1. Each planet describes about the stm anellipse, the sun being at one focus.

2. The straight line joining a planet to thesun sweeps over equal areas in equal intervalsof time.The first law gives the shape of the path that

each planet describes about the sun: the second,the speed with which the planet moves in variousparts of its orbit. In order that the areas sweptover each day by the line joining the planet tothe sun shall always be equal, the planet mustmove faster when nearer the sun than at othertimes. Now these two laws are exemplified in the


following diagram, which, however, does notrepresent the real path of any definite planet : theeccentricity of the ellipse being much exaggerated.For the actual orbits depart so slightly fromcircles, that, in a diagram drawn to scale, the eye

Fig. 4. The Orbit of tlie Earth

could hardly distinguish the difference betweenellipse and circle.The half major axis of the ellipse, or the dis-

tance CA, is called the " mean distance," and inthe case of the earth this is about 93,000,000 miles.This distance of the sun from the earth is so great

44 Nautical Science

that the mind fails to grasp it unless some concreteillustration is used. A seasoned walker can aver-age s miles per hour and if he walk 20 hours eachday he will average 100 miles per day. Walkingthus day after day and year after year such apedestrian would require nearly twenty-six cent-uries to cover the distance between here andthe sun. Again another illustration. Tlie greatturbine ship Mauretania, the largest and fastest ofthe great ocean liners, made 624 nautical milesbetween noon of one day and noon of the next.This is at the rate of nearly 29 ordinary, or land,miles per hour. Now if the Mauretania travelledat that average speed day and night, without astop, she would require nearly four centuries topass over a distance equal to that of the sun fromthe earth. Had Columbus sailed from Spain inthe Mauretania and voyaged toward the sun hewould but now have reached his destination.The sun is at one focus, S, and the distance

C S between S and the centre determines the shapeof the curve. The ratio of CS to CA is called the" eccentricity " of the orbit, and this eccentricitydiffers widely for the various planets. In thecase of the earth it is about ^; the focus beingabout 1,500,000 miles from the centre of the orbit.The point at which the planet approaches the sunmost closely is called the " perihelion " ; the point atwhich it attains its greatest distance, " aphelion."In this elliptic orbit the earth travels about the sunfrom west to east, moving at every point at such a


speed that the law of areas holds true. When atperihelion the earth will in one week pass from Pto R, when at aphelion, a somewhat less distancefrom A to B, in the same interval. The areasof the sectors PSR and ASB are equal, and inthe diagram these equal areas are shaded. Theearth passes through perihelion on or about thefirst of the year, and, thus being nearer the sunin winter, it passes over one half, or 180, of its

orbit faster than it does in summer. In fact thenorthern winter is about three days shorter thanthe summer.As a whole the earth receives nearly six per

cent, more heat in twenty-four hours in December,than it does in a corresponding interval in June.For the amoimt of heat received increases as thesquare of the distance from the sun decreases, andin December the earth is about three per cent,nearer the sun than in June. But December ismidsummer in the southern hemisphere and hencethe southern summer should be hotter than thenorthern. On the other hand the southern sum-mer is three days shorter than the northernand this shortness of the summer about counter-balances the extra amount of heat received eachday, so on the whole there is no radical differencebetween the summers in the two hemispheres.Far different, however, is the winter climate in

the two hemispheres : the southern winter is bothlonger and colder than the northern. This applies,of course, only to the hemispheres as wholes. The

46 Nautical Science

climate of any particular place is so modified bylocal conditions that it is next to impossible tomake definite comparisons of two widely sepa-rated points and to determine that one actuallyreceives less heat than the other. But if the twohemispheres were identical as to land, water, eleva-tions, forests, etc., then it is clear that of twoplaces similarly situated on opposite sides of theequator the southern one would have the colderwinter, and the hottest day in summer.

NOTES AND PRACTICAL APPLICATIONS

Astronomical Constants:Parallax of sun 8" .80General precession (1900) 50" .2564Constant of nutation 9" .21Constant of aberration 20"

.47

Time required for light totravel from sun to earth 498'

.5

Earth's Orbit:

Longitude of perihelion (1900) 101 13' 15". oObliquity of ecliptic (1900) 23 27' 8". 26Mean daily motion in orbit 0 59' 8". 1928Eccentricity of orbit o. 01675

Mean distance of earth from sun, 92,897,000 milesGreatest distance " " " 94,458,000 "

Least distance of " " " 91,336,000 "

Length of Julian year, 365.25 days =365*Length of Tropical year, 365.2422 days = 365''

S" 48" 45 "-5

1

Length of Sidereal year, 365.2564 days =365 "^

6 " 9 " 8^97

47

CHAPTER III

THE SUN

THE heavenly bodies may be divided into twoclasses: the so-called "fixed stars" and the

bodies of the solar system. The fixed stars arecountless in number. They are seen always in thesame portions of the heavens and appear in themost powerful of telescopes as mere points of lightwithout form, size, or shape : the bodies of the solarsystem on the other hand are few in number,they wander through the heavens visiting thedifferent constellations, and by the aid of thetelescope their shape, size, and surface conditionsmay be studied. Of all these celestial bodies

stars, sun, moon, and planets^the most importantto the inhabitants of the earth is the sun.The countless myriads of stars and the numerous

planets could be blotted out of existence withoutsensibly affecting our daily life ; the moon mightbe shattered into fragments and dispersed through-out space without materially changing the con-ditions under which we live and exist ; the nights

48

The Sun 49

would be dark, the tides and currents which sweepour coasts would be radically modified, and thelengths of the day and the year might even bechanged to an appreciable amount, but we couldstill go on living our lives, pursuing our businessand our pleasures as we do to-day. But if thesun ceased to shine the days of the world wouldbe numbered.The sun is the centre from which is derived the

heat, the energy, the life of the earth. In winterthe sun does not rise so far, nor remain so longabove our horizon as in summer, and to the differ-ing amounts of heat thus given us are ascribedour ever-varying seasons. The variations inclimate, the difference between the torrid heat ofthe tropics and the rigours of an arctic winter, arecaused by the radically different amotmts of solarheat received. A sensible increase or diminutionof the solar radiation would modify the climateof the entire world. A radical decrease in theamotmt of heat received from the sun would causethe polar ice to spread toward the equator, wouldproduce an age of ice and snow and bring deathand destruction to the inhabitants of our world.The earth, undoubtedly, has internal heat of itsown, but if the sun ceased to warm the atmosphere,for even a single month, the earth would grow coldand ttninhabitable.From the earliest times the principal facts

about the sun, those which are of special inter-est to the navigator, have been known. From

so Nautical Science

pre-historic ages the path of the sun through the

heavens has been recognised and the length ofthe year known to within very narrow limits.One hundred and thirty years before the Christianera Hipparchus had determined the length ofthe year, with an error of less than seven minutes

;

three centuries before Christ, Aristarchus hadmeasured the relative distances and sizes of theearth, and moon, and the sim. He knew thesun as a vast globe many times larger thanthe earth and some millions of miles distant.

During the twenty and more centuries whichhave elapsed since Aristarchus lived and madehis crude measures, many wonderful inventionshave been made, giant telescopes have been con-structed, and powerful methods of mathematicalanalysis brought into use. Corresponding ad-vances have been made in our knowledge ofthe size and distance of the sun. It is now knownthat the stin is a great globe between 860,000and 870,000 miles in diameter and nearly 93,000,-000 miles distant. The direct determination ofthis distance is impossible. From the laws ofplanetary motion, however, we know the correctshapes and the relative sizes of aU the planetaryorbits ; we have a correct map of the solar system,but a map without a scale. If any distance on themap be foimd, the scale can be at once determined,and all other distances found. Now, at times. Marsapproaches the earth much closer than the sun,and at these times the distance between the earth

The Sun 51

and Mars may be found and the scale of thewhole map determined. This distance is found by-means of "parallax"

a, very long name for a verysimple thing. Every navigator is familiar withthe "bow and beam" or "four-point bearing,"by which a ship's distance from a rock or light-house may be found. A vessel sailing due westfinds a light on her starboard bow bearing north-west ; after running on her course for five miles bythe patent log the light is abeam, or bears north;at this moment the light will be five miles distant,the distance rim by the log and the distance of thevessel from the shore being exactly equal. Nowthis change in the apparent direction of the light-house, caused by a real change in the vessel's posi-tion, is what is called in astronomy, "parallax."And by means of this parallax or change inbearing, together with the distance travelled bythe ship, the distance from the lighthouse canbe fotuid by simple geometry.In astronomy the parallax of a body. Mars for

example, is the difference in direction in which itis seen by an observer, or observers, in two differ-ent positions. And as with the ship, as soon asthe parallax and the distance through which theobserver has moved is known, then the distanceof Mars can be found. But, while in the caseof the vessel the change of bearing, or parallax,is four points, in astronomy the parallax of Mars isonly 20" or a trifle less than ^imF of a point. Thebest direct measvirement of this little shift was

52 Nautical Science

that made by Sir David Gill on Ascension Islandin 1877. The method he used was simple, effec-tive, and easily understood. The planet must beobserved from two or more different positions:

now Gill utiHsed the daily rotation of the earth

on its axis to carry him from point to point as hemade his observations, just as the ship carries thenavigator by the lighthouse as he makes his"bow and beam" bearing. In the early eveningas the planet was just rising above the easternhorizon he observed carefully its direction, itsbearing, as shown by its place among the stars.Six hours later the earth had made a quarterrevolution on its axis and Gill had been carriednearly six thousand miles to the eastward. Againhe measured the position of the planet in relationto the fixed stars, and the apparent shift or changeof position among the stars since the earlierobservation was the parallax. The two observa-tions were never actually made just six hoursapart: one was made in the early evening andthe other just before sunrise the next morning;but by noting the time which elapsed between thetwo observations, the distance through which hehad been carried by the rotation of the earth couldbe readily calculated, and this together with thecorresponding shift of Mars enabled him tocompute the distance of the planet.The Island of Ascension was chosen for these

observations because it is but 8 from the equator,and consequently the daily path of the observer

The Sun 53

is nearly the longest possible. At the pole anobserver would be stationary and the methodinapplicable. For the accurate measurement ofthe shift Gill took with him a heliometer, the mostdelicate instrument known to astronomy. Withit he made over 350 determinations of the parallaxof Mars, and these measurements are probably themost precise of modem astronomy; the probableerror in the determination of the planet's positionon any single evening being only about iV of asecond of arc, or 400,000 ' of a compass point.The sun itself is a globe of incandescent gases

and vapours and so nearly spherical in shape thatthe most accurate measures of modem times havefailed to show any distinct departure from thatform. Newcomb and Ambronn regard the helio-meter measures as conclusive evidence that thesun is sensibly a sphere. Yet these measures areso difficult to carry out with accuracy, that toomuch weight should not be placed upon them.All the other bodies of the solar system, like the.earth, show distinct elliptical discs, and it isbarely possible that the sun may be ellipsoidalto a very minute extent. It is certain, however,that the extreme difference between the equatorialand polar diameters of the sun cannot exceedo'-'.as, or, in other words, that the equatorialdiameter does not exceed the polar by so muchas one hundred miles.The great size of the sun as compared to the

earth can best be shown by illustrations. If the

54 Nautical Science

American fleet could have proceeded directlyaround the world, steaniing day and night at itsaverage seagoing speed, it would have completelycircumnavigated the globe in one hxindred days.Proceeding at the same rate it would take such afleet thirty-one years to complete a voyage aroundthe sun. Again, so vast is the sun, that were it ahollow globe, the earth and moon could be trans-ported and placed within the hollow ; the earth atthe centre and the moon in her orbit, 250,000 milesfrom the earth, would never be but little morethan half way out towards the sun's surface.When the sun is viewed through a telescope its

surface is often found to be covered with dark, ir-regular spots. And these dark sun-spots are seento be in motion ; when watched from day to daythey appear to travel slowly across the luminousdisc. They appear on the eastern edge of the sun,move slowly toward the centre, cross the disc,and disappear at the western limb. Whether thespots pass through the centre, or along a shorterchord above or below the centre, the actual timeof crossing the disc is always about the samenumber of days. In this motion of the spots is re-cognised an actual rotation of the sun just as theearth rotates each day about its axis. In the caseof the sun, however, the rotation is extremelyslow and stately, each stm day being abouttwenty-six of our days in length. There is,however, a marked difference between the rota-tion of the sun and the earth: the sun does not

I'LA'IE 1\'

Solar Cyclones, Photographed at the Carnegie Solar Obseivatoiy

The Sun 55

rotate as a whole. Spots near the equator com-plete an entire revolution in a much shorterperiod of time than do spots in high latitudes.This equatorial acceleration is somewhat morethan two and a half days ; a spot on the equatorrequiring not quite twenty-five days to completea single circuit, while a spot in latitude 45requires twenty-seven and one-half days. Spec-troscopic investigations show that this peculiaritycannot be explained by a mere drift of the spotsover the surface of the sun, for the entire surfaceparticipates in this rotation. The latest resultsobtained by Adams at the Mount Wilson Observ-atory indicate that particles at the equator of thesun rotate in 24.6 days and that the speed ofrotation steadily decreases from the equatortowards the pole. In latitude 50 the period ofrotation is about 28.8 days, in latitude 60, 31.3,while in latitude 80, the particles composingthe surface of the sun require nearly 35.5 daysto complete one circuit.

This rotation is proof sufficient that the visiblesurface of the sun is not a solid rigid body; itmust be liquid or gaseous. The earth's equatorcrosses the west coast of Africa a few miles northof the mouth of the Congo River, while far to thenorth and upon the same meridian of longitude isto be found Genoa in latitude 45, and Cristiania,the capital of Norway, in latitude 60. Nowif the earth rotated as does the sun, then a dayin Africa would be 24, a day in Italy 28, and a

S6 Nautical Science

day in Norway over 31 hours long. At the endof one Norwegian day, Genoa would have slipped40 to the east and be where now is the CaspianSea, Africa would have slipped 100 and havetaken the place of Borneo. At the end of threeand a half days Africa would have occupied allpositions on the equator, and again be founddirectly south of Norway, but Italy would be lostin the deep waters of the Pacific to the eastwardof Japan.

While the matter near the surface of the sunmust thus be very tenuous, yet as a whole thesun is much more dense than any gas known onthe earth. Its average density is nearly one anda half times that of water, about the same as thelighter rocks on the earth's surface. This averagedensity is found from the known diameter of thesun and from the total amoimt of matter whichit contains. This latter can be calculated fromthe force of attraction, which the sun exerts uponthe earth and upon the other bodies of the solarsystem, and this force of attraction can be meas-ured by the length of time required for eachplanet to travel about the sun; by the lengthof the year for example. It can readily be shownthat if the amount of matter in the sun werequadrupled, then the year would be only onehalf as long as at present.

If the sun and earth were at the same distancefrom a given body then the sun would attract thatbody 330,000 times more powerfully than does

The Sun 57

the earth. The sun contains 330,000 times asmuch matter as the earth. Yet this matter fillssuch a large globe (the sun's diameter is notimes that of the earth) that the average densityof the sun is only about one quarter that of theearth. And at the sun's surface, moreover, theattraction of gravity is only twenty-eight timesthat upon the surface of the earth. Here if a smallbody be dropped it falls 16 feet in the first second,on the sun such a body would fall 444 feet and atthe end of the second second it would be movingwith the speed of a cannon-ball. A man who hereweighs 175 pounds would, if transported to the sun,weigh nearly two and a half tons, and would becrushed imder his own weight.The spectroscope shows that the sun is com-

posed of very much the same kind of matter asis the earth. Most of the ordinary elementsof which our earth and rocks are composed arefound in the sun in the form of incandescent gases.Sodium, carbon, iron, lead, copper, silver, andmany other terrestrial elements are as commonon the sun as they are on the earth ; in fact, so faras chemical constitution, the sun seems to benothing more than an immensely large andintensely heated earth.The effective temperature of the sun's visible

surface is at least 10,000 Fahrenheit. Some ideaof what this means may be gathered when it isremembered that lead melts at about 800, castiron at a little over 2000, and that the tempera-

58 Nautical Science

ture of the molten metal in a blast furnace is under4000. Of course this estimate of the sun's tem-perature is more or less approximate, for from

the very nature of the problem it is impossible toreach an accurate conclusion. We cannot put athermometer in the sun and directly measure itstemperature. But we know that the characterof the radiation emitted from a body dependsupon its temperature. When a cannon-baU isheated, it first sends out rays which can be feltas heat, but which do not affect the eye. Ifplaced in a dark room, the heat from the ball canbe felt at some distance, but the ball itself cannotbe seen. As the ball becomes hotter it turns a dull-red and becomes faintly visible. After a while,as its temperature rises, it becomes white hot.The kind of radiation given off by a body thusaffords an indication as to its temperature, andwe can study the character of the sun's light, andthus indirectly estimate its temperature.

Another similar problem relates to the amountof heat, or energy, given off by the sun and receivedby the earth. Heat and temperature are notmerely different words for the same thing; theyare essentially different, heat is a form of energy,while temperature is the amount of heat ineach molecule of a body. Temperature representsrelative concentration of heat; it is a measure ofintensity, not of quantity. A body may containvery little heat and yet be at a high temperature.A pint of boiling water contains far more heat

The Sun 59

than the flame of a candle, but the temperatureof the flame is the higher. It takes twice as muchheat to raise a quart of water to the boihngpoint as it does for a single pint

;yet when both are

boiling, the temperatures are the same. Quantityof heat may thus be measured in terms of theamount of water it will raise from one temperatureto another, and the unit quantity is termed a"calorie." Thus temperatures are measured bydegrees, quantities of heat by calories.Now while the temperature of the sun is more

or less a matter of inference and speculation, thequantity of heat emitted by it and received bythe earth can be measured with considerableaccuracy. The presence of the atmosphere in-troduces some diflficulty, however; for the sun'srays must pass through many miles of atmospherebefore they reach the measuring apparatus,and in this passage a large proportion of theenergy is absorbed. Langley found that nearly40% of the stm's energy thus failed to reach thesurface of the earth, but it is not to be assumedthat this absorbed energy is lost to the earth ; onthe contrary, it warms the atmosphere and helpstowards making our globe habitable.The latest researches show that the total quan-

tity of heat and light received by the earth fromthe sun is tremendous. In each hour sufficientheat falls upon the upper layers of the earth's at-mosphere to melt a sheet of ice nine tenths of aninch thick ; in a year the heat from the sun would

6o Nautical Science

melt a sheet of ice covering the entire surface of the

earth and 164 feet thick. Another way of illus-trating the immense amount of energy receivedfrom the sun is by means of the mechanicalpower it would produce if completely utilised.Upon every six and a half square feet of the earth'ssurface there is received on a cloudless day,

when the sun is directly overhead, suflficient energyto develop one horse-power. An engine of ahundred horse-power will drive a small steamer,or furnish electricity enough to light a smallvillage, and each city lot receives at high noonsolar energy enough to run four such engines.Upon the deck of the Lusitania there is pouredenergy sufficient to develop five thousand horse-power. Unfortunately, however, this energy can-

not be successfully utilised in rtinning steamers andfactories, for it is extremely variable. A passingcloud will interrupt the flow of solar energy, andin the morning or the afternoon, or upon stormydays, a very small part only of the solar energyactually reaches the earth's surface and becomesavailable as power. Some solar engines havebeen constructed, which run successfully during afew hours of a bright, clear day, but they havenever been made a commercial success.

This heat energy which the sun is constantlypouring forth must come from some almost inex-haustible supply. It cannot come from combus-tion, for if the sun were solid coal and were burningin pure oxygen, it could not continue to supply

The Sun 61

heat at the present rate for so long as five thousandyears. In that period the sun would be entirelyburnt up and would cease to exist. Yet we knowthat the sun has existed for many millions of yearsand during immeasurable ages has given forthheat and light without stint. The heat of thesun is derived from the motions of its constituentparticles of matter. Heat is a mode of motion,and heat may be transformed into motion, ormotion transformed into heat. When a movingbody is stopped its energy of motion appears asheat and it makes no difference whether thestoppage be sudden or gradual, the total amountof heat produced is the same. A brick from thetop of a tall building, a shooting star from theunknown wilds that surround us, each on strikingthe earth imparts a little heat. Every meteor,every body that falls into the sun, and an enormousnumber there must be, increases its store of heat.By its fall into the sun each particle of matterproduces five thousand times as much heat as anequal weight of the best coal when burnt underthe most favourable conditions. Were the earthto fall into the sun enough heat would be generatedto last for ninety-five years; if the entire systemof planets collapsed on the sun there would beliberated sufficient heat to supply the solarfurnaces for over 46,000 years. Now the sun isgradually falling into itself, the outer layers arefalling towards the centre ; it is shrinking, growingsmaller. And this contraction, this falling in

62 Nautical Science

of the outer particles of the sun, produces theimmense store of energy on which we are con-tinually drawing. With the present size of thesun it is only necessary that its diameter bedecreasing about 220 feet a year, four miles acentury, in order that the supply of heat energymay continue the same year after year. Thiscontraction is so slow as to be impossible todetect with any instrument now in use ; after thelapse of many centuries the shrinkage wUl haveproceeded far enough for us to measure.The visible surface, or "photosphere," of the

sun is not equally bright throughout. The centralportion of the disc is the most brilliant, the edgesbeing quite dark in comparison. This gradualdecrease in brilliancy from the centre outward isdue to an invisible atmosphere of permanentgases which surrounds the visible portion of thesun. This enveloping layer of vapours absorbsa portion of the light emitted by the hotter centralphotosphere and absorbs a greater proportionof the light from the edge of the disc, for the lightfrom this portion of the sun must pass diagonallythrough this envelope and thus traverse a muchlonger path inside the absorbing vapours thanthe light which comes from the centre. Besidesthis darkening of the limb, the photosphereshows several other characteristic phenomena,among which the most striking are the darkspots, which have been mentioned in connectionwith the sun's rotation.

The Sun 63

These spots appear either singly or in groups,and occasionally one is so large as to be easilyvisible to the unaided eye. Against the sur-rounding brilliant surface of the sun they appeara deep velvety black, but this colour is only rela-tive. The darkest part of the blackest spot is inreality far more brilliant than the electric arc.These sun spots are short lived ; they seldom lastfor more than three or four months, but during thisshort period they sometimes reach an enormousgrowth. Not infrequently a spot measures 20,000miles in diameter, although the average is muchless. In March 1905, a spot covered -g^ partof the sun's disc. It was clearly visible withoutthe aid of a telescope and its area was nearlyforty times that of the entire surface of the earth.

It is now quite well established that these

spots are cavities, or local depressions in the solar

surface. But it is not certain that the floor ofthis cavity is below the average level of the solarsurface. Certain observations seem to indicatethat in the neighbourhood of a spot the wholesurface is raised and that the spot is a depressionin this elevated portion, like a crater on the top of

a low motmtain. This crater-like formation ofthe spots offers a plausible explanation of theirdark appearance. It is probable that in theneighbourhood of a spot eruptions take place andheated matter is ejected. The removal of thesupporting material causes the surface to sink

in and this sink is filled by the colder gases and

64 Nautical Science

vapours of the solar atmosphere. Thus the lightfrom the bottom of the well must pass througha much greater thickness of these cool vapoursthan the light from the surrounding surface,and in this passage a great proportion of the lightis absorbed, and the spot is made relativelydark.

The spots are confined to certain well-definedzones of the sun's surface: few have been foundat the equator and none have ever been observednearer the poles than latitude 45. Further theyare periodic; their average number waxes andwanes in regular periods of eleven years. Duringa minimum practically no spots are visible, daysand weeks often passing without a single spotmarring the brilliant solar surface. Then a fewsmall spots appear, and gradually the ntmiberand the size of the spots increase, until after alapse of some five and a half years portions of thesurface are constantly covered with large andsmall spots. Hardly a day passes, at the timeof a maximum, without several spots beingvisible, and occasionally the spots are so numerousas to form two great belts around the sun, oneon each side of the equator. This periodicityin the sun-spots is difficult to explain. It isprobable, however, that the eleven-year cycle isa natural period, due to the physical conditionof the sun as a rotating, cooling mass of gas;due to causes inherent in the sun itself and notto any outside influence.

The Sun 65

While to the practical man the appearanceof these spots on the sun may be regarded as amatter of little importance, yet it can be clearlyshown that they have a direct influence on theearth- an influence which may materially affectthe lives and well being of her inhabitants. Thespots have a direct connection with magneticand electric storms on the earth; when spots arenumerous, magnetic storms are frequent, and themagnetic needle is in a constant state of agitation.Again they may affect the average temperatureof the earth, and even have some influence onstorms, rainfall, and the like. While, however,such influence may be suspected, it has not beenconclusively proved, except in the case of electricand magnetic phenomena. It is certain that thecentral portion of a spot radiates less heat thanthe surrounding parts of the sun's surface, butwhether the sun as a whole gives out less heat,when spotted, than it does at other times, is notknown. The fact that spots exist on the sunshows that the activity of the sun is then greater,and the greater activity may overcome the lackof heat in the spots themselves. Newcomb madean exhaustive investigation and reached the con-clusion that the world as a whole is a fractionof a degree cooler at those times when spots areless numerous on the sun, than at times of a sun-spot maximum.

While under ordinary circumstances, the spotsare the most conspicuous features of the solar

66 Nautical Science

surface, yet at times other striking phenomena areobserved. This is especially the case during the

few brief moments of a total solar eclipse. Whenthe moon cuts off the last ray of direct stmlight,

there instantaneously appears around the blackdisc of our satellite a brilliant, broad white,flickering halo, while close to the edge of the moonmay be seen two or three bright red fla,mes. Thehalo is the mysterious and elusive "corona," thered flames, the ' ' prominences. " By the aid of thespectroscope these prominences may now be seenand studied at any time, but the corona has neverbeen seen except during a solar eclipse. Thestudy of its nature is thus limited to a few moments(four or five minutes at the most) every few years.For this reason, whenever an eclipse occurs, ex-peditions are fitted out and sent to the mostfavourable locations, and the astronomer utilisesevery moment of totality in obtaining photographsand spectographs for measurement and study.The prominences are eruptions from the layer

of permanent vapours which surround the photo-sphere ; their brilliant colour being due to thepresence of hydrogen. These protuberances areof all sorts of fantastic shapes and some of themreach to an immense height. Young records aprominence which extended 350,000 miles beyondthe edge of the sun. Great as this distance mayseem, the corona extends even farther. Thisbrilliant halo is made up of an intricate systemof rays and streamers, which undergo periodic

The Sun 67

changes in size and shape. The corona apparentlyconsists- of minute solid, liquid, and gaseousparticles; matter ejected from the sun, meteoricmatter, and minute dust-like planets. It is ex-tremely tenuous, containing less matter percubic inch than the best vacuum we can produceon the earth: the amount of matter in the coronais equivalent to a single dust particle in everyfourteen cubic yards.

NOTES AND PRACTICAL APPLICATIONS

Dimensions of the Sun:Mean apparent semi-diameter i6' o".oGreatest " " i6' i6".4Least " " is' 44".

2

Mean semi-diameter 432,400 miles.

Rotation of Sun:The periods of rotation of different parts of thesun are as follows:

Latitude

CHAPTER IV

the stars and planets

The Solar System

JUST as the earth revolves about the sun,so do coimtless other bodies'

^planets, planet-

oids, and comets. All these together form onegreat unique group, the solar system, of which thesun is absolute ruler, the czar. In the heavensmight makes right and the strong rule the weak,and the stm rules over his system because of hisvastly superior strength, or mass. The sun con-tains over three hundred thousand times as muchmatter as the earth, nearly one thousand times asmuch as all the other bodies of the system put to-gether, and it is this great superiority of massthat enables the sun to keep its attendant planetsand satellites in order, to control their motionsand to cause them to revolve in an orderly arrayof ellipses.

All the various bodies, planets and comets, re-volve about the sun in ellipses, and in each andevery case the sun is at one focus of the ellipse.

Yet in actual shape these paths differ widely;69

70 Nautical Science

the orbits of the great planets are nearly circtilar

;

whfle those of many comets are extremely long,narrow ovals, reaching out to untold distances

from the sun. The paths of the major planetslie very nearly in a single plane, the greatest

inclination to the ecliptic being a trifle over 7.On the other hand the paths of the comets lie inall sorts of positions, apparently without regardto order or arrangement. But, whatsoever theshape of the ellipse, howsoever it may lie in space,the body, be it planet or comet, travels about thesun always sweeping over equal areas in equalintervals of time.

Five of the larger planets. Mercury, Venus, Mars,Jupiter, and Saturn, are among the most brilliantobjects of the heavens; they have been watchedand their motions studied from pre-historic times.Two great planets have been discovered sincethe invention of the telescope, and these two,Uranus and Neptune, are invisible to the tinaidedeye. Together with the earth, these bodies arethe eight important members of the solar system.They are ranged about the sim in the order of theirperiodic times, or the lengths of their respectiveyears. Mercury lies nearest the great central orb,then come, in order, Venus, the Earth, Mars,Jupiter, Saturn, Uranus, and finally Neptune, theoutermost planet, some thirty times as far from thesun as the earth. Mercury requires but eighty-eight days to traverse its path about the sun,Neptime nearly one hundred and sixty-five years.

The Stars and Planets 71

Now there is a direct relation between the dis-tances of the planets from the sun and the lengthsof their respective years. This rather complicatedrelation was discovered by Kepler, and is knownas the third law of planetary motion. It maybe stated as follows

:

"The squares of the times of revolution of anytwo planets about the sun are proportional to thecubes of their mean distances from the sun."

This law is shown by the figures in the followingtable

:

Planets

72 Nautical Science

watching a planet through a long period of time,it will be foimd to return again and again to thesame position relative to the sun, and this period,the length of its year, can be obtained with greataccuracy.

It must be noted, however, that this law ofKepler does not give the distance in miles ; but onlyin terms of some other distance, that of the earthfrom the sun for example. From this law therelative sizes of the orbits can be determined,and a correct map of the solar system may bedrawn, but the scale of the map will be unknown.In order to find the scale of the map, to find thevarious distances in miles, one distance on the mapmust be measured. This is measured by meansof parallax, and the distance between Mars andthe earth, as has been seen, is the best for thispurpose.

To convey an accurate idea of the dimensionsand relative distances of the various bodies of thesolar system by means of a chart or diagram isweU-nigh impossible. The mechanical contriv-ances, or orreries, which purport to show themotions of the planets, are more than useless,for they cannot be constructed on anythinglike an approximate scale. A general impressionas to the distances and motions of the planetsmay be gathered however from the following illus-tration. On the top of City Hall, New York City,place a great spherical lantern, or search-light,twenty feet in diameter to represent the sun;


then Mercury will be represented by a smallplum, on the circumference of a circle 820 feetradius, or at the comer of Broadway and ThomasStreet ; Venus by an orange at the corner of Leon-ard Street, 1550 feet from City Hall; the earthby a large orange at White Street, 2150 feetdistant; Mars by a good-sized plum at GrandStreet, three-fifths of a mile away

;Jupiter by an

ordinary library globe two feet in diameter, placedtwo miles away in the middle of Madison Square

;

Saturn by a slightly smaller globe in the officeof the new Plaza Hotel at 59th Street, some fourmiles from the starting-point ; Uranus by a foot-ball on the Athletic Field of Columbia Universityat 1 1 6th Street, and Neptime by a large-size toyballoon in Bronx Park, a little over twelve milesfrom City Hall. In its orbit about the centralluminary, this toy balloon, representing Neptune,will pass over the town of Hackensack, the citiesof Passaic, Orange, and Newark, over the hillsof Staten Island and the sands of RockawayBeach, rettirning by way of Jamaica and Flushing,finally crossing the East River at Whitestone.To imitate the motions of the planets in theseorbits Mercury must move at the rate of threefeet an hour ; Venus not quite two feet per hour

;

the earth nineteen inches; Mars fifteen inches,

Jupiter eight, Satiim six, Uranus four, andNeptune only about three and a half inches perhour. This latter planet would require 165 yearsto complete its circuit of New York.

74 Nautical Science

The Planets

In physical condition the various planets

differ as widely as they do in size. Three of them,Mercury, Venus, and Mars, are not unlike theearth in size and in general characteristics. Theyare, in all probability, solid, cool bodies similar

to the earth, and like the earth surroundedby atmospheres of cool vapours. The outerplanets, Jupiter, Saturn, Uranus, and Neptune,on the other hand, are huge bodies, many timesthe size of the earth, and more nearly resemblingthe stm than the earth in their physical character-istics. They are globes of gases and vapours,so hot as to be nearly, if not actually at times,self-luminous. They may each contain a smallsolid nucleus, but the great bulk of these bodiesconsists of an immense gaseous atmosphere,filled with minute liquid particles; the whole atan extremely high temperature.Of the actual surface conditions on Venus and

Mercury little is definitely known. Mercuryis a very difficult object to observe on accotmtof its proximity to the sun. It is never visibleat night ; it must be examined either in the twilightjust before simrise or after sunset, or in fulldaylight. In either case the glare of the sunrenders the planet indistinct, and the heat of thesun disturbs our atmosphere and makes "goodseeing " extremely rare. The surface of the planetis probably rough and irregular, and not unlike that


of the moon, and to make the resemblance to themoon more complete, Mercury has little or noatmosphere. Still further, Mercury rotates uponits axis once in eighty-eight days ; its day and itsyear are of the same length. Thus the planetalways presents the same face toward the sun,and on that side reigns perpetual day, and onthe other perpetual night, a night of unbroken,unimaginable cold.Venus resembles the earth more nearly than

any other heavenly body. It is almost a counter-part of the earth in density and in size ; its diameterbeing 7830 miles, or only 120 miles less than thatof our planet. Venus is shrouded in deep banksof atmospheric clouds, which effectually veilher mysteries from our gaze. Her atmosphere isconsiderably more dense than that of the earth, andthe sunlight is reflected from the upper surface ofclouds and vapours, and reaches our telescopeswithout ever having penetrated to the actualsurface of the planet. Some few semi-permanentmarkings on the planet's disc have indeed beennoted from time to time, but whether these werecloud forms or the tops of moimtains, is not fully

established. There is no clear, undisputed, evi-

dence that any particular one of these markingsreally forms a permanent feature of the surface.

More is certainly known about Mars thanabout any other heavenly body, and yet verylittle is actually known in regard to the conditionson the surface of that ruddy planet. In many

76 Nautical Science

respects, however, Mars is a miniature earth; its

diameter is 4210 mUes, and its surface area is aHttle more than the total area of dry land uponthe earth. Like the earth, Mars rotates about anaxis inclined to the plane of its orbit, and thelength of a Martian day is very nearly equal toone of our own. The mean of a n^lmber of thebest modem determinations gives the length ofone complete axial rotation of Mars as equal to24'' 37" 22^65 and this makes each Martiansolar day 24'' 39" 35" long.

Mars is surrounded by a very light and trans-parent atmosphere, and through this manystriking and permanent features of the planet'ssurface are visible. The most noticeable of theseare the brilliant white "polar caps," first recog-nised by Sir William Herschel in 1784. Thesecaps alternately wax and wane with the changingseasons on Mars; during the long winter in thenorthern hemisphere, the cap at the north polesteadily increases in size, only to diminish duringthe next summer, when it is exposed to the directrays of the sun. The behaviour of the polar capsproves without question the presence in theMartian atmosphere of vapours, which are con-densed and precipitated by cold and which areevaporated by heat. These vapours are in allprobability water vapours, and the caps someform of snow and ice, or possibly hoar-frost.

Outside the polar caps the surface of the planetis rough, uneven, and shows a mass of faint

Plate VI

Drawing of Mars by E. E. Barnard, Made with the36-inch Lick Telescope


detail, which appears differently to differentobservers. The main part of the disc appears adeep, ruddy colour, and against this orange back-groiuid darker, grey-green spots and markingsare seen. The lighter portions were formerlythought to be continents and the darker portionsseas and oceans. It is now known, however,that the grey spots and markings are not seas, thatthey are really rough and irregular portions of thesurface, that in fact there is practically no freewater on the Martian surface. Mars is a dryplanet. In just what way, however, these darkmarkings differ from the lighter coloured portionsof the surface is not definitely known. By someinvestigators the orange hues are called desertsands and the dark markings irrigated plains.But such an artificial explanation is not necessary.There are in all likelihood different coloured rocksand soils on Mars, just as there are on the earthand on the moon. The deep red clays of NewJersey are radically different from the dazzlingsands of the coast. The moon, which has neitherair nor water, has light and dark patches.Some of the darker markings appear to be long,

straight, streaks. They are the so-called ' ' canals, '

'

or channels, so named by Schiaparelli, who firstnoted them in 1877. For many years the realityof this discovery was doubted, but during the lastfew years many astronomers have observed themore prominent channels and some few of themhave even been photographed. To-day the reality

78 Nautical Science

of some few of the more prominent of these mark-ings cannot be doubted. These broad channels,however, must not be confused with the system offine, sharp, lines, now so prominent in the drawingsof Flammarion and Lowell . The existence of theselatter, the "canals" of Lowell, is, at least, open toserious question. Keeler, Campbell, and Barnard,using the largest and best telescopes in the world,have failed to observe them. According toNewcomb the canaliform appearance as depictedby Lowell "is not to be regarded as a pure illusionon the one hand, or an exact representation ofobjects on the other. It grows out of the spon-taneous action of the eye in shaping slight andirregular combinations of light and shade, toominute to be separately made out, into regularforms."

The term canal, which has been applied to theseindistinct markings, is an unfortunate one. Theword implies the existence of water and thepresence of beings of sufficient intelligence andmechanical ability to construct elaborate works.Flammarion in France and Lowell in this countryassert that the word is correctly used, that thesemarkings are really canals and that Mars isinhabited. But this is pure speculation andimagination. There is no conclusive proof thatthe lines, or canals, really exist as drawn; theyare probably to a large extent illusions andfigments of defective vision. There is not theslightest trace of any artificial work on Mars itself;


the artificiality is in the drawings, not in theplanet. There is no evidence of any kind, pointingtoward the existence of conscious life upon Mars.So far as we know it is not impossible for life ofsome form to exist there, but, if it does, we, as yet,do not know it.

The Stars

Sharply distinguished from the planets, orwanderers, are the "fixed" stars. These appearas mere points of light and always maintain thesame relative positions in the heavens. Thousandsof years ago, when the shepherds first trod theplains of Chaldea, the "Great Dipper" hung in thenorthern sky just as it hangs to-night, and as itwill hang for thousands of years to come. Yetthese bodies are not absolutely fixed in space.In reality they are all in motion and in rapidmotion, some moving one way, some another.It is their immense distance from us that makesthis motion inappreciable. Great as may appearthe distance between the sun and the earth, yetthis distance shrinks to a mere nothing as comparedto the distance from the earth to a star, and fromstar to star. The nearest star is more than 200,000times as far from us as is the sun. Expressedin miles, the figure representing this distance

would be so enormous as to convey no distinctimpression. A special tmit has, therefore, beeninventeda imit represented by the distance

8o Nautical Science

traversed by light in one year. In one second lighttravels over 186,000 miles, nearly eight timesaround the earth's equator; in 8J minutes lightreaches us from the sun, covers the distance thatit would take the Mauretania over foiir centuriesto travel. Yet the nearest star is over four"light years" distant; it is so far away that itrequires over four years for its light to reach us.When we look at the stars to-night, we see them,not as they are, but as they were years, evencenturies ago. Polaris, the North Star, is distantsome sixty light years ; had it been blotted out ofexistence at the time the Monitor fought theMerrimac, we shovild as yet be unaware of thecatastrophe.

The stars appear to be countless in number, yet,in reality, comparatively few can be distinguishedby an unaided eye. In the whole heavens thereare not more than six thousand which are brightenough to be clearly located and counted, and lessthan one half of these can be seen at any one time.Even on a clear, moonless night, it is doubtfulwhether the sharpest eye can detect more thantwo thousand separate and distinct stars. Onemay, indeed, be conscious of a backgroimd of light,or of luminous points, but no eye can separate itinto clearly visible stars. Where the eye fails, how-ever, a small telescope even is successful. With anopera-glass the whole sky seems filled with stars,and over one himdred thousand may be seenand counted 5 with the Yerkes, or other great.

The Stars and Planets 8i

telescope a hundred millions may be distinguished.The photographic plate reveals countless myriadsthat otherwise wotild for ever remain invisibleand unknown.Now each and every one of these stars is a sun;

is a vast globe of gas and vapour, intensely hot andin a continuous state of violent agitation, radiatingforth heat and light; its every pulsation feltthroughout the viniverse. So closely, indeed, domany of the stars resemble the sun, that thelight which they emit cannot be distinguishedfrom sunlight. Some of them are vastly largerand hotter than our sun, others smaller and cooler,yet may our sun be regarded as a typical star, andfrom our knowledge of it, we can form a tolerablycorrect conception of the nature and constitutionof the other heavenly bodies.The stars differ among themselves in brightness,

and they may be classified accordingly. Theearly Greek astronomers divided the iioo or sostars which they knew into six groups, or " magni-tudes." In the first group they placed a dozen ormore of the brightest stars; in the sixth groupwas the mass of stars just visible to the unaidedeye, while the stars of intermediate brightnesswere arbitrarily classed as of the second, third,or fourth magnitude. The word magnitude asused in this connection refers to brightness only,and the greater the magnitude the fainter the star.Small magnitudes mean bright stars, large mag-nitudes faint stars. In these early groupings

82 Nautical Science

of the stars, the comparison of the brightness ofone star with that of another was a mere eye

estimateone star appeared brighter than theother. To-day, however, there are instruments

by means of which this comparison can be quicklyand accurately made, and the relative amount oflight received from the two stars measured withprecision. A definite scale of magnitude has,therefore, been adopted and is now in use in allpublications.

On this absolute scale of star magnitudes, astar of the first magnitude gives out 2 J times( #100) as much light as a star of the second, andthis star in turn is 2 J times as bright as one ofthe third magnitude. The ratio between thelight of a star and that of another, one magnitudefainter, is thus constant and equal to 2^. Hencea sixth magnitude star is exactly 100 times fainterthan a star of the first magnitude; one hundredstars of the sixth

old - nautical science

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