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+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
+%                                                                         %
+% The Project Gutenberg EBook of Mathematical Geography, by Willis E. Johnson
+%                                                                         %
+% This eBook is for the use of anyone anywhere at no cost and with        %
+% almost no restrictions whatsoever.  You may copy it, give it away or    %
+% re-use it under the terms of the Project Gutenberg License included     %
+% with this eBook or online at www.gutenberg.org                          %
+%                                                                         %
+%                                                                         %
+% Title: Mathematical Geography                                           %
+%                                                                         %
+% Author: Willis E. Johnson                                               %
+%                                                                         %
+% Release Date: February 21, 2010 [EBook #31344]                          %
+%                                                                         %
+% Language: English                                                       %
+%                                                                         %
+% Character set encoding: ISO-8859-1                                      %
+%                                                                         %
+% *** START OF THIS PROJECT GUTENBERG EBOOK MATHEMATICAL GEOGRAPHY ***    %
+%                                                                         %
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+\begin{verbatim}
+The Project Gutenberg EBook of Mathematical Geography, by Willis E. Johnson
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Mathematical Geography
+
+Author: Willis E. Johnson
+
+Release Date: February 21, 2010 [EBook #31344]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK MATHEMATICAL GEOGRAPHY ***
+\end{verbatim}
+
+%% -----File: 001.png---Folio 1-------
+\index{Axis, changes in position of!inclination of|see{\hyperref[idx:ooe]{Obliquity of ecliptic}.}}%
+\index{Ciudad Juarez|see{\hyperref[idx:j]{Juarez}.}}%
+\index{Date line|see{\hyperref[idx:idl]{International date line}.}}%
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+\index{Satellite|see{\hyperref[idx:m]{Moon}.}}%
+\index{Solar day|see{\hyperref[idx:d]{Day}.}}%
+\index{Vernal equinox|see{\hyperref[idx:e]{Equinox}.}}%
+\index{Weight|see{\hyperref[idx:g]{Gravity}.}}%
+\mainmatter
+\pdfbookmark[0]{MATHEMATICAL GEOGRAPHY}{MATHEMATICAL GEOGRAPHY}
+
+
+\begin{center}
+\TitleStretch
+\TitleHuge\selectfont\bfseries
+MATHEMATICAL GEOGRAPHY
+
+\vstretch{1}
+\mdseries\normalsize
+BY\\[1ex]
+
+\large WILLIS E. JOHNSON, \textsc{Ph.B}.\\[1ex]
+\small\textit{\TitleNoStretch VICE PRESIDENT AND PROFESSOR OF GEOGRAPHY AND\\
+SOCIAL SCIENCES, NORTHERN NORMAL AND\\
+INDUSTRIAL SCHOOL, ABERDEEN,\\
+SOUTH DAKOTA}
+
+\vstretch{2}
+\includegraphics{./images/abcmark.pdf}
+\vstretch{2}
+
+\normalsize
+\MakeLowercase{\large\scshape NEW YORK}   $\because$
+\MakeLowercase{\large\scshape CINCINNATI} $\because$
+\MakeLowercase{\large\scshape CHICAGO}\\[1ex]
+
+\large
+AMERICAN BOOK COMPANY
+\end{center}
+\clearpage
+%% -----File: 002.png---Folio 2-------
+
+\begin{center}
+\vstretch{1}
+\textsc{Copyright, 1907,\\by}
+
+WILLIS E. JOHNSON
+
+\rule[0.5ex]{2em}{0.5pt}
+
+\textit{Entered at Stationers' Hall, London}
+
+\rule[0.5ex]{2em}{0.5pt}
+
+\small JOHNSON MATH. GEO.
+\vstretch{1}
+\end{center}
+
+\clearpage
+\thispagestyle{empty}
+\begin{center}
+\small
+Produced by Peter Vachuska, Chris Curnow, Nigel Blower and
+the Online Distributed Proofreading Team at
+http://www.pgdp.net
+\end{center}
+
+\vfill
+{%
+  \setlength{\parindent}{0pt}
+	\setlength{\parskip}{6pt plus 2pt minus 1pt}
+  \subsection*{{\normalsize\centering\itshape Transcriber's Notes}}
+  \small
+  A small number of minor typographical errors and inconsistencies
+  have been corrected. Some references to page numbers and page ranges
+  have been altered in order to make them suitable for an eBook.
+  Such changes, as well as factual and calculation errors that were
+  discovered during transcription, have been documented in the
+  \LaTeX\ source as follows:
+  {\ttfamily\footnotesize\%[**TN:~text~of~note]}
+}
+%% -----File: 003.png---Folio 3-------
+
+\contentspage
+
+\SpecialChapter{Preface}
+\SpecialChapterRule
+\pdfbookmark[1]{Preface}{Preface}
+
+%set up page headers
+\fancypagestyle{plain}{%
+  \fancyhf{}%
+  \fancyfoot[C]{\smallsize\thepage}}
+
+\pagestyle{fancy}
+\setlength\headheight{14.5pt}
+\fancyhf{}
+\fancyhead[C]{\smallsize\leftmark}
+\fancyhead[R]{\thepage}
+
+\First{In} the greatly awakened interest in the common-school
+subjects during recent years, geography has received a
+large share. The establishment of chairs of geography in
+some of our greatest universities, the giving of college
+courses in physiography, meteor\-ology, and commerce,
+and the general extension of geography courses in normal
+schools, academies, and high schools, may be cited as
+evidence of this growing appreciation of the importance of
+the subject.
+
+While physiographic processes and resulting land forms
+occupy a large place in geographical control, the earth in
+its simple mathematical aspects should be better understood
+than it generally is, and mathematical geography
+deserves a larger place in the literature of the subject than
+the few pages generally given to it in our physical geographies
+and elementary astronomies. It is generally
+conceded that the mathematical portion of geography
+is the most difficult, the most poorly taught and least
+understood, and that students require the most help in
+understanding it. The subject-matter of mathematical
+geography is scattered about in many works, and no one
+book treats the subject with any degree of thoroughness,
+or even makes a pretense at doing so. It is with the
+view of meeting the need for such a volume that this
+work has been undertaken.
+
+Although designed for use in secondary schools and for
+teachers' preparation, much material herein organized
+%% -----File: 004.png---Folio 4-------
+may be used in the upper grades of the elementary school.
+The subject has not been presented from the point of
+view of a little child, but an attempt has been made to
+keep its scope within the attainments of a student in a
+normal school, academy, or high school. If a very short
+course in mathematical geography is given, or if students
+are relatively advanced, much of the subject-matter may
+be omitted or given as special reports.
+
+To the student or teacher who finds some portions too
+difficult, it is suggested that the discussions which seem
+obscure at first reading are often made clear by additional
+explanation given farther on in the book. Usually the
+second study of a topic which seems too difficult should be
+deferred until the entire chapter has been read over carefully.
+
+The experimental work which is suggested is given for
+the purpose of making the principles studied concrete and
+vivid. The measure of the educational value of a laboratory
+exercise in a school of secondary grade is not found
+in the academic results obtained, but in the attainment of
+a conception of a process. The student's determination
+of latitude, for example, may not be of much value if its
+worth is estimated in terms of facts obtained, but the
+forming of the conception of the process is a result of
+inestimable educational value. Much time may be wasted,
+however, if the student is required to rediscover the facts
+and laws of nature which are often so simple that to see
+is to accept and understand.
+
+Acknowledgments are due to many eminent scholars
+for suggestions, verification of data, and other valuable
+assistance in the preparation of this book.
+
+To President George W.~Nash of the Northern Normal
+\index{Nash, George W.}%
+and Industrial School, who carefully read the entire manuscript
+%% -----File: 005.png---Folio 5-------
+and proof, and to whose thorough training, clear
+insight, and kindly interest the author is under deep
+obligations, especial credit is gratefully accorded. While
+the author has not availed himself of the direct assistance
+of his sometime teacher, Professor Frank E.~Mitchell, now
+\index{Mitchell, Frank E.}%
+head of the department of Geography and Geology of the
+State Normal School at Oshkosh, Wisconsin, he wishes
+formally to acknowledge his obligation to him for an
+abiding interest in the subject. For the critical examination
+of portions of the manuscript bearing upon fields
+in which they are acknowledged authorities, grateful
+acknowledgment is extended to Professor Francis P.~Leavenworth,
+\index{Leavenworth, Francis P.}%
+head of the department of Astronomy of
+the University of Minnesota; to Lieutenant-Commander
+E.~E.~Hayden, head of the department of Chronometers
+\index{Hayden, E. E.}%
+and Time Service of the United States Naval Observatory,
+Washington; to President F.~W.~McNair of the Michigan
+\index{McNair, F. W.}%
+College of Mines; to Professor Cleveland Abbe of the
+\index{Abbe, Cleveland}%
+United States Weather Bureau; to President Robert S.~Woodward
+\index{Woodward, R. S.}%
+of the Carnegie Institution of Washington; to
+Professor T.~C.~Chamberlin, head of the department of
+\index{Chamberlin, T. C.}%
+Geology of the University of Chicago; and to Professor
+Charles R.~Dryer, head of the department of Geography
+\index{Dryer, Charles R.}%
+of the State Normal School at Terre Haute, Indiana. For
+any errors or defects in the book, the author alone is
+responsible.
+%% -----File: 006.png---Folio 6-------
+%% -----File: 006.png---Folio 7-------
+
+\clearpage
+\pdfbookmark[1]{Contents}{Contents}
+
+\fancyhead[C]{\smallsize CONTENTS}
+
+{\setlength{\topsep}{0pt}
+\tableofcontents}
+
+%% -----File: 007.png---Folio 8-------
+%% -----File: 008.png---Folio 9-------
+
+\Chapter{I}{Introductory}
+\fancyhead[C]{\smallsize\leftmark}
+
+\Section{Observations and Experiments}
+
+\Paragraph{Observations of the Stars.} On the first clear evening,
+\index{Observations of stars}%
+\index{Big Dipper}
+\index{Ursa Major}%
+\index{England}%
+observe the ``Big Dipper''\footnote
+  {In Ursa Major, commonly called the ``Plow,'' ``The Great
+  Wagon,'' or ``Charles's Wagon'' in England, Norway, Germany, and
+  other countries.}
+and the polestar. In September
+\index{Polestar@Polestar\phantomsection\label{idx:p}, (\emph{see} \hyperref[idx:ns]{North star})}%
+and in December, early in the evening, they will be
+nearly in the positions represented in Figure~\figureref{i008}{1}. Where
+is the Big Dipper
+later in the evening?
+Find out by observations.
+
+\includegraphicsright{i008}{Fig.~1}
+
+\index{Cassiopeia@Cassiopeia (k\u{a}s\;s\u{\i}\;\={o}\;p\={e}$'$y\.{a})}%
+Learn readily to
+pick out Cassiopeia's
+Chair and the Little
+Dipper. Observe
+\index{Little Dipper}%
+their apparent motions
+also. Notice
+the positions of stars
+in different portions of the sky and observe where they are
+later in the evening. Do the stars around the polestar
+remain in the same position in relation to each other,---the
+Big Dipper always like a dipper, Cassiopeia's Chair
+%% -----File: 009.png---Folio 10-------
+always like a chair, and both always on opposite sides of
+the polestar? In what sense may they be called ``fixed''
+\index{Fixed stars}%
+stars (see pp.~\pageref{page:108}, \pageref{page:265})?
+
+Make a sketch of the Big Dipper and the polestar,
+\index{Polestar@Polestar\phantomsection\label{idx:p}, (\emph{see} \hyperref[idx:ns]{North star})}%
+recording the date and time of observation. Preserve
+your sketch for future reference, marking it Exhibit~1.
+A month or so later, sketch again at the same time of
+night, using the same sheet of paper with a common
+polestar for both sketches. In making your sketches
+be careful to get the angle formed by a line through
+the ``pointers'' and the polestar with a perpendicular to
+the horizon. This angle can be formed by observing the
+side of a building and the pointer line. It can be
+measured more accurately in the fall months with a pair
+of dividers having straight edges, by placing
+one outer edge next to the perpendicular
+side of a north window and opening the
+dividers until the other outside edge is
+parallel to the pointer line (see Fig.~\figureref{i009}{2}).
+Now lay the dividers on a sheet of paper
+and mark the angle thus formed, representing
+the positions of stars with asterisks.
+Two penny rulers pinned through the ends
+will serve for a pair of dividers.
+
+\includegraphicsleft{i009}{Fig.~2}
+
+\Paragraph{Phases of the Moon.}\nblabel{page:9} Note the position
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+\index{Phases of the moon}%
+\index{Sun|(}%
+of the moon in the sky on successive nights at the same
+hour. Where does the moon rise? Does it rise at the
+same time from day to day? When the full moon may
+be observed at sunset, where is it? At sunrise? When
+there is a full moon at midnight, where is it? Assume
+it is sunset and the moon is high in the sky, how much of
+the lighted part can be seen?
+
+Answers to the foregoing questions should be based upon
+%% -----File: 010.png---Folio 11-------
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+first-hand observations. If the questions cannot easily
+be answered, begin observations at the first opportunity.
+Perhaps the best time to begin is when both sun and moon
+may be seen above the horizon. At each observation
+notice the position of the sun and of the moon, the portion
+of the lighted part which is turned toward the earth, and
+bear in mind the simple fact that \emph{the moon always shows a
+lighted half to the sun}. If the moon is rising when the sun
+is setting, or the sun is rising when the moon is setting,
+the observer must be standing directly between them, or
+approximately so. With the sun at your back in the east
+and facing the moon in the west, you see the moon as
+though you were at the sun. How much of the lighted
+part of the moon is then seen? By far the best apparatus
+for illustrating the phases of the moon is the sun and
+moon themselves, especially when both are observed above
+the horizon.
+
+\Paragraph{The Noon Shadow.} Some time early in the term from
+a convenient south window, measure upon the floor the
+length of the shadow when it is shortest during the
+day. Record the measurement and the date and time of
+day. Repeat the measurement each week. Mark this
+Exhibit~2.
+
+\sloppy
+\includegraphicsright{i011-1}{Fig.~3}
+
+On a south-facing window sill, strike a north-south line
+\index{North, line}%
+(methods for doing this are discussed on pp.~\pageref{page:61},~\pageref{page:130}).
+Erect at the south end of this line a perpendicular board,
+say six inches wide and two feet long, with the edge next
+the north-south line. True it with a plumb line; one
+\index{Plumb line}%
+made with a bullet and a thread will do. This should
+be so placed that the shadow from the edge of the board
+may be recorded on the window sill from 11~o'clock, \AM,
+until 1~o'clock, \PM{} (see Fig.~\figureref{i011-1}{3}).
+
+\fussy
+Carefully cut from cardboard a semicircle and mark the
+%% -----File: 011.png---Folio 12-------
+degrees, beginning with the
+middle radius as zero. Fasten
+this upon the window sill
+with the zero meridian coinciding
+with the north-south
+line. Note accurately the
+clock time when the shadow
+from the perpendicular board
+crosses the line, also where
+the shadow is at twelve
+o'clock. Record these facts
+with the date and preserve as
+Exhibit~3. Continue the observations
+every few days.
+
+\includegraphicsleft{i011-2}{Fig.~4}
+
+\Paragraph{The Sun's Meridian Altitude.}  When the shadow
+\index{Altitude, of noon sun}%
+\index{Sun|)}%
+is due north, carefully
+measure the angle formed
+by the shadow and a level
+line. The simplest way is
+to draw the window shade
+down to the top of a sheet
+of cardboard placed very
+nearly north and south with
+the bottom level and then
+draw the shadow line, the
+lower acute angle being the
+one sought (see Fig.~\figureref{i011-2}{4}).
+Another way is to drive a
+pin in the side of the window
+casing, or in the edge of the
+vertical board (Fig.~\figureref{i011-1}{3}); fasten a thread to it and connect
+the other end of the thread to a point on the sill where the
+shadow falls. A still better method is shown on p.~\pageref{page:172}.
+%% -----File: 012.png---Folio 13-------
+
+Since the shadow is north, the sun is as high in the sky
+as it will get during the day, and the angle thus measured
+gives the highest altitude of the sun for the day. Record
+\index{Altitude, of noon sun}%
+the measurement of the angle with the date as Exhibit~4.
+Continue these records from week to week, especially
+noting the angle on one of the following dates: March~21,
+June~22, September~23, December~22. This angle on
+March~21 or September~23, if subtracted from~$90°$, will
+equal the latitude\footnote{This is explained on p.~\pageref{page:170}.} of the observer. %[**TN: 'pp. 170, 171' in original text]
+
+\Section{A Few Terms Explained}
+
+\includegraphicsright[14]{i012}{Fig.~5}
+
+\Paragraph{\nbstretchyspace Centrifugal Force.} The literal meaning of the word
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}|(}%
+suggests its current meaning. It comes from the Latin
+\textit{centrum}, center; and
+\textit{fugere}, to flee. A centrifugal
+force is one
+directed away from a
+center. When a stone
+is whirled at the end of
+a string, the pull which
+the stone gives the
+string is called centrifugal
+force. Because
+of the inertia of the
+stone, the whirling
+motion given to it
+by the arm tends to
+make it fly off in a straight line (Fig.~\figureref{i012}{5}),---and this
+it will do if the string breaks. The measure of the
+centrifugal force is the tension on the string. If the
+string be fastened at the end of a spring scale and the
+%% -----File: 013.png---Folio 14-------
+stone whirled, the scale will show the amount of the centrifugal
+force which is given the stone by the arm that
+whirls it. \nblabel{page:14}The amount of this force\footnotemark~($C$) varies with the
+  \footnotetext{On the use of symbols, such as~$C$ for centrifugal force, $\phi$ for latitude,
+etc., see Appendix, p.~\pageref{page:307}.}
+mass of the body~($m$), its velocity~($v$), and the radius
+of the circle~($r$) in which it moves, in the following ratio:
+\[
+C = \frac{mv^2}{r}.
+\]
+
+The instant that the speed becomes such that the available
+strength of the string is less than the value of $\dfrac{mv^2}{r}$,
+however slightly, the stone will cease to follow the curve
+and will immediately take a motion at a uniform speed
+in the straight line with which its motion happened to
+coincide at that instant (a tangent to the circle at the point
+reached at that moment).
+
+\Subparagraph{Centrifugal Force on the Surface of the Earth.}\nblabel{page:14b} The
+rotating earth imparts to every portion of it, save along
+the axis, a centrifugal force which varies according to the
+foregoing formula, $r$~being the distance to the axis, or the
+radius of the parallel. It is obvious that on the surface
+of the earth the centrifugal force due to its rotation is
+greatest at the equator and zero at the poles.
+
+At the equator centrifugal force~($C$) amounts to about
+$\frac{1}{289}$ that of the earth's attraction~($g$), and thus an object
+there which weighs $288$~pounds is lightened just one pound
+by centrifugal force, that is, it would weigh $289$~pounds
+were the earth at rest. At latitude~30°, $C = \dfrac{g}{385}$ (that is,
+%% -----File: 014.png---Folio 15-------
+centrifugal force is $\tfrac{1}{385}$ the force of the earth's attraction);
+at~45°, $C = \dfrac{g}{578}$; at~60°, $C = \dfrac{g}{1156}$.
+
+For any latitude the ``lightening effect'' of centrifugal
+force due to the earth's rotation equals $\dfrac{g}{289}$~times the
+square of the cosine of the latitude ($C = \dfrac{g}{289} × \cos^2 \phi$).
+By referring to the \hyperref[page:311]{table of cosines} in the Appendix, the
+student can easily calculate the ``lightening'' influence
+of centrifugal force at his own latitude. For example,
+say the latitude of the observer is~40°.
+\[
+\operatorname{Cosine} 40° = .7660.\qquad \frac{g}{289} × .7660^2 = \frac{g}{492}.
+\]
+
+Thus the earth's attraction for an object on its surface
+at latitude~40° is 492~times as great as centrifugal force
+there, and an object weighing~491 pounds at that latitude
+would weigh one pound more were the earth at rest.\footnote
+  {These calculations are based upon a spherical earth and make no
+  allowances for the oblateness.}
+
+\Paragraph{Centripetal Force.} A centripetal (\textit{centrum}, center; \textit{petere},
+\index{Centripetal force@Centripetal force \indexglossref{Centripetal force}}%
+to seek) force is one directed toward a center, that is, at
+right angles to the direction of motion of a body. To
+distinguish between centrifugal force and centripetal
+force, the student should realize that forces never occur
+singly but only in pairs and that in any force action there
+are always \emph{two bodies} concerned. Name them $A$~and~$B$.
+Suppose~$A$ pushes or pulls~$B$ with a certain strength.
+This cannot occur except~$B$ pushes or pulls~$A$ by the same
+amount and in the opposite direction. This is only a
+simple way of stating Newton's third law that to every
+\index{Newton, Isaac}%
+%% -----File: 015.png---Folio 16-------
+action ($A$~on~$B$) there corresponds an equal and opposite
+reaction ($B$~on~$A$).
+
+Centrifugal force is the \emph{reaction} of the body against the
+centripetal force which holds it in a curved path, and it
+\index{Centripetal force@Centripetal force \indexglossref{Centripetal force}}%
+must always exactly equal the centripetal force. In the
+case of a stone whirled at the end of a string, the necessary
+force which the string exerts on the stone to keep it in a
+curved path is centripetal force, and the reaction of the
+stone upon the string is centrifugal force.
+
+The formulas for centripetal force are exactly the same
+as those for centrifugal force. Owing to the rotation of
+the earth, a body at the equator describes a circle with
+uniform speed. The attraction of the earth supplies the
+centripetal force required to hold it in the circle. The
+earth's attraction is greatly in excess of that which is
+required, being, in fact, 289~times the amount needed.
+\emph{The centripetal force in this case is that portion of the attraction
+which is used to hold the object in the circular course.}
+The excess is what we call the weight of the body or the
+force of gravity.
+
+If, therefore, a spring balance suspending a body at the
+equator shows 288~pounds, we infer that the earth really
+pulls it with a force of 289~pounds, but one pound of this
+pull is expended in changing the direction of the motion
+of the body, that is, the value of centripetal force is one
+pound. The body pulls the earth to the same extent,
+that is, the centrifugal force is also one pound. At the
+poles neither centripetal nor centrifugal force is exerted
+upon bodies and hence the weight of a body there is the
+full measure of the attraction of the earth.
+
+\includegraphicsright{i016-1}{Fig.~6}
+
+\sloppy
+\nblabel{page:16}\Paragraph{Gravitation.} Gravitation is the all-pervasive force by
+\index{Gravitation|(}%
+vir\-tue of which every particle of matter in the universe
+is constantly drawing toward itself every other particle
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}|)}%
+%% -----File: 016.png---Folio 17-------
+of matter, however distant. The amount of this attractive
+force existing between two bodies depends upon
+(1)~the amount of matter in them, and (2)~the distance
+they are apart.
+
+\fussy
+There are thus two laws of gravitation. The first law,
+the greater the mass, or amount of matter, the greater the
+attraction, is due to the fact that each particle of matter
+has its own independent attractive force, and the more
+there are of the particles,
+the greater
+is the combined
+attraction.
+
+\Subparagraph{The Second Law
+Explained.} In general
+terms the law
+is that the nearer
+an object is, the
+greater is its attractive
+force. Just
+as the heat and
+light of a flame are
+greater the nearer one gets to it (Fig.~\figureref{i016-1}{6}), because more rays
+are intercepted, so the nearer an object is, the greater is its
+attraction. The ratio of the increase of the power of gravitation
+as distance decreases, may be seen from Figures~\figureref{i016-2}{7} and~\figureref{i017}{8}.
+%% -----File: 017.png---Folio 18-------
+
+\includegraphicsmid{i016-2}{Fig.~7}
+\includegraphicsmid{i017}{Fig.~8}
+
+Two lines, $AD$ and $AH$ (Fig.~\figureref{i016-2}{7}), are twice as far apart
+at~$C$ as at~$B$ because twice as far away; three times as far
+apart at~$D$ as at~$B$ because three times as far away, etc.
+Now light radiates out in every direction, so that light
+coming from point~$A'$ (Fig.~\figureref{i017}{8}), when it reaches~$B'$ will be
+spread over the square of~$B' F'$\DPtypo{}{;}
+at~$C'$, on the square~$C' G'$;
+at~$D'$ on the square~$D' H'$, etc. $C'$~being twice as far
+away from~$A'$ as~$B'$, the side~$C' G'$ is twice that of~$B' F'$,
+as we observed in Fig.~\figureref{i016-2}{7}, and its square is four times as
+great. Line~$D' H'$ is three times as far away, is three
+times as long, and its square is nine times as great. The
+light being spread over more space in the more distant
+objects, it will light up a given area less. The square
+at~$B'$ receives all the light within the four radii, the
+same square at~$C'$ receives one fourth of it, at~$D'$ one
+ninth, etc. The amount of light \emph{decreases as the square of
+the distance increases}. The force of gravitation is exerted
+in every direction and varies in exactly the same way.
+Thus the second law of gravitation is that the force varies
+\index{Gravitation|)}%
+inversely as the square of the distance.
+
+\Paragraph{Gravity.} The earth's attractive influence is called
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+\emph{gravity}. The weight of an object is simply the measure of
+%% -----File: 018.png---Folio 19-------
+the force of gravity. An object on or above the surface
+of the earth weighs less as it is moved away from the
+center of gravity.\footnote
+  {For a more accurate and detailed discussion of gravity, see p.~\pageref{sec:gravity}.}
+It is difficult to realize that what we
+call the weight of an object is simply the excess of attraction
+which the earth possesses for it as compared with
+other forces acting upon it, and that it is a purely relative
+affair, the same object having a different weight in different
+places in the solar system. Thus the same pound-weight
+taken from the earth to the sun's surface would weigh $27$~pounds there, only one sixth of a pound at the surface of
+\index{Sun}%
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on sun}%
+the moon, over $2\tfrac{1}{2}$~pounds on Jupiter, etc. If the earth
+\index{Jupiter}%
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Jupiter}%
+were more dense, objects would weigh more on the surface.
+Thus if the earth retained its present size but contained as
+much matter as the sun has, the strongest man in the world
+could not lift a silver half dollar, for it would then weigh
+over five tons. A pendulum clock would then tick $575$~times
+as fast. On the other hand, if the earth were no
+denser than the sun, a half dollar would weigh only a
+trifle more than a dime now weighs, and a pendulum clock
+would tick only half as fast.
+
+From the table on p.~\pageref{page:266} giving the masses and distances
+of the sun, moon, and principal planets, many
+\index{Planets}%
+interesting problems involving the laws of gravitation
+may be suggested. To illustrate, let us take the problem
+``What would you weigh if you were on the moon?''
+
+\Paragraph{Weight on the Moon.}\nblabel{page:19} The mass of the moon, that is,
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on moon}%
+the amount of matter in it, is $\tfrac{1}{81}$ that of the earth.
+Were it the same size as the earth and had this mass, one
+pound on the earth would weigh a little less than one
+eightieth of a pound there. According to the first law of
+gravitation we have this proportion:
+
+1. $\text{Earth's attraction} : \text{Moon's attraction} \dblcolon 1 : \tfrac{1}{81}$.
+%% -----File: 019.png---Folio 20-------
+
+But the radius of the moon is $1081$~miles, only a little
+more than one fourth that of the earth. Since a person
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on moon}%
+on the moon would be so much nearer the center of gravity
+than he is on the earth, he would weigh much more there
+than here if the moon had the same mass as the earth.
+According to the second law of gravitation we have this
+proportion:
+
+2. $\text{Earth's attraction} : \text{Moon's attraction} \dblcolon \dfrac{1}{4000^2} : \dfrac{1}{1081^2}$. %[**TN: Indentation matched to 1. above]
+
+We have then the two proportions:
+\begin{align*}
+\text{1.\quad Att.\ Earth} : \text{Att.\ Moon} &\dblcolon 1 : \tfrac{1}{81}.\\
+\text{2.\quad Att.\ Earth} : \text{Att.\ Moon} &\dblcolon \dfrac{1}{4000^2} : \dfrac{1}{1081^2}.
+\end{align*}
+
+Combining these by multiplying, we get
+\[
+\text{Att.\ Earth} : \text{Att.\ Moon} \dblcolon 6 : 1.
+\]
+
+Therefore six pounds on the earth would weigh only
+one pound on the moon. Your weight, then, divided by
+six, represents what it would be on the moon. There
+you could jump six times as high---if you could live to
+jump at all on that cold and almost airless satellite (see
+p.~\pageref{page:263}). %[**TN: 'pp. 263, 264' in original text]
+
+\Paragraph{The Sphere, Circle, and Ellipse.} A \emph{sphere} is a solid
+\index{Circle defined}%
+\index{Sphere, defined}%
+bounded by a curved surface all points of which are equally
+distant from a point within called the center.
+
+A \emph{circle} is a plane figure bounded by a curved line all
+points of which are equally distant from a point within
+called the center. In geography what we commonly call
+circles such as the equator, parallels, and meridians, are
+really only the circumferences of circles. Wherever used
+%% -----File: 020.png---Folio 21-------
+\index{Circle defined}%
+in this book, unless otherwise stated, the term circle
+refers to the circumference.
+
+\includegraphicsleft{i021-1}{Fig.~9} %[**TN: period added after 'Minor Axis' on illustration]
+
+Every circle is conceived to be divided into 360 equal
+parts called degrees. The greater the size of the circle,
+the greater is the length of each degree. A \emph{radius} of a
+circle or of a sphere is a straight line from the boundary
+to the center. Two radii forming a straight line constitute
+a \emph{diameter}.
+
+Circles on a sphere dividing it into two hemispheres are
+called \emph{great circles}. Circles on a sphere dividing it into
+unequal parts are called \emph{small circles}.
+
+All great circles on the same sphere bisect each other,
+regardless of the angle at which they cross one another.
+That this may be clearly seen, with a globe before you test
+these two propositions:
+
+\textit{a}.  A point $180°$ in any direction from one point in a
+great circle must lie in the same circle.
+
+\textit{b}.  Two great circles on the same sphere must cross
+somewhere, and the point $180°$ from the one where they
+cross, lies in both of the circles, thus each great circle
+divides the other into two equal parts.
+
+An angle is the difference in direction of two lines which,
+if extended, would meet. Angles are measured by using
+the meeting point as the center of a circle and finding the
+fraction of the circle, or number of degrees of the circle,
+included between the lines. It is well to practice estimating
+different angles and then to test the accuracy of
+the estimates by reference to a graduated quadrant or
+circle having the degrees marked.
+
+\includegraphicsright{i021-2}{Fig.~10}
+
+\sloppy
+An \emph{ellipse} is a closed plane curve such that the sum of
+\index{Ellipse@Ellipse \indexglossref{Ellipse}|(}%
+the distances from one point in it to two fixed points within,
+called \emph{foci}, is equal to the sum of the distances from any
+other point in it to the foci. The ellipse is a conic section
+%% -----File: 021.png---Folio 22-------
+formed by cutting a right cone by a plane passing obliquely
+through its opposite sides (see \glossref{Ellipse} in Glossary).
+
+\fussy
+\nblabel{page:22}To construct an ellipse,
+drive two pins at points
+for foci, say three inches
+apart. With a loop of
+non-elastic cord, say ten
+inches long, mark the
+boundary line as represented
+in Figure~\figureref{i021-2}{10}.\index{Ellipse@Ellipse \indexglossref{Ellipse}|)}%
+
+\Paragraph{\nbstretchyspace Orbit of the Earth.}
+\index{Orbit, of earth}%
+The orbit of the earth
+is an ellipse. To lay off
+an ellipse which shall
+quite correctly represent
+the shape of the earth's
+orbit, place pins one
+tenth of an inch apart and make a loop of string $12.2$~inches
+long.  This loop
+can easily be made
+by driving two pins
+$6.1$~inches apart
+and tying a string
+looped around
+them.
+
+\Paragraph{Shape of the
+Earth.} The earth
+is a spheroid, or a
+\index{Spheroid}%
+solid approaching
+a sphere (see \glossref{Spheroid}
+in Glossary).
+The diameter upon which it rotates is called the \emph{axis}.
+The ends of the axis are its \emph{poles}. Imaginary lines on the
+\index{Axis, changes in position of!defined}%
+\index{North, line!pole}%
+\index{Pole, celestial!terrestrial}%
+%% -----File: 022.png---Folio 23-------
+surface of the earth extending from pole to pole are called
+\index{Meridian}%
+\index{Meridian!circle}%
+\emph{meridians}.\footnote
+  {The term meridian is frequently used to designate a great circle
+  passing through the poles. In this book such a circle is designated a
+  \emph{meridian circle}, since each meridian is numbered regardless of its opposite
+  meridian.}
+While any number of meridians may be
+conceived of, we usually think of them as one degree apart.
+We say, for example, the ninetieth meridian, meaning the
+meridian ninety degrees from the prime or initial meridian.
+What kind of a circle is a meridian circle? Is it a true
+circle? Why?
+
+The \emph{equator} is a great circle midway between the poles.
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+
+\emph{Parallels} are small circles parallel to the equator.
+\index{Parallels}%
+
+It is well for the student to bear in mind the fact that
+it is the earth's rotation on its axis that determines most of
+\index{Rotation of earth@Rotation of earth\phantomsection\label{idx:r}}%
+the foregoing facts. A sphere at rest would not have
+equator, meridians, etc.
+%% -----File: 023.png---Folio 24-------
+
+\Chapter{II}{The Form of the Earth}
+\index{Proofs, form of earth|(}%
+\index{Form of the earth|(}%
+
+\Section{The Earth a Sphere}
+
+\Paragraph{Circumnavigation.} The statements commonly given as
+proofs of the spherical form of the earth would often apply
+as well to a cylinder or an egg-shaped or a disk-shaped
+body. ``People have sailed around it,'' ``The shadow of
+the earth as seen in the eclipse of the moon is always circular,''
+\index{Eclipse}%
+etc., do not in themselves prove that the earth is a
+sphere. They might be true if the earth were a cylinder
+or had the shape of an egg. ``But men have sailed around
+it in different directions.'' So might they a lemon-shaped
+body. To make a complete proof, we must show that men
+have sailed around it in practically every direction and
+have found no appreciable difference in the distances in
+the different directions.
+
+\Paragraph{Earth's Shadow always Circular.} The shadow of the
+earth as seen in the lunar eclipse is always circular. But
+a dollar, a lemon, an egg, or a cylinder may be so placed
+as always to cast a circular shadow. When in addition
+to this statement it is shown that the earth presents many
+different sides toward the sun during different eclipses of
+the moon and the shadow is always circular, we have a
+proof positive, for nothing but a sphere casts a circular
+shadow when in many different positions. The fact that
+eclipses of the moon are seen in different seasons and at
+different times of day is abundant proof that practically
+%% -----File: 024.png---Folio 25-------
+all sides of the earth are turned toward the sun during
+different eclipses.
+
+\includegraphicsright{i024-1}{Fig.~11. Ship's rigging distinct. Water hazy.}
+
+\Paragraph{Almost Uniform Surface Gravity.} An object has almost
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+exactly the same weight in
+different parts of the earth
+(that is, on the surface),
+showing a practically common
+distance from different points
+on the earth's surface to the
+center of gravity. This is
+ascertained, not by carrying
+an object all over the earth
+and weighing it with a pair
+of spring scales (why not
+balances?); but by noting the
+time of the swing of the
+pendulum, for the rate of its swing varies according
+to the force of gravity.
+
+\includegraphicsleft{i024-2}{Fig.~12. Water distinct. Rigging ill-defined.}
+
+\Paragraph{Telescopic Observations.} If
+we look through a telescope
+at a distant object over a
+level surface, such as a body
+of water, the lower part is
+hidden by the intervening
+curved surface. (Figs.~\figureref{i024-2}{11},~\figureref{i024-2}{12}.)
+This has been observed in
+many different places, and the
+rate of curvature seems uniform
+everywhere and in every
+direction. Persons ascending
+in balloons or living on high
+elevations note the appreciably earlier time of sunrise
+or later time of sunset at the higher elevation.
+%% -----File: 025.png---Folio 26-------
+
+\Paragraph{Shifting of Stars and Difference in Time.} The proof
+which first demonstrated the curvature of the earth, and
+one which the student should clearly understand, is the
+disappearance of stars from the southern horizon and the
+rising higher of stars from the northern horizon to persons
+traveling north, and the sinking of northern stars and the
+rising of southern stars to south-bound travelers. After
+people had traveled far enough north and south to make
+an appreciable difference in the position of stars, they
+observed this apparent rising and sinking of the sky. Now
+two travelers, one going north and the other going south,
+will see the sky apparently elevated and depressed at the
+same time; that is, the portion of the sky that is rising for
+one will be sinking for the other. Since it is impossible
+that the stars be both rising and sinking at the same
+time, only one conclusion can follow,---the movement of
+the stars is apparent, and the path traveled north and
+south must be curved.
+
+Owing to the rotation of the earth one sees the same
+stars in different positions in the sky east and west, so the
+proof just given simply shows that the earth is curved in
+a north and south direction. Only when timepieces were
+invented which could carry the time of one place to different
+portions of the earth could the apparent positions
+of the stars prove the curvature of the earth east and
+west. By means of the telegraph and telephone we
+have most excellent proof that the earth is curved east
+and west.
+
+If the earth were flat, when it is sunrise at Philadelphia
+\index{Philadelphia, Pa.}%
+it would be sunrise also at St.~Louis and Denver. Sun
+\index{Denver, Col.}%
+\index{St.~Louis, Mo.}%
+rays extending to these places which are so near together
+as compared with the tremendous distance of the sun, over
+ninety millions of miles away, would be almost parallel
+%% -----File: 026.png---Folio 27-------
+on the earth and would strike these points at about the
+same angle. But we know from the many daily messages
+between these cities that sun time in Philadelphia is an
+\index{Philadelphia, Pa.}%
+hour later than it is in St.~Louis and two hours later than
+\index{St.~Louis, Mo.}%
+in Denver.
+\index{Denver, Col.}%
+
+When we know that the curvature of the earth north
+\index{Curvature of surface of earth, rate of}%
+\index{Rate of curvature of earth's surface}%
+and south as observed by the general and practically
+uniform rising and sinking of the stars to north-bound and
+south-bound travelers is the same as the curvature east
+and west as shown by the difference in time of places
+east and west, we have an excellent proof that the earth is
+a sphere.
+
+\Paragraph{Actual Measurement.} Actual measurement in many
+different places and in nearly every direction shows a practically
+uniform curvature in the different directions. In
+digging canals and laying watermains, an allowance must
+always be made for the curvature of the earth; also in
+surveying, as we shall notice more explicitly farther on.
+
+A simple rule for finding the amount of curvature for
+any given distance is the following:
+
+\emph{Square the number of miles representing the distance, and
+two thirds of this number represents in feet the departure
+from a straight line.}
+
+Suppose the distance is $1$~mile. That number squared
+is~$1$, and two thirds of that number of feet is $8$~inches.
+Thus an allowance of $8$~inches must be made for $1$~mile.
+If the distance is $2$~miles, that number squared is~$4$, and
+two thirds of $4$~feet is $2$~feet, $8$~inches. An object, then,
+$1$~mile away sinks $8$ inches below the level line, and at $2$~miles
+it is below $2$~feet, $8$~inches.
+
+To find the distance, the height from a level line being
+given, we have the converse of the foregoing rule:
+
+\emph{Multiply the number representing the height in feet by~$1\tfrac{1}{2}$,
+%% -----File: 027.png---Folio 28-------
+and the square root of this product represents the number of
+miles distant the object is situated.}
+
+\index{Rate of curvature of earth's surface}%
+\index{Curvature of surface of earth, rate of}%
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+\index{Oblateness of earth|(}%
+The following  table is  based upon  the more accurate
+formula:
+\begin{center}
+$\text{Distance (miles) } = 1.317 \sqrt{\text{height (feet)}.}$
+\end{center}
+{\smallsize\nblabel{page:28a}
+\[
+\begin{array}{c|c||c|c||c|c}
+\hline
+\tablespacertop%
+\text{~Ht.\ ft.~} & \text{Dist.\ miles} &
+\text{~Ht.\ ft.~} & \text{Dist.\ miles} &
+\text{~Ht.\ ft.~} & \text{Dist.\ miles}\tablespacerbot\\
+\hline
+\tablespacertop%
+\Z1 & 1.32 & \Z50 & \Z9.31 & \Z170 & 17.17\\
+\Z2 & 1.86 & \Z55 & \Z9.77 & \Z180 & 17.67\\
+\Z3 & 2.28 & \Z60 &  10.20 & \Z190 & 18.15\\
+\Z4 & 2.63 & \Z65 &  10.62 & \Z200 & 18.63\\
+\Z5 & 2.94 & \Z70 &  11.02 & \Z300 & 22.81\\
+\Z6 & 3.23 & \Z75 &  11.40 & \Z400 & 26.34\\
+\Z7 & 3.48 & \Z80 &  11.78 & \Z500 & 29.45\\
+\Z8 & 3.73 & \Z85 &  12.14 & \Z600 & 32.26\\
+\Z9 & 3.95 & \Z90 &  12.49 & \Z700 & 34.84\\
+ 10 & 4.16 & \Z95 &  12.84 & \Z800 & 37.25\\
+ 15 & 5.10 &  100 &  13.17 & \Z900 & 39.51\\
+ 20 & 5.89 &  110 &  13.81 &  1000 & 41.65\\
+ 25 & 6.59 &  120 &  14.43 &  2000 & 58.90\\
+ 30 & 7.21 &  130 &  15.02 &  3000 & 72.13\\
+ 35 & 7.79 &  140 &  15.58 &  4000 & 83.30\\
+ 40 & 8.33 &  150 &  16.13 &  5000 & 93.10\\
+ 45 & 8.83 &  160 &  16.66 & \text{Mile} & 95.70\tablespacerbot\\
+\hline
+\end{array}
+\]
+}%end smallsize
+
+
+\Section{The Earth an Oblate Spheroid}\nblabel{page:28}
+\index{Spheroid|(}%
+
+\index{Cayenne@Cayenne (k\u{\i}\;\u{e}n$'$), French Guiana}%
+\index{Louis XIV., King of France}%
+\index{Richer@Richer (re\;sh\={a}y$'$), John}%
+\index{Paris, France}%
+\index{Pendulum clock}%
+\Paragraph{Richer's Discovery.} In the year 1672 John Richer, the
+astronomer to the Royal Academy of Sciences of Paris,
+was sent by Louis~XIV to the island of Cayenne to make
+certain astronomical observations. His Parisian clock had
+its pendulum, slightly over $39$~inches long, regulated to
+beat seconds. Shortly after his arrival at Cayenne, he
+noticed that the clock was losing time, about two and a
+half minutes a day. Gravity, evidently, did not act with
+so much force near the equator as it did at Paris. The
+astronomer found it necessary to shorten the pendulum
+nearly a quarter of an inch to get it to swing fast enough.
+%% -----File: 028.png---Folio 29-------
+
+Richer reported these interesting facts to his colleagues
+\index{Richer@Richer (re\;sh\={a}y$'$), John}%
+at Paris, and it aroused much discussion. At first it was
+thought that greater centrifugal force at the equator,
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}}%
+counteracting the earth's attraction more there than elsewhere,
+was the explanation. The difference in the force
+of gravity, however, was soon discovered to be too great
+to be thus accounted for. The only other conclusion was
+that Cayenne must be farther from the center of gravity
+\index{Cayenne@Cayenne (k\u{\i}\;\u{e}n$'$), French Guiana}%
+than Paris (see the discussion of Gravity, Appendix,
+\index{Paris, France}%
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+p.~\pageref{sec:gravity}; also Historical Sketch, pp.~\pageref{page:273}--\pageref{page:275}).
+
+Repeated experiments show it to be a general fact that
+pendulums swing faster on the surface of the earth as one
+approaches the poles. Careful measurements of arcs of
+meridians prove beyond question that the earth is flattened
+toward the poles, somewhat like an oblate spheroid.
+Further evidence is found in the fact that the sun and
+planets, so far as ascertained, show this same flattening.
+\index{Proofs, form of earth|)}%
+
+\Paragraph{Cause of Oblateness.} The cause of the oblateness is
+the rotation of the body, its flattening effects being more
+marked in earlier plastic stages, as the earth and other
+planets are generally believed to have been at one time.
+The reason why rotation causes an equatorial bulging
+is not difficult to understand. Centrifugal force increases
+away from the poles toward the equator and gives a lifting
+or lightening influence to portions on the surface. If the
+earth were a sphere, an object weighting $289$~pounds at
+the poles would be lightened just one pound if carried to
+the swiftly rotating equator (see p.~\pageref{page:280}). The form given
+the earth by its rotation is called an oblate spheroid or an
+ellipsoid of rotation.
+
+\Paragraph{Amount of Oblateness.} To represent a meridian circle
+\index{Meridian}%
+\index{Diameter of earth|(}%
+accurately, we should represent the polar diameter about
+$\frac{1}{300}$~part shorter than the equatorial diameter. That this
+%% -----File: 029.png---Folio 30-------
+difference is not perceptible to the unaided eye will be
+apparent if the construction of such a figure is attempted,
+say ten inches in diameter in one direction and $\frac{1}{30}$~of an
+inch less in the opposite direction. The oblateness of
+Saturn is easily perceptible, being thirty times as great as
+\index{Saturn}%
+that of the earth, or one tenth (see p.~\pageref{page:257}). Thus an
+ellipsoid nine inches in polar diameter (minor axis) and
+ten inches in equatorial diameter (major axis) would represent
+the form of that planet.
+
+Although the oblateness of the earth seems slight when
+represented on a small scale and for most purposes may be
+ignored, it is nevertheless of vast importance in many
+problems in surveying, astronomy, and other subjects.
+Under the discussion of \hyperref[page:282]{latitude} it will be shown how this
+oblateness makes a difference in the lengths of degrees of
+latitude, and in the Appendix it is shown how this equatorial
+bulging shortens the length of the year and changes
+the inclination of the earth's axis (see \hyperref[page:286]{Precession of the
+Equinoxes} and \hyperref[page:286a]{Motions of the Earth's Axis}).
+
+\Paragraph{Dimensions of the Spheroid.}\nblabel{page:30} It is of very great importance
+\index{Circumference of earth}%
+in many ways that astronomers and surveyors know
+as exactly as possible the dimensions of the spheroid.
+Many men have made estimates based upon astronomical
+facts, pendulum experiments and careful surveys, as to the
+equatorial and polar diameters of the earth. Perhaps the
+most widely used is the one made by A.~R. Clarke, for many
+\index{Clarke, A. R.|(}%
+years at the head of the English Ordnance Survey, known
+as the Clarke Spheroid of~1866.
+
+\begin{tabularspheroid}{Clarke Spheroid of 1866.}
+\tablespacertop%
+  A. & Equatorial diameter \dotfill & $7,926.614$ miles\\
+  B. & Polar diameter      \dotfill & $7,899.742$ miles\\
+     & Oblateness $\dfrac{A - B}{A}$ \dotfill & $\dfrac{1}{295}$
+\end{tabularspheroid}
+%% -----File: 030.png---Folio 31-------
+
+It is upon this spheroid of reference that all of the
+work of the United States Geological Survey and of the
+\index{Survey}%
+\index{United States|(}%
+\index{United States Geological Survey}%
+United States Coast and Geodetic Survey is based, and
+\index{United States Coast and Geodetic Survey}%
+upon which most of the dimensions given in this book are
+determined.
+
+In 1878 Mr.~Clarke made a recalculation, based upon
+additional information, and gave the following dimensions,
+though it is doubtful whether these approximations are
+any more nearly correct than those of~1866.
+\begin{tabularspheroid}{Clarke Spheroid of 1878.}
+\tablespacertop%
+  A. & Equatorial diameter \dotfill & $7,926.592$ miles\\
+  B. & Polar diameter      \dotfill & $7,899.580$ miles\\
+     & Oblateness $\dfrac{A - B}{A}$ \dotfill & $\dfrac{1}{293.46}$
+\end{tabularspheroid}
+
+Another standard spheroid of reference often referred
+to, and one used by the United States Governmental
+Surveys before~1880, when the Clarke spheroid was
+adopted, was calculated by the distinguished Prussian
+astronomer, F.~H. Bessel, and is called the
+\index{Bessel, F. W.}%
+\begin{tabularspheroid}{Bessel Spheroid of 1841.}
+\tablespacertop%
+  A. & Equatorial diameter \dotfill & $7,925.446$ miles\\
+  B. & Polar diameter      \dotfill & $7,898.954$ miles\\
+     & Oblateness $\dfrac{A - B}{A}$ \dotfill & $\dfrac{1}{299.16}$
+\end{tabularspheroid}
+\index{Circumference of earth}%
+\index{Diameter of earth|)}%
+
+Many careful pendulum tests and a great amount of
+scientific triangulation surveys of long arcs of parallels
+\index{Triangulation}%
+and meridians within recent years have made available
+considerable data from which to determine the true
+dimensions of the spheroid. In~1900, the United States
+Coast and Geodetic Survey completed the measurement
+of an arc across the United States along the 39th~parallel
+%% -----File: 031.png---Folio 32-------
+from Cape May, New Jersey, to Point Arena, California,
+\index{Point Arena, Calif.}%
+\index{Cape May, N. J.}%
+\index{California}%
+\index{New Jersey}%
+through $48°~46'$ of longitude, or a distance of about $2,625$
+miles. This is the most extensive piece of geodetic surveying
+ever undertaken by any nation and was so carefully
+done that the total amount of probable error does not
+amount to more than about eighty-five feet. A long arc
+has been surveyed diagonally from Calais, Maine, to
+\index{Calais, Me.}%
+\index{Maine}%
+New Orleans, Louisiana, through $15°~1'$ of latitude and
+$22°~47'$ of longitude, a distance of $1,623$ miles. Another
+long arc will soon be completed along the 98th~meridian
+\index{Meridian}%
+across the United States. Many shorter arcs have also
+been surveyed in this country.
+
+The English government undertook in 1899 the gigantic
+task of measuring the arc of a meridian extending the
+entire length of Africa, from Cape Town to Alexandria.
+\index{Cape Town, Africa}%
+\index{Alexandria, Egypt}%
+This will be, when completed, $65°$~long, about half on
+each side of the equator, and will be of great value in
+determining the oblateness. Russia and Sweden have
+\index{Russia}%
+\index{Sweden}%
+lately completed the measurement of an arc of $4°~30'$ on
+the island of Spitzbergen, which from its high latitude,
+\index{Spitzbergen}%
+$76°$~to $80°~30'$~N., makes it peculiarly valuable. Large
+arcs have been measured in India, Russia, France, and
+\index{France}%
+\index{India}%
+other countries, so that there are now available many times
+as much data from which the form and dimensions of the
+earth may be determined as Clarke or Bessel had.
+\index{Bessel, F. W.}%
+\index{Clarke, A. R.|)}%
+
+The late Mr.~Charles~A. Schott, of the United States
+\index{Schott, C. A.}%
+\index{United States Coast and Geodetic Survey}%
+\index{Survey}%
+Coast and Geodetic Survey, in discussing the survey of the
+39th~parallel, with which he was closely identified, said:\footnote
+  {In his Transcontinental Triangulation and the American Arc of
+\index{Triangulation}%
+  the Parallel.}
+
+``Abundant additional means for improving the existing
+deductions concerning the earth's figure are now at hand,
+and it is perhaps not too much to expect that the International
+%% -----File: 032.png---Folio 33-------
+Geodetic Association may find it desirable in the
+near future to attempt a new combination of all available
+arc measures, especially since the two large arcs of the
+parallel, that between Ireland and Poland and that of the
+\index{Ireland}%
+\index{Poland}%
+United States of America, cannot fail to have a paramount
+influence in a new general discussion.''
+
+\index{Proofs, form of earth|(}%
+A spheroid is a solid nearly spherical. An oblate spheroid
+is one flattened toward the poles of its axis of rotation.
+The earth is commonly spoken of as a sphere. It would
+be more nearly correct to say it is an oblate spheroid.
+This, however, is not strictly accurate, as is shown in the
+succeeding discussion.
+
+\Section{The Earth a Geoid}
+\index{Geoid@Geoid (j\={e}$'$oid)|(}%
+
+\Paragraph{Conditions Producing Irregularities.} If the earth had
+been made up of the same kinds of material uniformly
+distributed throughout its mass, it would probably have
+assumed, because of its rotation, the form of a regular
+oblate spheroid. But the earth has various materials
+\index{Spheroid|)}%
+unevenly distributed in it, and this has led to many slight
+variations from regularity in form.
+
+\Paragraph{Equator Elliptical.} Pendulum experiments and measurements
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+indicate not only that meridians are elliptical but
+that the equator itself may be slightly elliptical, its longest
+axis passing through the earth from $15°$~E. to $165°$~W. and
+its shortest axis from $105°$~E. to $75°$~W\@. The amount of this
+oblateness of the equator is estimated at about $\frac{1}{4,000}$ or a
+difference of two miles in the lengths of these two diameters
+of the equator. Thus the meridian circle passing through
+central Africa and central Europe ($15°$~E.) and around
+near Behring Strait ($165°$~W.) may be slightly more oblate
+\index{Behring Strait}%
+than the other meridian circles, the one which is most
+\index{Oblateness of earth|)}%
+%% -----File: 033.png---Folio 34-------
+nearly circular passing through central Asia ($105°$~E.),
+\index{Asia}%
+eastern North America, and western South America
+\index{South America}%
+($75°$~W.).
+
+\includegraphicsmid{i033}{Fig.~13. Gravimetric lines showing variation in force of gravity}
+\index{Gravimetric lines, map showing}%
+
+\Paragraph{United States Curved Unequally.} It is interesting to
+note that the dimensions of the degrees of the long arc
+of the 39th~parallel surveyed in the United States bear out
+\index{United States|)}%
+to a remarkable extent the theory that the earth is slightly
+flattened longitudinally, making it even more than that
+just given, which was calculated by Sir John Herschel and
+\index{Herschel, John}%
+A.~R. Clarke. The average length of degrees of longitude
+\index{Clarke, A. R.}%
+from the Atlantic coast for the first $1,500$ miles corresponds
+closely to the Clarke table, and thus those degrees are
+longer, and the rest of the arc corresponds closely to the
+Bessel table and shows shorter degrees.
+%% -----File: 034.png---Folio 35-------
+\begin{center}
+\smallsize
+\settowidth{\TmpLen}{Diff.\ in}
+\begin{tabular}{@{}l@{\,}|@{\,}c@{\,}|@{\,}c@{\,}|@{\,}c@{\,}|@{\,}c@{\,}}
+\hline
+
+& \parbox{\TmpLen}{\centering\tablespacertop Diff.\ in long.\tablespacerbot} &
+  \parbox{\TmpLen}{\centering Length\\of $1°$} & Clarke & Bessel\\
+\hline
+\tablespacertop%
+Cape May to Wallace (Kansas)      &  $26.661°$  & $53.829$ mi. & $53.828$~mi. & \dotfill\\
+\index{Kansas}%
+Wallace to Uriah (Calif.)\dotfill &  $21.618°$  & $53.822$ mi. & \dotfill     & $53.821$~mi.\tablespacerbot\\
+\hline
+\end{tabular}
+\index{Bessel, F. W.}%
+\index{Clarke, A. R.}%
+\index{California}%
+\index{Cape May, N. J.}%
+\index{Wallace, Kan.}%
+\end{center}
+
+\Paragraph{Earth not an Ellipsoid of Three Unequal Axes.} This
+oblateness of the meridians and oblateness of the equator
+led some to treat the earth as an ellipsoid of three
+unequal axes: (1)~the longest equatorial axis, (2)~the
+shortest equatorial axis, and (3)~the polar axis. It has
+been shown, however, that meridians are not true ellipses,
+for the amount of flattening northward is not quite the
+same as the amount southward, and the mathematical
+center of the earth is not exactly in the plane of the equator.
+
+\Paragraph{Geoid Defined.} The term \emph{geoid}, which means ``like the
+earth,'' is now applied to \emph{that figure which most nearly corresponds
+to the true shape of the earth}. Mountains, valleys,
+and other slight deviations from evenness of surfaces are
+treated as departures from the geoid of reference. The
+following definition by Robert~S. Woodward, President of
+\index{Woodward, R. S.}%
+the Carnegie Institution of Washington, very clearly
+\index{Washington, D. C.}%
+\index{Carnegie Institution of Washington}%
+explains what is meant by the geoid.\footnote
+  {Encyclopaedia Americana.}%
+\index{Proofs, form of earth|)}%
+
+``Imagine the mean sea level, or the surface of the sea
+freed from the undulations due to winds and to tides.
+This mean sea surface, which may be conceived to extend
+through the continents, is called the geoid. It does not
+coincide exactly with the earth's spheroid, but is a slightly
+wavy surface lying partly above and partly below the
+spheroidal surface, by small but as yet not definitely known
+amounts. The determination of the geoid is now one of
+the most important problems of geophysics.''
+%% -----File: 035.png---Folio 36-------
+
+An investigation is now in progress in the United States
+\index{United States}%
+for determining a new geoid of reference upon a plan never
+followed hitherto. The following is a lucid description\footnote
+  {Given at the International Geographic Congress, 1904.}
+of the plan by John~F. Hayford, Inspector of Geodetic
+\index{Hayford, J. F.}%
+Work, United States Coast and Geodetic Survey.
+\index{Survey}%
+\index{United States Coast and Geodetic Survey}%
+
+\Paragraph{Area Method of Determining Form of the Earth.} ``The
+\index{Area method of determining geoid}%
+arc method of deducing the figure of the earth may be
+illustrated by supposing that a skilled workman to whom is
+given several stiff wires, each representing a geodetic arc,
+either of a parallel or a meridian, each bent to the radius
+deduced from the astronomic observations of that arc, is
+told in what latitude each is located on the geoid and then
+requested to construct the ellipsoid of revolution which
+will conform most closely to the bent wires. Similarly,
+the area method is illustrated by supposing that the workman
+is given a piece of sheet metal cut to the outline of
+the continuous triangulation which is supplied with necessary
+astronomic observations, and accurately molded to fix
+the curvature of the geoid, as shown by the astronomic
+observations, and that the workman is then requested to
+\DPtypo{contruct}{construct} the ellipsoid of revolution which will conform
+\index{Ellipsoid of rotation@Ellipsoid of rotation \indexglossref{Spheroid}}%
+most accurately to the bent sheet. Such a bent sheet
+essentially includes within itself the bent wires referred to
+in the first illustration, and, moreover, the wires are now
+held rigidly in their proper relative positions. The sheet is
+much more, however, than this rigid system of bent lines,
+for each arc usually treated as a line is really a belt of
+considerable width which is now utilized fully. It is obvious
+that the workman would succeed much better in constructing
+accurately the required ellipsoid of revolution
+from the one bent sheet than from the several bent wires.
+When this proposition is examined analytically it will be
+%% -----File: 036.png---Folio 37-------
+seen to be true to a much greater extent than appears
+from this crude illustration.''
+
+``The area of irregular shape which is being treated as a
+\index{Area method of determining geoid}%
+single unit extends from Maine to California and from
+\index{California}%
+\index{Maine}%
+Lake Superior to the Gulf of Mexico. It covers a range of~$57°$
+\index{Gulf of Mexico}%
+in longitude and~$19°$ in latitude, and contains $477$
+astronomic stations. This triangulation with its numerous
+accompanying astronomical observations will, even without
+combination with similar work in other countries,
+furnish a remarkably strong determination of the figure
+and size of the earth.''
+
+It is possible that at some distant time in the future the
+dimensions and form of the geoid will be so accurately
+known that instead of using an oblate spheroid of reference
+(that is, a spheroid of such dimensions as most closely
+correspond to the earth, treated as an oblate spheroid such
+as the Clarke Spheroid of 1866), as is now done, it will be
+\index{Clarke, A. R.}%
+possible to treat any particular area of the earth as having
+its own peculiar curvature and dimensions.
+
+\Paragraph{Conclusion.} What is the form of the earth? We went
+\index{Oblateness of earth}%
+to considerable pains to prove that the earth is a sphere.
+That may be said to be its general form, and in very many
+calculations it is always so treated. For more exact calculations,
+the earth's departures from a sphere must be
+borne in mind. The regular geometric solid which the
+earth most nearly resembles is an oblate spheroid. Strictly
+speaking, however, the form of the earth (not considering
+such irregularities as mountains and valleys) must be
+called a \emph{geoid}.
+
+
+\Section{Directions on the Earth}
+
+\Paragraph{On a Meridian Circle.} Think of yourself as standing
+\index{Meridian}%
+on a great circle of the earth passing through the poles.
+\index{Pole, celestial!terrestrial}%
+\index{Geoid@Geoid (j\={e}$'$oid)|)}%
+%% -----File: 037.png---Folio 38-------
+Pointing from the northern horizon by way of your feet
+\index{Horizon@Horizon \indexglossref{Horizon}|(}%
+to the southern horizon, you have pointed to all parts
+of the meridian circle beneath you. Your arm has
+\index{Meridian}%
+swung through an angle of~$180°$, but you have pointed
+through all points of the meridian circle, or $360°$~of it.
+Drop your arm~$90°$, or from the horizon to the nadir,
+\index{Nadir@Nadir \indexglossref{Nadir}}%
+and you have pointed through half of the meridian
+circle, for $180°$~of latitude. It is apparent, then, that for
+every degree you drop your arm, you point through
+a space of two degrees of latitude upon the earth
+beneath.
+
+The north pole is, let us say, $45°$~from you. Drop
+\index{Pole, celestial!terrestrial}%
+your arm $22\frac{1}{2}°$~from the northern horizon, and you will
+point directly toward the north pole (Fig.~\figureref{i037}{14}). \emph{Whatever
+your latitude, drop your arm half as many degrees from
+the northern horizon as you are degrees from the pole, and you
+will point directly toward that pole.}\footnote
+  {The angle included between a tangent and a chord is measured by
+  one half the intercepted arc.}
+
+\includegraphicsleft{i037}{Fig.~14}
+
+You may be so accustomed to thinking of the north
+pole as northward in a
+horizontal line from you
+that it does not seem
+real to think of it as
+below the horizon. This
+is because one is liable
+to forget that he is
+living on a ball. To
+point to the horizon is
+to point away from the earth.
+
+\includegraphicsright{i038-1}{Fig.~15}
+
+\Paragraph{A Pointing Exercise.} It may not be easy or even
+\index{Pointing exercise|(}%
+essential to learn exactly to locate many places in relation
+to the home region, but the ability to locate readily
+%% -----File: 038.png---Folio 39-------
+some salient points greatly clarifies one's sense of location
+and conception of the earth as a ball.
+
+The following exercise
+is designed for
+students living not far
+from the 45th~parallel.
+Since it is impossible
+to point the arm or
+pencil with accuracy
+at any given angle, it
+is roughly adapted for
+the north temperate
+latitudes (Fig.~\figureref{i038-1}{15}).
+Persons living in the
+southern states may
+use Figure~\figureref{i038-2}{16}, based
+on the 30th~parallel.
+The student should make the necessary readjustment for
+his own latitude.
+
+\includegraphicsleft{i038-2}{Fig.~16}
+
+Drop the arm from
+the northern horizon
+quarter way down, or~$22\frac{1}{2}°$,
+and you are
+pointing toward the
+north pole (Fig.~\figureref{i038-1}{15}).
+Drop it half way
+down, or $45°$~from the
+horizon, and you are
+pointing $45°$ the other
+side of the north pole,
+or half way to the
+equator, on the same parallel but on the opposite side of
+the earth, in opposite longitude. Were you to travel half
+%% -----File: 039.png---Folio 40-------
+way around the earth in a due easterly or westerly direction,
+you would be at that point. Drop the arm $22\frac{1}{2}°$~more,
+or $67\frac{1}{2}°$~from the horizon, and you are pointing $45°$~farther
+south or to the equator on the opposite side of the
+earth. Drop the arm $22\frac{1}{2}°$~more, or $90°$~from the horizon,
+toward your feet, and you are pointing toward our antipodes,
+$45°$~south of the equator on the meridian opposite
+ours. Find where on the earth this point is. Is the
+familiar statement, ``digging through the earth to China,''
+based upon a correct idea of positions and directions on
+the earth?
+
+From the southern horizon drop the arm~$22\frac{1}{2}°$, and you
+are pointing to a place having the same longitude but on
+the equator. Drop the arm $22\frac{1}{2}°$~more, and you point to
+a place having the same longitude as ours but opposite
+latitude, being $45°$~south of the equator on our meridian.
+Drop the arm $22\frac{1}{2}°$~more, and you point toward the south
+pole. Practice until you can point directly toward any of
+these seven points without reference to the diagram.
+\index{Horizon@Horizon \indexglossref{Horizon}|)}%
+\index{Pointing exercise|)}%
+
+\Section{Latitude and Longitude}
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!origin of term}%
+\index{Longitude, origin of term}%
+
+\Paragraph{Origin of Terms.} Students often have difficulty in
+remembering whether it is latitude that is measured east
+and west, or longitude. When we recall the fact that
+to the people who first used these terms the earth was
+believed to be longer east and west than north and south,
+and now we know that owing to the oblateness of the
+earth this is actually the case, we can easily remember that
+longitude (from the Latin \textit{longus}, long) is measured east
+and west. The word latitude is from the Latin \textit{latitudo},
+which is from \textit{latus}, wide, and was originally used to
+designate measurement of the ``width of the earth,'' or
+north and south.
+%% -----File: 040.png---Folio 41-------
+
+\Paragraph{Antipodal Areas.} From a globe one can readily ascertain
+\index{Antipodal@Antipodal (\u{a}n\;t\u{\i}p$'$\={o}\;dal) areas!map showing}%
+the point which is exactly opposite any given one on
+the earth. The map showing antipodal areas indicates
+\index{Map}%
+at a glance what portions of the earth are opposite each
+other; thus Australia lies directly through the earth from
+\index{Australia}%
+mid-Atlantic, the point antipodal to Cape Horn is in
+\index{Cape Horn}%
+central Asia,~etc.
+\index{Asia}%
+
+\includegraphicsmid{i040}{Fig.~17. Map of Antipodal Areas}
+
+\ParagraphNoSpace{Longitude} is measured on parallels and is reckoned from
+some meridian selected as standard, called the \emph{prime
+\index{Meridian!prime}%
+meridian}. The meridian which passes through the Royal
+Observatory at Greenwich, near London, has long been the
+\index{London, England}%
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+prime meridian most used. In many countries the
+meridian passing through the capital is taken as the prime
+meridian. Thus, the Portuguese use the meridian of the
+\index{Lisbon, Portugal}%
+\index{Portugal}%
+Naval Observatory in the Royal Park at Lisbon, the
+\index{Paris, France}%
+%% -----File: 041.png---Folio 42-------
+French that of the Paris Observatory, the Greeks that of
+the Athens Observatory, the Russians that of the Royal
+\index{Athens, Greece}%
+Observatory at Pulkowa, near St.~Petersburg.
+
+In the maps of the United States the longitude is often
+\index{United States}%
+reckoned both from Greenwich and Washington. The
+\index{Washington, D. C.}%
+latter city being a trifle more than $77°$~west of Greenwich,
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+a meridian numbered at the top of the map as $90°$~west
+\index{Map}%
+\index{Meridian!prime}%
+from Greenwich, is numbered at the bottom as $13°$~west
+from Washington. Since the United States Naval Observatory,
+the point in Washington reckoned from, is $77°~3'~81''$
+west from Greenwich, this is slightly inaccurate.
+Among all English speaking people and in most nations of
+the world, unless otherwise designated, the longitude of a
+place is understood to be reckoned from Greenwich.
+
+\emph{The longitude of a place} is the arc of the parallel intercepted
+between it and the prime meridian. Longitude
+may also be defined as the arc of the equator intercepted
+between the prime meridian and the meridian of the
+place whose longitude is sought.
+
+Since longitude is measured on parallels, and parallels
+grow smaller toward the poles, degrees of longitude are
+shorter toward the poles, being degrees of smaller circles.
+
+\ParagraphNoSpace{Latitude} is measured on a meridian and is reckoned
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!lengths of degrees|(}%
+from the equator. The number of degrees in the arc of
+a meridian circle, from the place whose latitude is sought
+to the equator, is its latitude. Stated more formally, the
+latitude of a place is the arc of the meridian intercepted
+between the equator and that place. (See \glossref{Latitude} in
+Glossary.) What is the greatest number of degrees of
+latitude any place may have? What places have no
+latitude?
+
+
+\sloppy
+\Subparagraph{Comparative Lengths of Degrees of Latitude.} If the earth
+were a perfect sphere, meridian circles would be true
+\includegraphicsright{i042}{Fig.~18} %[**TN: Figure placed mid paragraph to avoid poor line break after 'Comparative']
+%% -----File: 042.png---Folio 43-------
+mathematical circles. Since the earth is an oblate spheroid,
+\index{Oblateness of earth}%
+meridian circles, so called, curve less rapidly toward the
+poles. Since the curvature is greatest near the equator,
+\index{Curvature of surface of earth, rate of}%
+\index{Rate of curvature of earth's surface}%
+one would have to travel less distance on a meridian there
+to cover a degree of curvature, and a degree of latitude is
+thus shorter near the equator. Conversely, the meridian
+being slightly flattened
+toward the
+poles, one would
+travel farther there
+to cover a degree
+of latitude, hence
+degrees of latitude
+are longer toward
+the poles. Perhaps
+this may be seen
+more clearly from
+Figure~\figureref{i042}{18}.
+
+\fussy
+While all circles
+have~$360°$, the degrees
+of a small
+circle are, of course,
+shorter than the degrees of a greater circle. Now an
+arc of a meridian near the equator is obviously a part
+of a smaller circle than an arc taken near the poles and,
+consequently, the degrees are shorter. Near the poles,
+because of the flatness of a meridian there, an arc of a
+meridian is a part of a larger circle and the degrees are
+longer. As we travel northward, the North star (polestar)
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+rises from the horizon. In traveling from the equator on
+a meridian, one would go $68.7$~miles to see the polestar
+rise one degree, or, in other words, to cover one degree of
+curvature of the meridian. Near the pole, where the earth
+%% -----File: 043.png---Folio 44-------
+is flattest, one would have to travel $69.4$~miles to cover one
+degree of curvature of the meridian. The average length
+\index{Curvature of surface of earth, rate of}%
+\index{Rate of curvature of earth's surface}%
+of a degree  of latitude throughout the United States is
+almost exactly $69$~miles.
+\index{Form of the earth|)}%
+
+\Paragraph{Table of Lengths of Degrees.} The following table
+\index{Longitude@Longitude \indexglossref{Longitude}!lengths of degrees}%
+\index{Meridian!length of degrees of}%
+shows the length of each degree of the parallel and of the
+meridian at every degree of latitude. It is based upon
+the Clarke spheroid of~1866.
+\index{Clarke, A. R.}%
+\begin{center}
+\smallsize\nblabel{page:44}
+\begin{tabular}{%
+@{}>{\bfseries}c@{\,}|>{$}c<{$}|>{$}c<{$}||%
+@{\,}>{\bfseries}c@{\,}|>{$}c<{$}|>{$}c<{$}||%
+@{\,}>{\bfseries}c@{\,}|>{$}c<{$}|>{$}c<{$}@{}}%
+\hline
+\settowidth{\TmpLen}{Lat.}%
+\parbox[c]{\TmpLen}{\centering\normalfont Lat.} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\tablespacertop\centering Deg.\\ Par.\\ Miles\tablespacerbot} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\centering Deg.\\ Mer.\\ Miles} &
+%
+\settowidth{\TmpLen}{Lat.}%
+\parbox[c]{\TmpLen}{\centering\normalfont Lat.} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\centering Deg.\\ Par.\\ Miles} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\centering Deg.\\ Mer.\\ Miles} &
+%
+\settowidth{\TmpLen}{Lat.}%
+\parbox[c]{\TmpLen}{\centering\normalfont Lat.} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\centering Deg.\\ Par.\\ Miles} &
+\settowidth{\TmpLen}{Miles}%
+\parbox[c]{\TmpLen}{\centering Deg.\\ Mer.\\ Miles} \\
+%
+\hline
+\tablespacertop%
+\Z0\rlap{°} & 69.172 & 68.704 & 31\rlap{°}& 59.345 & 68.890 & 61\rlap{°}& 33.623 & 69.241 \\
+\Z1  & 69.162 & 68.704 & 32 & 58.716 & 68.901 & 62 & 32.560 & 69.251 \\
+\Z2  & 69.130 & 68.705 & 33 & 58.071 & 68.912 & 63 & 31.488 & 69.261 \\
+\Z3  & 69.078 & 68.706 & 34 & 57.407 & 68.923 & 64 & 30.406 & 69.271 \\
+\Z4  & 69.005 & 68.708 & 35 & 56.725 & 68.935 & 65 & 29.315 & 69.281 \\
+\Z5  & 68.911 & 68.710 & 36 & 56.027 & 68.946 & 66 & 28.215 & 69.290 \\
+\Z6  & 68.795 & 68.712 & 37 & 55.311 & 68.958 & 67 & 27.106 & 69.299 \\
+\Z7  & 68.660 & 68.715 & 38 & 54.579 & 68.969 & 68 & 25.988 & 69.308 \\
+\Z8  & 68.504 & 68.718 & 39 & 53.829 & 68.981 & 69 & 24.862 & 69.316 \\
+\Z9  & 68.326 & 68.721 & 40 & 53.063 & 68.993 & 70 & 23.729 & 69.324 \\
+ 10 & 68.129 & 68.725 & 41 & 52.281 & 69.006 & 71 & 22.589 & 69.332 \\
+ 11 & 67.910 & 68.730 & 42 & 51.483 & 69.018 & 72 & 21.441 & 69.340 \\
+ 12 & 67.670 & 68.734 & 43 & 50.669 & 69.030 & 73 & 20.287 & 69.347 \\
+ 13 & 67.410 & 68.739 & 44 & 49.840 & 69.042 & 74 & 19.127 & 69.354 \\
+ 14 & 67.131 & 68.744 & 45 & 48.995 & 69.054 & 75 & 17.960 & 69.360 \\
+ 15 & 66.830 & 68.751 & 46 & 48.136 & 69.066 & 76 & 16.788 & 69.366 \\
+ 16 & 66.510 & 68.757 & 47 & 47.261 & 69.079 & 77 & 15.611 & 69.372 \\
+ 17 & 66.169 & 68.764 & 48 & 46.372 & 69.091 & 78 & 14.428 & 69.377 \\
+ 18 & 65.808 & 68.771 & 49 & 45.469 & 69.103 & 79 & 13.242 & 69.382 \\
+ 19 & 65.427 & 68.778 & 50 & 44.552 & 69.115 & 80 & 12.051 & 69.386 \\
+ 20 & 65.026 & 68.786 & 51 & 43.621 & 69.127 & 81 & 10.857 & 69.390 \\
+ 21 & 64.606 & 68.794 & 52 & 42.676 & 69.139 & 82 &  9.659 & 69.394 \\
+ 22 & 64.166 & 68.802 & 53 & 41.719 & 69.151 & 83 &  8.458 & 69.397 \\
+ 23 & 63.706 & 68.811 & 54 & 40.749 & 69.163 & 84 &  7.255 & 69.400 \\
+ 24 & 63.228 & 68.820 & 55 & 39.766 & 69.175 & 85 &  6.049 & 69.402 \\
+ 25 & 62.729 & 68.829 & 56 & 38.771 & 69.186 & 86 &  4.842 & 69.404 \\
+ 26 & 62.212 & 68.839 & 57 & 37.764 & 69.197 & 87 &  3.632 & 69.405 \\
+ 27 & 61.676 & 68.848 & 58 & 36.745 & 69.209 & 88 &  2.422 & 69.407 \\
+ 28 & 61.122 & 68.858 & 59 & 35.716 & 69.220 & 89 &  1.211 & 69.407 \\
+ 29 & 60.548 & 68.869 & 60 & 34.674 & 69.230 & 90 &  0.000 & 69.407 \\
+ 30 & 59.956 & 68.879 &    &        &        &    &        & \tablespacerbot \\
+\hline
+\end{tabular}
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!lengths of degrees|)}%
+\end{center}
+%% -----File: 044.png---Folio 45-------
+
+\Chapter{III}{The Rotation of the Earth}
+
+\Section{The Celestial Sphere}\nblabel{page:45}
+\index{Celestial latitude!sphere|(}%
+
+\Paragraph{Apparent Dome of the Sky.} On a clear night the stars
+\index{Star, distance of a}%
+\index{Distances, of planets!of stars}%
+twinkling all over the sky seem to be fixed in a dark dome
+fitting down around the horizon. This apparent concavity,
+studded with heavenly bodies, is called the celestial sphere.
+Where the horizon is free from obstructions, one can see
+\index{Refraction of light}%
+half\footnote
+  {No allowance is here made for the refraction of rays of light or the
+  slight curvature of the globe in the locality.}
+of the celestial sphere at a given time from the same
+place.
+
+\includegraphicsmid{i044}{Fig.~19}
+\begin{flushright}
+\vspace{-8\baselineskip}%[**TN: move back vertically to place text over graphics]
+\begin{tabular}{p{0.3\textwidth}@{}p{0.6\textwidth}}
+&
+\smallsize
+If these lines met at a point $50,000$ miles
+distant, the difference in their direction
+could not be measured. Such is the ratio
+of the diameter of the earth and the distance
+\index{Diameter of earth}%
+to the very nearest of stars.
+\end{tabular}
+\vspace{2\baselineskip}%[**TN: advance again to continue main text]
+\end{flushright}
+
+A line from one side of the horizon over the zenith point
+to the opposite side of the horizon is half of a great circle
+of the celestial sphere. The horizon line extended to the
+celestial sphere is a great circle. Owing to its immense
+distance, a line from an observer at~$A$ (Fig.~\figureref{i044}{19}), pointing
+to a star, will make a line apparently parallel to one from~$B$
+to the same star. The most refined measurements at
+%% -----File: 045.png---Folio 46-------
+present possible fail to show any angle whatever between
+them.
+
+We may note the following in reference to the celestial
+sphere. (1)~The earth seems to be a mere point in the
+center of this immense hollow sphere. (2)~The stars,
+however distant, are apparently fixed in this sphere.
+(3)~Any plane from the observer, if extended, will divide
+the celestial sphere into two equal parts. (4)~Circles
+may be projected on this sphere and positions on it indicated
+by degrees in distance from established circles or
+points.
+
+\includegraphicsright{i046-1}{Fig.~20}
+
+\Paragraph{Celestial Sphere seems to Rotate.} The earth rotates on
+its axis (the term rotation applied to the earth refers to
+its daily or axial motion). To us, however, the earth
+seems stationary and the celestial sphere seems to rotate.
+Standing in the center of a room and turning one's body
+around, the objects in the room seem to rotate around in
+the opposite direction. The point overhead will be the
+only one that is stationary. Imagine a fly on a rotating
+sphere. If it were on one of the poles, that is, at the end
+of the axis of rotation, the object directly above it would
+constantly remain above it while every other fixed object
+would seem to swing around in circles. Were the fly to
+walk to the equator, the point directly away from the
+globe would cut the largest circle around him and the
+stationary points would be along the horizon.
+
+\Paragraph{Celestial Pole.} The point in the celestial sphere directly
+\index{Celestial latitude!pole}%
+\index{Pole, celestial}%
+above the pole and in line with the axis has no motion.
+It is called the celestial pole. The star nearest the pole
+of the celestial sphere and directly above the north pole
+of the earth is called the North star, and the star nearest
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+the southern celestial pole the South star. It may be of
+\index{South, on map!star|(}%
+interest to note that as we located the North star by reference
+%% -----File: 046.png---Folio 47-------
+to the Big Dipper, the South star is located by reference
+to a group of stars known as the Southern Cross.
+\index{Southern Cross}%
+
+\Paragraph{Celestial Equator.} A great circle is conceived to extend
+\index{Equator@Equator \indexglossref{Equator}!celestial}%
+\index{Celestial equator}%
+around the celestial sphere $90°$~from
+the poles (Fig.~\figureref{i046-1}{20}). This
+is called the \emph{celestial equator}.
+The axis of the earth, if prolonged,
+would pierce the celestial
+poles, almost pierce the
+North and South stars, and
+the equator of the earth if extended
+would coincide with the
+celestial equator.
+
+\includegraphicsleft{i046-2}{Fig.~21}
+
+\sloppy
+\Paragraph{At the North Pole.} An
+\index{Pole, celestial!terrestrial}%
+\index{Celestial latitude!pole}%
+\index{North, line!pole}%
+observer at the north pole
+will see the North star almost exactly overhead, and
+as the earth turns around under his feet it will remain
+constantly overhead (Fig.~\figureref{i046-2}{21}). Half way, or $90°$~from
+the North star, is the celestial equator around the
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+horizon. As the earth
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+rotates,---though it
+seems to us perfectly
+still,---the stars
+around the sky seem
+to swing in circles in
+the opposite direction.
+The planes of the star
+paths are parallel to
+the horizon. The
+same half of the celestial sphere can be seen all of the
+time, and stars below the horizon always remain so.
+
+\fussy
+All stars south of the celestial equator being forever
+invisible at the north pole, Sirius, the brightest of the
+\index{Sirius@Sirius (s\u{\i}r$'$\u{\i}\;us)}%
+%% -----File: 047.png---Folio 48-------
+stars, and many of the beautiful constellations, can never
+be seen from that place. How peculiar the view of the
+heavens must be from the pole, the Big Dipper, the
+\index{Big Dipper}%
+Pleiades, the Square of Pegasus, and other star groups
+\index{Pleiades@Pleiades (pl\={e}$'$yä\;d\={e}z)}%
+\index{Pegasus@Pegasus (p\u{e}g$'$a\;s\u{u}s), Square of}%
+\index{Square of Pegasus}%
+swinging eternally around in courses parallel to the
+horizon. When the sun, moon, and planets are in the
+portion of their courses north of the celestial equator,
+they, of course, will be seen throughout continued rotations
+of the earth until they pass below the celestial equator,
+when they will remain invisible again for long periods.
+
+The direction of the daily apparent rotation of the stars
+is from left to right (westward), the direction of the
+hands of a clock looked at from above. Lest the direction
+of rotation at the North pole be a matter of memory
+rather than of insight, we may notice that in the United
+States and Canada when we face southward we see the
+\index{United States}%
+\index{Canada}%
+sun's daily course in the direction left to right (westward),
+and going poleward the direction remains the same though
+the sun approaches the horizon more and more as we
+approach the North pole.
+
+\includegraphicsright{i048-1}{Fig.~22}
+
+\Paragraph{At the South Pole.} An observer at the South pole, at
+the other end of the axis, will see the South star directly
+overhead, the celestial equator on the horizon, and the
+plane of the star circles parallel with the horizon. The
+direction of the apparent rotation of the celestial sphere
+is from right to left, counter-clockwise. If a star is seen
+at one's right on the horizon at six o'clock in the morning,
+at noon it will be in front, at about six o'clock at night at
+his left, at midnight behind him, and at about six o'clock
+in the morning at his right again.
+
+\Paragraph{At the Equator.} An observer at the equator sees the
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+stars in the celestial sphere to be very different in their
+positions in relation to himself. Remembering that he is
+%% -----File: 048.png---Folio 49-------
+standing with the line of his body at right angles to the
+axis of the earth, it is easy to understand why all the stars
+of the celestial sphere seem to be shifted around $90°$ from
+where they were at the poles. The celestial equator is a
+great circle extending
+from east to west directly
+overhead. The
+North star is seen
+on the northern horizon
+and the South
+star on the southern
+\index{South, on map!star|)}%
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+horizon. The planes
+of the circles followed
+by stars in their daily
+orbits cut the horizon
+at right angles, the horizon being parallel to the axis. At
+the equator one can see the entire celestial sphere, half at
+one time and the other half about twelve hours later.
+
+\includegraphicsleft{i048-2}{Fig.~23}
+
+\Paragraph{Between Equator
+and Poles.} At places
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+between the equator
+and the poles, the observer
+is liable to feel
+that a star rising due
+east ought to pass
+the zenith about six
+hours later instead
+of swinging slantingly
+around as it actually
+seems to do. This is because one forgets that the axis
+is not squarely under his feet excepting when at the
+equator. There, and there only, is the axis at right
+angles to the line of one's body when erect. The
+%% -----File: 049.png---Folio 50-------
+apparent rotation of the celestial sphere is at right angles
+to the axis.
+
+\Paragraph{Photographing the Celestial Sphere.} Because of the
+\index{Photographing}%
+earth's rotation, the entire celestial sphere seems to rotate.
+Thus we see stars daily circling around, the polestar
+always stationary. When stars are photographed, long
+exposures are necessary that their faint light may affect
+the sensitive plate of the camera, and the photographic
+instruments must be constructed so that they will move
+at the same rate and in the same direction as the stars,
+otherwise the stars will leave trails on the plate. When
+the photographic instrument thus follows the stars in
+their courses, each is shown as a speck on the plate and
+comets, meteors, planets, or asteroids, moving at different
+\index{Asteroids}%
+\index{Comets}%
+\index{Meteors}%
+\index{Planets}%
+rates and in different directions, show as traces.
+
+\Paragraph{Rotation of Celestial Sphere is Only Apparent.} For a long
+time it was believed that the heavenly bodies rotated
+around the stationary earth as the center. It was only
+about five hundred years ago that the astronomer Copernicus
+\index{Copernicus@Copernicus (k\={o}\;per$'$n\u{\i}\;k\u{u}s)}%
+established the fact that the motion of the sun and
+stars around the earth is only apparent, the earth rotating.
+We may be interested in some proofs that this is the case.
+It seems hard to believe at first that this big earth, $25,000$
+miles in circumference can turn around once in a day.
+``Why, that would give us a whirling motion of over a
+thousand miles an hour at the equator.'' ``Who could
+stick to a merry-go-round going at the rate of a thousand
+miles an hour?'' When we see, however, that the sun
+$93,000,000$ miles away, would have to swing around in a
+course of over $580,000,000$ miles per day, and the stars, at
+their tremendous distances, would have to move at unthinkable
+rates of speed, we see that it is far easier to believe
+that it is the earth and not the celestial sphere that rotates
+%% -----File: 050.png---Folio 51-------
+daily. We know by direct observation that other planets,
+the sun and the moon, rotate upon their axis, and may
+reasonably infer that the earth does too.
+
+So far as the whirling motion at the equator is concerned,
+it does give bodies a slight tendency to fly off, but the
+amount of this force is only $\tfrac{1}{289}$ as great as the attractive
+influence of the earth; that is, an object which would
+weigh $289$~pounds at the equator, were the earth at rest,
+weighs a pound less because of the centrifugal force of
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}}%
+rotation (see p.~\pageref{page:14b}).
+
+\Section{Proofs of the Earth's Rotation}
+
+\index{Proofs, form of earth!rotation of earth|(}%
+\index{Rotation, proofs of}%
+\Paragraph{Eastward Deflection of Falling Bodies.} Perhaps the
+\index{Eastward deflection of falling objects|(}%
+simplest proof of the rotation of the earth is one pointed
+out by Newton, although he had no means of demonstrating
+\index{Newton, Isaac}%
+it. With his clear vision \DPtypo{be}{he} said that if the earth
+rotates and an object were dropped from a considerable
+height, instead of falling directly toward the center of
+the earth in the direction of the plumb line,\footnote
+  {The slight geocentric deviations of the plumb line are explained
+  on p.~\pageref{page:281}.} %[**TN:'pp. 281-282' in original text]
+\index{Plumb line}%
+it would be
+deflected toward the east. Experiments have been made
+in the shafts of mines where air currents have been shut off
+and a slight but unmistakable eastward tendency has been
+observed.
+
+During the summer of~1906, a number of newspapers
+and magazines in the United States gave accounts of the
+\index{United States}%
+eastward falling of objects dropped in the deep mines of
+northern Michigan, one of which (Shaft No.~3 of the Tamarack
+\index{Michigan}%
+\index{Tamarack mine}%
+mine) is the deepest in the world, having a vertical
+depth of over one mile (and still digging!). It was stated
+that objects dropped into such a shaft never reached the
+\index{Celestial latitude!sphere|)}%
+%% -----File: 051.png---Folio 52-------
+bottom but always lodged among timbers on the east
+side. Some papers added a touch of the grewsome by
+implying that among the objects found clinging to the east
+side are ``pieces of a dismembered human body'' which
+were not permitted to fall to the bottom because of the rotation
+of the earth. Following is a portion of an account\footnote
+{In the \textit{Mining and Scientific Press}, July~14, 1906.}
+\index{Mining and Scientific Press|(}%
+by F.~W.~McNair, President of the Michigan College of
+\index{Michigan!College of Mines}%
+Mines.
+
+\Subparagraph{McNair's Experiment.} ``Objects dropping into the shaft
+\index{McNair, F. W.}%
+under ordinary conditions nearly always start with some
+horizontal velocity, indeed it is usually due to such initial
+velocity in the horizontal that they get into the shaft
+at all. Almost all common objects are irregular in shape,
+and, drop one of them ever so carefully, contact with the
+air through which it is passing soon deviates it from
+the vertical, giving it a horizontal velocity, and this when
+the air is quite still. The object slides one way or another
+on the air it compresses in front of it. Even if the body
+is a sphere, the air will cause it to deviate, if it is rotating
+about an axis out of the vertical. Again, the air in the
+shaft is in ceaseless motion, and any obliquity of the
+currents would obviously deviate the falling body from
+the vertical, no matter what its shape. If the falling
+object is of steel, the magnetic influence of the air mains
+and steam mains which pass down the shaft, and which
+invariably become strongly magnetic, may cause it to
+swerve from a vertical course \ldots\DPtypo{}{.} %[**TN: final period added for consistency with elsewhere]
+
+``A steel sphere, chosen because it was the only convenient
+object at hand, was suspended about one foot
+from the timbers near the western corner of the compartment.
+The compartment stands diagonally with reference
+to the cardinal points. Forty-two hundred feet below
+%% -----File: 052.png---Folio 53-------
+a clay bed was placed, having its eastern edge some five
+feet east of the point of suspension of the ball. When
+the ball appeared to be still the suspending thread was
+burned, and the instant of the dropping of the ball was
+indicated by a prearranged signal transmitted by telephone
+to the observers below, who, watch in hand, waited
+for the sphere to strike the bed of clay. It failed to
+appear at all. Another like sphere was hung in the center
+of the compartment and the trial was repeated with the
+same result. The shaft had to be cleared and no more
+trials were feasible. Some months later, one of the spheres,
+presumably the latter one, was found by a timberman
+where it had lodged in the timbers $800$~feet from the
+surface.
+
+\includegraphicsleft{i053}{Fig.~24}
+
+``It is not probable, however, that these balls lodged
+because of the earth's rotation alone\ldots. The matter is
+really more complicated than the foregoing discussion
+implies. It has received mathematical treatment from
+the great Gauss. According to his results, the deviation
+\index{Gauss}%
+to the east for a fall of $5,000$~feet at the Tamarack mine
+\index{Tamarack mine}%
+should be a little under three feet. Both spheres had that
+much to spare before striking the timbers. It is almost
+certain, therefore, that others of the causes mentioned in
+the beginning acted to prevent a vertical fall. At any
+rate, these trials serve to emphasize the unlikelihood that
+an object which falls into a deep vertical shaft, like those
+at the Tamarack mine, will reach the bottom, even when
+some care is taken in selecting it and also to start it vertically.
+
+``If the timbering permits lodgment, as is the case in
+most shafts, it may truthfully be said that if a shaft is
+deep in proportion to its cross section few indeed will be
+the objects falling into it which will reach the bottom,
+%% -----File: 053.png---Folio 54-------
+and such objects are more likely to lodge on the easterly
+side than on any other.''
+
+\includegraphicsright{i054}{Fig.~25}
+
+\sloppy
+\Paragraph{The Foucault Experiment.} Another simple demonstration
+\index{Deviation, of pendulum|(}%
+\index{Foucault@Foucault (foo\;ko$'$), experiment, with gyroscope!with pendulum|(}%
+\index{Pendulum clock}%
+of the earth's rotation is by the celebrated Foucault
+experiment. In~1851, the French physicist, M.~Leon Foucault,
+suspended from the dome of the Pantheon, in Paris,
+\index{Paris, France}%
+a heavy iron ball by wire two hundred feet long. A pin
+was fastened to the lowest
+side of the ball so that when
+swinging it traced a slight
+mark in a layer of sand placed
+beneath it. Carefully the
+long pendulum was set swinging.
+It was found that the
+path gradually moved around
+toward the right. Now either
+the \DPtypo{pedulum}{pendulum} changed its
+plane or the building was
+gradually turned around. By
+experimenting with a ball
+suspended from a ruler one
+can readily see that gradually
+turning the ruler will not
+change the plane of the
+swinging pendulum. If the
+pendulum swings back and forth in a north and south direction,
+the ruler can be entirely turned around without changing
+the direction of the pendulum's swing. If at the north
+pole a pendulum was set swinging toward a fixed star, say
+\index{Pole, celestial!terrestrial|(}%
+Arcturus, it would continue swinging toward the same
+\index{Arcturus (ark\;tu$'$rus)}%
+star and the earth would thus be seen to turn around in
+a day. The earth would not seem to turn but the pendulum
+would seem to deviate toward the right or clockwise.
+\index{Eastward deflection of falling objects|)}%
+\index{Mining and Scientific Press|)}%
+%% -----File: 054.png---Folio 55-------
+
+\fussy
+\Subparagraph{Conditions for Success.} The Foucault experiment has
+been made in many places at different times. To be successful
+there should be a long slender wire, say forty feet
+or more in length, down the well of a stairway. The weight
+suspended should be heavy and spherical so that the
+impact against the air may not cause it to slide to one
+side, and there
+should be protection
+against drafts
+of air. A good sized
+circle, marked off
+in degrees, should
+be placed under it,
+with the center
+exactly under the
+ball when at rest.
+From the rate of
+the deviation the
+latitude may be
+easily determined
+or, knowing the
+latitude, the deviation
+may be calculated.
+
+\Subparagraph{To Calculate Amount of Deviation.} At first thought
+it might seem as though the floor would turn completely
+around under the pendulum in a day, regardless of the
+latitude. It will be readily seen, however, that it is only
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by Foucault experiment}%
+at the pole that the earth would make one complete rotation
+under the pendulum in one day\index{Sidereal, clock!day}%
+\footnote
+  {Strictly speaking, in one sidereal day.}
+or show a deviation
+of $15°$ in an hour. At the equator the pendulum will
+show no deviation, and at intermediate latitudes the rate
+%% -----File: 055.png---Folio 56-------
+of deviation varies. Now the ratio of variation from the
+pole considered as \emph{one} and the equator as \emph{zero} is shown
+in the table of ``natural sines'' (p.~\pageref{page:311}). It can be
+demonstrated that the number of degrees the plane of the
+pendulum will deviate in one hour at any latitude is found
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by Foucault experiment}%
+by multiplying $15°$~by the sine of the latitude.
+\begin{align*}
+d &= \text{deviation}\\
+\phi &= \text{latitude}\\
+\therefore\quad d&= \sin \phi × 15°.
+\end{align*}
+Whether or not the student has a very clear conception of
+what is meant by ``the sine of the latitude'' he may easily
+calculate the deviation or the latitude where such a pendulum
+experiment is made.
+
+\Subparagraph{Example.} Suppose the latitude is~$40°$. Sine~$40° = .6428$.
+The hourly deviation at that latitude, then, is
+$.6428 × 15°$ or $9.64°$. Since the pendulum deviates~$9.64°$
+in one hour, for the entire circuit it will take as many
+hours as that number of degrees is contained in~$360°$ or
+about $37\frac{1}{3}$~hours. It is just as simple to calculate one's
+latitude if the amount of deviation for one hour is known.
+Suppose the plane of the pendulum is observed to deviate
+$9°$~in an hour.
+\begin{align*}
+\text{Sine of the latitude} &× 15° = 9°.\\
+\therefore \quad \text{Sine of the latitude}
+  &= \tfrac{9}{15} \quad \text{or} \quad.6000.
+\end{align*}
+From the \hyperref[page:311]{table of sines} we find that this sine, $.6000$, corresponds
+more nearly to that of~$37°$ ($.6018$) than to the sine
+of any other whole degree, and hence $37°$~is the latitude
+where the hourly deviation is~$9°$. At that latitude it would
+take forty hours ($360 ÷ 9 = 40$) for the pendulum to
+make the entire circuit.
+\index{Pole, celestial!terrestrial|)}%
+%% -----File: 056.png---Folio 57-------
+
+\smallskip%[**TN: since page break comes before actual table]
+\Subparagraph{Table of Variations.} The following table shows the
+deviation of the plane of the pendulum for one hour and
+the time required to make one entire rotation.
+\begin{center}
+\smallsize\nblabel{page:57}
+\begin{tabular}{@{}c@{\;}|c|c||@{\;}c@{\;}|c|c@{}}
+\hline
+\settowidth{\TmpLen}{Latitude.}%
+\parbox[c]{\TmpLen}{Latitude.} &
+\settowidth{\TmpLen}{Deviation.}%
+\parbox[c]{\TmpLen}{\tablespacertop\centering%
+Hourly\\Deviation.\tablespacerbot} &
+\settowidth{\TmpLen}{Pendulum.}%
+\parbox[c]{\TmpLen}{\centering
+Circuit of\\Pendulum.} &
+%
+\settowidth{\TmpLen}{Latitude.}%
+\parbox[c]{\TmpLen}{Latitude.} &
+\settowidth{\TmpLen}{Deviation.}%
+\parbox[c]{\TmpLen}{\centering%
+Hourly\\Deviation.} &
+\settowidth{\TmpLen}{Pendulum.}%
+\parbox[c]{\TmpLen}{\centering
+Circuit of\\Pendulum.} \\
+%
+\hline
+\tablespacertop%
+\Z5\rlap{°} & \Z1.31\rlap{°} &  275 hrs. & 50\rlap{°} & 11.49\rlap{°} & 31 hrs.\\
+ 10         & \Z2.60         &  138\ph   & 55         & 12.28         & 29\ph\\
+ 15         & \Z3.88         & \Z93\ph   & 60         & 12.99         & 28\ph\\
+ 20         & \Z5.13         & \Z70\ph   & 65         & 13.59         & 26\ph\\
+ 25         & \Z6.34         & \Z57\ph   & 70         & 14.09         & 25\rlap{.5}\ph\\
+ 30         & \Z7.50         & \Z48\ph   & 75         & 14.48         & 24\rlap{.8}\ph\\
+ 35         & \Z8.60         & \Z42\ph   & 80         & 14.77         & 24\rlap{.5}\ph\\
+ 40         & \Z9.64         & \Z37\ph   & 85         & 14.94         & 24\rlap{.1}\ph\\
+ 45         &  10.61         & \Z34\ph   & 90         & 15.00         & 24\rlap{.0}\ph\tablespacerbot\\
+\hline
+\end{tabular}
+\index{Deviation, of pendulum|)}%
+\index{Foucault@Foucault (foo\;ko$'$), experiment, with gyroscope!with pendulum|)}%
+\index{Proofs, form of earth!rotation of earth|)}%
+\end{center}
+
+\Paragraph{Other Evidence.} Other positive evidence of the rotation
+of the earth we have in the fact that the equatorial winds
+north of the equator veer toward the east and polar winds
+toward the west---south of the equator exactly opposite---and
+this is precisely the result which would follow from the
+earth's rotation. Cyclonic winds in the northern hemisphere
+in going toward the area of low pressure veer toward
+the right and anti-cyclonic winds also veer toward the
+right in leaving areas of high pressure, and in the southern
+hemisphere their rotation is the opposite. No explanation
+of these well-known facts has been satisfactorily advanced
+other than the eastward rotation of the earth, which easily
+accounts for them.
+
+Perhaps the best of modern proofs of the rotation of
+the earth is demonstrated by means of the spectroscope.
+\index{Spectroscope}%
+A discussion of this is reserved until the principles are
+explained (p.~\pageref{page:107}) in connection with the proofs of %[**TN: 'pp. 107, 108' in original text]
+the earth's revolution.
+%% -----File: 057.png---Folio 58-------
+
+\Section{Velocity of Rotation}
+\index{Velocity of rotation}%
+
+The velocity of the rotation at the surface, in miles per
+hour, in different latitudes, is as follows:
+\begin{center}
+\smallsize\nblabel{page:58}
+\begin{tabular}{@{}c|c||c|c||c|c@{}}
+\hline
+\tablespacertop
+Latitude. & Velocity. &
+Latitude. & Velocity. &
+Latitude. & Velocity.\tablespacerbot \\
+\hline
+\tablespacertop%
+\Z0 &  1038 & 44 & 748 & 64 &   456 \\
+\Z5 &  1034 & 45 & 735 & 66 &   423 \\
+ 10 &  1022 & 46 & 722 & 68 &   390 \\
+ 15 &  1002 & 47 & 709 & 70 &   356 \\
+ 20 & \Z975 & 48 & 696 & 72 &   322 \\
+ 25 & \Z941 & 49 & 682 & 74 &   287 \\
+ 30 & \Z899 & 50 & 668 & 76 &   252 \\
+ 32 & \Z881 & 51 & 654 & 78 &   216 \\
+ 34 & \Z861 & 52 & 640 & 80 &   181 \\
+ 36 & \Z840 & 53 & 626 & 82 &   145 \\
+ 38 & \Z819 & 54 & 611 & 84 &   109 \\
+ 39 & \Z807 & 55 & 596 & 86 &  \Z73 \\
+ 40 & \Z796 & 56 & 582 & 88 &  \Z36 \\
+ 41 & \Z784 & 58 & 551 & 89 &  \Z18 \\
+ 42 & \Z772 & 60 & 520 & 89\rlap{$\tfrac{1}{2}$} & \Z\Z9 \\
+ 43 & \Z760 & 62 & 488 & 90 & \Z\Z0\tablespacerbot \\
+\hline
+\end{tabular}
+\end{center}
+
+\sloppy
+\Paragraph{Uniform Rate of Rotation.} There are theoretical grounds
+for believing that the rate of the earth's rotation is getting
+gradually slower. As yet, however, not the slightest
+variation has been discovered. Before attacking the
+somewhat complex problem of time, the student should
+clearly bear in mind the fact that the earth rotates on its
+axis with such unerring regularity that this is the most
+perfect standard for any time calculations known to
+science.
+
+\fussy
+\Section{Determination of Latitude}
+\index{Altitude, of noon sun!of polestar or celestial pole|(}%
+\index{Celestial latitude!pole}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by altitude of circumpolar star|(}%
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+\index{South, on map!star}%
+
+\Paragraph{Altitude of Celestial Pole Equals Latitude.} Let us return,
+in imagination, to the equator. Here we may see the North
+star on the horizon due north of us, the South star on the
+%% -----File: 058.png---Folio 59-------
+horizon due south, and halfway between these two points,
+extending from due east through the zenith to due west,
+is the celestial equator. If we travel northward we shall
+be able to see objects which were heretofore hidden from
+view by the curvature of the earth. We shall find that
+the South star becomes hidden from sight for the same
+reason and the North star seems to rise in the sky. The
+celestial equator no longer extends through the point
+directly overhead but is somewhat to the south of the
+zenith, though it still intersects the horizon at the east
+and west points. As we go farther north this rising of
+the northern sky and sinking of the southern sky becomes
+greater. If we go halfway to the north pole we shall find
+the North star halfway between the zenith and the northern
+horizon, or at an altitude of~$45°$ above the horizon. For
+every degree of curvature of the earth we pass over,
+going northward, the North star rises one degree from
+the horizon. At New Orleans the North star is $30°$~from
+\index{New Orleans, La.}%
+the horizon, for the city is $30°$~from the equator. At
+Philadelphia, $40°$~north latitude, the North star is $40°$~from
+\index{Philadelphia, Pa.}%
+the horizon. South of the equator the converse of
+this is true. The North star sinks from the horizon and
+the South star rises as one travels southward from the
+\index{South, on map!star}%
+equator. \emph{The altitude of the North star is the latitude of
+a place north of the equator and the altitude of the South
+star is the latitude of a place south of the equator.} It is
+obvious, then, that the problem of determining latitude is
+the problem of determining the altitude of the celestial
+pole.
+
+\Paragraph{To Find Your Latitude.} By means of the compasses
+and scale, ascertain the altitude of the North star. This
+can be done by placing one side of the compasses on
+a level window sill and sighting the other side toward
+%% -----File: 059.png---Folio 60-------
+the North star, then measuring the angle thus formed.
+Another simple process for ascertaining latitude is to
+determine the altitude of a star not far from the North
+star when it is highest and when it is lowest; the average
+of these altitudes is the altitude of the pole, or the latitude.
+This may easily be done in latitudes north of~$38°$ during
+the winter, observing, say, at $6$~o'clock in the morning
+and at $6$~o'clock in the evening. This is simple in that
+it requires no tables. Of course such measurements are
+very crude with simple instruments, but with a little
+care one will usually be surprised at the accuracy of his
+results.
+
+\includegraphicsmid{i059}{Fig.~26}
+
+Owing to the fact that the North star is not exactly at
+the north pole of the celestial sphere, it has a slight rotary
+\index{Pole, celestial!terrestrial}%
+motion. It will be more accurate, therefore, if the observation
+is made when the Big Dipper and Cassiopeia are
+\index{Big Dipper}%
+\index{Cassiopeia@Cassiopeia (k\u{a}s\;s\u{\i}\;\={o}\;p\={e}$'$y\.{a})}%
+in one of the positions ($A$~or~$B$) represented by Figure~\figureref{i059}{26}.
+In case of these positions the altitude of the North star
+will give the true latitude, it then being the same altitude
+as the pole of the celestial sphere. In case of position~$D$,
+the North star is about $1\frac{1}{4}°$~below the true pole, hence
+%% -----File: 060.png---Folio 61-------
+${1\frac{1}{4}}°$~must be added to the altitude of the star. In case of
+position~$C$, the North star is ${1\frac{1}{4}}°$~above the true pole, and
+\index{Celestial latitude!pole}%
+\index{Pole, celestial!terrestrial}%
+that amount must be subtracted from its altitude. \nblabel{page:61}It is
+obvious from the diagrams that a true north and south
+line can be struck when the stars are in positions $C$~and~$D$,
+\index{North, line}%
+by hanging two plumb lines so that they lie in the same
+plane as the zenith meridian line through Mizar and Delta
+Cassiopeiæ. Methods of determining latitude will be further
+\index{Cassiopeia@Cassiopeia (k\u{a}s\;s\u{\i}\;\={o}\;p\={e}$'$y\.{a})}%
+discussed on pp.~\pageref{page:172}--\pageref{page:174}. The instrument commonly
+used in observations for determining latitude is the meridian
+circle, or, on shipboard, the sextant. Read the description
+\index{Sextant}%
+of these instruments in any text on astronomy.
+\index{Altitude, of noon sun!of polestar or celestial pole|)}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by altitude of circumpolar star|)}%
+
+\Section{Queries}
+
+In looking at the heavenly bodies at night do the stars,
+moon, and planets all look as though they were equally
+distant, or do some appear nearer than others? The fact
+that people of ancient times believed the celestial sphere
+to be made of metal and all the heavenly bodies fixed or
+moving therein, would indicate that to the observer who is
+not biased by preconceptions, all seem equally distant.
+If they did not seem equally distant they would not
+assume the apparently spherical arrangement.
+
+The declination, or distance from the celestial equator,
+of the star (Benetnasch) at the end of the handle of the
+\index{Benetnasch}%
+Big Dipper is~$50°$. How far is it from the celestial pole?
+\index{Big Dipper}%
+At what latitude will it touch the horizon in its swing
+under the North star? How far south of the equator could
+one travel and still see that star at some time?
+%% -----File: 061.png---Folio 62-------
+
+\Chapter{IV}{Longitude and Time}
+
+\Section{Solar Time}
+
+\Paragraph{Sun Time Varies.} The sun is the world's great time-keeper.
+\index{Sun!fast or slow}%
+\index{Proofs, form of earth!rotation of earth}%
+He is, however, a slightly erratic one. At the
+equator the length of day equals the length of night the
+year through. At the poles there are six months day and
+six months night, and at intermediate latitudes the time
+of sunrise and of sunset varies with the season. Not only
+does the time of sunrise vary, but the time it takes the sun
+apparently to swing once around the earth also varies.
+Thus from noon by the sun until noon by the sun again is
+sometimes more than twenty-four hours and sometimes
+less than twenty-four hours. The reasons for this variation
+will be taken up in the \hyperref[chap:VI]{chapter} on the earth's revolution.
+
+\Paragraph{Mean Solar Day.}  By a mean solar day is meant the
+\index{Time@Time \indexglossref{Time}, apparent solar}%
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!solar}%
+average interval of time from sun noon to sun noon.
+While the apparent solar day varies, the mean solar day
+is exactly twenty-four hours long. A sundial does not
+\index{Sundial}%
+record the same time as a clock, as a usual thing, for the
+sundial records apparent solar time while the clock records
+mean solar time.
+
+\Paragraph{Relation of Longitude to Time.} The sun's apparent daily
+\index{Longitude@Longitude \indexglossref{Longitude}!and time|(}%
+journey around the earth with the other bodies of the
+\index{Celestial latitude!sphere}%
+celestial sphere gives rise to day and night\footnote
+  {Many thoughtlessly assume that the fact of day and night is a
+  proof of the earth's rotation.}
+It takes the
+sun, on the average, twenty-four hours apparently to swing
+%% -----File: 062.png---Folio 63-------
+once around the earth. In this daily journey it crosses
+$360°$~of longitude, or $15°$~for each hour. It thus takes
+four minutes for the sun's rays to sweep over one degree
+of longitude. Suppose it is noon by the sun at the 90th~meridian,
+in four minutes the sun will be over the 91st~meridian,
+in four more minutes it will be noon by the sun
+on the 92d~meridian, and so on around the globe.
+
+Students are sometimes confused as to the time of day
+in places east of a given meridian as compared with the
+time in places west of it. When the sun is rising here, it
+has already risen for places east of us, hence their time is
+after sunrise or later than ours. If it is noon by the
+sun here, at places east of us, having already been noon
+there, it must be past noon or later in the day. \emph{Places
+to the east have later time because the sun reaches them first.}
+To the westward the converse of this is true. If the sun
+is rising here, it has not yet risen for places west of us and
+their time is before sunrise or earlier. When it is noon by
+the sun in Chicago, the shadow north, it is past noon by
+\index{Chicago, Ill.}%
+the sun in Detroit and other places eastward and before
+\index{Detroit, Mich.}%
+noon by the sun in Minneapolis and other places westward.
+\index{Minneapolis, Minn.}%
+
+\Paragraph{How Longitude is Determined.} A man when in London,
+\index{London, England}%
+\index{Longitude@Longitude \indexglossref{Longitude}!how determined|(}%
+longitude~$0°$, set his watch according to mean solar time
+there. When he arrived at home he found the mean solar
+time to be six hours earlier (or slower) than his watch,
+which he had not changed. Since his watch indicated
+later time, London must be east of his home, and since the
+sun appeared six hours earlier at London, his home must
+be $6 × 15°$, or~$90°$, west of London. While on shipboard
+at a certain place he noticed that the sun's shadow was due
+north when his watch indicated 2:30~o'clock,~\PM. Assuming
+that both the watch and the sun were ``on time'' we
+readily see that since London time was two and one half
+%% -----File: 063.png---Folio 64-------
+hours later than the time at that place, he must have been
+west of London $2\frac{1}{2} × 15°$, or~$37°~30'$.
+\index{London, England}%
+
+\Paragraph{Ship's Chronometer.} Every ocean vessel carries a very
+\index{Chronometer@Chronometer (kr\={o}\;n\u{o}m$'$\={e}\;ter)}%
+accurate watch called a chronometer. This is regulated
+to run as perfectly as possible and is set according to the
+mean solar time of some well known meridian. Vessels
+from English speaking nations all have their chronometers
+set with Greenwich time. By observing the time according
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+to the sun at the place whose longitude is sought and
+comparing that time with the time of the prime meridian
+as indicated by the chronometer, the longitude is reckoned.
+For example, suppose the time according to the
+sun is found by observation to be 9:30~o'clock,~\AM, and
+the chronometer indicates 11:20~o'clock,~\AM. The prime
+meridian, then, must be east as it has later time. Since
+the difference in time is one hour and fifty minutes and
+there are $15°$~difference in longitude for an hour's difference
+in time, the difference in longitude must be $1\frac{5}{6} × 15°$,
+or~$27°~30'$.
+
+The relation of longitude and time should be thoroughly
+mastered. From the \hyperref[page:88]{table} at the close of this chapter,
+giving the longitude, of the principal cities of the world,
+one can determine the time it is in those places when it is
+noon at home. Many other problems may also be suggested.
+It should be borne in mind that it is the \emph{mean
+solar time} that is thus considered, which in most cities is
+not the time indicated by the watches and clocks there.
+People all over Great Britain set their timepieces to agree
+\index{Great Britain}%
+with Greenwich time, in Ireland with Dublin, in France
+\index{Dublin, Ireland}%
+\index{France}%
+\index{Ireland}%
+with Paris, etc. (see \hyperref[page:81]{``Time used in Various Countries''} at
+\index{Paris, France}%
+the end of this chapter).
+
+\Paragraph{Local Time.}\nblabel{page:64} The mean solar time of any place is often
+\index{Time@Time \indexglossref{Time}, apparent solar!local}%
+called its local time. This is the average time indicated
+%% -----File: 064.png---Folio 65-------
+by the sundial. All places on the same meridian have the
+\index{Sundial}%
+same local time. Places on different meridians must of
+necessity have different local time, the difference in time
+being four minutes for every degree's difference in longitude.
+
+\Section{Standard Time}\nblabel{page:65}
+\index{Time@Time \indexglossref{Time}, apparent solar!standard|(}%
+\index{Standard time|(}%
+
+\Paragraph{Origin of Present System.} Before the year~1883, the
+\index{Time@Time \indexglossref{Time}, apparent solar!confusion}%
+people of different cities in the United States commonly
+\index{United States}%
+used the local time of the meridian passing through the city.
+Prior to the advent of the railroad, telegraph, and telephone,
+little inconvenience was occasioned by the prevalence of so
+many time systems. But as transportation and communication
+became rapid and complex it became very difficult to
+adjust one's time and calculations according to so many
+standards as came to prevail. Each railroad had its own
+arbitrary system of time, and where there were several
+railroads in a city there were usually as many species of
+``railroad time'' besides the local time according to
+longitude.
+
+``Before the adoption of standard time there were sometimes
+as many as five different kinds of time in use in a
+single town. The railroads of the United States followed
+fifty-three different standards, whereas they now use five.
+The times were very much out of joint.''\footnote
+  {The \textit{Scrap Book}, May,~1906.}
+\index{Scrap Book}%
+
+\includegraphicssideways{i065}{Fig.~27. Standard Time Belts}
+
+His inability to make some meteorological calculations
+in 1874 because of the diverse and doubtful character of
+the time of the available weather reports, led Professor
+Cleveland Abbe, for so many years connected with the
+\index{Abbe, Cleveland}%
+United States Weather service, to suggest that a system of
+standard time should be adopted. At about the same time
+several others made similar suggestions and the subject was
+soon taken up in an official way by the railroads of the
+\index{Longitude@Longitude \indexglossref{Longitude}!how determined|)}%
+%% -----File: 065.png---Folio 66-------
+%% -----File: 066.png---Folio 67-------
+country under the leadership of William F.~Allen, then secretary
+\index{Allen, W. F.}%
+of the General Time Convention of Railroad Officials.
+As a result of his untiring efforts the railway associations
+endorsed his plan and at noon of Sunday, November~18,
+1883, the present system was inaugurated.
+
+\Paragraph{Eastern Standard Time.} According to the system all
+\index{Meridian!standard time|(}%
+\index{Eastern time, in Europe!in the United States}%
+cities approximately within $7\frac{1}{2}°$ of the 75th meridian use
+the mean solar time of that meridian, the clocks and
+watches being thus just five hours earlier than those of
+Greenwich. This belt, about $15°$ wide, is called the eastern
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+standard time belt. The 75th meridian passes through the
+eastern portion of Philadelphia, so the time used throughout
+the eastern portion of the United States corresponds
+to Philadelphia local mean solar time.%
+\index{Philadelphia, Pa.}%
+
+\Paragraph{Central Standard Time.} The time of the next belt is the
+\index{Central time, in Europe!in the United States}%
+mean solar time of the 90th meridian or one hour slower
+than eastern standard time. This meridian passes through
+or very near Madison, Wisconsin, St.~Louis, and New
+\index{St.~Louis, Mo.}%
+\index{New Orleans, La.}%
+\index{Madison, Wis.}%
+\index{Wisconsin}%
+Orleans, where mean local time is the same as standard
+time. When it is noon at Washington, D.~C, it is $11$~o'clock, \AM,
+\index{Washington, D. C.}%
+at Chicago, because the people of the former
+\index{Chicago, Ill.}%
+city use eastern standard time and those at the latter use
+central standard time.
+
+\Paragraph{Mountain Standard Time.} To the west of the central
+\index{Mountain time belt}%
+standard time belt lies the mountain region where the
+time used is the mean solar time of the 105th meridian.
+This meridian passes through Denver, Colorado, and its
+\index{Denver, Col.}%
+\index{Colorado}%
+clocks as a consequence indicate the same time that the
+mean sun does there. As the standard time map shows,
+all the belts are bounded by irregular lines, due to the
+fact that the people of a city usually use the same time
+that their principal railroads do, and where trains change
+their time depends in a large measure upon the convenience
+%% -----File: 067.png---Folio 68-------
+to be served. This belt shows the anomaly of being
+bounded on the east by the central time belt, on the west
+by the Pacific time belt, and on the \emph{south} by the same belts.
+\index{Pacific time belt}%
+The reasons why the mountain standard time belt tapers
+\index{Mountain time belt}%
+to a point at the south and the peculiar conditions which
+consequently result, are discussed under the topic ``Four
+Kinds of Time around El Paso'' (p.~\pageref{page:75}).
+\index{El Paso, Tex.}%
+
+\Paragraph{Pacific Standard Time.} People living in the states bordering
+or near the Pacific Ocean use the mean solar time
+\index{Pacific Ocean}%
+of the 120th meridian and thus have three hours earlier
+time than the people of the Atlantic coast states. This
+meridian forms a portion of the eastern boundary of
+California.
+\index{California}%
+
+In these great time belts\footnote
+  {For a discussion of the time used in other portions of North
+  America and elsewhere in the world see pp.~\pageref{page:81}--\pageref{page:87}.}
+all the clocks and other timepieces
+differ in time by whole hours. In addition to astronomical
+observatory clocks, which are regulated according
+to the mean local time of the meridian passing through the
+observatory, there are a few cities in Michigan, Georgia,
+\index{Georgia}%
+\index{Michigan}%
+New Mexico, and elsewhere in the United States, where
+\index{New Mexico}%
+mean local time is still used.\nblabel{page:68}
+
+\Paragraph{Standard Time in Europe.} In many European countries
+standard time based upon Greenwich time, or whole hour
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+changes from it, is in general use, although there are many
+more cities which use mean local time than in the United
+States. \emph{Western European time}, or that of the meridian
+\index{Meridian!standard time|)}%
+\index{Western European time}%
+of Greenwich, is used in Great Britain, Spain, Belgium, and
+\index{Belgium}%
+\index{Great Britain}%
+\index{Spain}%
+Holland. \emph{Central European time}, one hour later than that
+\index{Central time, in Europe}%
+\index{Holland}%
+of Greenwich, is used in Norway, Sweden, Denmark, Luxemburg,
+\index{Denmark}%
+\index{Luxemburg}%
+\index{Norway}%
+\index{Sweden}%
+Germany, Switzerland, Austria-Hungary, Servia, and
+\index{Austria-Hungary}%
+\index{Germany}%
+\index{Servia}%
+\index{Switzerland}%
+Italy. \emph{Eastern European time}, two hours later than that
+\index{Eastern time, in Europe}%
+\index{Italy}%
+of Greenwich, is used in Turkey, Bulgaria, and Roumania.
+\index{Bulgaria}%
+\index{Roumania}%
+%% -----File: 068.png---Folio 69-------
+
+\Section{Telegraphic Time Signals}
+\index{Telegraphic time signals}%
+\index{Time@Time \indexglossref{Time}, apparent solar!signals|(}%
+
+\Paragraph{Getting the Time.} An admirable system of sending time
+signals all over the country and even to Alaska, Cuba, and
+\index{Alaska}%
+\index{Cuba}%
+Panama, is in vogue in the United States, having been
+\index{Panama}%
+\index{United States}%
+established in August,~1865. The Naval Observatories at
+\index{United States Naval Observatory|(}%
+Washington, D.~C., and Mare Island, California, send out
+the signals during the five minutes preceding noon each
+day.
+
+It is a common custom for astronomical observatories to
+correct their own clocks by careful observations of the stars.
+The Washington Observatory sends telegraphic signals to
+all the cities east of the Rocky Mountains and the Mare
+Island Observatory to Pacific cities and Alaska. A few
+\index{Mare Island Naval Observatory}%
+railroads receive their time corrections from other observatories.
+Goodsell Observatory, Carleton College, Northfield,
+\index{Carleton College, Northfield, Minn.}%
+\index{Goodsell Observatory, Northfield, Minn.}%
+\index{Northfield, Minn.}%
+Minnesota, has for many years furnished time to the
+Great Northern, the Northern Pacific, the Great Western,
+and the Sault Ste.~Marie railway systems. Allegheny
+Observatory sends out time to the Pennsylvania system
+\index{Allegheny Observatory, Allegheny, Pa.}%
+and the Lick Observatory to the Southern Pacific system.
+\index{Lick Observatory}%
+
+\index{Time@Time \indexglossref{Time}, apparent solar!how determined}%
+\Subparagraph{How Time is Determined at the United States Naval
+Observatory.} The general plan of correcting clocks at the
+United States Naval Observatories by stellar observations
+is as follows: A telescope called a meridian transit is situated
+\index{Transit instrument}%
+in a true north-south direction mounted on an east-west
+axis so that it can be rotated in the plane of the
+meridian but not in the slightest degree to the east or
+west. Other instruments used are the chronograph and
+the sidereal clock. The chronograph is an instrument
+\index{Clock, sidereal}%
+\index{Sidereal, clock}%
+\index{Chronograph@Chronograph (kr\u{o}n$'$\={o}\;graph)}%
+which may be electrically connected with the clock and
+which automatically makes a mark for each second on a
+sheet of paper fastened to a cylinder. The sidereal clock
+%% -----File: 069.png---Folio 70-------
+is regulated to keep time with the stars---not with the
+sun, as are other clocks. The reason for this is because
+the stars make an apparent circuit with each rotation of
+the earth and this, we have observed, is unerring while
+the sun's apparent motion is quite irregular.
+
+To correct the clock, an equatorial or high zenith star
+is selected. A well known one is chosen since the exact
+time it will cross the meridian of the observer (that is, be
+at its highest point in its apparent daily rotation) must be
+calculated. The chronograph is then started, its pen and
+ink adjusted, and its electrical wires connected with the
+clock. The observer now sights the telescope to the point
+where the expected star will cross his meridian and, with
+his hand on the key, he awaits the appearance of the star.
+As the star crosses each of the eleven hair lines in the field
+of the telescope, the observer presses the key which automatically
+marks upon the chronographic cylinder. Then
+by examining the sheet he can tell at what time, \emph{by the
+clock}, the star crossed the center line. He then calculates
+just what time the clock \emph{should} indicate and the difference
+is the error of the clock. By this means an error of one
+tenth of a second can be discovered.
+
+\Paragraph{The Sidereal Clock.} The following facts concerning the
+\index{Clock, sidereal}%
+\index{Sidereal, clock}%
+sidereal clock may be of interest. It is marked with
+twenty-four hour spaces instead of twelve. Only one
+moment in the year does it indicate the same time as
+ordinary timepieces, which are adjusted to the average sun.
+When the error of the clock is discovered the clock is
+not at once reset because any tampering with the clock
+would involve a slight error. The correction is simply
+noted and the rate of the clock's gaining or losing time is
+calculated so that the true time can be ascertained very
+precisely at any time by referring to the data showing the
+%% -----File: 070.png---Folio 71-------
+clock error when last corrected and the rate at which it
+varies.
+
+A while before noon each day the exact sidereal time is
+calculated; this is converted into local mean solar time and
+this into standard time. The Washington Naval Observatory
+converts this into the standard time of the~75th
+meridian or Eastern time and the Mare Island Observatory
+\index{Eastern time, in Europe!in the United States}%
+\index{Mare Island Naval Observatory}%
+\index{Meridian!standard time}%
+into that of the 120th meridian or Pacific time.
+
+\Paragraph{Sending Time Signals.}\nblabel{page:71} By the coöperation of telegraph
+\index{Signals, time|(}%
+companies, the time signals which are sent out daily from
+the United States Naval Observatories reach practically
+\index{United States}%
+every telegraph station in the country. They are sent
+out at noon, 75th meridian time, from Washington, which
+\index{Washington, D. C.}%
+is 11~o'clock, \AM, in cities using Central time and 10~o'clock, \AM,
+\index{Central time, in Europe!in the United States}%
+where Mountain time prevails; and at noon,
+120th meridian time, they are sent to Pacific coast cities
+from the Mare Island Observatory---three hours after
+Washington has flashed the signal which makes correct
+time accessible to sixty millions of our population living
+east of the Rockies.
+
+Not only are the time signals sent to the telegraph
+stations and thence to railway offices, clock makers and
+repairers, schools, court houses, etc., but the same telegraphic
+signal that marks noon also actually sets many
+thousands of clocks, their hands whether fast or slow automatically
+flying to the true mark in response to the electric
+current. In a number of cities of the United States,
+nineteen at present, huge balls are placed upon towers or
+\index{Time@Time \indexglossref{Time}, apparent solar!ball}%
+buildings and are automatically dropped by the electric
+noon signal. The time ball in Washington is conspicuously
+placed on the top of the State, War, and Navy building
+and may be seen at considerable distances from many
+parts of the city.
+%% -----File: 071.png---Folio 72-------
+
+\includegraphicsmid{i071}{Fig.~28}
+
+A few minutes before noon each day, one wire at each
+telegraphic office is cleared of all business and ``thousands
+of telegraph operators sit in silence, waiting for the click
+of the key which shall tell them that the `master clock'
+\index{Washington, D. C.}%
+in Washington has begun to speak.''\footnote
+  {From ``What's the Time,'' \textit{Youth's Companion}, May~17 and June~14,
+\index{Youth's Companion}%
+  1906.} At five minutes
+before twelve the instrument begins to click off the seconds.
+Figure~\figureref{i071}{28} (adapted from a cut appearing in Vol.~IV, Appendix~IV,
+United States Naval Observatory Publications)
+graphically shows which second beats are sent along the
+wires during each of the five minutes before noon by the
+transmitting clock at the Naval Observatory.
+
+\Subparagraph{Explanation of the Second Beats.} It will be noticed
+that the twenty-ninth second of each minute is omitted.
+This is for the purpose of permitting the observer to
+distinguish, without counting the beats, which is the one
+denoting the middle of each minute; the five seconds at
+the end of each of the first four minutes are omitted to
+mark the beginning of a new minute and the last ten
+seconds of the fifty-ninth minute are omitted to mark
+conspicuously the moment of noon. The omission of the
+%% -----File: 072.png---Folio 73-------
+last ten seconds also enables the operator to connect
+his wire with the clock to be automatically set or the
+time ball to be dropped. The contact marking noon is
+prolonged a full second, not only to make prominent this
+important moment but also to afford sufficient current
+to do the other work which this electric contact must
+perform.
+
+\Subparagraph{Long Distance Signals.} Several times in recent years
+special telegraphic signals have been sent out to such distant
+points as Madras, Mauritius, Cape Town, Pulkowa
+(near St.~Petersburg), Rome, Lisbon, Madrid, Sitka,
+Buenos Ayres, Wellington, Sydney, and Guam. Upon
+\index{Buenos Aires@Buenos Aires (b\={o}$'$n\u{u}s \={a}$'$r\u{\i}z), Argentina}%
+\index{Cape Town, Africa}%
+\index{Lisbon, Portugal}%
+\index{Madras@Madras (ma\;dr\u{a}s$'$), India}%
+\index{Madrid, Spain}%
+\index{Mauritius@Mauritius (ma\;r\u{\i}sh$'$\;\u{\i}\;\u{u}s) Island}%
+\index{Pulkowa, Russia}%
+\index{Rome, Italy}%
+\index{St.~Petersburg, Russia}%
+\index{Sitka, Alaska}%
+\index{Wellington, New Zealand}%
+\index{Guam}%
+these occasions ``our standard clock may fairly be said to
+be heard in `the remotest ends of the earth,' thus anticipating
+the day when wireless telegraphy will perhaps allow
+of a daily international time signal that will reach every
+continent and ocean in a small fraction of a second.''\index{Hayden, E. E.}%
+\footnote
+  {``The Present Status of the Use of Standard Time,'' by Lieut.\
+  Commander E.~E.~Hayden, U.~S.~Navy.}
+
+These reports have been received at widely separated
+stations within a few seconds, being received at the Lick
+Observatory in $0.05\s$, Manila in $0.11\s$, Greenwich in
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+\index{Manila, Philippine Is.}%
+\index{Lick Observatory}%
+$1.33\s$, and Sydney, Australia, in $2.25\s$.
+\index{Signals, time|)}%
+\index{Time@Time \indexglossref{Time}, apparent solar!signals|)}%
+\index{United States Naval Observatory|)}%
+
+\Section{Confusion from Various Standards}
+\index{Time@Time \indexglossref{Time}, apparent solar!confusion|(}%
+
+Where different time systems are used in the same
+community, confusion must of necessity result. The
+following editorial comment in the \emph{Official Railway Guide}
+\index{Official Railway Guide|(}%
+for November,~1900, very succinctly sets forth the condition
+which prevailed in Detroit as regards standard and
+\index{Detroit, Mich.}%
+local time.
+
+``The city of Detroit is now passing through an agitation
+which is a reminiscence of those which took place throughout
+%% -----File: 073.png---Folio 74-------
+the country about seventeen years ago, when standard
+time was first adopted. For some reason, which it
+is difficult to explain, the city fathers of Detroit have
+refused to change from the old local time to the standard,
+notwithstanding the fact that all of the neighboring cities---Cleveland,
+Toledo, Columbus, Cincinnati, etc.,---in
+\index{Cincinnati, O.}%
+\index{Cleveland, O.}%
+\index{Columbus, O.}%
+\index{Toledo, O.}%
+practically the same longitude, had made the change years
+ago and realized the benefits of so doing. The business
+men of Detroit and visitors to that city have been for a
+long time laboring under many disadvantages owing to
+the confusion of standards, and they have at last taken
+the matter into their own hands and a lively campaign,
+with the coöperation of the newspapers, has been
+organized during the past two months. Many of the
+hotels have adopted standard time, regardless of the
+city, and the authorities of Wayne County, in which
+Detroit is situated, have also decided to hold court on
+Central Standard time, as that is the official standard of
+\index{Central time, in Europe!in the United States}%
+the state of Michigan. The authorities of the city have
+\index{Michigan}%
+so far not taken action. It is announced in the newspapers
+that they probably will do so after the election,
+and by that time, if progress continues to be made, the
+only clock in town keeping the local time will be on the
+town hall. All other matters will be regulated by standard
+time, and the hours of work will have been altered
+accordingly in factories, stores, and schools. Some
+opposition has been encountered, but this, as has been
+the case in every city where the change has been made,
+comes from people who evidently do not comprehend the
+effects of the change. One individual, for instance, writes
+to a newspaper that he will decline to pay pew rent in
+any church whose clock tower shows standard time; he
+refuses to have his hours of rest curtailed. How these will
+%% -----File: 074.png---Folio 75-------
+be affected by the change he does not explain. Every
+visitor to Detroit who has encountered the difficulties
+which the confusion of standards there gives rise to, will
+rejoice when the complete change is effected.''
+
+The longitude of Detroit being $83°$~W., it is seven degrees
+east of the 90th meridian, hence the local time used in the
+\index{Meridian!standard time}%
+city was twenty-eight minutes faster than Central time
+and thirty-two minutes slower than Eastern time. In
+Gainesville, Georgia, mean local sun time is used in the city,
+\index{Gainesville, Ga.}%
+\index{Georgia}%
+while the Southern railway passing through the city uses
+Eastern time and the Georgia railway uses Central time.
+\index{Official Railway Guide|)}%
+
+\includegraphicsmid{i074}{Fig.~29}
+
+\Paragraph{Four Kinds of Time Around El~Paso.}\nblabel{page:75} Another place of
+\index{Central time, in Europe!in the United States}%
+\index{Eastern time, in Europe!in the United States}%
+\index{El Paso, Tex.}%
+peculiar interest in connection with this subject is El~Paso,
+Texas, from the fact that four different systems are employed.
+The city, the Atchison, Topeka, and Santa~Fe,
+and the El~Paso and Southwestern railways use Mountain
+\index{Mountain time belt}%
+time. The Galveston, Harrisburg, and San Antonio, and
+\index{Galveston, Tex.}%
+the Texas and Pacific railways use Central time. The
+Southern Pacific railway uses Pacific time. The Mexican
+Central railway uses Mexican standard time.
+%% -----File: 075.png---Folio 76-------
+From this it will be seen that when clocks in Strauss,
+\index{Strauss, N. M.}%
+\index{New Mexico}%
+N.~M., a few miles from El~Paso, are striking twelve, the
+clocks in El~Paso are striking one; in Ysleta, a few miles
+\index{Ysleta@Ysleta (\u{\i}s\;l\={a}$'$tä), Tex.}%
+\index{El Paso, Tex.}%
+east, they are striking two; while across the river in Juarez,
+\index{Juarez@Juarez (hoo\;ä$'$reth)\phantomsection\label{idx:j}, Mexico}%
+Mexico, the clocks indicate 12:24.
+
+\Paragraph{Time Confusion for Travelers.} The confusion which
+prevails where several different standards of time obtain
+is well illustrated in the following extract from ``The
+Impressions of a Careless Traveler'' by Lyman Abbott,
+\index{Impressions of a Careless Traveler, quoted}%
+\index{Abbott, Lyman}%
+in the \textit{Outlook}, Feb.~28, 1903.
+\index{Outlook, The}%
+
+``The changes in time are almost as interesting and
+quite as perplexing as the changes in currency. Of course
+our steamer time changes every day; a sharp blast on the
+whistle notifies us when it is twelve o'clock, and certain
+of the passengers set their watches accordingly every
+day. I have too much respect for my faithful friend to
+meddle with him to this extent, and I keep my watch
+unchanged and make my calculations by a mental comparison
+of my watch with the ship's time. But when we
+are in port we generally have three times---ship's time,
+local time, and railroad time, to which I must in my own
+case add my own time, which is quite frequently neither.
+In fact, I kept New York time till we reached Genoa;
+\index{Genoa, Italy}%
+\index{New York}%
+since then I have kept central Europe railroad time.
+\index{Central time, in Europe}%
+Without changing my watch, I am getting back to that
+standard again, and expect to find myself quite accurate
+when we land in Naples.''
+
+\Section{The Legal Aspect of Standard Time}
+\index{Legal aspect of standard time|(}%
+
+The legal aspect of standard time presents many
+interesting features. Laws have been enacted in many
+different countries and several of the states of this country
+legalizing some standard of time. Thus in Michigan,
+\index{Michigan}%
+\index{Time@Time \indexglossref{Time}, apparent solar!confusion|)}%
+%% -----File: 076.png---Folio 77-------
+Minnesota, and other central states the legal time is the
+\index{Central time, in Europe!in the United States}%
+mean solar time of longitude $90°$ west of Greenwich.
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+When no other standard is explicitly referred to, the
+time of the central belt is the legal time in force. Similarly,
+legal time in Germany was declared by an imperial decree
+\index{Germany}%
+dated March~12, 1903, as follows:\index{Hayden, E. E.}%
+\footnote
+  {Several of the following quotations are taken from the ``Present
+  Status of the Use of Standard Time,'' by E.~E.~Hayden.}
+
+\begin{SmallText}
+``We, Wilhelm, by the grace of God German Emperor, King of
+\index{Wilhelm II., Emperor}%
+Prussia, decree in the name of the Empire, the Bundesrath and Reichstag
+concurring, as follows:
+
+``The legal time in Germany is the mean solar time of longitude $15°$
+east from Greenwich.''
+\end{SmallText}
+
+Greenwich time for Great Britain, and Dublin time for
+\index{Great Britain}%
+Ireland, were legalized by an act of Parliament as follows:
+\index{Ireland}%
+\index{Parliament}%
+
+\begin{SmallText}
+\First{A Bill} to remove doubts as to the meaning of expressions relative
+to time occurring in acts of Parliament, deeds, and other legal instruments.
+
+Whereas it is expedient to remove certain doubts as to whether
+expressions of time occurring in acts of Parliament, deeds, and other
+legal instruments relate in England and Scotland to Greenwich time,
+and in Ireland to Dublin time, or to the mean astronomical time in
+each locality:
+
+Be it therefore enacted by the Queen's most Excellent Majesty,
+by and with the advice and consent of the Lords, spiritual and temporal,
+and Commons in the present Parliament assembled, and by
+the authority of the same, as follows (that is to say):
+
+1. That whenever any expression of time occurs in any act of
+Parliament, deed, or other legal instrument, the time referred to
+shall, unless it is otherwise specifically stated, be held in the case of
+Great Britain to be Greenwich mean time and in the case of Ireland,
+Dublin mean time.
+
+2. This act may be cited as the statutes (definition of time) act, 1880.
+\end{SmallText}
+
+Seventy-fifth meridian time was legalized in the District
+\index{Meridian!standard time}%
+of Columbia by the following act of Congress:
+
+\begin{SmallText}
+\First{An Act} to establish a standard of time in the District of Columbia.
+\index{District of Columbia}%
+Be it enacted by the Senate and House of Representatives of the
+%% -----File: 077.png---Folio 78-------
+United States of America in Congress assembled, That the legal
+\index{United States}%
+standard of time in the District of Columbia shall hereafter be the
+mean time of the seventy-fifth meridian of longitude west from
+\index{Meridian!standard time}%
+Greenwich.
+
+\textsc{Section~2.} That this act shall not be so construed as to affect
+existing contracts.
+
+Approved, March~13, 1884.
+\end{SmallText}
+
+In New York eastern standard time is legalized in
+\index{Eastern time, in Europe!in the United States}%
+\index{New York}%
+section~28 of the Statutory Construction Law as follows:
+
+\begin{SmallText}
+The standard time throughout this State is that of the 75th~meridian
+of longitude west from Greenwich, and all courts and public offices, and
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+legal and official proceedings, shall be regulated thereby. Any act
+required by or in pursuance of law to be performed at or within a prescribed
+time, shall be performed according to such standard time.
+\end{SmallText}
+
+A New Jersey statute provides that the time of the
+\index{New Jersey}%
+same meridian shall be that recognized in all the courts and
+public offices of the State, and also that ``the time named
+in any notice, advertisement, or contract shall be deemed
+and taken to be the said standard time, unless it be otherwise
+expressed.'' In Pennsylvania also it is provided
+\index{Pennsylvania}%
+that ``on and after July~1, 1887, the mean solar time of
+the seventy-fifth meridian of longitude west of Greenwich,
+commonly called eastern standard time,'' shall be the
+standard in all public matters; it is further provided that
+the time ``in any and all contracts, deeds, wills, and
+notices, and in the transaction of all matters of business,
+public, legal, commercial, or otherwise, shall be construed
+with reference to and in accordance with the said standard
+hereby adopted, unless a different standard is therein
+expressly provided for.''
+
+Where there is no standard adopted by legal authority,
+difficulties may arise, as the following clipping from the
+\index{New York Sun}\textit{New York Sun}, November~25, 1902, illustrates:
+%% -----File: 078.png---Folio 79-------
+
+\begin{multicols}{2}
+\smallsize
+\begin{center}
+\textbf{\normalsize WHAT'S NOON IN A FIRE
+POLICY?}
+
+\shoughtbreak
+
+\textbf{Solar Noon or Standard Time
+Noon---Courts Asked to Say.}
+
+\shoughtbreak
+\end{center}
+
+\noindent\hangindent1em\emph{Fire in Louisville at 11:45~a.m., Standard
+\index{Louisville, Ky.}%
+Time, Which Was 12:02~1-2~p.m.\
+Solar Time---Policies Expired at
+Noon and 13~Insurance Companies
+Wont Pay.} %[**TN: As in original text, no apostrophe]
+
+Whether the word ``noon,''
+which marks the beginning and
+expiration of all fire insurance
+policies, means noon by standard
+time, or noon by solar time, is a
+question which is soon to be
+fought out in the courts of Kentucky,
+\index{Kentucky}%
+in thirteen suits which
+have attracted the attention of
+fire insurance people all over the
+world. The suits are being
+brought by the Peaslee-Gaulbert
+Company and the Louisville Lead
+and Color Company of Louisville,
+and \$19,940.70 of insurance
+money depends on the result.
+
+Now, although the policies in
+these companies all state that
+they were in force from noon of
+April~1, 1901, to noon of April~1,
+1902, not one of them says what
+kind of time that period of the
+day is to be reckoned in. In
+Louisville the solar noon is $17\frac{1}{2}$~minutes
+earlier than the standard
+noon, so that a fire occurring
+in the neighborhood of noon on
+the day of a policy's expiration,
+may easily be open to attack.
+
+The records of the Louisville
+fire department show that the fire
+that destroyed the buildings of
+the two companies was discovered
+at 11:45~o'clock Louisville
+standard time in the forenoon of
+April~1, last. The fire began in
+the engine room of the main factory
+and spread to the two other
+buildings which were used mainly
+as warehouses. When the fire
+department recorded the time of
+the fire's discovery it figured, of
+course, by standard time. Solar
+time would make it just two and
+a half minutes after noon. If
+noon in the policies means noon
+by solar time, of course the thirteen
+companies are absolved from
+any responsibility for the loss.
+If it means noon by standard
+time, of course they must pay.
+
+When the insurance people got
+the claims of the companies they
+declined to pay, and when asked
+for an explanation declared that
+noon in the policies meant noon
+by solar time. The burned-out
+companies immediately began suit,
+and in their affidavits they say
+that not only is standard time
+the official time of the State of
+Kentucky and the city of Louisville,
+but it is also the time upon
+which all business engagements
+and all domestic and social engagements
+are reckoned. They
+state further that they are prepared
+to show that in~1890 the
+city of Louisville passed an ordinance
+making standard time the
+official time of the city, that all
+legislation is dated according to
+standard time, and that the governor
+of the state is inaugurated
+at noon according to the same
+measurement of time.
+
+Solar time, state the companies,
+can be found in use in Louisville
+by only a few banking institutions
+which got charters many
+years ago that compel them to
+use solar time to this day. Most
+banks, they say, operate on standard
+time, although they keep
+clocks going at solar time so as to
+do business on that basis if
+requested. Judging by standard
+time the plaintiffs allege their fire
+took place fifteen minutes before
+their policies expired.
+
+The suits will soon come to trial,
+and, of course, will be watched with
+great interest by insurance people.
+\end{multicols}
+%% -----File: 079.png---Folio 80-------
+
+\Paragraph{Iowa Case.} An almost precisely similar case occurred
+\index{Iowa}%
+at Creston, Iowa, September~19, 1897. In this instance
+\index{Creston, Iowa}%
+the insurance policies expired ``at 12~o'clock at noon,''
+and the fire broke out at two and a half minutes past
+noon according to standard time, but at fifteen and one-half
+minutes before local mean solar noon. In each of
+these cases the question of whether standard time or local
+mean solar time was the accepted meaning of the term
+was submitted to a jury, and in the first instance the verdict
+was in favor of standard time, in the Iowa case the
+verdict was in favor of local time.
+
+\Paragraph{Early Decision in England.} In~1858 and thus prior to
+\index{England}%
+the formal adoption of standard time in Great Britain, it
+\index{Great Britain}%
+was held that the time appointed for the sitting of a court
+must be understood as the mean solar time of the place
+where the court is held and not Greenwich time, unless it be
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+so expressed, and a new trial was granted to a defendant
+who had arrived at the local time appointed by the court
+but found the court had met by Greenwich time and the
+case had been decided against him.
+
+\Paragraph{Court Decision in Georgia.} In a similar manner a court
+\index{Georgia}%
+in the state of Georgia rendered the following opinion:
+
+\begin{SmallText}
+``The only standard of time in computation of a day, or hours of a
+day, recognized by the laws of Georgia is the meridian of the sun; and
+a legal day begins and ends at midnight, the mean time between meridian
+and meridian, or 12~o'clock \textit{post meridiem}. An arbitrary and artificial
+standard of time, fixed by persons in a certain line of business,
+cannot be substituted at will in a certain locality for the standard
+recognized by the law.''
+\end{SmallText}
+
+\Paragraph{Need for Legal Time Adoption on a Scientific Basis.} There
+is nothing in the foregoing decisions to determine whether
+mean local time, or the time as actually indicated by the
+sun at a particular day, is meant. Since the latter sometimes
+%% -----File: 080.png---Folio 81-------
+\index{United States Naval Observatory}%
+varies as much as fifteen minutes faster or slower
+than the average, opportunities for controversies are multiplied
+when no scientifically accurate standard time is
+adopted by law.
+
+Even though statutes are explicit in the definition of
+time, they are still subject to the official interpretation
+of the courts, as the following extracts show:
+
+\begin{SmallText}
+Thomas Mier took out a fire insurance policy on his saloon at
+11:30 standard time, the policy being dated noon of that day. At
+the very minute that he was getting the policy the saloon caught fire
+and was burned. Ohio law makes standard time legal time, and the
+company refused to pay the \$2,000 insurance on Mier's saloon. The
+case was fought through to the Supreme Court, which decided that
+``noon'' meant the time the sun passed the meridian at Akron, which is
+\index{Akron, O.}%
+\index{Meridian!standard time|(}%
+at 11:27 standard time. The court ordered the insurance company to
+pay.---\textit{Law Notes}, June, 1902.
+
+In the 28th Nebraska Reports a case is cited in which judgment by
+\index{Nebraska}%
+\index{Law Notes, quoted}%
+default was entered against a defendant in a magistrate's court who
+failed to make an appearance at the stipulated hour by standard time,
+but arrived within the limit by solar time. He contested the ruling
+of the court, and the supreme judiciary of the state upheld him in the
+contest, although there was a Nebraska statute making standard time
+the legal time. The court held that ``at noon'' must necessarily
+mean when the sun is over the meridian, and that no construction
+could reasonably interpret it as indicating 12~o'clock standard time.
+\end{SmallText}
+\index{Legal aspect of standard time|)}%
+
+\Section{Time Used in Various Countries}\nblabel{page:81}
+
+The following table is taken, by permission, largely
+from the abstracts of official reports given in Vol.~IV,
+Appendix~IV of the Publications of the United States
+Naval Observatory, 1905. The time given is fast or slow
+as compared with Greenwich mean solar time.
+
+\begin{SmallText}
+\index{Time@Time \indexglossref{Time}, apparent solar!in various countries|(}%
+\index{Time@Time \indexglossref{Time}, apparent solar!signals|(}%
+\index{Signals, time|(}%
+\index{Telegraphic time signals}%
+\setlength\parindent{0.5\parindent}
+\CTime{Argentina}, $4$~h.\ $16$~m.\ $48.2$~s.\ slow. Official time is referred to the meridian
+of Cordoba. At 11~o'clock,~\AM, a daily signal is telegraphed
+from the Cordoba Observatory.
+\index{Cordoba@Cordoba (k\={o}r$'$d\={o}\;b\.{a}), Argentina}%
+\index{Argentina@Argentina (är\;jen\;te$'$na)}%
+%% -----File: 081.png---Folio 82-------
+
+\CTime{Austria-Hungary}, $1$~h.\ fast. Standard time does not exist except for
+\index{Austria-Hungary}%
+the service of railroads where it is in force, not by law, but by order
+of the proper authorities.
+
+\CTime{Belgium.} Official time is calculated from $0$ to $24$~hours, zero corresponding
+\index{Brussels, Belgium}%
+\index{Belgium}%
+to midnight at Greenwich. The Royal Observatory at
+Brussels communicates daily the precise hour by telegraph.
+
+\CTime{British Empire.}
+\index{British Empire}%
+
+\CSubTime{Great Britain.} The meridian of Greenwich is the standard time
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+meridian for England, Isle of Man, Orkneys, Shetland Islands,
+\index{Orkneys, The}%
+\index{Shetland Is.}%
+\index{England}%
+\index{Isle of Man}%
+and Scotland.
+\index{Scotland}%
+
+\CSubTime{Ireland}, $0$~h.\ $25$~m.\ $21.1$~s.\ slow. The meridian of Dublin is the
+\index{Ireland}%
+\index{Dublin, Ireland}%
+standard time meridian.
+
+\CSubTime{Africa} (English Colonies), $2$~h.\ fast. Standard time for Cape Colony,
+Natal, Orange River Colony, Rhodesia and Transvaal.
+\index{Natal, Africa}%
+\index{Rhodesia, Africa}%
+\index{Cape Colony, Africa}%
+\index{Orange River Colony}%
+\index{Transvaal}%
+
+\CSubTime{Australia.}
+
+{\setlength\parindent{2\parindent}
+\CSubTime{New South Wales, Queensland, Tasmania and Victoria}, $10$~h.\ fast.
+\index{New South Wales}%
+\index{Queensland, Australia}%
+\index{Tasmania}%
+\index{Victoria, Australia}%
+
+\CSubTime{South Australia and Northern Territory}, $9$~h.\ $30$~m.\ fast.
+\index{South Australia}%
+}
+
+\CSubTime{Canada.}
+
+{\setlength\parindent{2\parindent}
+\CSubTime{Alberta and Saskatchewan}, $7$~h.\ slow.
+\index{Alberta, Canada}%
+\index{Saskatchewan, Canada}%
+
+\CSubTime{British Columbia}, $8$~h.\ slow.
+\index{British Columbia}%
+
+\CSubTime{Keewatin and Manitoba}, $6$~h.\ slow.
+\index{Keewatin, Canada}%
+\index{Manitoba, Canada}%
+
+\CSubTime{Ontario and Quebec}, $5$~h.\ slow.
+\index{Quebec, Canada}%
+\index{Ontario, Canada}%
+
+\CSubTime{New Brunswick, Nova Scotia, and Prince Edward Island}, $4$~h.\ slow.
+\index{New Brunswick, Canada}%
+\index{Nova Scotia, Canada}%
+\index{Prince Edward Island, Can.}%
+}
+
+\CSubTime{Chatham Island}, $11$~h.\ $30$~m.\ fast.
+\index{Chatham Islands}%
+
+\CSubTime{Gibraltar}, Greenwich time.
+\index{Gibraltar, Spain}%
+
+\CSubTime{Hongkong}, $8$~h.\ fast.
+\index{Hongkong}%
+
+\CSubTime{Malta}, $1$~h.\ fast.
+\index{Malta}%
+
+\CSubTime{New Zealand}, $11$~h.\ $30$~m.\ fast.
+\index{New Zealand}%
+
+\CSubTime{India.} Local mean time of the Madras Observatory, $5$~h.\ $20$~m.\ $59.1$~s.,
+\index{Madras@Madras (ma\;dr\u{a}s$'$), India}%
+\index{India}%
+is practically used as standard time for India and Ceylon, being
+\index{Ceylon@Ceylon (s\={e}\;l\u{o}n$'$)}%
+telegraphed daily all over the country; but for strictly local use it
+is generally converted into local mean time. It is proposed soon
+to adopt the standard time of $5$~h.\ $30$~m.\ fast of Greenwich for India
+and Ceylon, and $6$~h.\ $30$~m.\ fast of Greenwich for Burmah.
+\index{Burmah}%
+
+\CSubTime{Newfoundland}, $3$~h.\ $30$~m.\ $43.6$~s.\ slow. (Local mean time of
+\index{Newfoundland}%
+St.~John's.)
+\index{St.~John's, Newfoundland}%
+
+\CTime{Chile}, $4$~h.\ $42$~m.\ $46.1$~s.\ slow. The official railroad time is furnished by
+\index{Chile@Chile (ch\={e}$'$l\={a})}%
+\index{Santiago@Santiago (sän\;t\={e}\;ä$'$g\={o}), Chile}%
+the Santiago Observatory. It is telegraphed over the country daily
+at 7 o'clock, \AM. The city of Valparaiso uses the local time,
+\index{Valparaiso@Valparaiso (väl\;p\={a}\;r\={\i}$'$s\={o}), Chile}%
+$4$~h.\ $46$~\DPtypo{h}{m}.\ $34.1$~\DPtypo{m}{s}.
+slow, of the observatory at the Naval School located
+there.
+%% -----File: 082.png---Folio 83-------
+
+\CTime{China}. An observatory is maintained by the Jesuit mission at
+\index{China}%
+Zikawei near Shanghai, and a time ball suspended from a mast on
+\index{Time@Time \indexglossref{Time}, apparent solar!ball}%
+\index{Zikawei@Zikawei (z\u{\i}\;kä$'$w\={e}), China}%
+\index{Shanghai@Shanghai (sh\u{a}ng$'$h\={\i}), China}%
+the French Bund in Shanghai is dropped electrically precisely at
+noon each day. This furnishes the local time at the port of
+Shanghai $8$~h.\ $5$~m.\ $43.3$~s.\ fast, which is adopted by the railway and
+telegraph companies represented there, as well as by the coastwise
+shipping. From Shanghai the time is telegraphed to other ports.
+The Imperial Railways of North China use the same time, taking
+it from the British gun at Tientsin and passing it on to the stations
+\index{Tientsin@Tientsin (t\={e}\;\u{e}n$'$ts\={e}n), China}%
+of the railway twice each day, at 8~o'clock~\AM{} and at 8~o'clock~\PM.
+Standard time, $7$~h.\ and $8$~h.\ fast, is coming into use all along the
+east coast of China from Newchwang to Hongkong.
+\index{Newchwang, China}%
+\index{Hongkong}%
+
+\CTime{Colombia}. Local mean time is used at Bogota, $4$~h.\ $56$~m.\ $54.2$~s.\ slow,
+\index{Colombia}%
+taken every day at noon in the observatory. The lack of effective
+telegraphic service makes it impossible to communicate the time
+as corrected at Bogota to other parts of the country, it frequently
+\index{Bogota@Bogota (b\={o}\;g\={o}\;tä$'$), Columbia}%
+taking four and five days to send messages a distance of from $50$ to
+$100$~miles.
+
+\CTime{Costa Rica}, $5$~h.\ $36$~m.\ $16.9$~s.\ slow. This is the local mean time of the
+\index{Costa Rica}%
+Government Observatory at San José.
+\index{San Jose@San Jose (h\={o}\;s\={a}$'$), Costa Rica}%
+
+\CTime{Cuba}, $5$~h.\ $29$~m.\ $26$~s.\ slow. The official time of the Republic is the civil
+\index{Cuba}%
+mean time of the meridian of Havana and is used by the railroads
+and telegraph lines of the government. The Central Meteorological
+Station gives the time daily to the port and city of Havana as well
+as to all the telegraph offices of the Republic.
+\index{Havana, Cuba}%
+
+\CTime{Denmark}, $1$~h.\ fast. In Iceland, the Faroe Islands and the Danish
+\index{Denmark}%
+\index{Iceland}%
+\index{Danish West Indies}%
+\index{Faroe@Faroe (f\={a}$'$r\={o}), Islands}%
+West Indies, local mean time is used.
+
+\CTime{Egypt}, $2$~h.\ fast. Standard time is sent out electrically by the standard
+\index{Egypt}%
+clock of the observatory to the citadel at Cairo, to Alexandria, Port
+\index{Cairo@Cairo (k\={\i}$'$r\={o}), Egypt}%
+\index{Alexandria, Egypt}%
+\index{Port Said (sä\;\={e}d$'$), Egypt}%
+\index{Wady-Halfa@Wady-Halfa (wä$'$d\={e}\;häl$'$fä), Egypt}%
+Said and Wady-Halfa.
+
+\CTime{Equador}, $5$~h.\ $14$~m.\ $6.7$~s.\ slow. The official time is that of the meridian
+\index{Equador}%
+of Quito, corrected daily from the National Observatory.
+\index{Quito@Quito (k\={e}$'$t\={o}), Equador}%
+
+\CTime{France}, $0$~h.\ $9$~m.\ $20.9$~s.\ fast. Legal time in France, Algeria and Tunis is
+\index{Algeria}%
+\index{France}%
+\index{Tunis}%
+local mean time of the Paris Observatory. Local mean time is
+considered legal in other French colonies.
+
+\CTime{German Empire}.
+
+\CSubTime{Germany}, $1$~h.\ fast.
+\index{Germany}%
+
+\CSubTime{Kiaochau}, $8$~h.\ fast.
+\index{Kiaochau@Kiaochau (k\={e}\;ä\;\={o}\;chow$'$), China}%
+
+\CSubTime{Southwest Africa}, $1$~h.\ fast.
+
+It is proposed to adopt standard time for the following:
+
+\CSubTime{Bismarck Archipelago}, Carolines, Mariane Islands and New Guinea,
+\index{Carolines, the}%
+\index{Bismarck Archipelago}%
+\index{Mariane Islands}%
+\index{New Guinea}%
+$10$\DPtypo{}{~h.}\ fast.
+%% -----File: 083.png---Folio 84-------
+
+\CSubTime{German East Africa}, $2$~h.\ fast or $2$~h.\ $30$~m.\ fast.
+\index{Germany}%
+\index{German East Africa}%
+
+\CSubTime{Kamerun}, $1$~h.\ fast.
+\index{Kamerun, Africa}%
+
+\CSubTime{Samoa} (after an understanding with the U. S.), $12$~h.\ fast.
+\index{Samoa}%
+
+\CSubTime{Toga}, Greenwich time.
+\index{Toga Is.}%
+
+\CTime{Greece,} $1$~h.\ $34$~m.\ $52.9$~s.\ fast. By royal decree of September 14, 1895, the
+\index{Greece}%
+\index{Athens, Greece}%
+time in common use is that of the mean time of Athens, which is
+transmitted from the observatory by telegraph to the towns of
+the kingdom.
+
+\CTime{Holland.} The local time of Amsterdam, $0$~h.\ $19$~m.\ $32.3$~s.\ fast, is
+\index{Amsterdam, Holland}%
+\index{Holland}%
+generally used, but Greenwich time is used by the post and telegraph
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+administration and the railways and other transportation companies.
+The observatory at Leyden communicates the time twice
+\index{Leyden, Holland}%
+a week to Amsterdam, The Hague, Rotterdam and other cities,
+\index{Hague, The, Holland}%
+and the telegraph bureau at Amsterdam signals the time to all
+the other telegraph bureaus every morning.
+
+\CTime{Honduras.} In Honduras the half hour nearest to the meridian of
+\index{Honduras}%
+Tegucigalpa, longitude $87°~12'$ west from Greenwich, is generally
+\index{Tegucigalpa, Honduras}%
+used. Said hour, $6$~h.\ slow, is frequently determined at the National
+Institute by means of a solar chronometer and communicated by
+telephone to the Industrial School, where in turn it is indicated to
+the public by a steam whistle. The central telegraph office communicates
+it to the various sub-offices of the Republic, whose
+clocks generally serve as a basis for the time of the villages, and in
+this manner an approximately uniform time is established throughout
+the Republic.
+
+\CTime{Italy}, $1$~h.\ fast. Adopted by royal decree of August 10, 1893. This
+\index{Italy}%
+time is kept in all government establishments, ships of the Italian
+Navy in the ports of Italy, railroads, telegraph offices, and Italian
+coasting steamers. The hours are numbered from $0$ to $24$,
+beginning with midnight.
+
+\CTime{Japan.} Imperial ordinance No.\ 51, of 1886: ``The meridian that
+\index{Japan}%
+passes through the observatory at Greenwich, England, shall be
+the zero ($0$) meridian. Longitude shall be counted from the above
+meridian east and west up to $180$ degrees, the east being positive
+and the west negative. From January 1, 1888, the time of the
+135th degree east longitude shall be the standard time of Japan.''
+This is $9$~h.\ fast.\\
+Imperial ordinance No. 167, of 1895: ``The standard time hitherto
+used in Japan shall henceforth be called central standard time. The
+time of the 120th degree east longitude shall be the standard time
+of Formosa, the Pescadores, the Yaeyama, and the Miyako groups,
+\index{Miyako@Miyako (m\={e}\;yä$'$k\={o}) Islands}%
+\index{Pescadores@Pescadores (p\u{e}sk\={a}d\={o}r$'$\={e}z) Is.}%
+\index{Yaeyama@Yaeyama (y\={e}\;yä$'$mä) Is.}%
+\index{Formosa}%
+and shall be called western standard time. This ordinance shall
+take effect from the first of January, 1896.'' This is $8$~h.\ fast.
+%% -----File: 084.png---Folio 85-------
+
+\CTime{Korea}, $8$~h.\ $30$~m.\ fast. Central standard time of Japan is telegraphed
+\index{Korea@Korea (k\={o}\;r\={e}$'$a)}%
+\index{Japan}%
+daily to the Imperial Japanese Post and Telegraph Office at Seoul.
+\index{Seoul@Seoul (s\={a}\;\={o}\=ol$'$), Korea}%
+Before December, 1904, this was corrected by subtracting $30$~m.,
+which nearly represents the difference in longitude, and was then
+used by the railroads, street railways, and post and telegraph offices,
+and most of the better classes. Since December 1, 1904, the Japanese
+post-offices and railways in Korea have begun to use central
+standard time of Japan. In the country districts the people use
+sundials to some extent.
+
+\CTime{Luxemburg}, $1$~h.\ fast, the legal and uniform time.
+\index{Luxemburg}%
+
+\CTime{Mexico}, $6$~h.\ $36$~m.\ $26.7$~s.\ slow. The National Astronomical Observatory
+\index{Mexico}%
+of Tacubaya regulates a clock twice a day which marks the local
+\index{Tacubaya@Tacubaya (\phonTacubaya), Mexico}%
+mean time of the City of Mexico, and a signal is raised twice a week
+at noon upon the roof of the national palace, such signal being
+used to regulate the city's public clocks. This signal, the clock at
+the central telegraph office, and the public clock on the cathedral,
+serve as a basis for the time used commonly by the people. The
+general telegraph office transmits this time daily to all of its branch
+offices. Not every city in the country uses this time, however,
+since a local time, very imperfectly determined, is more commonly
+observed. The following railroad companies use standard City of
+Mexico time corrected daily by telegraph: Central, Hidalgo, Xico
+\index{Xico, Mexico}%
+\index{Hidalgo, Mexico}%
+and San Rafael, National and Mexican. The Central and National
+\index{San Rafael@San Rafael (rä\;fä\;\u{e}l$'$), Mexico}%
+railroads correct their clocks to City of Mexico time daily by means
+of the noon signal sent out from the Naval Observatory at Washington
+\index{Washington, D. C.}%
+(see page~\pageref{page:71}) and by a similar signal from the observatory
+at St.~Louis, Missouri. The Nacozari, and the Cananea, Yaqui River
+\index{St.~Louis, Mo.}%
+\index{Yaqui River, Mexico}%
+and Pacific railroads use Mountain time, $7$~h.\ slow, and the Sonora
+railroad uses the local time of Guaymas, $7$~h.\ $24$~m.\ slow.
+\index{Guaymas, Mexico}%
+
+\CTime{Nicaragua}, $5$~h.\ $45$~m.\ $10$~s.\ slow. Managua time is issued to all public
+\index{Nicaragua}%
+\index{Managua@Managua (mä\;nä$'$guä), Nicaragua}%
+offices, railways, telegraph offices and churches in a zone that
+extends from San Juan del Sur, latitude $11°~15'~44''$~N., to El Ocotal,
+\index{San Juan del Sur, Nicaragua}%
+\index{El Ocotal@El Ocotal (\u{e}l\;\={o}k\;\={o}\;täl$'$), Nicaragua}%
+latitude $12°~46'$~N., and from El Castillo, longitude $84°~22'~37''$~W.,
+\index{El Castillo@El Castillo (\u{e}l\;käs\;t\={e}l$'$y\={o}), Nicaragua}%
+to Corinto, longitude $87°~12'~31''$ W\@. The time of the Atlantic
+\index{Corinto@Corinto (k\={o}\;r\={e}n$'$t\={o}), Nicaragua}%
+ports is usually obtained from the captains of ships.
+
+\CTime{Norway}, $1$~h.\ fast. Central European time is used everywhere throughout
+\index{Central time, in Europe}%
+\index{Norway}%
+the country. Telegraphic time signals are sent out once a
+week to the telegraph stations throughout the country from the
+observatory of the Christiania University.
+
+\CTime{Panama.} Both the local mean time of Colon, $5$~h.\ $19$~m.\ $39$~s.\ slow, and
+\index{Panama}%
+\index{Colon@Colon (k\={o}\;l\={o}n$'$), Panama}%
+eastern standard time of the United States, $5$~h.\ slow, are used. The
+latter time is cabled daily by the Central and South American Cable
+%% -----File: 085.png---Folio 86-------
+Company from the Naval Observatory at Washington, and will
+\index{Washington, D. C.}%
+probably soon be adopted as standard.
+
+\CTime{Peru}, $5$~h.\ $9$~m.\ $3$~s.\ slow. There is no official time. The railroad from
+\index{Peru}%
+Callao to Oroya takes its time by telegraph from the noon signal at
+\index{Callao@Callao (käl\;lä$'$\={o}), Peru}%
+\index{Oroya, Peru}%
+the naval school at Callao, which may be said to be the standard
+time for Callao, Lima, and the whole of central Peru. The railroad
+\index{Lima@Lima (l\={e}$'$ma), Peru}%
+from Mollendo to Lake Titicaca, in southern Peru, takes its time
+\index{Mollendo, Peru}%
+\index{Titicaca, Lake, Peru}%
+from ships in the Bay of Mollendo.
+
+\CTime{Portugal}, $0$~h.\ $36$~m.\ $44.7$~s.\ slow. Standard time is in use throughout
+\index{Portugal}%
+Portugal and is based upon the meridian of Lisbon. It is established
+\index{Lisbon, Portugal}%
+by the Royal Observatory in the Royal Park at Lisbon,
+and from there sent by telegraph to every railway station throughout
+Portugal having telegraphic communication. Clocks on railway
+station platforms are five minutes behind and clocks outside of
+stations are true.
+
+\CTime{Russia}, $2$~h.\ $1$~m.\ $18.6$~s.\ fast. All telegraph stations use the time of the
+\index{Russia}%
+Royal Observatory at Pulkowa, near St.~Petersburg. At railroad
+\index{Pulkowa, Russia}%
+\index{St.~Petersburg, Russia}%
+stations both local and Pulkowa time are given, from which it is
+to be inferred that for all local purposes local time is used.
+
+\CTime{Salvador}, $5$~h.\ $56$~m.\ $32$~s.\ slow. The government has established a national
+observatory at San Salvador which issues time on Wednesdays and
+\index{Salvador@Salvador (säl\;vä\;d\={o}r)}%
+\index{San Salvador, Salvador}%
+Saturdays, at noon, to all public offices, telegraph offices, railways,
+etc., throughout the Republic.
+
+\CTime{Santo Domingo}, $4$~h.\ $39$~m.\ $32$~s.\ slow. Local mean time is used, but there
+\index{Santo Domingo}%
+is no central observatory and no means of correcting the time. The
+time differs from that of the naval vessels in these waters by about
+30 minutes.
+
+\CTime{Servia}, $1$~h.\ fast. Central European time is used by the railroad, telegraph
+\index{Central time, in Europe}%
+\index{Servia}%
+companies, and people generally. Clocks are regulated by
+telegraph from Budapest every day at noon.
+\index{Budapest@Budapest (boo$'$\;da\;pest), Hungary}%
+
+\CTime{Spain}, Greenwich time. This is the official time for use in governmental
+\index{Spain}%
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England|(}%
+offices in Spain and the Balearic Islands, railroad and
+\index{Balearic Is.}%
+telegraph offices. The hours are numbered from $0$ to $24$, beginning
+with midnight. In some portions local time is still used for private
+matters.
+
+\CTime{Sweden}, $1$~h.\ fast. Central European time is the standard in general
+\index{Sweden}%
+use. It is sent out every week by telegraph from the Stockholm
+\index{Stockholm, Sweden}%
+Observatory.
+
+\CTime{Switzerland}, $1$~h.\ fast. Central European time is the only legal time.
+\index{Central time, in Europe}%
+\index{Switzerland}%
+It is sent out daily by telegraph from the Cantonal Observatory at
+Neuchatel.%
+\index{Neuchatel, Switzerland}%
+%% -----File: 086.png---Folio 87-------
+
+\CTime{Turkey.} Two kinds of time are used, Turkish and Eastern European
+\index{Turkey}%
+\index{Eastern time, in Europe}%
+time, the former for the natives and the latter for Europeans. The
+railroads generally use both, the latter for the actual running of
+trains and Turkish time-tables for the benefit of the natives.
+Standard Turkish time is used generally by the people, sunset being
+the base, and twelve hours being added for a theoretical sunrise.
+The official clocks are set daily so as to read 12 o'clock at the theoretical
+sunrise, from tables showing the times of sunset, but the
+tower clocks are set only two or three times a week. The government
+telegraph lines use Turkish time throughout the empire, and
+St.~Sophia time, $1$~h.\ $56$~m.\ $53$~s.\ fast, for telegrams sent out of the
+country.
+
+\CTime{United States.} Standard time based upon the meridian of Greenwich,
+\index{United States}%
+varying by whole hours from Greenwich time, is almost universally
+used, and is sent out daily by telegraph to most of the country, and
+to Havana and Panama from the Naval Observatory at Washington,
+\index{Havana, Cuba}%
+\index{Panama}%
+and to the Pacific coast from the observatory at Mare Island Navy
+\index{Mare Island Naval Observatory}%
+Yard, California. For further discussions of standard time belts in
+the United States, see pp.~\pageref{page:65}--\pageref{page:68} and the U. S. standard time belt
+\hyperref[fig:i065]{map}. Insular possessions have time as follows:
+
+\CSubTime{Porto Rico}, $4$~h.\ slow, Atlantic standard time.
+\index{Porto Rico}%
+
+\CSubTime{Alaska}, $9$~h.\ slow, Alaska standard time.
+\index{Alaska}%
+
+\CSubTime{Hawaiian Islands}, $10$~h.\ $30$~m.\ slow, Hawaiian standard time.
+\index{Hawaiian (Sandwich) Islands}%
+
+\CSubTime{Guam}, $9$~h.\ $30$~m.\ fast, Guam standard time.
+\index{Guam}%
+
+\CSubTime{Philippine Islands}, $8$~h.\ fast, Philippine standard time.
+\index{Philippine Is.}%
+
+\CSubTime{Tutuila, Samoa}, $11$~h.\ $30$~m.\ slow, Samoan standard time.
+\index{Tutuila@Tutuila (too\;tw\={e}$'$lä), Samoa}%
+
+\CTime{Uruguay}, $3$~h.\ $44$~m.\ $48.9$~s.\ slow. The time in common use is the mean
+\index{Uruguay}%
+time of the meridian of the dome of the Metropolitan Church of
+Montevideo. The correct time is indicated by a striking clock in
+\index{Montevideo, Uruguay}%
+the tower of that church. An astronomical geodetic observatory,
+with meridian telescope and chronometers, has now been established
+and will in the future furnish the time. It is proposed to
+install a time ball for the benefit of navigators at the port of Montevideo.
+An electric time service will be extended throughout the
+country, using at first the meridian of the church and afterwards
+\index{Meridian!standard time|)}%
+that of the national observatory, when constructed.
+
+\CTime{Venezuela}, $4$~h.\ $27$~m.\ $43.6$~s. The time is computed daily at the Caracas
+\index{Caracas@Caracas (kä\;rä$'$käs), Venezuela}%
+\index{Venezuela}%
+Observatory from observations of the sun and is occasionally telegraphed
+to other parts of Venezuela. The cathedral clock at Caracas
+is corrected by means of these observations. Railway time is at
+least five minutes later than that indicated by the cathedral clock,
+which is accepted as standard by the people. Some people take
+time from the observatory flag, which always falls at noon.\nblabel{page:87}
+\index{Signals, time|)}%
+\index{Time@Time \indexglossref{Time}, apparent solar!in various countries|)}%
+\index{Time@Time \indexglossref{Time}, apparent solar!signals|)}%
+\end{SmallText}
+%% -----File: 087.png---Folio 88-------
+
+\Section{Latitude and Longitude of Cities}
+
+The latitude and longitude of cities in the following
+table was compiled from  various sources.  Where possible,
+the exact place is given,  the abbreviation ``O'' standing
+for observatory, ``C'' for cathedral, etc.
+\index{Adelaide, Australia}%
+\index{Aden@Aden (ä$'$den), Arabia}%
+\index{Apia@Apia (ä\;p\={e}$'$ä), Samoa}%
+\index{Bankok, Siam}%
+\index{Bombay@Bombay (b\u{o}m\;b\={a}$'$), India}%
+\index{Bordeaux@Bordeaux (bôr\;d\={o}$'$), France}%
+\index{Buenos Aires@Buenos Aires (b\={o}$'$n\u{u}s \={a}$'$r\u{\i}z), Argentina}%
+\index{Cadiz@Cadiz (k\={a}$'$d\u{\i}z), Spain}%
+\index{Cairo@Cairo (k\={\i}$'$r\={o}), Egypt}%
+\index{Calcutta, India}%
+\index{Cayenne@Cayenne (k\u{\i}\;\u{e}n$'$), French Guiana}%
+\index{Christiania@Christiania (kr\u{\i}s\;t\={e}\;ä$'$n\={e}\;ä), Norway}%
+\index{Edinburgh@Edinburgh (\u{e}d$'$\u{\i}n\;b\u{u}r\;r\={o}), Scotland}%
+\index{Guiana, French}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!of principal cities|(}%
+\index{Longitude@Longitude \indexglossref{Longitude}!of principal cities|(}%
+
+{
+\smallsize\nblabel{page:88}
+\settowidth{\TmpLen}{Longitude from}
+\begin{longtable}{@{}>{\raggedright\hangindent1em}b{0.4\textwidth}<{\dotfill}|r@{\Z\Z}l@{\Z\Z}l|r@{\Z\Z}l@{\Z\Z}l@{}}
+\hline
+\hspace*{0.4\textwidth}
+& \multicolumn{3}{c|}{\parbox{\TmpLen}{\centering\tablespacertop Latitude\tablespacerbot}}
+& \multicolumn{3}{c}{\parbox{\TmpLen}{\centering Longitude from Greenwich}}\\
+\hline
+\hspace*{0.4\textwidth}&&&&&&\\[-1.5ex] %to force space after heading of each page of table
+\endhead
+Adelaide, S. Australia, Snapper Point & $\Z34°$ & $46'$ & $50''$ S & $138°$ & $30'$& $39''$ E \\
+Aden, Arabia, Tel.~Station & $12°$ & $46'$ & $40''$ N & $44°$ & $58'$ & $58''$ E \\
+\index{Arabia}%
+Alexandria, Egypt, Eunos Pt.  & $31°$ & $11'$ & $43''$ N & $29°$ & $51'$ & $40''$ E \\
+\index{Alexandria, Egypt}%
+\index{Egypt}%
+Amsterdam, Holland, Ch.   & $52°$ & $22'$ & $30''$ N & $4°$ & $53'$ & $04''$ E \\
+\index{Amsterdam, Holland}%
+\index{Holland}%
+Antwerp, Belgium, O.  & $51°$ & $12'$ & $28''$ N & $4°$ & $24'$ & $44''$ E \\
+\index{Antwerp, Belgium}%
+\index{Belgium}%
+Apia, Samoa, Ruge's Wharf  & $13°$ & $ 48'$ & $56''$ S & $171°$ & $44'$ & $56''$ W \\
+\index{Samoa}%
+Athens, Greece, O.   & $37°$ & $ 58'$ & $21''$ N & $23°$ & $43'$ & $55''$ E \\
+\index{Athens, Greece}%
+\index{Greece}%
+Bangkok, Siam, Old Br.~Fact.  & $13°$ & $ 44'$ & $20''$ N & $100°$ & $28'$ & $42''$ E \\
+\index{Siam}%
+Barcelona, Spain, Old Mole
+\index{Barcelona, Spain}%
+\index{Spain}%
+Light   & $41°$ & $ 22'$ & $10''$ N & $2°$ & $10'$ & $55''$ E \\
+Batavia, Java, O.   & $6°$ & $ 07'$ & $40''$ N & $106°$ & $48'$ & $25''$ E \\
+\index{Batavia, Java}%
+\index{Java}%
+Bergen, Norway, C.   & $60°$ & $ 23'$ & $37''$ N & $5°$ & $20'$ & $15''$ E \\
+\index{Bergen, Norway}%
+\index{Norway}%
+Berlin, Germany, O. &  $52°$ & $30'$ & $17''$ N &  $13°$ & $23'$ & $44''$ E \\
+\index{Berlin, Germany}%
+\index{Germany}%
+Bombay, India, O.  & $18°$ & $53'$ & $45''$ N & $72°$ & $48'$ & $58''$ E \\
+\index{India}%
+Bordeaux, France, O.  & $44°$ & $50'$ & $07''$ N & $00°$ & $31'$ & $23''$ W \\
+\index{France}%
+Brussels, Belgium, O.  & $50°$ & $51'$ & $11''$ N & $4°$ & $22'$ & $18''$ E \\
+\index{Brussels, Belgium}%
+Buenos Aires, Custom House & $34°$ & $36'$ & $30''$ S & $58°$ & $22'$ & $14''$ W \\
+Cadiz, Spain, O.  & $36°$ & $27'$ & $40''$ N & $6°$ & $12'$ & $20''$ W \\
+Cairo, Egypt, O.  & $30°$ & $04'$ & $38''$ N & $31°$ & $17'$ & $14''$ E \\
+Calcutta, Ft.~Wm.\ Semaphore & $22°$ & $33'$ & $25''$ N & $88°$ & $20'$ & $11''$ E \\
+Canton, China, Dutch Light & $23°$ & $06'$ & $35''$ N & $113°$ & $16'$ & $34''$ E \\
+\index{Canton, China}%
+\index{China}%
+Cape Horn, South Summit & $55°$ & $58'$ & $41''$ S & $67°$ & $16'$ & $15''$ W \\
+Cape Town, S.~Africa, O.  & $33°$ & $56'$ & $03''$ S & $18°$ & $28'$ & $40''$ E \\
+Cayenne, Fr.~Guiana, Landing & $4°$ & $ 56'$ & $20''$ N & $52°$ & $20'$ & $25''$ W \\
+Christiania, Norway, O.  & $59°$ & $54'$ & $44''$ N & $10°$ & $43'$ & $35''$ E \\
+Constantinople, Turkey, C. & $41°$ & $00'$ & $16''$ N & $28°$ & $58'$ & $59''$ E \\
+\index{Constantinople, Turkey}%
+\index{Turkey}%
+Copenhagen, Denmark, New O. & $55°$ & $41'$ & $14''$ N & $12°$ & $34'$ & $47''$ E \\
+\index{Copenhagen, Denmark}%
+\index{Denmark}%
+Dublin, Ireland, O.  & $53°$ & $23'$ & $13''$ N & $6°$ & $20'$ & $30''$ W \\
+\index{Dublin, Ireland}%
+\index{Ireland}%
+Edinburgh, Scotland, O.    & $55°$ & $57'$ & $23''$ N & $3°$ & $10'$ & $54''$ W \\
+\index{Scotland}%
+Florence, Italy, O.  & $43°$ & $46'$ & $04''$ N & $11°$ & $15'$ & $22''$ E \\
+\index{Florence, Italy}%
+\index{Italy}%
+Gibraltar, Spain, Dock Flag & $36°$ & $07'$ & $10''$ N & $5°$ & $21'$ & $17''$ W \\
+\index{Gibraltar, Spain}%
+Glasgow, Scotland, O.    & $55°$ & $52'$ & $43''$ N & $4°$ & $17'$ & $39''$ W \\
+\index{Glasgow, Scotland}%
+Hague, The, Holland, Ch.  & $52°$ & $04'$ & $40''$ N & $4°$ & $18'$ & $30''$ E \\
+\index{Hague, The, Holland}%
+Hamburg, Germany, O.  & $53°$ & $33'$ & $07''$ N & $9°$ & $58'$ & $25''$ E \\
+\index{Hamburg, Germany}%
+Havana, Cuba, Morro Lt.~H. & $23°$ & $09'$ & $21''$ N & $82°$ & $21'$ & $30''$ W \\
+\index{Cuba}%
+\index{Havana, Cuba}%
+Hongkong, China, C.    & $21°$ & $16'$ & $52''$ N & $114°$ & $09'$ & $31''$ E \\
+\index{Hongkong}%
+\index{Standard time|)}%
+\index{Time@Time \indexglossref{Time}, apparent solar!standard|)}%
+%% -----File: 088.png---Folio 89-------
+\index{Berkeley, Calif.}%
+\index{Boise@Boise (boi$'$z\={a}), Ida.}%
+\index{California}%
+\index{Chile@Chile (ch\={e}$'$l\={a})}%
+\index{Georgia}%
+\index{Holland}%
+\index{Madras@Madras (ma\;dr\u{a}s$'$), India}%
+\index{Maryland}%
+\index{Massachusetts}%
+\index{Melbourne, Australia}%
+\index{Michigan}%
+\index{Munich@Munich (m\={u}$'$n\u{\i}k), Germany}%
+\index{New South Wales}%
+\index{New York|(}%
+\index{North Dakota}%
+\index{Rotterdam, Holland}%
+\index{South Dakota|(}%
+\index{Sydney, Australia}%
+\index{Texas}%
+\index{Valparaiso@Valparaiso (väl\;p\={a}\;r\={\i}$'$s\={o}), Chile}%
+\index{Victoria, Australia}%
+\index{Wisconsin}%
+Jerusalem, Palestine, Ch. & $31°$ & $46'$ & $45''$ N & $35°$ & $13'$ & $25''$ E \\
+\index{Jerusalem}%
+\index{Palestine}%
+Leipzig, Germany, O.   & $51°$ & $20'$ & $06''$ N & $12°$ & $23'$ & $30''$ E \\
+\index{Germany}%
+\index{Leipzig, Germany}%
+Lisbon, Portugal, O. (Royal)  & $38°$ & $42'$ & $31''$ N & $9°$ & $11'$ & $10''$ W \\
+\index{Lisbon, Portugal}%
+\index{Portugal}%
+Liverpool, England, O.   & $53°$ & $24\DPtypo{''}{'}$ & $04''$ N & $3°$ & $04'$ & $16''$ W \\
+\index{England}%
+\index{Liverpool, England}%
+Madras, India, O.   & $13°$ & $04'$ & $06''$ N & $80°$ & $14'$ & $  51''$ E \\
+\index{India}%
+Marseilles, France, New O.  & $43°$ & $18'$ & $22''$ N & $5°$ & $23'$ & $43''$ E \\
+\index{France}%
+\index{Marseilles, France}%
+Melbourne, Victoria, O.   & $37°$ & $49'$ & $53''$ S & $144°$ & $58'$ & $  32''$ E \\
+Mexico, Mexico, O.   & $19°$ & $26'$ & $01''$ N & $99°$ & $06'$ & $39''$ W \\
+\index{Mexico}%
+Montevideo, Uruguay, C.   & $34°$ & $54'$ & $33''$ S & $56°$ & $12'$ & $15''$ W \\
+\index{Montevideo, Uruguay}%
+\index{Uruguay}%
+Moscow, Russia, O.   & $55°$ & $45'$ & $20''$ N & $37°$ & $32'$ & $36''$ E \\
+\index{Moscow, Russia}%
+\index{Russia}%
+Munich, Germany, O.   & $48°$ & $08'$ & $45''$ N & $11°$ & $36'$ & $  32''$ E \\
+Naples, Italy, O.   & $40°$ & $51'$ & $46''$ N & $14°$ & $14'$ & $44''$ E \\
+\index{Italy}%
+\index{Naples, Italy}%
+Panama, Cent.~Am., C.  & $8°$ & $57'$ & $06''$ N & $79°$ & $32'$ & $12''$ W \\
+\index{Panama}%
+Para, Brazil, Custom H.   & $1°$ & $26'$ & $59''$ S & $48°$ & $30'$ & $01''$ W \\
+\index{Brazil}%
+\index{Para, Brazil}%
+Paris, France, O.   & $48°$ & $50'$ & $11''$ N & $2°$ & $20'$ & $14''$ E \\
+\index{Paris, France}%
+Peking, China       & $39°$ & $56'$ & $00''$ N & $116°$ & $28'$ & $54''$ E \\
+\index{China}%
+\index{Peking, China}%
+Pulkowa, Russia, O.     & $59°$ & $46'$ & $19''$ N & $30°$ & $19'$ & $40''$ E \\
+\index{Pulkowa, Russia}%
+Rio de Janeiro, Brazil, O.   & $22°$ & $54'$ & $24''$ S & $43°$ & $10'$ & $21''$ W \\
+\index{Rio de Janeiro, Brazil}%
+Rome, Italy, O.   & $41°$ & $  53'$ & $54''$ N & $12°$ & $28'$ & $40''$ E \\
+\index{Rome, Italy}%
+Rotterdam, Holl., Time Ball  & $51°$ & $54'$ & $30''$ N & $4°$ & $28'$ & $50''$ E \\
+St.~Petersburg, Russia, see
+\index{St.~Petersburg, Russia}%
+Pulkowa \par
+Stockholm, Sweden, O.   & $59°$ & $20'$ & $35''$ N & $18°$ & $03'$ & $30''$ E \\
+\index{Stockholm, Sweden}%
+\index{Sweden}%
+Sydney, N.~S.~Wales, O.     & $33°$ & $51'$ & $41''$ S & $151°$ & $12'$ & $23''$ E \\
+Tokyo, Japan, O.   & $35°$ & $39'$ & $17''$ N & $139°$ & $44'$ & $30''$ E \\
+\index{Japan}%
+\index{Tokyo, Japan}%
+Valparaiso, Chile, Light House  & $33°$ & $01'$ & $30''$ S & $71°$ & $39'$ & $22''$ W\tablespacerbot \\
+\hline
+\multicolumn{7}{c}{\tablespacertop\textsc{United States}\tablespacerbot}\\\hline\tablespacertop
+\index{United States}%
+Aberdeen, S.~D., N.~N. \& I.~S.  & $45°$ & $27'$ & $50''$ N & $98°$ & $28'$ & $45''$ W \\
+\index{Aberdeen, S.~D.}%
+Albany, N.~Y., New O  & $42°$ & $39'$ & $13''$ N & $73°$ & $46'$ & $42''$ W \\
+\index{Albany, N.~Y.}%
+Ann Arbor, Mich., O.   & $42°$ & $16'$ & $48''$ N & $83°$ & $43'$ & $48''$ W \\
+\index{Ann Arbor, Mich.}%
+Annapolis, Md., O.   & $38°$ & $58'$ & $53''$ N & $76°$ & $29'$ & $08''$ W \\
+\index{Annapolis, Md.}%
+Atlanta, Ga., Capitol   & $33°$ & $45'$ & $19''$ N & $84°$ & $23'$ & $29''$ W \\
+\index{Atlanta, Ga.}%
+Attu Island, Alaska, Chichagoff
+\index{Alaska}%
+\index{Attu Island}%
+Harbor & $52°$ & $56'$ & $01''$ N & $173°$ & $12'$ & $24''$ E \\
+Augusta, Me., Baptist Ch.  & $44°$ & $18'$ & $52''$ N & $69°$ & $46'$ & $37''$ W \\
+\index{Augusta, Me.}%
+Austin, Tex.   & $32°$ & $00'$ & $40''$ N & $100°$ & $27'$ & $35''$ W \\
+\index{Austin, Tex.}%
+Baltimore, Md., Wash.~Mt.   & $39°$ & $17'$ & $48''$ N & $76°$ & $36'$ & $59''$ W \\
+\index{Baltimore, Md.}%
+Bangor, Me., Thomas Hill   & $44°$ & $48'$ & $23''$ N & $68°$ & $46'$ & $59''$ W \\
+\index{Bangor, Me.}%
+Beloit, Wis., College.  & $42°$ & $30'$ & $13''$ N & $89°$ & $\DPtypo{1}{01}'$ & $46''$ W \\
+\index{Beloit, Wis.}%
+Berkeley, Cal., O.   & $37°$ & $52'$ & $24''$ N & $122°$ & $15'$ & $41''$ W \\
+Bismarck, N.~D.     & $46°$ & $49'$ & $12''$ N & $100°$ & $45'$ & $08''$ W \\
+\index{Bismarck, N.~D.}%
+Boise, Idaho, Ast.~Pier   & $43°$ & $35'$ & $58''$ N & $116°$ & $13'$ & $04''$ W \\
+\index{Idaho}%
+Boston, Mass., State House  & $42°$ & $21'$ & $28''$ N & $71°$ & $03'$ & $50''$ W \\
+\index{Boston, Mass.}%
+%% -----File: 089.png---Folio 90-------
+\index{Alabama}%
+\index{Arkansas@Arkansas (\phonArkansas)}%
+\index{California}%
+\index{Cheyenne@Cheyenne (sh\={\i}\;\u{e}n$'$), Wyo.}%
+\index{Cincinnati, O.}%
+\index{Cleveland, O.}%
+\index{Colorado}%
+\index{Columbus, O.}%
+\index{Connecticut}%
+\index{Des Moines@Des Moines (de\;moin$'$), Iowa}%
+\index{Florida}%
+\index{Guthrie, Okla@Guthrie, Okla\DPtypo{}{.}}%
+\index{Honolulu, Hawaiian Islands}%
+\index{Illinois}%
+\index{Indiana}%
+\index{Kentucky}%
+\index{Los Angeles, Calif.}%
+\index{Louisiana}%
+\index{Manila, Philippine Is.}%
+\index{Massachusetts}%
+\index{Michigan}%
+\index{Minnesota}%
+\index{Mississippi}%
+\index{Missouri}%
+\index{Montana}%
+\index{Nebraska}%
+\index{New Hampshire}%
+\index{New Jersey}%
+\index{North Dakota}%
+\index{Oklahoma}%
+\index{Pennsylvania}%
+\index{South Carolina}%
+\index{Tennessee}%
+\index{Texas}%
+\index{Wisconsin}%
+\index{Wyoming}%
+Buffalo, N.~Y. & $42°$ & $53'$ & $03''$ N & $78°$ & $52'$ & $42''$ W \\
+\index{Buffalo, N.~Y.}%
+Charleston, S.~C., Lt.~House & $32°$ & $41'$ & $44''$ N & $79°$ & $52'$ & $58''$ W \\
+\index{Charleston, S.~C.}%
+Cheyenne, Wyo., Ast.~Sta. & $41°$ & $07'$ & $47''$ N & $104°$ & $48'$ & $52''$ W \\
+Chicago, Ill., O.  & $41°$ & $50'$ & $01''$ N & $87°$ & $36'$ & $36''$ W \\
+\index{Chicago, Ill.}%
+Cincinnati, Ohio  & $39°$ & $08'$ & $19''$ N & $84°$ & $26'$ & $00''$ W \\
+\index{Ohio}%
+Cleveland, Ohio, Lt.~H.  & $41°$ & $30'$ & $02''$ N & $81°$ & $42'$ & $10''$ W \\
+Columbia, S.~C.  & $33°$ & $59'$ & $12''$ N & $81°$ & $00'$ & $12''$ W \\
+\index{Columbia, S.~C}%
+Columbus, Ohio  & $39°$ & $57'$ & $40''$ N & $82°$ & $59'$ & $40''$ W \\
+Concord, N.~H.  & $43°$ & $11'$ & $48''$ N & $71°$ & $32'$ & $30''$ W \\
+\index{Concord, N.~H.}%
+Deadwood, S.~D., P.~O.  & $44°$ & $22'$ & $34''$ N & $103°$ & $43'$ & $19''$ W \\
+\index{Deadwood, S.~D.}%
+Denver, Col., O.  & $39°$ & $40'$ & $36''$ N & $104°$ & $59'$ & $23''$ W \\
+\index{Denver, Col.}%
+Des Moines, Iowa  & $41°$ & $35'$ & $08''$ N & $93°$ & $37'$ & $30''$ W \\
+\index{Iowa}%
+Detroit, Mich.  & $42°$ & $20'$ & $00''$ N & $83°$ & $02'$ & $54''$ W \\
+\index{Detroit, Mich.}%
+Duluth, Minn.  & $46°$ & $48'$ & $00''$ N & $92°$ & $06'$ & $10''$ W \\
+\index{Duluth, Minn.}%
+Erie, Pa., Waterworks  & $42°$ & $07'$ & $53''$ N & $80°$ & $05'$ & $51''$ W \\
+\index{Erie, Pa.}%
+Fargo, N.~D., Agri.~College & $46°$ & $52'$ & $04''$ N & $96°$ & $47'$ & $11''$ W \\
+\index{Fargo, N.~D.}%
+Galveston, Tex., C.  & $29°$ & $18'$ & $17''$ N & $94°$ & $47'$ & $26''$ W \\
+\index{Galveston, Tex.}%
+Guthrie, Okla.  & $35°$ & $51'$ & $48''$ N & $100°$ & $26'$ & $24''$ W \\
+Hartford, Conn.  & $41°$ & $45'$ & $59''$ N & $72°$ & $40'$ & $45''$ W \\
+\index{Hartford, Conn.}%
+Helena, Mont.  & $46°$ & $35'$ & $36''$ N & $111°$ & $52'$ & $45''$ W \\
+\index{Helena, Mont.}%
+Honolulu, Sandwich Islands & $21°$ & $18'$ & $12''$ N & $157°$ & $51'$ & $34''$ W \\
+Indianapolis, Ind.  & $39°$ & $47'$ & $00''$ N & $86°$ & $05'$ & $00''$ W \\
+\index{Indianapolis, Ind.}%
+Jackson, Miss.  & $31°$ & $16'$ & $00''$ N & $91°$ & $36'$ & $18''$ W \\
+\index{Jackson, Miss.}%
+Jacksonville, Fla., M.~E. Ch. & $30°$ & $19'$ & $43''$ N & $81°$ & $39'$ & $14''$ W \\
+\index{Jacksonville, Fla.}%
+Kansas City, Mo.  & $39°$ & $06'$ & $08''$ N & $94°$ & $35'$ & $19''$ W \\
+\index{Kansas City, Mo.}%
+Key West, Fla., Light House & $24°$ & $32'$ & $58''$ N & $81°$ & $48'$ & $04''$ W \\
+\index{Key West, Fla.}%
+Lansing, Mich., Capitol  & $42°$ & $43'$ & $56''$ N & $84°$ & $33'$ & $23''$ W \\
+\index{Lansing, Mich.}%
+Lexington, Ky., Univ. & $38°$ & $02'$ & $25''$ N & $84°$ & $30'$ & $21''$ W \\
+\index{Lexington, Ky.}%
+Lincoln, Neb.  & $40°$ & $55'$ & $00''$ N & $96°$ & $52'$ & $00''$ W \\
+\index{Lincoln, Neb.}%
+Little Rock, Ark.  & $34°$ & $40'$ & $00''$ N & $92°$ & $12'$ & $00''$ W \\
+\index{Little Rock, Ark.}%
+Los Angeles, Cal., Ct.~House & $34°$ & $03'$ & $05''$ N & $118°$ & $14'$ & $32''$ W \\
+Louisville, Ky.  & $38°$ & $15'$ & $08''$ N & $85°$ & $45'$ & $29''$ W \\
+\index{Louisville, Ky.}%
+Lowell, Mass.  & $42°$ & $22'$ & $00''$ N & $71°$ & $04'$ & $00''$ W \\
+\index{Lowell, Mass.}%
+Madison, Wis., O. & $43°$ & $04'$ & $37''$ N & $89°$ & $24'$ & $27''$ W \\
+\index{Madison, Wis.}%
+Manila, Luzon, C.  & $14°$ & $35'$ & $31''$ N & $120°$ & $58'$ & $03''$ E \\
+\index{Luzon}%
+Memphis, Tenn.  & $35°$ & $08'$ & $38''$ N & $90°$ & $03'$ & $00''$ W \\
+\index{Memphis, Tenn.}%
+Milwaukee, Wis., Ct.~House & $43°$ & $02'$ & $32''$ N & $87°$ & $54'$ & $18''$ W \\
+\index{Milwaukee, Wis.}%
+Minneapolis, Minn., O. & $44°$ & $58'$ & $38''$ N & $93°$ & $14'$ & $02''$ W \\
+\index{Minneapolis, Minn.}%
+Mitchell, S.~D.  & $43°$ & $49'$ & $00''$ N & $98°$ & $00'$ & $14''$ W \\
+\index{Mitchell, S.~D.}%
+Mobile, Ala., Epis.~Church  & $30°$ & $41'$ & $26''$ N & $88°$ & $02'$ & $28''$ W \\
+\index{Mobile, Ala.}%
+Montgomery, Ala.  & $32°$ & $22'$ & $46''$ N & $86°$ & $17'$ & $57''$ W \\
+\index{Montgomery, Ala.}%
+Nashville, Tenn., O.  & $36°$ & $08'$ & $54''$ N & $86°$ & $48'$ & $00''$ W \\
+\index{Nashville, Tenn.}%
+Newark, N.~J., M.~E.~Ch. & $40°$ & $44'$ & $06''$ N & $74°$ & $10'$ & $12''$ W \\
+\index{Newark, N.~J.}%
+New Haven, Conn., Yale.  & $41°$ & $18'$ & $28''$ N & $72°$ & $55'$ & $45''$ W \\
+\index{New Haven, Conn.}%
+New Orleans, La., Mint  & $29°$ & $57'$ & $46''$ N & $90°$ & $03'$ & $28''$ W \\
+\index{New Orleans, La.}%
+New York, N.~Y., City Hall & $40°$ & $42'$ & $44''$ N & $74°$ & $00'$ & $24''$ W \\
+Northfield, Minn., O.  & $44°$ & $27'$ & $42''$ N & $93°$ & $08'$ & $57''$ W \\
+\index{Northfield, Minn.}%
+%% -----File: 090.png---Folio 91-------
+\index{California}%
+\index{District of Columbia}%
+\index{Florida}%
+\index{Georgia}%
+\index{Minnesota}%
+\index{Missouri}%
+\index{Nebraska}%
+\index{Nevada}%
+\index{Newark, N.~J.}%
+\index{New Jersey}%
+\index{New Mexico}%
+\index{North Carolina}%
+\index{Oregon}%
+\index{Pago Pago@Pago Pago (pron.\;pango,\;pango), Samoa}%
+\index{Pittsburg, Pa.}%
+\index{Providence, R.~I.}%
+\index{Rhode Island}%
+\index{Sacramento, Calif.}%
+\index{San Francisco, Calif.}%
+\index{West Virginia}%
+Ogden, Utah, O.   & $41°$ & $13'$ & $08''$ N & $111°$ & $59'$ & $45''$ W \\
+\index{Ogden, Utah}%
+\index{Utah}%
+Olympia, Wash.   & $47°$ & $03'$ & $00''$ N & $122°$ & $57'$ & $00''$ W \\
+\index{Olympia, Wash.}%
+Omaha, Neb.   & $41°$ & $16'$ & $50''$ N & $95°$ & $57'$ & $33''$ W \\
+\index{Omaha, Neb.}%
+Pago Pago, Samoa   & $14°$ & $18'$ & $06''$ S & $170°$ & $42'$ & $31''$ W \\
+\index{Samoa}%
+Philadelphia, Pa., State House  & $39°$ & $56'$ & $53''$ N & $75°$ & $09'$ & $03''$ W \\
+\index{Philadelphia, Pa.}%
+Pierre, S.~D., Capitol.   & $44°$ & $22'$ & $50''$ N & $100°$ & $20'$ & $26''$ W \\
+\index{Pierre, S.~D.}%
+Pittsburg, Pa.   & $40°$ & $26'$ & $34''$ N & $80°$ & $02'$ & $38''$ W \\
+Point Barrow (highest latitude
+\index{Point Barrow}%
+in the United States)  & $71°$ & $27'$ & $00''$ N & $156°$ & $15'$ & $00''$ W \\
+Portland, Ore.   & $45°$ & $30'$ & $00''$ N & $122°$ & $40'$ & $30''$ W \\
+\index{Portland, Ore.}%
+Princeton, N.~J., O.   & $40°$ & $20'$ & $58''$ N & $74°$ & $39'$ & $24''$ W \\
+\index{Princeton, N.~J.}%
+Providence, R.~I., Unit.~Ch.  & $41°$ & $49'$ & $28''$ N & $71°$ & $24'$ & $20''$ W \\
+Raleigh, N.~C.   & $35°$ & $47'$ & $00''$ N & $78°$ & $40'$ & $00''$ W \\
+\index{Raleigh, N.~C.}%
+Richmond, Va., Capitol    & $37°$ & $32'$ & $19''$ N & $77°$ & $27'$ & $02''$ W \\
+\index{Richmond, Va.}%
+Rochester, N.~Y., O.   & $43°$ & $09'$ & $17''$ N & $77°$ & $35'$ & $27''$ W \\
+\index{Rochester, N.~Y.}%
+Sacramento, Cal.  & $38°$ & $33'$ & $38''$ N & $121°$ & $26'$ & $00''$ W \\
+St.~Louis, Mo.   & $38°$ & $38'$ & $04''$ N & $90°$ & $12'$ & $16''$ W \\
+\index{St.~Louis, Mo.}%
+St.~Paul, Minn.   & $44°$ & $52'$ & $56''$ N & $93°$ & $05'$ & $00''$ W \\
+\index{St.~Paul, Minn.}%
+San Francisco, Cal., C.~S.~Sta.  & $37°$ & $47'$ & $55''$ N & $122°$ & $24'$ & $32''$ W \\
+San Juan, Porto Rico, Morro
+\index{Porto Rico}%
+\index{San Juan, Porto Rico}%
+Light House   & $18°$ & $28'$ & $56''$ N & $66°$ & $07'$ & $28''$ W \\
+Santa Fe, N.~M.   & $35°$ & $41'$ & $19''$ N & $105°$ & $56'$ & $45''$ W \\
+\index{Santa Fe, N.~M.}%
+Savannah, Ga., Exchange   & $32°$ & $04'$ & $52''$ N & $81°$ & $05'$ & $26''$ W \\
+\index{Savannah, Ga.}%
+Seattle, Wash., C.~S.~Ast.~Sta.  & $47°$ & $35'$ & $54''$ N & $122°$ & $19'$ & $59''$ W \\
+\index{Seattle, Wash.}%
+Sitka, Alaska, Parade Ground  & $57°$ & $02'$ & $52''$ N & $135°$ & $19'$ & $31''$ W \\
+\index{Alaska}%
+\index{Sitka, Alaska}%
+Tallahassee, Fla.   & $30°$ & $25'$ & $00''$ N & $84°$ & $18'$ & $00''$ W \\
+\index{Tallahassee, Fla.}%
+Trenton, N.~J. Capitol   & $40°$ & $13'$ & $14''$ N & $74°$ & $46'$ & $13''$ W \\
+\index{Trenton, N.~J.}%
+Virginia City, Nev.   & $39°$ & $17'$ & $36''$ N & $119°$ & $39'$ & $06''$ W \\
+\index{Virginia City, Nev.}%
+\index{Virginia}%
+Washington, D.~C., O.   & $38°$ & $53'$ & $39''$ N & $77°$ & $03'$ & $06''$ W \\
+\index{Washington}%
+\index{Washington, D.~C.}%
+Wheeling, W.~Va.   & $40°$ & $05'$ & $16''$ N & $80°$ & $44'$ & $30''$ W \\
+\index{Wheeling, W.~Va.}%
+Wilmington, Del., Town Hall  & $39°$ & $44'$ & $27''$ N & $75°$ & $33'$ & $03''$ W \\
+\index{Wilmington, Del.}%
+\index{Winona, Minn.}Winona, Minn.   & $44°$ & $04'$ & $00''$ N & $91°$ & $30'$ & $00''$ W \tablespacerbot\\\hline
+\end{longtable}
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England|)}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!of principal cities|)}%
+\index{Longitude@Longitude \indexglossref{Longitude}!and time|)}%
+\index{Longitude@Longitude \indexglossref{Longitude}!of principal cities|)}%
+\index{New York|)}%
+\index{South Dakota|)}%
+}% end \smallsize
+%% -----File: 091.png---Folio 92-------
+
+\Chapter{V}{Circumnavigation and Time}
+
+\Paragraph{Magellan's Fleet.} When the sole surviving ship of
+\index{Magellan's fleet}%
+Magellan's fleet returned to Spain in~1522 after having
+\index{Spain}%
+circumnavigated the globe, it is said that the crew were
+greatly astonished that their calendar and that of the
+Spaniards did not correspond. They landed, according to
+their own reckoning, on September~6, but were told it was
+September~7\@. At first they thought they had made a mistake,
+and some time elapsed before they realized that they
+had lost a day by going around the world with the sun.
+Had they traveled toward the east, they would have
+gained a day, and would have recorded the same date as
+September~8.
+
+\begin{quote}
+\smallsize
+``My pilot is dead of scurvy: may \\
+I ask the longitude, time and day?'' \\
+The first two given and compared; \\
+The third,---the commandante stared! \\
+\\
+``The \emph{first} of June? I make it second,''\\
+Said the stranger, ``Then you've wrongly reckoned!''
+
+\index{Harte, Bret}%
+\hspace{4em}---\textsc{Bret Harte}, in \textit{The Lost Galleon}.
+\end{quote}
+
+The explanation of this phenomenon is simple. In
+traveling westward, in the same way with the sun, one's
+days are lengthened as compared with the day at any
+fixed place. When one has traveled~$15°$ westward, at whatever
+rate of speed, he finds his watch is one hour behind
+the time at his starting point, if he changes it according
+to the sun. He has thus lost an hour as compared with
+%% -----File: 092.png---Folio 93-------
+the time at his starting point. After he has traveled~$15°$
+farther, he will set his watch back two hours and thus
+record a loss of two hours. And so it continues throughout
+the twenty-four belts of~$15°$ each, losing one hour in
+each belt; by the time he arrives at his starting point
+again, he has set his hour hand back twenty-four hours
+and has lost a day.
+
+\includegraphicsmid{i092}{Fig.~30}
+
+{% adjust margin round wrapfig to squeeze image onto page
+\setlength\intextsep{0pt}
+\Paragraph{Westward Travel---Days are Lengthened.} To make this
+\index{London, England|(}%
+clearer, let us suppose a traveler starts from London Monday
+noon, January~1st, traveling westward~$15°$ each day.
+On Tuesday, when he finds he is~$15°$ west of London, he
+sets his watch back an hour. It is then noon by the sun
+where he is.
+\includegraphicsright{i094}{Fig. 31} %[**TN: inserted mid-paragraph - may need fixing if pagination changed]
+He says, ``I left Monday noon, it is now
+%% -----File: 093.png---Folio 94-------
+Tuesday noon; therefore I have been out one day.'' The
+tower clock at London and his chronometer set with it,
+however, indicate a different view. They say it is Tuesday,
+1~o'clock, \PM, and he has been out a day and an hour.
+The next day the process is repeated. The traveler having
+covered another space of $15°$ westward, sets his watch
+back a second hour and says, ``It is Wednesday noon and
+I have been out just two days.'' The London clock, however,
+says Wednesday,~2 o'clock, \PM---two days and
+two hours since he left. The third day this occurs again,
+the traveler losing a third hour; and what to him seems
+three days, Monday noon to Thursday noon, is in reality
+by London time three days and three hours.
+Each of his days is really a little more than twenty-four hours long,
+for he is going with the sun. By the time he arrives at
+London again he finds what to him was twenty-four days
+is, in reality, twenty-five days, for he has set his watch
+back an hour each day for twenty-four days, or an entire
+day. To have his calendar correct, he must omit a day,
+that is, move the date ahead one day to make up the date
+lost from his reckoning. It is obvious that this will be
+true whatever the rate of travel, and the day can be omitted
+from his calendar anywhere in the journey and the error
+corrected.
+
+\Paragraph{Eastward Travel---Days are Shortened.} Had our traveler
+gone eastward, when he had covered $15°$ of longitude
+he would set his watch ahead one hour and then say,
+``It is now Tuesday noon. I have been out one day.''
+The London clock would indicate~11 o'clock, \AM, of
+Tuesday, and thus say his day had but twenty-three
+hours in it, the traveler having moved the hour hand
+ahead one space. He has gained one hour. The second
+day he would gain another hour, and by the time he arrived
+%% -----File: 094.png---Folio 95-------
+at London again, he would
+have set his hour hand ahead
+twenty-four hours or one
+full day. To correct his calendar,
+somewhere on his voyage
+he would have to repeat
+a day.
+
+\Paragraph{The International Date
+Line.} It is obvious from
+\index{International date line@International date line\phantomsection\label{idx:idl}}%
+the foregoing explanation
+that somewhere and sometime
+in circumnavigation, a
+day must be omitted in traveling
+westward and a day
+repeated in traveling eastward.
+Where and when the
+change is made is a mere
+matter of convenience. The
+theoretical location of the
+date line commonly used is
+the~180th meridian. This
+\index{Meridian|(}%
+line where a traveler's calendar
+needs changing varies
+as do the boundaries of the
+standard time belts and for
+the same reason. While
+the change could be made
+at any particular point on
+a parallel, it would make a
+serious inconvenience were
+the change made in some
+places. Imagine, for example,
+the~90th meridian,
+%% -----File: 095.png---Folio 96-------
+west of Greenwich, to be the line used. When it was
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+Sunday in Chicago, New York, and other eastern points,
+\index{Chicago, Ill.}%
+\index{New York}%
+it would be Monday in St.~Paul, Kansas City, and western
+\index{St.~Paul, Minn.}%
+\index{Kansas City, Mo.}%
+points. A traveler leaving Minneapolis on Sunday night
+\index{Minneapolis, Minn.}%
+would arrive in Chicago on Sunday morning and thus
+have two Sundays on successive days. Our national holidays
+and elections would then occur on different days
+in different parts of the country. To reduce to the
+minimum such inconveniences as necessarily attend changing
+one's calendar, the change is made where there is a
+relatively small amount of travel, away out in the Pacific
+\index{Pacific Ocean}%
+Ocean. Going westward across this line one must set his
+calendar ahead a day; going eastward, back a day.
+} %end scope for adjusting wrapfig parameters
+
+\sloppy
+As shown in Figures~\figureref{i094}{31} and~\figureref{i099}{32}, this line begins on the~180th
+meridian far to the north, sweeps to the eastward
+around Cape Deshnef, Russia, then westward beyond the~180th
+\index{Cape Deshnef, Siberia}%
+\index{Deshnef, Cape}%
+\index{Russia}%
+meridian seven degrees that the Aleutian islands
+\index{Aleutian Is.}%
+may be to the east of it and have the same day as
+continental United States; then the line extends to the
+180th meridian which it follows southward, sweeping
+somewhat eastward to give the Fiji and Chatham islands
+\index{Fiji Islands}%
+\index{Chatham Islands}%
+the same day as Australia and New Zealand. The following
+\index{Australia}%
+\index{New Zealand}%
+is a letter, by C.~B.~T. Moore, commander, U.~S.~N.,
+\index{Moore, C. B. T.}%
+Governor of Tutuila, relative to the accuracy of the map
+\index{Tutuila@Tutuila (too\;tw\={e}$'$lä), Samoa}%
+in this book:
+
+\fussy
+\begin{SmallText}
+\hfill\textit{Pago-Pago, Samoa}, December~1, 1906.\hspace*{2em}
+\index{Pago Pago@Pago Pago (pron.\;pango,\;pango), Samoa}%
+\index{Samoa}%
+
+\smallskip\textsc{Dear Sir:}---The map of your Mathematical Geography is
+correct in placing Samoa to the east of the international date line.
+The older geographies were also right in placing these islands west
+of the international date line, because they used to keep the same date
+as Australia and New Zealand, which are west of the international
+date line.
+
+The reason for this mistake is that when the London Missionary
+Society sent its missionaries to Samoa they were not acquainted with
+\index{London, England|)}%
+%% -----File: 096.png---Folio 97-------
+the trick of changing the date at the 180th~meridian, and so carried
+into Samoa, which was east of the date line, the date they brought
+\index{Samoa}%
+with them, which was, of course, one day ahead.
+
+This false date was in force at the time of my first visit to Samoa,
+in 1889. While I have no record to show when the date was
+corrected, I believe that it was corrected at the time of the annexation
+of the Samoan Islands by the United States and by Germany.
+\index{Germany}%
+\index{United States}%
+The date in Samoa is, therefore, the same date as in the United
+States, and is one day behind what it is in Australia and New Zealand;
+\index{Australia}%
+\index{New Zealand}%
+
+Example: To-day is the 2d~day of December in Auckland, and the
+\index{Auckland, New Zealand}%
+1st~day of December in Tutuila.
+\index{Tutuila@Tutuila (too\;tw\={e}$'$lä), Samoa}%
+
+\hfill Very respectfully, \qquad\qquad \textsc{C.~B.~T. Moore}, \hspace*{2em}
+
+\hfill \textit{Commander, U.~S. Navy,}
+
+\hfill \textit{Governor.}
+
+\medskip
+
+\noindent \textsc{Mr.~Willis~E. Johnson}, \\
+\indent\textit{Vice President Northern Normal and Industrial School,}\\
+\indent\indent\textit{Aberdeen, South Dakota.}
+\end{SmallText}
+
+``It is fortunate that the 180th~meridian falls where
+it does. From Siberia to the Antarctic continent this
+\index{Siberia}%
+imaginary line traverses nothing but water. The only
+land which it passes at all near is one of the archipelagoes
+of the south Pacific; and there it divides but a handful of
+\index{Pacific Ocean}%
+volcanoes and coral reefs from the main group. These
+islands are even more unimportant to the world than
+insignificant in size. Those who tenant them are few,
+and those who are bound to these few still fewer\dots.
+There, though time flows ceaselessly on, occurs that
+unnatural yet unavoidable jump of twenty-four hours;
+and no one is there to be startled by the fact,---no one to
+be perplexed in trying to reconcile the two incongruities,
+continuous time and discontinuous day. There is nothing
+but the ocean, and that is tenantless\dots. Most fortunate
+was it, indeed, that opposite the spot where man was most
+destined to think there should have been placed so little
+\index{Chosön, Land of the Morning Calm (Korea)}%
+\index{Lowell, Percival}%
+to think about.''\footnote
+  {From \textit{Chosön}, by Percival Lowell.}
+%% -----File: 097.png---Folio 98-------
+
+\Paragraph{Where Days Begin.} When it is~11:30 o'clock, \PM, on
+Saturday at Denver, it is~1:30 o'clock, \AM, Sunday, at
+\index{Denver, Col.}%
+New York, It is thus evident that parts of two days
+\index{New York}%
+exist at the same time on the earth. Were one to travel
+around the earth with the sun and as rapidly it would be
+perpetually noon. When he has gone around once, one
+day has passed. Where did that day begin? Or, suppose
+we wished to be the first on earth to hail the new
+year, where could we go to do so? The midnight line,
+just opposite the sun, is constantly bringing a new day
+somewhere. Midnight ushers in the new year at Chicago.
+\index{Chicago, Ill.}%
+Previous to this it was begun at New York. Still east
+of this, New Year's Day began some time before. If we
+keep going around eastward we must surely come to
+some place where New Year's Day was first counted, or we
+shall get entirely around to New York and find that the
+New Year's Day began the day before, and this midnight
+would commence it again. As previously stated, the date
+line commonly accepted nearly coincides with the~180th
+meridian. Here it is that New Year's Day first dawns
+and each new day begins.
+
+\Paragraph{The Total Duration of a Day.} While a day at any
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!total duration of a}%
+particular place is twenty-four hours long, each day lasts
+on earth at least forty-eight hours. Any given day, say
+Christmas, is first counted as that day just west of the
+date line. An hour later Christmas begins~$15°$ west of
+that line, two hours later it begins~$30°$ west of it, and so on
+around the globe. The people just west of the date line
+who first hailed Christmas have enjoyed twelve hours of
+it when it begins in England, eighteen hours of it when
+\index{England}%
+it begins in central United States, and twenty-four hours
+\index{United States}%
+of it, or the whole day, when it begins in western Alaska,
+\index{Alaska}%
+just east of the date line. Christmas, then, has existed
+%% -----File: 098.png---Folio 99-------
+twenty-four hours on the globe, but having just begun in
+western Alaska, it will tarry twenty-four hours longer
+among mankind, making forty-eight hours that the day
+blesses the earth.
+
+If the date line followed the meridian~$180°$ without
+any variation, the total duration of a day would be exactly
+forty-eight hours as just explained. But that line is quite
+irregular, as previously described and as shown on the
+map. Because of this irregularity of the date line the
+same day lasts somewhere on earth over \emph{forty-nine hours}.
+Suppose we start at Cape Deshnef, Siberia, longitude~$169°$
+\index{Deshnef, Cape}%
+\index{Cape Deshnef, Siberia}%
+\index{Siberia}%
+West, a moment after midnight of the~3d of July. The~4th
+of July has begun, and, as midnight sweeps around
+westward, successive places see the beginning of this day.
+When it is the~4th in London it has been the~4th at
+\index{London, England}%
+Cape Deshnef twelve hours and forty-four minutes. When
+the glorious day arrives at New York, it has been seventeen
+\index{New York}%
+hours and forty-four minutes since it began at Cape
+Deshnef. When it reaches our most western point on this
+continent, Attu Island,~$173°$~E., it has been twenty-five
+\index{Attu Island}%
+hours and twelve minutes since it began at Cape Deshnef.
+Since it will last twenty-four hours at Attu Island, forty-nine
+hours and twelve minutes will have elapsed since the
+beginning of the day until the moment when all places
+on earth cease to count it that day.
+
+\includegraphicsmid{i099}{Fig.~32}
+
+\Paragraph{When Three Days Coëxist.} Portions of three days
+exist at the same time between~11:30 o'clock,~\AM, and
+12:30~o'clock, \PM, London time. When it is Monday
+noon at London, Tuesday has begun at Cape Deshnef,
+but Monday morning has not yet dawned at Attu Island;
+nearly half an hour of Sunday still remains there.
+
+\Paragraph{Confusion of Travelers.} Many stories are told of the
+confusion to travelers who pass from places reckoning
+%% -----File: 099.png---Folio 100-------
+one day across this line, to places having a different day.
+``If it is such a deadly sin to work on Sunday, one or the
+other of Mr.~A and Mr.~B coming one from the east,
+the other from the west of the~180th meridian, must, if
+\index{Meridian|)}%
+he continues his daily vocations, be in a bad way. Some
+of our people in the Fiji are in this unenviable position,
+\index{Fiji Islands}%
+as the line~$180°$ passes through Loma-Loma. I went
+from Fiji to Tonga in Her Majesty's ship \emph{Nymph} and
+\index{Tonga Is.}%
+arrived at our destination on Sunday, according to our
+reckoning from Fiji, but on Saturday, according to the
+proper computation west from Greenwich. We, however,
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+found the natives all keeping Sunday. On my asking
+the missionaries about it they told me that the missionaries
+to that group and Samoa having come from
+\index{Samoa}%
+%% -----File: 100.png---Folio 101-------
+the westward, had determined to observe their Sabbath
+day, as usual, so as not to subject the natives to any
+puzzle, and agreed to put the dividing line farther off,
+between them and Hawaii, somewhere in the broad ocean
+\index{Hawaiian (Sandwich) Islands}%
+where no metaphysical natives or `intelligent' Zulus
+could cross-question them.''\footnote{Mr. E. L. Layard, at the British Consulate, Noumea, New Caledonia,
+\index{Layard, E. L.}%
+\index{New Caledonia}%
+\index{Noumea, New Caledonia}%
+as quoted in a pamphlet on the International Date Line by
+\index{Collins, Henry}%
+Henry Collins.}
+
+``A party of missionaries bound from China, sailing
+\index{China}%
+west, and nearing the line without their knowledge, on
+Saturday posted a notice in the cabin announcing that
+`To-morrow being Sunday there will be services in this
+cabin at 10 \AM' The following morning at 9, the captain
+tacked up a notice declaring that `This being Monday
+there will be no services in this cabin this morning.'"
+
+{\nbstretchyspace%
+It should be remembered that this line, called ``international,''}
+\index{International date line@International date line\phantomsection\label{idx:idl}}%
+has not been adopted by all nations as a hard
+and fast line, making it absolutely necessary to change
+the date the moment it is crossed. A ship sailing, say,
+from Honolulu, which has the same day as North America
+\index{Honolulu, Hawaiian Islands}%
+\index{North America}%
+and Europe, to Manila or Hongkong, having a day later,
+\index{Europe}%
+\index{Manila, Philippine Is.|(}%
+\index{Manila, Philippine Is.!change of date at}%
+\index{Philippine Is.}%
+may make the change in date at any time between these
+distant points; and since several days elapse in the passage,
+the change is usually made so as to have neither
+two Sundays in one week nor a week without a Sunday.
+Just as the traveler in the United States going from a
+\index{United States|(}%
+place having one time standard to a place having a different
+one would find it necessary to change his watch
+but could make the change at any time, so one passing
+from a place having one day to one reckoning another,
+could suit his convenience as to the precise spot where
+he make the change. This statement needs only the
+%% -----File: 101.png---Folio 102-------
+modification that as all events on a ship must be regulated
+by a common timepiece, changed according to
+longitude, so the community on board in order to adjust
+to a common calendar must accept the change when made
+by the captain.
+
+\Paragraph{Origin and Change of Date Line.} The origin of this
+line is of considerable interest. The day adopted in any
+region depended upon the direction from which the
+people came who settled the country. For example,
+people who went to Australia, Hongkong, and other English
+\index{Australia}%
+\index{Hongkong}%
+possessions in the Orient traveled around Africa or
+\index{Africa}%
+across the Mediterranean. They thus set their watches
+\index{Mediterranean}%
+ahead an hour for every~$15°$. ``For two centuries after
+the Spanish settlement the trade of Manila with the
+western world was carried on \emph{via} Acapulco and Mexico''
+\index{Acapulco, Mexico}%
+\index{Mexico}%
+(Ency.\ Brit.). Thus the time which obtained in the
+\index{Encyclopaedia Britannica}%
+Philippines was found by setting watches backwards an
+\index{Philippine Is.}%
+hour for every $15°$, and so it came about that the calendar
+of the Philippines was a day earlier than that of Australia,
+Hongkong, etc. The date line at that time was very indefinite
+and irregular. In~1845 by a decree of the Bishop of
+Manila, who was also Governor-General, Tuesday, December~31,
+was stricken from the calendar; the day after
+Monday, December~30, was Wednesday, January~1, 1846.
+This cutting the year to~364 days and the week to~6 days
+gave the Philippines the same day as other Asiatic places,
+and shifted the date line to the east of that archipelago.
+Had this change never been made, all of the possessions
+of the United States would have the same day.
+
+For some time after the acquisition of Alaska the people
+\index{Alaska}%
+living there, formerly citizens of Russia, used the day later
+\index{Russia}%
+than ours, and also used the Russian or Julian calendar,
+twelve days later than ours. As people moved there from
+%% -----File: 102.png---Folio 103-------
+the United States, our system gradually was extended, but
+\index{United States|)}%
+for a time both systems were in vogue. This made affairs
+confusing, some keeping Sunday when others reckoned the
+same day as Saturday and counted it as twelve days later
+in the calendar, New Year's Day, Christmas, etc., coming
+at different times. Soon, however, the American system
+prevailed to the entire exclusion of the Russian, the
+inhabitants repeating a day, and thus having eight days
+in one week. While the Russians in their churches in
+Alaska are celebrating the Holy Mass on our Sunday,
+\index{Alaska}%
+their brethren in Siberia, not far away, and in other parts
+\index{Siberia}%
+of Russia, are busy with Monday's duties.
+\index{Russia}%
+
+\begin{SmallText}
+\Paragraph{\smallsize Date Line East of Fiji Islands.} Fiji, No~XIV, 1879: An ordinance
+\index{Fiji Islands}%
+enacted by the governor of the colony of Fiji, with the advice
+and consent of the legislative council thereof, to provide for a universal
+day throughout the colony.
+
+\emph{Whereas}, according to the ordinary rule of noting time, any given
+time would in that part of the colony lying to the east of the meridian
+of~$180°$ from Greenwich be noted as of a day of the week and month
+different from the day by which the same time would be noted in the
+part of the colony lying to the west of such meridian; and
+
+\emph{Whereas}, by custom the ordinary rule has been set aside and time
+has been noted throughout the colony as though the whole were situated
+to the west of such meridian; and
+
+\emph{Whereas}, in order to preclude uncertainty for the future it is expedient
+that the above custom should be legalized; therefore
+
+\hangindent2\parindent\hspace{.5\parindent}\emph{Be it enacted by the governor, with the advice and consent of the
+legislative council, as follows:}
+
+Time in this colony shall be noted as if the whole colony were
+situated to the west of the meridian of $180°$ from Greenwich.
+
+(\emph{Exempli gratia}---To-day, which according to the ordinary rule
+for noting time is on the island of Ovalau the~5th day of June, and
+on the island of Vanua-Balevu the~4th day of June, would by this
+ordinance be deemed as the~5th day of June,~1879, in the whole
+colony.)
+
+\Paragraph{\smallsize Problem.} Assuming it was 5~\AM, Sunday, May~1, 1898, when the
+naval battle of Manila began, what time was it in Milwaukee, the city
+\index{Milwaukee, Wis.}%
+\index{Wisconsin}%
+using standard time and Dewey using the local time of $120°$ east?
+\index{Dewey, George}%
+\end{SmallText}
+\index{Manila, Philippine Is.|)}%
+%% -----File: 103.png---Folio 104-------
+
+\Chapter{VI}{The Earth's Revolution}
+
+\Section{Proofs of Revolution}
+\index{Proofs, form of earth!revolution of earth|(}%
+\index{Revolution@Revolution \indexglossref{Revolution}|(}%
+
+\First{For} at least~2400 years the theory of the revolution
+of the earth around the sun has been advocated, but only
+in modern times has the fact been demonstrated beyond
+successful contradiction. The proofs rest upon three sets
+of astronomical observations, all of which are of a delicate
+and abstruse character, although the underlying principles
+are easily understood.
+
+\Paragraph{Aberration of Light.}\nblabel{page:104} When rain is falling on a calm day
+\index{Aberration of light@Aberration of light \indexglossref{Aberration}|(}%
+the drops will strike the top of one's head if he is standing
+still in the rain; but if one moves, the direction of the
+drops will seem to have changed, striking one in the face
+more and more as the speed is increased (Fig.~\figureref{i104}{33}). Now
+light rays from the sun, a star, or other heavenly body,
+strike the earth somewhat slantingly, because the earth is
+moving around the sun at the rate of over a thousand
+miles per minute. Because of this fact the astronomer
+must tip his telescope slightly to the east of a star in order
+to see it when the earth is in one side of its orbit, and to
+the west of it when in the opposite side of the orbit. The
+necessity of this tipping of the telescope will be apparent
+if we imagine the rays passing through the telescope are
+like raindrops falling through a tube. If the tube is carried
+forward swiftly enough the drops will strike the sides
+of the tube, and in order that they may pass directly
+through it, the tube must be tilted forward somewhat,
+%% -----File: 104.png---Folio 105-------
+the amount varying with (\emph{a})~the rate of its onward motion,
+and (\emph{b})~the rate at which the raindrops are falling.
+
+Since the telescope must at one time be tilted one way
+to see a star and at another season tilted an equal amount
+in the opposite direction, each star thus seems to move
+about in a tiny orbit, varying from a circle to a straight
+line, depending upon the position of the star, but in every
+case the major axis is~$41''$, or twice the greatest angle at
+which the telescope must be tilted forward.
+
+\includegraphicsmid{i104}{Fig.~33}
+
+Each of the millions of stars has its own apparent aberrational
+orbit, no two being exactly alike in form, unless
+the two chance to be exactly the same distance from the
+plane of the earth's orbit. Assuming that the earth
+%% -----File: 105.png---Folio 106-------
+revolves around the sun, the precise form of this aberrational
+orbit of any star can be calculated, and observation
+invariably confirms the calculation. Rational minds cannot
+conceive that the millions of stars, at varying distances,
+can all actually have these peculiar annual motions,
+six months toward the earth and six months from it, in
+addition to the other motions which many of them (and
+probably all of them, see p.~\pageref{page:265b}) have. The discovery %[**TN: 'pp.265-267' in original text]
+and explanation of these facts in~1727 by James
+\index{Bradley, James}%
+Bradley (see p.~\pageref{page:278}), the English Astronomer Royal, forever
+put at rest all disputes as to the revolution of the earth.
+\index{Aberration of light@Aberration of light \indexglossref{Aberration}|)}%
+
+\Paragraph{Motion in the Line of Sight.} If you have stood near by
+\index{Motion in the line of sight|(}%
+when a swiftly moving train passed with its bell ringing,
+you may have noticed a sudden change in the tone of the
+bell; it rings a lower note immediately upon passing. The
+pitch of a note depends upon the rate at which the sound
+waves strike the ear; the more rapid they are, the higher
+is the pitch. Imagine a boy throwing chips\footnote{This illustration is adapted from Todd's New Astronomy, p.~432.} into a river
+\index{Todd, David}%
+at a uniform rate while walking down stream toward a
+bridge and then while walking upstream away from the
+bridge. The chips will be closer together as they pass
+under the bridge when the boy is walking toward it than
+when he is walking away from it. In a similar way the
+sound waves from the bell of the rapidly approaching
+locomotive accumulate upon the ear of the listener, and
+the pitch is higher than it would be if the train were stationary,
+and after the train passes the sound waves will be
+farther apart, as observed by the same person, who will
+hear a lower note in consequence.
+
+\Subparagraph{Color varies with Rate of Vibration.} Now in a precisely
+\index{Vibrations, color}%
+\index{Color vibrations}%
+similar manner the colors in a ray of light vary in the rate
+%% -----File: 106.png---Folio 107-------
+\index{Color vibrations}%
+\index{Vibrations, color}%
+of vibration. The violet is the most rapid,\footnote
+  {The rate of vibration per second for each of the colors in a ray
+  of light is as follows:
+  \begin{center}
+  \begin{tabular}{p{0.2\textwidth}@{}p{0.2\textwidth}p{0.2\textwidth}@{}p{0.2\textwidth}}
+  Violet\dotfill & $756.0 × 10^{12}$ & Yellow\dotfill & $508.8 × 10^{12}$ \\
+  Indigo\dotfill & $698.8 × 10^{12}$ & Orange\dotfill & $457.1 × 10^{12}$ \\
+  Blue\dotfill   & $617.1 × 10^{12}$ & Red\dotfill    & $393.6 × 10^{12}$ \\
+  Green\dotfill  & $569.2 × 10^{12}$ &                &
+  \end{tabular}
+  \end{center}
+  Thus the violet color has $756.0$~millions of millions of vibrations each
+  second; indigo, $698.8$~millions of millions, etc.}
+indigo about
+one tenth part slower, blue slightly slower still, then green,
+yellow, orange, and red. The spectroscope is an astronomical
+\index{Spectroscope}%
+instrument which spreads out the line of light
+from a celestial body into a band and breaks it up into
+its several colors. If a ringing bell rapidly approaches us,
+or if we approach it, the tone of the bell sounds higher
+than if it recedes from us or if we recede from it. If we
+rapidly approach a star, or a star approaches us, its color
+shifts toward the violet end of the spectroscope; and if we
+rapidly recede from it, or it recedes from us, its color shifts
+toward the red end. Now year after year the thousands
+of stars in the vicinity of the plane of the earth's pathway
+show in the spectroscope this change toward violet at one
+season and toward red at the opposite season. The farther
+from the plane of the earth's orbit a star is located,
+the less is this annual change in color, since the earth
+neither approaches nor recedes from stars toward the
+poles. Either the stars near the plane of the earth's
+orbit move rapidly toward the earth at one season, gradually
+stop, and six months later as rapidly recede, and stars
+away from this plane approach and recede at rates diminishing
+exactly in proportion to their distance from this
+plane, \emph{or the earth itself swiftly moves about the sun}.
+
+\Subparagraph{Proof of the Rotation of the Earth.}\nblabel{page:107} The same set of
+\index{Proofs, form of earth!rotation of earth}%
+\index{Fixed stars}%
+\index{Star, distance of a!motions of}%
+%% -----File: 107.png---Folio 108-------
+facts and reasoning applies to the rotation of the earth.
+In the evening a star in the east shows a color approaching
+the violet side of the spectroscope, and this gradually shifts
+toward the red during the night as the star is seen higher
+in the sky, then nearly overhead, then in the west. Now
+either the star swiftly approaches the earth early in the
+evening, then gradually pauses, and at midnight begins to
+go away from the earth faster and faster as it approaches
+the western horizon, or the earth rotates on its axis,
+toward a star seen in the east, neither toward nor from it
+when nearly overhead, and away from it when seen near
+the west. Since the same star rises at different hours
+throughout the year it would have to fly back and forth
+toward and from the earth, two trips every day, varying
+its periods according to the time of its rising and setting.
+Besides this, when a star is rising at Calcutta it shows the
+violet tendency to observers there (Calcutta is rotating
+toward the star when the star is rising), and at the same
+moment the same star is setting at New Orleans and thus
+shows a shift toward the red to observers there. Now the
+distant star cannot possibly be actually rapidly approaching
+Calcutta and at the same time be as rapidly receding
+\index{Calcutta, India}%
+from New Orleans. The spectroscope, that wonderful
+\index{New Orleans, La.}%
+instrument which has multiplied astronomical knowledge
+during the last half century, demonstrates, with mathematical
+certainty, the rotation of the earth, and multiplies
+millionfold the certainty of the earth's revolution.
+
+\Subparagraph{Actual Motions of Stars.}\nblabel{page:108} Before leaving this topic we
+should notice that other changes in the colors of stars show
+that some are actually approaching the earth at a uniform
+rate, and some are receding from it. Careful observations
+at long intervals show other changes in the positions
+of stars. The latter motion of a star is called its
+%% -----File: 108.png---Folio 109-------
+\emph{proper motion} to distinguish it from the apparent motion
+it has in common with other stars due to the motions of
+the earth. The spectroscope also assists in the demonstration
+\index{Spectroscope}%
+that the sun with the earth and the rest of the
+planets and their attendant satellites is moving rapidly
+toward the constellation Hercules.
+
+\Subparagraph{Elements of Orbit Determined by the Spectroscope.} As
+an instance of the use of the spectroscope in determining
+motions of celestial bodies, we may cite the recent calculations
+of Professor \DPtypo{Kustner}{Küstner}, Director of the Bonn Observatory.
+\index{Küstner, Professor}%
+\index{Bonn Observatory}%
+Extending from June~24, 1904, to January~15, 1905,
+he made careful observations and photographs of the
+spectrographic lines shown by Arcturus. He then made
+\index{Arcturus (ark\;tu$'$rus)}%
+\index{Spectrograph}%
+calculations based upon a microscopic examination of
+the photographic plates, and was able to determine (\emph{a})~the
+size of the earth's orbit, (\emph{b})~its form, (\emph{c})~the rate of the
+earth's motion, and (\emph{d}) the rate at which the solar system
+and Arcturus are approaching each other ($10,849$ miles per
+hour, though not in a direct line).
+
+\Paragraph{The Parallax of Stars.}\nblabel{page:109} Since the days of Copernicus
+\index{Copernicus@Copernicus (k\={o}\;per$'$n\u{\i}\;k\u{u}s)}%
+\index{Parallax}%
+\index{Fixed stars}%
+\index{Proper motion of stars}%
+\index{Star, distance of a!motions of}%
+(1473--1543) the theory of the revolution of the earth
+around the sun has been very generally accepted. Tycho
+Brahe (1546--1601), however, and some other astronomers,
+\index{Brahe (brä), Tycho}%
+rejected this theory because they argued that if the
+earth had a motion across the great distance claimed for its
+orbit, stars would change their positions in relation to the
+earth, and they could detect no such change. Little did
+they realize the tremendous distances of the stars. It was
+not until~1838 that an astronomer succeeded in getting
+the orbital or heliocentric parallax of a star. The German
+astronomer Bessel then discovered that the faint star 61~Cygni
+\index{Bessel, F. W.}%
+\index{Cygnus@Cygnus (s\u{\i}g$'$n\u{u}s; plural and possessive singular, cygni)}%
+is annually displaced to the extent of~$0.4''$. Since
+then about forty stars have been found to have measurable
+\index{Motion in the line of sight|)}%
+%% -----File: 109.png---Folio 110-------
+parallaxes, thus multiplying the proofs of the motion of
+the earth around the sun.
+
+\includegraphicsleft{i109}{Fig.~34}
+
+\Subparagraph{Displacement of a Star Varies with its Distance.} Figure~\figureref{i109}{34}
+shows that the amount of
+the displacement of a star
+in the background of the
+heavens owing to a change
+in the position of the earth,
+varies with the distance of
+the star. The nearer the
+star, the greater the displacement;
+in every instance, however,
+this apparent shifting of
+a star is exceedingly minute,
+owing to the great distance
+(see pp.~\pageref{page:45},~\pageref{page:246}) of the very
+nearest of the stars.
+
+Since students often confuse
+the apparent orbit of a
+star described under aberration
+of light with that due to the parallax, we may make
+\index{Aberration of light@Aberration of light \indexglossref{Aberration}}%
+the following comparisons:
+\setlength{\TmpLen}{\parindent}
+\begin{center}
+\smallsize
+\begin{tabular}{@{}p{0.5\textwidth - 1em}@{\hspace{2em}}p{0.5\textwidth - 1em}@{}}
+\hfil\textsc{Aberrational Orbit}\tablespacerbot & \hfil\textsc{Parallactic Orbit}\\
+\hspace{\TmpLen}1. The earth's rapid motion
+causes the rays of light to slant
+(apparently) into the telescope so
+that, as the earth changes its
+direction in going around the sun,
+the star seems to shift slightly
+about. &
+\hspace{\TmpLen}1. As the earth moves about
+in its orbit the stars seem to
+move about upon the background
+of the celestial sphere.\\
+\hspace{\TmpLen}2.~This orbit has the same
+maximum width for all stars,
+however near or distant. &
+\hspace{\TmpLen}2.~This orbit varies in width
+with the distance of the star; the
+nearer the star, the greater the
+width.
+\end{tabular}
+\end{center}
+%% -----File: 110.png---Folio 111-------
+
+\Section{Effects of Earth's Revolution}
+
+\Paragraph{Winter Constellations Invisible in Summer.} You have
+\index{Winter constellations}%
+doubtless observed that some constellations which are
+visible on a winter's night cannot be seen on a summer's
+night. In January, the beautiful constellation Orion may
+\index{Orion@Orion (o\;r\={\i}$'$on)}%
+be seen early in the evening and the whole night through;
+in July, not at all. That this is due to the revolution of
+the earth around the sun may readily be made apparent.
+In the daytime we cannot easily see the stars around the
+sun, because of its great light and the peculiar properties
+of the atmosphere; six months from now the earth will
+have moved halfway around the sun, and we shall be
+between the sun and the stars he now hides from view,
+and at night the stars now invisible will be visible.
+
+\includegraphicsmid{i110}{Fig.~35}
+
+If you have made a record of the observations suggested
+in Chapter~\hyperref[chap:I]{I}, you will now find that Exhibit~I (Fig.~\figureref{i110}{35}),
+shows that the Big Dipper and other star groups have
+\index{Big Dipper}%
+slightly changed their relative positions for the same time
+of night, making a little more than one complete rotation
+during each twenty-four hours. In other words, the stars
+\index{Proofs, form of earth!revolution of earth|)}%
+%% -----File: 111.png---Folio 112-------
+have been gaining a little on the sun in the apparent daily
+swing of the celestial sphere around the earth.
+
+\includegraphicsmid{i111}{Fig.~36}
+
+The reasons for this may be understood from a careful
+study of Figure~\figureref{i111}{36}. The outer circle, which should be
+indefinitely great, represents the celestial sphere; the inner
+ellipse, the path of the earth around the sun. Now the sun
+does not seem to be, as it really is, relatively near the
+earth, but is projected into the celestial sphere among the
+%% -----File: 112.png---Folio 113-------
+stars. When the earth is at point~$A$ the sun is seen among
+\index{Sun!apparent motions of}%
+the stars at~$a$; when the earth has moved to~$B$ the sun
+seems to have moved to~$b$, and so on throughout the annual
+\index{Orbit, of earth}%
+orbit. \emph{The sun, therefore, seems to creep around the celestial
+sphere among the stars at the same rate and in the same
+direction as the earth moves in its orbit.} If you walk around
+a room with someone standing in the center, you will see
+that his image may be projected upon the wall opposite,
+and as you walk around, his image on the wall will move
+around in the same direction. Thus the sun seems to move
+in the celestial sphere in the same direction and at the same
+rate as the earth moves around the sun.
+
+\Paragraph{Two Apparent Motions of the Sun: Daily Westward,
+Annual Eastward.} The sun, then, has two apparent
+motions,\allowbreak---a daily swing around the earth with the celestial
+sphere, and this annual motion in the celestial sphere among
+the stars. The first motion is in a direction opposite to that
+of the earth's rotation and is from east to west, the second
+is in the same direction as the earth's revolution and is
+from west to east. If this is not readily seen from the
+foregoing statements and the diagram, think again of the
+rotation of the earth making an apparent rotation of
+the celestial sphere in the opposite direction, the reasons
+why the sun and moon seem to rise in the east and set in
+the west; then think of the motion of the earth around the
+sun by which the sun is projected among certain stars
+and then among other stars, seeming to creep among
+them from west to east.
+
+After seeing this clearly, think of yourself as facing the
+rising sun and a star which is also rising. Now imagine
+the earth to have rotated once, a day to have elapsed,
+and the earth to have gone a day's journey in its orbit in
+the direction corresponding to upward. The sun would
+%% -----File: 113.png---Folio 114-------
+not then be on the horizon, but, the earth having moved
+``upward,'' it would be somewhat below the horizon.
+The same star, however, would be on the horizon, for the
+earth does not change its position in relation to the stars.
+After another rotation the earth would be, relative to the
+stars viewed in that direction, higher up in its orbit and
+the sun farther below the horizon when the star was just
+rising. In three months when the star rose the sun would
+be nearly beneath one's feet, or it would be midnight; in
+six months we should be on the other side of the sun,
+and it would be setting when the star was rising; in nine
+months the earth would have covered the ``downward''
+quadrant of its journey around the sun, and the star
+would rise at noon; twelve months later the sun and
+star would rise together again. If the sun and a star
+set together one evening, on the next evening the star
+would set a little before the sun, the next night earlier
+still.
+
+Since the sun passes around its orbit, $360°$, in a year,
+\index{Orbit, of earth}%
+$365$ days, it passes over a space of nearly one degree each
+day. The diameter of the sun as seen from the earth
+covers about half a degree of the celestial sphere. During
+one rotation of the earth, then, the sun creeps eastward
+among the stars about twice its own width. A star rising
+with the sun will gain on the sun nearly $\frac{1}{360}$~of a day
+during each rotation, or a little less than four minutes.
+The sun sets nearly four minutes later than the star with
+which it set the day before.
+
+\Paragraph{Sidereal Day. Solar Day.} The time from star-rise to
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!sidereal}%
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!solar}%
+star-rise, or an exact rotation of the earth, is called a
+\emph{sidereal day}. Its exact length is $23$~h.\ $56$~m.\ $4.09$~s. The
+time between two successive passages of the sun over a
+given meridian, or from noon by the sun until the next
+%% -----File: 114.png---Folio 115-------
+noon by the sun, is called a \emph{solar day}.\footnote
+  {A solar day is sometimes defined as the interval from sunrise to
+  sunrise again. This is true only at the equator. The length of the
+  solar day corresponding to February~12, May~15, July~27, or November~3,
+  is almost exactly twenty-four hours. The time intervening between
+  sunrise and sunrise again varies greatly with the latitude and season.
+  On the dates named a solar day at the pole is twenty-four hours long,
+  as it is everywhere else on earth. The time from sunrise to sunrise
+  again, however, is almost six months at either pole.}
+Its length varies
+somewhat, for reasons to be explained later, but averages
+twenty-four hours. When we say ``day,'' if it is not
+otherwise qualified, we usually mean an average solar
+day divided into twenty-four hours, from midnight to
+midnight. The term ``hour,'' too, when not otherwise
+qualified, refers to one twenty-fourth of a mean solar
+day.
+
+\includegraphicsmid{i114}{Fig.~37}
+
+\Paragraph{Causes of Apparent Motions of the Sun.} The apparent
+motions of the sun are due to the real motions of the
+earth. If the earth moved slowly around the sun, the
+sun would appear to move slowly among the stars. Just
+as we know the direction and rate of the earth's rotation
+by observing the direction and rate of the apparent rotation
+%% -----File: 115.png---Folio 116-------
+of the celestial sphere, we know the direction and
+rate of the earth's revolution by observing the direction
+and rate of the sun's apparent annual motion.
+
+\includegraphicsmid{i115}{Fig.~38. Celestial sphere, showing zodiac}
+\index{Zodiac}%
+\index{Signs of zodiac}%
+
+\Paragraph{The Ecliptic.} The path which the center of the sun
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}}%
+seems to trace around the celestial sphere in its annual
+\index{Orbit, of earth|(}%
+orbit is called the \emph{ecliptic}.\footnote
+  {So called because eclipses can occur only when the moon crosses
+  the plane of the ecliptic.}
+\index{Eclipse}%
+The line traced by the center
+of the earth in its revolution about the sun is its orbit.
+Since the sun's apparent annual revolution around the sky
+is due to the earth's actual motion about the sun, the path
+of the sun, the ecliptic, must lie in the same plane with the
+%% -----File: 116.png---Folio 117-------
+earth's orbit. The earth's equator and parallels, if extended,
+would coincide with the celestial equator and
+parallels; similarly, the earth's orbit, if expanded in the
+same plane, would coincide with the ecliptic. We often
+use interchangeably the expressions ``plane of the earth's
+orbit'' and ``plane of the ecliptic.''
+
+\Paragraph{The Zodiac.}\nblabel{page:117} The orbits of the different planets and of
+\index{Zodiac}%
+the moon are inclined somewhat to the plane of the ecliptic,
+but, excepting some of the minor planets, not more
+than eight degrees. The moon and principal planets,
+therefore, are never more than eight degrees from the
+pathway of the sun. This belt sixteen degrees wide, with
+the ecliptic as the center, is called the zodiac (more fully
+discussed in the Appendix, p.~\pageref{page:293}). Since the sun appears
+to pass around the center of the zodiac once each year,
+the ancients, who observed these facts, divided it into
+twelve parts, one for each month, naming each part from
+some constellation in it. It is probably more nearly correct
+historically, to say that these twelve constellations
+got their names originally from the position of the sun in
+the zodiac. Libra, the Balance, probably got its name
+\index{Libra@Libra (li$'$bra)}%
+from the fact that in ancient days the sun was among the
+group of stars thus named about September~23, when the
+days and nights are equal, thus balancing. In some such
+way these parts came to be called the ``twelve signs of
+the zodiac,'' one for each month.
+
+The facts in this chapter concerning the apparent
+annual motion of the sun were well known to the ancients,
+possibly even more generally than they are to-day. The
+reason for this is because there were few calendars and
+almanacs in the earlier days of mankind, and people had
+to reckon their days by noting the position of the sun.
+Thus, instead of saying that the date of his famous
+%% -----File: 117.png---Folio 118-------
+journey to Canterbury was about the middle of April,
+\index{Canterbury Tales, quoted}%
+Chaucer says it was
+\index{Chaucer, quoted}%
+
+{\centering
+\begin{SmallText}
+\settowidth{\TmpLen}{The tendre croppes, and the younge sonne}
+\parbox{\TmpLen}{%
+When Zephirus eek with his sweete breeth \\
+Enspired hath in every holt and heath \\
+The tendre croppes, and the younge sonne \\
+Hath in the Ram his halfe course yronne.}\par
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation!sign of zodiac}%
+\end{SmallText}
+}
+
+Even if clothed in modern English such a description
+would be unintelligible to a large proportion of the students
+of to-day, and would need some such translation as
+the following.
+
+``When the west wind of spring with its sweet breath
+hath inspired or given new life in every field and heath
+to the tender crops, and the young sun (young because it
+had got only half way through the sign Aries, the Ram,
+which marked the beginning of the new year in Chaucer's
+day) hath run half his course through the sign the Ram.''
+
+\Paragraph{Obliquity of the Ecliptic.}\nblabel{page:118} The orbit of the earth is
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}!obliquity of}%
+\index{Obliquity of the ecliptic@Obliquity of the ecliptic\phantomsection\label{idx:ooe}}%
+not at right angles to the axis. If it were, the ecliptic
+would coincide with the celestial equator. The plane of
+the ecliptic and the plane of the celestial equator form an
+angle of nearly\footnotemark~$23\frac{1}{2}°$.
+\index{Nautical almanac@Nautical almanac\phantomsection\label{idx:na}}%
+\index{Newcomb, Simon}%
+  \footnotetext{The exact amount varies slightly from year to year. The following
+  table is taken from the Nautical Almanac, Newcomb's Calculations:
+\index{Almanac}%
+  \begin{center}
+  \settowidth{\TmpLen}{$23°~27'~6.86''$}
+  \begin{tabular}{@{}p{0.5\textwidth-\TmpLen-1em}@{}p{\TmpLen}@{\hspace{2em}}p{0.5\textwidth-\TmpLen-1em}@{}p{\TmpLen}@{}}
+  1903 \dotfill & $23°~27'~6.86''$ & 1906 \dotfill & $23°~27'~5.45''$ \\
+  1904 \dotfill & $23°~27'~6.39''$ & 1907 \dotfill & $23°~27'~4.98''$ \\
+  1905 \dotfill & $23°~27'~5.92''$ & 1908 \dotfill & $23°~27'~4.51''$
+  \end{tabular}
+  \end{center}}
+
+This is called the obliquity of the
+ecliptic. We sometimes speak of this as the inclination of
+the earth's axis from a perpendicular to the plane of its
+orbit.
+
+\includegraphicsright{i118}{Fig.~39}
+
+Since the plane of the ecliptic forms an angle of~$23\frac{1}{2}°$ with
+the plane of the equator, the sun in its apparent annual
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+course around in the ecliptic crosses the celestial equator
+%% -----File: 118.png---Folio 119-------
+twice each year, and at one season gets $23\frac{1}{2}°$~north of it,
+and at the opposite season $23\frac{1}{2}°$~south of it. The sun thus
+never gets nearer the pole of the celestial sphere than~$66\frac{1}{2}°$.
+On March~21 and September~23 the sun is on the celestial
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+equator. On June~21
+and December~22 the sun
+is $23\frac{1}{2}°$~from the celestial
+equator.
+
+\Paragraph{Earth's Orbit.} We have
+learned that the earth's orbit
+is an ellipse, and the sun is
+at a focus of it. While the
+eccentricity is not great, and
+when reduced in scale the
+orbit does not differ materially
+from a circle, the difference
+is sufficient to make an appreciable difference in the
+rate of the earth's motion in different parts of its orbit.
+Figure~\figureref{i284}{113}, p.~\pageref{fig:i284}, represents the orbit of the earth, greatly
+exaggerating the ellipticity. The point in the orbit nearest
+the sun is called perihelion (from \emph{peri}, around or near, and
+\index{Perihelion}%
+\emph{helios}, the sun). This point is about $91\frac{1}{2}$~million miles from
+the sun, and the earth reaches it about December~31st.
+The point in the earth's orbit farthest from the sun is
+called aphelion (from \emph{a}, away from, and \emph{helios}, sun). Its
+\index{Aphelion@Aphelion \indexglossref{Aphelion}}%
+distance is about $94\frac{1}{2}$~million miles, and the earth reaches
+it about July~1st.
+
+\Paragraph{Varying Speed of the Earth.} According to the law of
+gravitation, the earth moves faster in its orbit when near
+perihelion, and slower when near aphelion. In December
+and January the earth moves fastest in its orbit, and
+during that period the sun moves fastest in the ecliptic
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}}%
+and falls farther behind the stars in their rotation in the
+\index{Orbit, of earth|)}%
+%% -----File: 119.png---Folio 120-------
+celestial sphere. Solar days are thus longer then than
+they are in midsummer when the earth moves more slowly
+in its orbit and more nearly keeps up with the stars.
+
+Imagine the sun and a star are rising together January~1st.
+After one exact rotation of the earth, a sidereal day,
+the star will be rising again, but since the earth has moved
+rapidly in its course around the sun, the sun is somewhat
+farther behind the star than it would be in summer when
+the earth moved more slowly around the sun. At star-rise
+January~3d, the sun is behind still farther, and in
+the course of a few weeks the sun will be several minutes
+behind the point where it would be if the earth's orbital
+motion were uniform. The sun is then said to be slow of
+the average sun. In July the sun creeps back less rapidly
+in the ecliptic, and thus a solar day is more nearly the
+same length as a sidereal day, and hence shorter than the
+average.
+
+\includegraphicsleft{i119}{Fig.~40}
+
+Another factor modifies the foregoing statements. The
+daily courses of the stars swinging around with the celestial
+sphere are parallel and are at right angles to the axis.
+The sun in its annual
+path creeps diagonally
+across their courses.
+When farthest from the
+celestial equator, in June
+and in December, the
+sun's movement in the
+ecliptic is nearly parallel
+to the courses of the
+stars (Fig.~\figureref{i119}{40}); as it
+gets nearer the celestial equator, in March and in September,
+the course is more oblique. Hence in the latter
+part of June and of December, the sun, creeping back in
+%% -----File: 120.png---Folio 121-------
+the ecliptic, falls farther behind the stars and becomes
+slower than the average. In the latter part of March and
+of September the sun creeps in a more diagonal course and
+hence does not fall so far behind the stars in going the
+same distance, and thus becomes faster than the average
+(Fig.~\figureref{i120}{41}).
+
+\includegraphicsleft{i120}{Fig.~41}
+
+Some solar days being longer than others, and the
+sun being sometimes
+slow and sometimes
+fast, together with
+standard time adoptions
+whereby most
+places have their
+watches set by mean
+solar time at some
+given meridian, make
+it unsafe to set one's
+watch by the sun without making many corrections.
+
+The shortest day in the northern hemisphere is about
+December~22d; about that time the sun is neither fast nor
+slow, but it then begins to get slow. So as the days get
+longer the sun does not rise any earlier until about the
+second week of January. After Christmas one may notice
+the later and later time of sunsets. In schools in the
+northern states beginning work at 8~o'clock in the morning,
+it is noticed that the mornings are actually darker for a
+while after the Christmas holidays than before, though the
+shortest day of the year has passed.
+
+\Paragraph{Sidereal Day Shorter than Solar Day.} If one wanted
+to set his watch by the stars, he would be obliged to
+remember that sidereal days are shorter than solar days;
+if the star observed is in a certain position at a given time
+of night, it will be there nearly four minutes earlier the
+%% -----File: 121.png---Folio 122-------
+next evening. The Greek dramatist Euripides (480--407~\BC),
+\index{Euripides@Euripides (\={u}\;r\u{\i}p$'$\u{\i}\;d\={e}z)}%
+in his tragedy ``Rhesus,'' makes the Chorus say:
+
+\begin{SmallText}
+Whose is the guard? Who takes my turn? The first signs
+are setting, and the seven Pleiades are in the sky, and the Eagle
+\index{Pleiades@Pleiades (pl\={e}$'$yä\;d\={e}z)}%
+glides midway through the sky. Awake! See ye not the brilliancy
+of the moon? Morn, morn, indeed is approaching, and hither is one
+of the forewarning stars.
+
+\Section{\smallsize SUMMARY} %[**TN: italic 'Summary' in original - changed for consistency]
+
+Note carefully these propositions:
+\begin{slist}
+\item[1.] The earth's orbit is an ellipse.
+\index{Orbit, of earth}%
+
+\item[2.] The earth's orbital direction is the same as the direction of its
+axial motion.
+
+\item[3.] The rate of the earth's rotation is uniform, hence sidereal days
+are of equal length.
+
+\item[4.] The orbit of the earth is in nearly the same plane as that of the
+equator.
+
+\item[5.] The earth's revolution around the sun makes the sun seem to
+creep backward among the stars from west to east, falling
+behind them about a degree a day. The stars seem to swing
+around the earth, daily gaining about four minutes upon the
+sun.
+
+\item[6.] The rate of the earth's orbital motion determines the rate of the
+sun's apparent annual backward motion among the stars.
+
+\item[7.] The rate of the earth's orbital motion varies, being fastest when
+the earth is nearest the sun or in perihelion, and slowest when
+farthest from the sun or in aphelion.
+
+\item[8.] The sun's apparent annual motion, backward or eastward among
+the stars, is greater when in or near perihelion (December~31)
+than at any other time.
+
+\item[9.] The length of solar days varies, averaging $24$~hours in length.
+There are two reasons for this variation.
+\begin{ssublist}
+\item[\textit{a.}]  Because the earth's orbital motion is not uniform, it being faster
+when nearer the sun, and slower when farther from it.
+
+\item[\textit{b.}]  Because when near the equinoxes the apparent annual motion
+of the sun in the celestial sphere is more diagonal than when
+near the tropics.
+\end{ssublist}
+%% -----File: 122.png---Folio 123-------
+\item[10.] Because of these two sets of causes, solar days are more than $24$~hours
+in length from December~25 to April~15 and from June~15
+to September~1, and less than $24$~hours in length from April~15
+to June~15 and from September~1 to December~25.
+\end{slist}
+\end{SmallText}
+
+\Section{Equation of Time}
+\index{Equation of time@Equation of time \indexglossref{Equation of time}|(}%
+
+\Paragraph{Sun Fast or Sun Slow.} The relation of the apparent
+\index{Sun!fast or slow|(}%
+solar time to mean solar time is called the equation of
+time. As just shown, the apparent eastward motion of
+the sun in the ecliptic is faster than the average twice a
+year, and slower than the average twice a year. A fictitious
+sun is imagined to move at a uniform rate eastward
+in the celestial equator, starting with the apparent sun at
+the vernal equinox (see \glossref{Equinox} in Glossary)
+and completing
+its annual course around the celestial sphere in
+the same time in which the sun apparently makes its circuit
+of the ecliptic. While, excepting four times a year,
+the apparent sun is fast or slow as compared with this
+fictitious sun which indicates mean solar time, their difference
+at any moment, or the equation of time, may be
+accurately calculated.
+
+The equation of time is indicated in various ways. The
+usual method is to indicate the time by which the apparent
+sun is faster than the average by a minus sign, and the
+time by which it is slower than the average by a plus sign.
+The apparent time and the equation of time thus indicated,
+when combined, will give the mean time. Thus, if the sun
+indicates noon (apparent time), and we know the equation
+to be $-7$~m.\ (sun fast, $7$~m.), we know it is $11$~h.\ $53$~m.,~\AM{}
+by mean solar time.
+
+Any almanac shows the equation of time for any day of
+\index{Almanac|(}%
+the year. It is indicated in a variety of ways.
+
+\textit{a.} In the World Almanac it is given under the title
+\index{World Almanac}%
+%% -----File: 123.png---Folio 124-------
+``Sun on Meridian.'' The local mean solar time of the
+sun's crossing a meridian is given to the nearest second.
+Thus Jan.~1, 1908, it is given as $12$~h.\ $3$~m.\ $16$~s. We know
+from this that the apparent sun is $3$~m.\ $16$~s.\ slow of the
+average on that date.
+
+\textit{b.} In the Old Farmer's Almanac the equation of time is
+\index{Old Farmer's Almanac}%
+given in a column headed ``Sun Fast,'' or ``Sun Slow.''
+
+\textit{c.}~In some places the equation of time is indicated by
+the words, ``clock ahead of sun,'' and ``clock behind sun.''
+Of course the student knows from this that if the clock is
+ahead of the sun, the sun is slower than the average, and,
+conversely, if the clock is behind the sun, the latter must
+be faster than the average.
+
+\textit{d.} Most almanacs give times of sunrise and of sunset.
+Now half way between sunrise and sunset it is apparent
+noon. Suppose the sun rises at 7:24~o'clock, \AM, and
+sets at 4:43~o'clock, \PM. Half way between those times
+is 12:03$\frac{1}{2}$~o'clock, the time when the sun is on the
+meridian, and thus the sun is $3\frac{1}{2}$~minutes slow (Jan.~1, at
+New York).
+
+\textit{e. The Nautical Almanac}\footnote
+  {Prepared annually three years in advance, by the Professor of
+  Mathematics, United States Navy, Washington, D.~C\@. It is sold by
+  the Bureau of Equipment at actual cost of publication, one dollar.}
+\index{Nautical almanac@Nautical almanac\phantomsection\label{idx:na}}%
+\index{Washington, D. C.}%
+\index{District of Columbia}%
+has the most detailed and
+accurate \DPtypo{date}{data} obtainable.
+\hyperref[page:125]{Table~II} %[**TN: not labelled 'Table II' in original text]
+for each month gives
+in the column ``Equation of Time'' the number of minutes
+and seconds to be added to or subtracted from 12~o'clock
+noon at Greenwich for the apparent sun time. The
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England|(}%
+adjoining column gives the difference for one hour to be
+added when the sun is gaining, or subtracted when the sun
+is losing, for places east of Greenwich, and \textit{vice versa} for
+places west.
+
+Whether or not the student has access to a copy of the
+%% -----File: 124.png---Folio 125-------
+Nautical Almanac it may be of interest to notice the use
+of this table.
+
+\begin{center}
+\index{Declination@Declination \indexglossref{Declination}}%
+\scriptsize
+\newlength{\MyCola} \settowidth{\MyCola}{Thur.}%
+\newlength{\MyColb} \settowidth{\MyColb}{Declination}%
+\newlength{\MyColc} \settowidth{\MyColc}{$+00.00$}%
+\newlength{\MyCold} \settowidth{\MyCold}{Equation}%
+\newlength{\MyCole} \settowidth{\MyCole}{Ascension of}%
+\newlength{\MyRow}  \setlength{\MyRow}{28pt}%
+\setlength{\tabcolsep}{2pt}%
+\begin{tabular}{@{}l|r|c|c|r|r|c|c|c@{}}
+\hline\hline
+\multicolumn{9}{c}{\nblabel{page:125}\rule[-8pt]{0pt}{24pt}AT GREENWICH MEAN NOON.} \\
+\hline
+\multirow{2}{*}{\parbox[c]{\MyCola}{\centering \begin{sideways}Day of the week.\end{sideways}}}
+&\multirow{2}{*}{\begin{sideways}Day of the month.\end{sideways}}
+&\multicolumn{4}{c|}{\rule[-8pt]{0pt}{24pt}THE SUN'S}
+&\multirow{2}{*}{\parbox[c]{\MyCold}{\centering Equation\\of Time\\to be Sub-\\tracted\\from\\Mean\\Time}}
+&\multirow{2}{*}{\parbox[c]{\MyColc}{\centering~\\~\\~\\Diff.\ \\for\\1~hour}}
+&\multirow{2}{*}{\parbox[c]{\MyCole}{\centering~\\~\\Sidereal\\Time,\\or Right\\Ascension of\\Mean Sun}} \\
+\cline{3-6}
+&&\parbox[c]{\MyColb}{\centering Apparent\\Right\\Ascension}
+&\parbox[c]{\MyColc}{\centering Diff.\ \\for\\1~Hour}
+&\parbox[c]{\MyColb}{\rule{0pt}{\MyRow}\centering Apparent\\Declination\rule[-\MyRow]{0pt}{\MyRow}}
+&\parbox[c]{\MyColc}{\centering Diff.\ \\for\\1~Hour} &&& \\
+\hline
+\rule{0pt}{8pt}
+&&
+\PadTo{18}{\text{h}}~\PadTo{99}{\text{m}}~\PadTo{99.99}{\text{s}} &
+\text{s} &
+\PadTo{99}{°}~\PadTo[r]{99}{'}~\PadTo{99.9}{''} &
+\PadTo{99.99}{''} &
+\text{m}~\PadTo{99.99}{\text{s}} &
+\text{s} &
+\PadTo{99}{\text{h}}~\PadTo{99}{\text{m}}~\PadTo{99.99}{\text{s}} \\
+Wed. & 1 & $18~42~\Z9.88$ & $11.057$ & S.~$23~\Z5~47.3$  &$+11.13$ & $3~10.29$ & $1.200$ & $18~38~59.60$  \\
+Thur.& 2 & $18~46~35.09$  & $11.044$ &    $23~\Z1~\Z6.3$ & $12.28$ & $3~38.93$ & $1.188$ & $18~42~56.16$  \\
+Frid.& 3 & $18~50~59.99$  & $11.030$ &    $22~55~57.7$   & $13.42$ & $4~\Z7.28$& $1.174$ & $18~46~52.71$  \\
+\tablespacertop
+Sat. & 4 & $18~55~24.54$  & $11.015$ &    $22~50~21.8$   &$+14.56$ & $4~35.27$ & $1.158$ & $18~50~49.27$  \\
+\textit{SUN.} & 5 & $18~59~48.70$  & $10.098$ &    $22~44~18.6$   & $15.70$ & $5~\Z2.87$& $1.141$ & $18~54~45.83$  \\
+Mon. & 6 & $19~\Z4~12.45$ & $10.979$ &    $22~37~48.2$   & $16.82$ & $5~30.06$ & $1.123$ & $18~58~42.39$  \\
+\tablespacertop
+Tues.& 7 & $19~\Z8~35.74$ & $10.959$ &    $22~30~51.0$   &$+17.94$ & $5~56.80$ & $1.104$ & $19~\Z2~38.94$ \\
+Wed. & 8 & $19~12~58.56$  & $10.939$ &    $22~23~27.1$   & $19.04$ & $6~23.06$ & $1.083$ & $19~\Z6~35.50$ \\
+Thur.& 9 & $19~17~20.85$  & $10.918$ &    $22~15~36.8$   & $20.14$ & $6~48.79$ & $1.061$ & $19~10~32.06$  \\
+\tablespacertop
+Frid.&10 & $19~21~42.61$  & $10.895$ &    $22~\Z7~20.2$  &$+21.23$ & $7~13.99$ & $1.038$ & $19~14~28.62$  \\
+Sat. &11 & $19~26~\Z3.79$ & $10.871$ &    $21~58~37.7$   & $22.30$ & $7~38.62$ & $1.014$ & $19~18~25.17$  \\
+\textit{SUN.} &12 & $19~30~24.39$  & $10.846$ &    $21~49~29.5$   & $23.37$ & $8~\Z2.66$& $0.989$ & $19~22~21.73$\tablespacerbot  \\
+\hline
+\hline
+\multicolumn{9}{c}{\tablespacertop Part of a page from \textit{The American Ephemeris and Nautical Almanac}, Jan.~1908.}
+\index{Almanac|)}%
+\end{tabular}
+\end{center}
+
+This table indicates that at 12~o'clock noon, on the
+meridian of Greenwich on Jan.~1, 1908, the sun is slow $3$~m.\
+$10.29$~s., and is losing $1.200$~s.\ each hour from that moment.
+We know it is losing, for we find that on January~2 the
+sun is slow $3$~m.\ $38.93$~s., and by that time its rate of loss
+is slightly less, being $1.188$~s.\ each hour.
+
+Suppose you are at Hamburg on Jan.~1, 1908, when
+\index{Hamburg, Germany}%
+it is noon according to standard time of Germany, one
+hour before Greenwich mean noon. The equation of time
+will be the same as at Greenwich less $1.200$~s.\ for the hour's
+difference, or ($3~\text{m.}\ 10.29~\text{s.} - 1.200~\text{s.}$) $3$~m.\ $9.09$~s. If you
+are at New York on that date and it is noon, Eastern standard
+%% -----File: 125.png---Folio 126-------
+time, five hours after Greenwich noon, it is obvious
+that the sun is $5 × 1.200$~s.\ or $6$~s.\ slower than it was at
+Greenwich mean noon. The equation of time at New
+York would then be $3~\text{m.}\ 10.29~\text{s.} + 6~\text{s.}$\ or $3$~m.\ $16.29$~s.
+
+\includegraphicsfp{i126}{Fig.~42}
+
+\textit{f. The Analemma} graphically indicates the approximate
+\index{Analemma@Analemma \indexglossref{Analemma}, description of}%
+equation of time for any day of the year, and also indicates
+the declination of the sun (or its distance from the celestial
+equator). Since our year has $365\frac{1}{4}$~days, the equation of
+time for a given date of one year will not be quite the
+same as that of the same date in a succeeding year. That
+for 1910 will be approximately one fourth of a day or six
+hours later in each day than for~1909; that is, the table
+for Greenwich in 1910 will be very nearly correct for Central
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England|)}%
+United States in~1909. Since for the ordinary purposes
+\index{United States}%
+of the student using this book an error of a few
+seconds is inappreciable, the analemma will answer for
+most of his calculations.
+
+The vertical lines of the analemma represent the number
+of minutes the apparent sun is slow or fast as compared
+with the mean sun. For example, the dot representing
+February~25 is a little over half way between the
+lines representing sun slow $12$~m.\ and~$14$~m. The sun is then
+slow about $13$~m.\ $18$~s. It will be observed that April~15,
+June~15, September~1, and December~25 are on the central
+line. The equation of time is then zero, and the sun may
+be said to be ``on time.'' Persons living in the United
+States on the 90th~meridian will see the shadow due north
+at 12~o'clock on those days; if west of a standard time
+meridian one will note the north shadow when it is past
+12~o'clock, four minutes for every degree; and, if east of
+a standard time meridian, before 12~o'clock four minutes
+for each degree. Since the analemma shows how fast or
+slow the sun is each day, it is obvious that, knowing one's
+%% -----File: 126.png---Folio 127-------
+%% -----File: 127.png---Folio 128-------
+longitude, one can set his watch by the sun by reference
+to this diagram, or, having correct clock time, one can
+ascertain his longitude.
+\index{Equation of time@Equation of time \indexglossref{Equation of time}|)}%
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!representation of}%
+\index{Declination@Declination \indexglossref{Declination}}%
+\index{Sun!declination of}%
+
+\Section{Uses of the Analemma}\nblabel{page:128}
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!uses of|(}%
+
+\Paragraph{To Ascertain Your Longitude.} To do this your watch
+\index{Longitude@Longitude \indexglossref{Longitude}!how determined}%
+must show correct standard time. You must also have a
+\index{Time@Time \indexglossref{Time}, apparent solar!standard}%
+true north-south line.
+
+1. Carefully observe the time when the shadow is north.
+Ascertain from the analemma the number of minutes and
+seconds the sun is fast or slow.
+
+2. If fast, add that amount to the time by your watch;
+if slow, subtract. This gives your mean local time.
+
+3. Divide the minutes and seconds past or before twelve
+by four. This gives you the number of degrees and
+minutes you are from the standard time meridian. If
+the corrected time is before twelve, you are east of it; if
+after, you are west of it.
+
+4. Subtract (or add) the number of degrees you are
+east (or west) of the standard time meridian, and this is
+your longitude.
+
+For example, say the date is October~5th. 1.~Your
+watch says $12$~h.\ $10$~m.\ $30$~s.,~\PM, when the shadow is north.
+The analemma shows the sun to be $11$~m.\ $30$~s.\ fast. 2.~The
+sun being fast, you add these and get 12:22~o'clock,~\PM{}
+This is the mean local time of your place. 3.~Dividing
+the minutes past twelve by four, you get $5$~m.\ $30$~s. This is
+the number of degrees and minutes you are west from the
+standard meridian. If you live in the Central standard
+\index{Central time, in Europe!in the United States}%
+time belt of the United States, your longitude is $90°$ plus
+\index{United States}%
+$5°~30'$, or~$95°~30'$. If you are in the Eastern time belt,
+it is $75°$ plus $5°~30'$. If you are in Spain, it is $0°$ plus
+\index{Spain}%
+$5°~30'$, and so on.
+%% -----File: 128.png---Folio 129-------
+
+\Paragraph{To Set Your Watch.}\nblabel{page:129} To do this you must know your
+\index{Watch, to set by sun}%
+longitude and have a true north-south line.
+
+1. Find the difference between your longitude and that
+of the standard time meridian in accordance with which
+\index{Time@Time \indexglossref{Time}, apparent solar!standard}%
+you wish to set your watch. In Eastern United States the
+\index{United States}%
+standard time meridian is the~75th, in Central United
+States the~90th,~etc.
+
+2. Multiply the number of degrees and seconds of
+difference by four. This gives you the number of minutes
+and seconds your time is faster or slower than local time.
+If you are east of the standard meridian, your watch must
+be set slower than local time; if west, faster.
+
+3. From the analemma observe the position of the sun
+whe\-ther fast or slow and how much. If fast, subtract
+that time from the time obtained in step two; if slow, add.
+This gives you the time before or after twelve when the
+shadow will be north; before twelve if you are east of the
+standard time meridian, after twelve if you are west.
+
+4. Carefully set your watch at the time indicated in step
+three when the sun's shadow crosses the north-south line.
+
+For example, suppose your longitude is $87°~37'$~W.
+(Chicago). 1.~The difference between your longitude and
+\index{Chicago, Ill.}%
+\index{Chicago, Ill.}%
+your standard time meridian,~$90°$, is $2°~23'$. 2.~Multiplying
+this difference by four we get $9°~32'$, the minutes
+and seconds your time is slower than the sun's average
+time. That is, the sun on the average casts a north
+shadow at $11$~h.\ $50$~m.\ $28$~s.\ at your longitude. 3.~From the
+analemma we see the sun is $14$~m.\ $15$~s.\ slow on February~6.
+The time being slow, we add this to $11$~h.\ $50$~m.\ $28$~s.\ and
+get $12$~h.\ $4$~m.\ $43$~s., or $4$~m.\ $43$~s.\ past twelve when the
+shadow will be north. 4.~Just before the shadow is north
+get your watch ready, and the moment the shadow is north
+set it $4$~m.\ $43$~s.\ past twelve.
+%% -----File: 129.png---Folio 130-------
+\index{North, line}%
+
+\Paragraph{To Strike a North-South Line.}\nblabel{page:130} To do this you must
+know your longitude and have correct time.
+
+Steps 1,~2, and~3 are exactly as in the foregoing explanation
+how to set your watch by the sun. At the time you
+obtain in step~3 you know the shadow is north; then draw
+the line of the shadow, or, if out of doors, drive stakes or
+otherwise indicate the line of the shadow.
+
+\Paragraph{To Ascertain Your Latitude.} This use of the analemma
+is reserved for later discussion.
+
+\Paragraph{Civil and Astronomical Days.} The mean solar day of
+twenty-four hours reckoned from midnight is called a civil
+day, and among all Christian nations has the sanction of
+law and usage. Since astronomers work at night they
+reckon a day from noon. Thus the civil forenoon is
+dated a day ahead of the astronomical day, the afternoon
+\index{Astronomical day}%
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical}%
+being the last half of the civil day but the beginning of
+\index{Civil day}%
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!civil}%
+the astronomical day. Before the invention of clocks and
+watches, the sundial was the common standard for the
+time during each day, and this, as we have seen, is a constantly
+varying one. When clocks were invented it was
+found impossible to have them so adjusted as to gain or
+lose with the sun. Until 1815 a civil day in France was a
+\index{France}%
+day according to the actual position of the sun, and hence
+\index{Sun!fast or slow|)}%
+was a very uncertain affair.
+
+\Section{A Few Facts: Do You Understand Them?}
+
+1. A day of twenty-four hours as we commonly use the
+term, is not one rotation of the earth. A solar day is a
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!solar}%
+little more than one complete rotation and averages
+exactly twenty-four hours in length. This is a civil or
+legal day.
+
+2. A sidereal day is the time of one rotation of the
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!sidereal}%
+earth on its axis.
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!uses of|)}%
+%% -----File: 130.png---Folio 131-------
+
+3. There are $366$~rotations of the earth (sidereal days)
+in one year of $365$~days (solar days).
+
+4. A sundial records apparent or actual sun time, which
+\index{Sundial}%
+is the same as mean sun time only four times a year.
+
+5. A clock records mean sun time, and thus corresponds
+to sundial time only four times a year.
+
+6. In many cities using standard time the shadow of the
+sun is never in a north-south line when the clock strikes
+twelve. This is true of all cities more than $4°$~east or
+west of the meridian on which their standard time is based.
+
+7. Any city within $4°$~of its standard time meridian will
+have north-south shadow lines at twelve o'clock no more
+than four times a year at the most. Strictly speaking,
+practically no city ever has a shadow exactly north-south
+at twelve o'clock.
+\index{Revolution@Revolution \indexglossref{Revolution}|)}%
+%% -----File: 131.png---Folio 132-------
+
+\Chapter{VII}{Time and the Calendar}
+\index{Calendar|(}%
+
+``\First{In} the early days of mankind, it is not probable that
+there was any concern at all about dates, or seasons, or
+years. Herodotus is called the father of history, and his
+\index{Herodotus@Herodotus (he\;r\u{o}d$'$\;o\;tus)}%
+history does not contain a single date. Substantially
+the same may be said of Thucydides, who wrote only a
+\index{Thucydides@Thucydides (thu\;s\u{\i}d$'$\u{\i}\;d\={e}z)}%
+little later---somewhat over 400~\BC. If Geography and
+Chronology are the two eyes of history, then some histories
+are blind of the one eye and can see but little out of the
+\index{Farland, R. W.}%
+other.''\footnote
+  {R.~W. Farland in \textit{Popular Astronomy} for February, 1895.}
+\index{Popular Astronomy}%
+
+\Paragraph{Sidereal Year. Tropical Year.}\nblabel{page:132} As there are two kinds
+\index{Sidereal, clock!year}%
+\index{Year}%
+of days, solar and sidereal, there are two kinds of years,
+solar or tropical years, and sidereal years, but for very
+different reasons. The sidereal year is the time elapsing
+between the passage of the earth's center over a given
+point in its orbit until it crosses it again. For reasons
+\index{Orbit, of earth}%
+not properly discussed here (see Precession of the Equinoxes,
+p.~\pageref{page:286}), the point in the orbit where the earth is
+when the vertical ray is on the equator shifts slightly
+westward so that we reach the point of the vernal equinox
+a second time a few minutes before a sidereal year has
+elapsed. The time elapsing from the sun's crossing of the
+celestial equator in the spring until the crossing the next
+spring is a \emph{tropical}, year and is what we mean when we
+say ``a year.''\footnote
+  {A third kind of year is considered in astronomy, the anomalistic
+  year, the time occupied by the earth in traveling from perihelion to
+  perihelion again. Its length is $365$~d.\ $6$~h.\ $13$~m.\ $48.09$~s. The lunar year,
+  twelve new moons, is about eleven days shorter than the tropical
+  year. The length of a sidereal year is $365$~d.\ $6$~h.\ $9$~m.\ $8.97$~s.}
+Since it is the tropical year that we
+%% -----File: 132.png---Folio 133-------
+attempt to fit into an annual calendar and which marks
+the year of seasons, it is well to remember its length:
+\index{Year}%
+$365$~d.\ $5$~h.\ $48$~m.\ $45.51$~s.\ ($365.2422$~d.).  The adjustment
+of the days, weeks, and months into a calendar
+\index{Month@Month \indexglossref{Month}}%
+that does not change from year to year but brings
+the annual holidays around in the proper seasons, has
+been a difficult task for the human race to accomplish.
+If the length of the year were an even number of days
+and that number was exactly divisible by twelve,
+seven, and four, we could easily have seven days in a week,
+four weeks in a month, and twelve months in a year and
+have no time to carry over into another year or month.
+
+\Paragraph{The Moon the Measurer.} Among the ancients the
+moon was the great measurer of time, our word month
+comes from the word moon, and in connection with its
+changing phases religious feasts and celebrations were
+observed. Even to-day we reckon Easter and some other
+holy days by reference to the moon. Now the natural
+units of time are the solar day, the lunar month (about
+$29\frac{1}{2}$~days), and the tropical year. But their lengths are
+prime to each other. For some reasons not clearly known,
+but believed to be in accordance with the four phases of
+the moon, the ancient Egyptians and Chaldeans divided
+\index{Egypt}%
+\index{Chaldeans}%
+the month into four weeks of seven days each. The
+addition of the week as a unit of time which is naturally
+related only to the day, made confusion worse confounded.
+Various devices have been used at different times to make
+the same date come around regularly in the same season
+year after year, but changes made by priests who were
+ignorant as to the astronomical data and by more ignorant
+kings often resulted in great confusion. The very
+%% -----File: 133.png---Folio 134-------
+exact length of the solar year in the possession of the
+ancient Egyptians seems to have been little regarded.
+
+\Paragraph{Early Roman Calendar.} Since our calendar is the same
+\index{Calendar!early Roman}%
+\index{Roman calendar}%
+as that worked out by the Romans, a brief sketch of their
+system may be helpful. The ancient Romans seem to
+have had ten months, the first being March. We can see
+\index{Month@Month \indexglossref{Month}}%
+that this was the case from the fact that September means
+seventh; October, eighth; November, ninth; and December,
+tenth. It was possibly during the reign of Numa
+\index{Numa}%
+that two months were added, January and February.
+There are about $29\frac{1}{2}$~days in a lunar month, or from one
+new moon to the next, so to have their months conform
+to the moons they were given $29$~and~$30$ days alternately,
+beginning with January. This gave them twelve
+lunar months in a year of $354$~days. It was thought
+unlucky to have the number even, so a day was added for
+luck.
+
+This year, having but $355$~days, was over ten days too
+short, so festivals that came in the summer season would
+appear ten days earlier each year, until those dedicated
+to Bacchus, the god of wine, came when the grapes were
+\index{Bacchus}%
+still green, and those of Ceres, the goddess of the harvest,
+\index{Ceres}%
+before the heads of the wheat had appeared. To correct
+this an extra month was added, called Mercedonius, every
+\index{Mercedonius}%
+second year. Since the length of this month was not fixed
+by law but was determined by the pontiffs, it gave rise
+to serious corruption and fraud, interfering with the collection
+of debts by the dropping out of certain expected
+dates, lengthening the terms of office of favorites,~etc.
+
+\Paragraph{The Julian and the Augustan Calendars.} In the year
+\index{Caesar, Augustus!Julius}%
+\index{Julian calendar}%
+46~\BC, Julius Caesar, aided by the Egyptian astronomer,
+Sosigenes, reformed the calendar. He decreed that beginning
+\index{Sosigenes@Sosigenes (so\;s\u{\i}g$'$e\;n\={e}z)}%
+with January the months should have alternately $31$~and
+%% -----File: 134.png---Folio 135-------
+$30$~days, save February, to which was assigned $29$~days,
+and every fourth year an additional day. This
+made a year of exactly $365\tfrac{1}{4}$~days. Since the true year has
+$365$~days, $5$~hours, $48$~min., $45.51$~sec., and the Julian year
+had $365$~days, $6$~hours, it was $11$~min.,
+$14.49$~sec.\ too long.
+
+\begin{wrapfigure}{l}{0pt}
+\smallsize
+\begin{tabular}{@{}l@{}r@{}r}
+\multicolumn{2}{@{}c@{}}{\textsc{Julian}} &\textsc{Augustan} \\
+Jan. & 31 & 31 \\
+Feb. & 29--30 & 28--29 \\
+Mar. & 31 & 31 \\
+Apr. & 30 & 30 \\
+May & 31 & 31 \\
+June & 30 & 30 \\
+July & 31 & 31 \\
+Aug. & 30 & 31 \\
+Sept. & 31 & 30 \\
+Oct. & 30 & 31 \\
+Nov. & 31 & 30 \\
+Dec. & 30 & 31
+\end{tabular}
+\end{wrapfigure}
+
+During the reign of Augustus
+\index{Augustan calendar}%
+\index{Caesar, Augustus}%
+another day was taken from February
+and added to August in order
+that that month, the name of which
+had been changed from Sextilis to
+August in his honor, might have as
+many days in it as the month
+Quintilis, whose name had been
+changed to July in honor of Julius Caesar. To prevent the
+three months, July, August, and September, from having $31$
+days each, such an arrangement being considered unlucky,
+Augustus ordered that one day be taken from September
+and added to October, one from November and added to
+December. Thus we find the easy plan of remembering
+the months having 31 days, every other one, was disarranged,
+and we must now count our knuckles or learn:
+
+\begin{center}
+\smallsize
+\settowidth{\TmpLen}{\phantom{``}Which has four and twenty-four, till leap year gives it one day more.''}%
+\parbox{\TmpLen}{%
+``Thirty days hath September, April, June, and November. \\
+\phantom{``}All the rest have thirty-one, save the second one alone, \\
+\phantom{``}Which has four and twenty-four, till leap year gives it one day more.''}
+\end{center}
+
+\Paragraph{The Gregorian Calendar.} This Julian calendar, as it
+\index{Calendar!Augustan}%
+\index{Calendar!Julian}%
+\index{Gregorian calendar|(}%
+\index{Julian calendar}%
+is called, was adopted by European countries just as they
+adopted other Roman customs. Its length was $365.25$~days,
+whereas the true length of the year is $365.2422$~days.
+While the error was only $.0078$~of a day, in the
+course of centuries this addition to the true year began
+to amount to days. By 1582 the difference had amounted
+to about $13$~days, so that the time
+%% -----File: 135.png---Folio 136-------
+when the sun crosses the celestial equator, occurred the
+11th~of March. In that year Pope Gregory~XIII reformed
+the calendar so that the March equinox might occur on
+\index{Calendar!Gregorian}%
+March~21st, the same date as it did in the year 325~\AD,
+when the great Council of Nicæa was held which finally
+\index{Nicaea, Council of}%
+decided the method of reckoning Easter. One thousand
+two hundred and fifty-seven years had elapsed, each being
+$11$~min.\ $14$~sec.\ too long. The error of $10$~days was
+corrected by having the date following October~4th of that
+year recorded as October~15. To prevent a recurrence of
+the error, the Pope further decreed that thereafter the
+centurial years not divisible by~400 should not be counted
+as leap years. Thus the years 1600, 2000, 2400,~etc., are
+leap years, but the years 1700, 1900, 2100,~etc., are not
+leap years. This calculation reduces the error to a very
+low point, as according to the Gregorian calendar nearly
+$4000$ years must elapse before the error amounts to a
+single day.
+
+\sloppy
+The Gregorian calendar was soon adopted in all Roman
+Catholic countries, France recording the date after December 9th
+\index{France}%
+as December~20th. It was adopted by Poland in~1786,
+\index{Poland}%
+and by Hungary in~1787. Protestant Germany,
+\index{Hungary}%
+\index{Germany}%
+Denmark, and Holland adopted it in~1700 and Protestant
+\index{Denmark}%
+\index{Holland}%
+Switzerland in~1701. The Greek Catholic countries have
+\index{Switzerland}%
+not yet adopted this calendar and are now thirteen days
+behind our dates. Non-Christian countries have calendars
+of their own.
+
+\fussy
+In England and her colonies the change to the Gregorian
+\index{England}%
+system was effected in~1752 by having the date
+following September~2d read September~14. The change
+was violently opposed by some who seemed to think that
+changing the number assigned to a particular day modified
+time itself, and the members of the Government are
+%% -----File: 136.png---Folio 137-------
+said to have \DPtypo{heen}{been} mobbed in London by laborers who
+\index{London, England}%
+cried ``give us back our eleven days.''
+
+\includegraphicsright{i136}{Fig. 43. Page from Franklin's Almanac Showing Omission of Eleven Days, 1752.}
+\index{Franklin's almanac}%
+\Paragraph{\nbstretchyspace Old Style and New Style.} Dates of events occurring
+\index{New Style|(}%
+\index{Old Style|(}%
+before this change
+are usually kept as
+they were then written,
+the letters~\OS{}
+sometimes being
+written after the
+date to signify the
+old style of dating.
+To translate a date
+into the Gregorian or
+new style, one must
+note the century in
+which it occurred.
+For example, Columbus
+\index{Columbus, Christopher}%
+discovered land
+Oct.~12, 1492, \OS.
+According to the
+Gregorian calendar
+a change of~10 days
+was necessary in
+1582. In~1500, leap
+year was counted by
+the old style but
+should not have
+been counted by the
+new style. Hence,
+in the century ending
+1500, only~9 days
+difference had been made. So the discovery of America
+occurred October~12,~\OS{} or October~21,~\NS. English
+%% -----File: 137.png---Folio 138-------
+historians often write such dates October~$\dfrac{12}{21}$, the upper date
+referring to old style and the lower to new style.
+
+A historian usually follows the dates in the calendar used
+\index{Calendar!early Roman}%
+by his country at the time of the event. If, however, the
+event refers to two nations having different calendars, both
+dates are given. Thus, throughout Macaulay's ``History
+\index{Macaulay's History of England}%
+of England'' one sees such dates as the following: Avaux,
+$\dfrac{\text{July}\ 27}{\text{Aug.}\ 6}$, 1689. (Vol.~III\@.) A few dates in American history
+prior to September, 1752, have been changed to agree
+with the new style. Thus Washington was born Feb.~11,
+\index{Washington, George}%
+1731,~\OS, but we always write it Feb.~22, 1732. The %[**TN: original text omitted period after O.S]
+reason why all such dates are not translated into new
+style is because great confusion would result, and, besides,
+some incongruities would obtain. Thus the principal ship
+of Columbus was wrecked Dec.~25, 1492, and Sir Isaac
+\index{Columbus, Christopher}%
+Newton was born Dec.~25, 1642, and since in each case
+\index{Newton, Isaac}%
+this was Christmas, it would hardly do to record them as
+Christmas, Jan.~3, 1493, in the former instance, or as
+Christmas, Jan.~4, 1643, in the latter case, as we should
+have to do to write them in new style.
+
+\Paragraph{The Beginning of the Year.} With the ancient Romans
+\index{Roman calendar}%
+\index{Caesar, Augustus!Julius}%
+the year had commenced with the March equinox, as
+we notice in the names of the last months, September,
+October, November, December, meaning 7th, 8th, 9th,
+10th, which could only have those names by counting
+back to March as the first month. By the time of Julius
+Caesar the December solstice was commonly regarded as
+the beginning of the year, and he confirmed the change,
+making his new year begin January first. The later
+Teutonic nations for a long time continued counting the
+beginning of the year from March~25th. In~1563, by an
+\index{Gregorian calendar|)}%
+%% -----File: 138.png---Folio 139-------
+edict of Charles~IX, France changed the time of the beginning
+\index{Charles IX., King of France}%
+\index{France}%
+of the year to January first. In~1600 Scotland made
+\index{Scotland}%
+the same change and England did the same in~1752 when
+\index{England}%
+the Gregorian system was adopted there. Dates between
+the first of January and the twenty-fifth of March from
+1600 to~1752 are in one year in Scotland and another year
+in England. In Macaulay's ``History of England'' (Vol.~III,
+\index{Macaulay's History of England}%
+p.~258), he gives the following reference: ``Act.\ Parl.\ Scot.,
+Mar.~19, 1689--90.'' The date being between January~1st
+and March~25th in the interval between 1600 and
+1752, it was recorded as the year~1689 in England, and a
+year later, or~1690, in Scotland---Scotland dating the new
+year from January~1st, England from March~25th. This
+explains also why Washington's birthday was in 1731,~\OS,
+\index{Washington, George}%
+and 1732,~\NS, since English colonies used the same
+system of dating as the mother country.
+
+\Paragraph{Old Style is still used in England's Treasury Department.}
+``The old style is still retained in the accounts
+of Her Majesty's Treasury. This is why the Christmas
+dividends are not considered due until Twelfth Day, and
+the midsummer dividends not till the 5th~of July, and in
+just the same way it is not until the 5th~of April that
+Lady Day is supposed to arrive. There is another piece
+of antiquity in the public accounts. In the old times, the
+year was held to begin on the 25th~of March, and this
+change is also still observed in the computations over
+which the Chancellor of the Exchequer presides. The
+consequence is, that the first day of the financial year is
+the 5th~of April, being old Lady Day, and with that day
+\index{London Times}%
+\index{Times, London}%
+the reckonings of our annual budgets begin and end.''---\textit{London
+Times},\footnote
+  {Under the date of September~10, 1906, the same authority says
+  that the facts above quoted obtain in England at the present time.}
+Feb.~16, 1861.
+%% -----File: 139.png---Folio 140-------
+
+\Paragraph{\nbstretchyspace Greek Catholic Countries Use Old Style.} The Greek
+\index{Old Style|)}%
+Catholic countries, Russia, some of the Balkan states and
+\index{Balkan States}%
+\index{Russia}%
+Greece, still employ the old Julian calendar which now,
+\index{Calendar!Julian}%
+\index{Julian calendar}%
+with their counting 1900 as a leap year and our not
+counting it so, makes their dates $13$~days behind ours.
+Dates in these countries recorded by Protestants or Roman
+Catholics or written for general circulation are commonly
+recorded in both styles by placing the Gregorian date
+under the Julian date. For example, the date we celebrate
+as our national holiday would be written by an
+American in Russia as $\dfrac{\text{June}\ 21}{\text{July}\ 4}$. The day we commemorate
+as the anniversary of the birth of Christ, Dec.~$\dfrac{12}{25}$; the
+day they commemorate $\dfrac{\text{Dec.}\ 25, 1906} {\text{Jan.}\ 7, 1907}$. It should be
+remembered that if the date is before 1900 the difference
+will be less than thirteen days. Steps are being
+taken in Russia looking to an early revision of the
+calendar.
+
+\Paragraph{Mohammedan and Jewish Calendars.} The old system
+\index{Calendar!Mohammedan}%
+\index{Mohammedan calendar}%
+employed before the time of the Caesars is still used by
+the Mohammedans and the Jews. The year of the former
+is the lunar year of $354\frac{11}{30}$~days, and being about $.03$~of
+a year too short to correspond with the solar year, the
+same date passes through all seasons of the year in the
+course of $33$~years. Their calendar dates from the year
+of the Hegira, or the flight of Mohammed, which occurred
+\index{Hegira}%
+July, 622~\AD. If their year was a full solar year, their
+date corresponding to 1900 would be $622$~years less than
+that number, or 1278, but being shorter in length there are
+more of them, and they write the date 1318, that year
+beginning with what to us was May~1. That is to say,
+\index{New Style|)}%
+%% -----File: 140.png---Folio 141-------
+what we called May~1, 1900, they called the first day of
+their first month, Muharram, 1318.
+
+\Paragraph{Chinese Calendar.} The Chinese also use a lunar calendar;
+\index{Calendar!Chinese}%
+\index{Chinese calendar}%
+that is, with months based upon the phases of the
+moon, each month beginning with a new moon. Their
+months consequently have $29$~and~$30$ days alternately.
+To correct the error due to so short a year, seven out of
+every nineteen years have thirteen months each. This
+still leaves the average year too short, so in every cycle of
+sixty years, twenty-two extra months are intercalated.
+
+\Paragraph{Ancient Mexican Calendar.} The ancient Mexicans had a
+\index{Calendar!ancient Mexican}%
+calendar of $18$~months of $20$~days each and five additional
+days, with every fourth year a leap year. Their year began
+with the vernal equinox.
+
+\Paragraph{Chaldean Calendar.}\label{page:141} Perhaps the most ancient calendar
+\index{Calendar!Chaldean}%
+of which we have record, and the one which with modifications
+became the basis of the Roman calendar which we
+have seen was handed down through successive generations
+to us, was the calendar of the Chaldeans. Long
+\index{Chaldeans}%
+before Abraham left Ur of the Chaldees (see Genesis~xi,~31;
+\index{Ur, ancient Chaldean city}%
+\index{Abraham}%
+\index{Genesis}%
+Nehemiah~ix,~7, etc.)\ that city had a royal observatory,
+\index{Nehemiah}%
+and Chaldeans had made subdivisions of the celestial sphere
+and worked out the calendar upon which ours is based.
+
+Few of us can fail to recall how hard fractions were
+when we first studied them, and how we avoided them in
+our calculations as much as possible. For exactly the
+same reason these ancient Chaldeans used the number~$60$
+as their unit wherever possible, because that number
+being divisible by more numbers than any other less than~$100$,
+its use and the use of any six or a multiple of six
+avoided fractions. Thus they divided circles into $360$~degrees
+($6 × 60$), each degree into $60$~minutes, and each
+minute into $60$~seconds. They divided the zodiac into
+\index{Zodiac}%
+%% -----File: 141.png---Folio 142-------
+spaces of $30°$~each, giving us the plan of twelve months
+in the year. Their divisions of the day led to our $24$~hours,
+each having $60$~minutes, with $60$~seconds each.
+They used the week of seven days, one for each of the
+heavenly bodies that were seen to move in the zodiac.
+This origin is suggested in the names of the days of the
+week.
+
+\Section{Days of the Week}
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!week}%
+
+\begin{center}
+\scriptsize%
+\setlength{\tabcolsep}{2pt}%
+\begin{tabular}{l|c|c|c|c|c}
+\hline
+\settowidth{\TmpLen}{4. Wednesday}%
+\parbox[c]{\TmpLen}{\centering \tablespacertop Modern\\English\tablespacerbot} &
+\settowidth{\TmpLen}{Celestial}%
+\parbox[c]{\TmpLen}{\centering Celestial\\Origin} &
+\settowidth{\TmpLen}{Dies Mercurii}%
+\parbox[c]{\TmpLen}{\centering Roman} &
+\settowidth{\TmpLen}{Dimanche}%
+\parbox[c]{\TmpLen}{\centering Modern\\French} &
+\settowidth{\TmpLen}{Thor (thunderer)}%
+\parbox[c]{\TmpLen}{\centering Ancient\\Saxon} &
+\settowidth{\TmpLen}{Donnerstag}%
+\parbox[c]{\TmpLen}{\centering Modern German} \\
+\hline\tablespacertop
+1. Sunday & Sun & Dies Solis & Dimanche & Sunnan-daeg & Sonntag\tablespacerbot \\
+\hline\tablespacertop
+2. Monday & Moon & Dies Lunæ & Lundi & Monan-daeg & Montag\tablespacerbot \\
+\hline
+3. Tuesday & Mars & Dies Martis & Mardi &
+\settowidth{\TmpLen}{Tiew or Tuesco}% [**TN: this cell not centered in original]
+\parbox[c]{\TmpLen}{\centering\tablespacertop Mythical God\\Tiew or Tuesco\\Tues-daeg\tablespacerbot} & Dienstag \\
+\hline
+4. Wednesday & Mercury & Dies Mercurii & Mereredi &
+\settowidth{\TmpLen}{Woden's-daeg}%
+\parbox[c]{\TmpLen}{\centering\tablespacertop Woden\\Woden's-daeg\tablespacerbot} &
+\settowidth{\TmpLen}{(Mid-week)}%
+\parbox[c]{\TmpLen}{\centering (Mid-week)\\Mittwoche} \\
+\hline
+5. Thursday & Jupiter & Dies Jovis & Jeudi &
+\settowidth{\TmpLen}{Thor (thunderer)}%
+\parbox[c]{\TmpLen}{\centering\tablespacertop Thor (thunderer)\\Thor-daeg\tablespacerbot} & Donnerstag \\
+\hline
+6. Friday & Venus & Dies Veneris & Vendredi &
+\settowidth{\TmpLen}{Frigedaeg}%
+\parbox[c]{\TmpLen}{\centering\tablespacertop Friga\\Frigedaeg\tablespacerbot} & Freitag \\
+\hline
+7. Saturday & Saturn & Dies Saturni & Samedi & Saeter-daeg &
+\settowidth{\TmpLen}{Samstag or}%
+\parbox[c]{\TmpLen}{\centering\tablespacertop Samstag or\\Sonnabend\tablespacerbot} \\
+\hline
+\end{tabular}
+\end{center}
+
+\Paragraph{Complex Calendar Conditions in Turkey.} ``But it is in
+\index{Calendar!Mohammedan|(}%
+\index{Calendar!Turkish}%
+\index{Turkey|(}%
+\index{Abbott, Lyman|(}%
+\index{Impressions of a Careless Traveler, quoted|(}%
+\index{Outlook, The|(}%
+\index{Turkish calendar|(}%
+Turkey that the time problem becomes really complicated,
+very irritating to him who takes it seriously, very funny
+to him who enjoys a joke. To begin with, there are four
+years in Turkey---a Mohammedan civil year, a Mohammedan
+\index{Mohammedan calendar|(}%
+religious year, a Greek or Eastern year, and a European
+or Western year. Then in the year there are both
+lunar months depending on the changes of the moon, and
+months which, like ours, are certain artificial proportions
+of the solar year. Then the varieties, of language in
+%% -----File: 142.png---Folio 143-------
+Turkey still further complicate the calendars in customary
+use. I brought away with me a page from the diary
+which stood on my friend's library table, and which is
+customarily sold in Turkish shops to serve the purpose of
+a calendar; and I got from my friend the meaning of the
+hieroglyphics, which I record here as well as I can remember
+them. This page represents one day. Numbering the
+compartments in it from left to right, it reads as follows:
+\includegraphicsrightwidth[1]{i142}{Fig.~44}{0.52\textwidth}
+\begin{SmallText}
+\noindent\parbox[t]{0.44\textwidth}{%[**TN: width here plus width of graphics above = textwidth minus a little gap]
+\setlength{\parindent}{0pt}
+\begin{list}{}{%
+  \setlength\itemindent{-1.5em}%
+  \setlength\labelwidth{2em}%
+  \setlength\labelsep{0.5em}%
+  \setlength\leftmargin{3em}%
+  \setlength\itemsep{0pt plus 1pt}%
+  \setlength\parsep{0pt}%
+  \setlength\topsep{0pt}%
+}
+\item[1.] March, 1318 (Civil Year).
+
+\item[2.] March, 1320 (Religious Year).
+
+\item[3.] Thirty-one days (Civil Year).
+
+\item[4.] Wednesday.
+
+\item[5.] Thirty days (Religious Year).
+
+\item[6.] 27 (March: Civil Year).
+
+\item[7.] (March: Religious Year.)
+
+\item[8.] March, Wednesday (Armenian).
+
+\item[9.] April, Wednesday (French)
+
+\item[10.] March, Wednesday (Greek)
+
+\item[11.] Ecclesiastical Day (French R.~C. Church).
+
+\item[12.]  March, Wednesday (Russian).
+
+\item[13.] Month Day (Hebrew).
+
+\item[14.] Month Day (Old Style).
+\index{Old Style}%
+
+\item[15.] Month Day (New Style).
+\index{New Style}%
+
+\item[16.] Ecclesiastical Day (Armenian).
+
+\item[17.] Ecclesiastical Day (Greek)
+
+\item[18.] Midday, 5:35, 1902; Midday, 5:21.
+\end{list}
+}
+\end{SmallText}
+
+``I am not quite clear in my mind now as to the meaning
+of the last section, but I think it is that noon according to
+European reckoning, is twenty-one minutes past five according
+%% -----File: 143.png---Folio 144-------
+\index{Time@Time \indexglossref{Time}, apparent solar!confusion}%
+to Turkish reckoning. For there is in Turkey, added
+to the complication of year, month, and day, a further
+complication as to hours. The Turks reckon, not from an
+artificial or conventional hour, but from sunrise, and their
+reckoning runs for twenty-four hours. Thus, when the
+sun rises at 6:30 our noon will be 5:30, Turkish time. The
+Turkish hours, therefore, change every day. The steamers
+on the Bosphorus run according to Turkish time, and
+\index{Bosphorus}%
+one must first look in the time-table to see the hour, and
+then calculate from sunrise of the day what time by his
+European clock the boat will start. My friends in Turkey
+\index{Turkey|)}%
+had apparently gotten used to this complicated calendar,
+\index{Calendar!Jewish}%
+with its variable years and months and the constantly
+changing hours, and took it as a matter of course.''\footnote
+  {The Impressions of a Careless Traveler, by Lyman Abbott.---\textit{The
+Outlook}, Feb.~28, 1903.}
+\index{Abbott, Lyman|)}%
+\index{Impressions of a Careless Traveler, quoted|)}%
+\index{Mohammedan calendar|)}%
+\index{Outlook, The|)}%
+\index{Turkish calendar|)}%
+
+\Paragraph{Modern Jewish Calendar.} The modern Jewish calendar
+employs also a lunar year, but has alternate years lengthened
+by adding extra days to make up the difference
+between such year and the solar year. Thus one year
+will have $354$ days, and another $22$ or $23$ days more.
+Sept.~23, 1900, according to our calendar, was the beginning
+of their year~5661.
+
+Many remedies have been suggested for readjusting
+our calendar so that the same date shall always recur on
+\index{Calendar!Mohammedan|)}%
+the same day of the week. While it is interesting for the
+student to speculate on the problem and devise ways of
+meeting the difficulties, none can be suggested that does
+not involve so many changes from our present system that
+it will be impossible for a long, long time to overcome
+social inertia sufficiently to accomplish a reform.
+
+If the student becomes impatient with the complexity
+of the problem, he may recall with profit these words of
+%% -----File: 144.png---Folio 145-------
+John Fiske: ``It is well to simplify things as much as
+\index{Fiske, John}%
+possible, but this world was not so put together as to save
+us the trouble of using our wits.''
+
+\Paragraph{Three Christmases in One Year.} ``Bethlehem, the
+\index{Bethlehem}%
+\index{Christmases, three in one year}%
+home of Christmases, is that happy Utopia of which every
+American child dreams---it has more than one Christmas.
+In fact, it has three big ones, and, strangely enough, the
+one falling on December~25th of our calendar is not the
+greatest of the three. It is, at least, the first. Thirteen
+days after the Latin has burned his Christmas incense in
+the sacred shrine, the Greek Church patriarch, observing
+that it is Christmas-time by his slower calendar, catches up
+the Gloria, and bows in the Grotto of the Nativity for the
+devout in Greece, the Balkan states, and all the Russias.
+\index{Balkan States}%
+After another period of twelve days the great Armenian
+\index{Armenian Church}%
+Church of the East takes up the anthem of peace and
+good-will, and its patriarch visits the shrine.''\footnote
+{Ernest~I. Lewis in \textit{Woman's Home Companion}, December,~1903.}
+\index{Lewis, Ernest~I.}%
+
+\Paragraph{Topics for Special Reports.} The gnomon. The clepsydra.
+Other ancient devices for reckoning time. The
+week. The Metonic cycle and the Golden Number. The
+calculation of Easter. The Roman calendar. Names of
+the months and days of the week. Calendar reforms.
+The calendar of the French Revolution. The Jewish
+calendars. The Turkish calendar.
+\index{Calendar|)}%
+%% -----File: 145.png---Folio 146-------
+
+\Chapter{VIII}{Seasons}
+\index{Seasons|(}%
+
+\Paragraph{Vertical and Slanting Rays of the Sun.} He would be
+\index{Vertical ray of sun}%
+unobservant, indeed, who did not know from first-hand
+experience that the morning and evening rays of the sun
+do not feel so warm as those of midday, and, if living outside
+the torrid zone, that rays from the low winter sun in
+some way lack the heating power of those from the high
+summer sun. The reason for this difference may not be
+so apparent. The vertical rays are not warmer than the
+slanting ones, but the more nearly vertical the sun, the
+more heat rays are intercepted by a given surface. If
+you place a tub in the rain and tip it so that the rain falls
+in slantingly, it is obvious that less water will be caught
+than if the tub stood at right angles to the course of the
+raindrops. But before we take up in detail the effects of
+the shifting rays of the sun, let us carefully examine the
+conditions and causes of the shifting.
+
+\Paragraph{Motions of the Earth.} The direction and rate of the
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+earth's \emph{rotation} are ascertained from the direction and
+rate of the apparent rotation of the celestial sphere. The
+direction and rate of the earth's \emph{revolution} are ascertained
+from the apparent revolution of the sun among the stars
+of the celestial sphere. Just as any change in the rotation
+of the earth would produce a corresponding change in the
+apparent rotation of the celestial sphere, so any change
+in the revolution of the earth would produce a corresponding
+change in the apparent revolution of the sun.
+
+Were the sun to pass among the stars at right angles to
+%% -----File: 146.png---Folio 147-------
+the celestial equator, passing through the celestial poles,
+we should know that the earth went around the sun in a
+\index{Orbit, of earth}%
+path whose plane was perpendicular to the plane of the
+equator and was in the plane of the axis. In such an
+event the sun at some time during the year would shine
+vertically on each point on the earth's surface. Seasons
+would be nearly the same in one portion of the earth
+as in another. The sun would sometimes cast a north
+shadow at any given place and sometimes a south shadow.
+Were the sun always in the celestial equator, the ecliptic
+coinciding with it, we should know that the earth traveled
+around the sun at right angles to the axis. The vertical
+\index{Vertical ray of sun}%
+ray of the sun would then always be overhead at noon on
+the equator, and no change in season would occur. Were
+the plane of the earth's orbit at an angle of~$45°$ from the
+equator the ecliptic would extend half way between the
+poles and the equator, and the sun would at one time get
+within~$45°$ of the North star and six months later~$45°$
+from the South star. The vertical ray on the earth would
+then travel from~$45°$ south latitude to~$45°$ north latitude,
+and the torrid zone would be~$90°$ wide.
+
+\Paragraph{Obliquity of the Ecliptic.}\nblabel{page:147} But we know that the vertical
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}!obliquity of}%
+\index{Obliquity of the ecliptic@Obliquity of the ecliptic\phantomsection\label{idx:ooe}}%
+ray never gets farther north or south of the equator than
+about~$23 \tfrac{1}{2}°$, or nearer the poles than about~$66 \tfrac{1}{2}°$. The
+plane of the ecliptic or of the earth's orbit is, then, inclined
+at an angle of~$66 \tfrac{1}{2}°$ to the axis, or at an angle of $23 \tfrac{1}{2}°$ to
+the plane of the equator. This obliquity of the ecliptic
+varies slightly from year to year, as is shown on
+pp.~\pageref{page:118},~\pageref{page:288}.
+
+\Paragraph{Equinoxes.} The sun crosses the celestial equator twice
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+a year, March~20 or~21, and September~22 or~23,\footnote
+  {The reason why the date shifts lies in the construction of our
+  calendar, which must fit a year of $365$~days, $5$~h.\ $48$~m.\ $45.51$~s. The time
+  of the vernal equinox in 1906 was March~21, 7:46~\AM, Eastern
+  standard time. In 1907 it occurred $365$~days, $5$~h.\ $48$~m.\ $45.51$~s.\ later, or
+  at 1:35~\PM, March~21. In 1908, being leap year, it will occur $366$~days,
+  %[**TN: factual error: actually 365 days which is the reason the date changes from March 21 to 20 in leap year]
+  $5$~h.\ $48$~m.\ $45.51$~s.\ later, or at about 7:24~\PM, March~20. The same facts
+  are true of the solstices; they occur June~21--22 and December~22--23.}
+varying
+%% -----File: 147.png---Folio 148-------
+from year to year, the exact date for any year being easily
+found by referring to any almanac. These dates are
+called equinoxes (equinox; \textit{æquus}, equal; \textit{nox}, night), for
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+the reason that the days and nights are then twelve
+hours long everywhere on earth. March~21 is called
+the vernal (spring) equinox, and September~23 is called
+the autumnal equinox, for reasons obvious to those
+who live in the northern hemisphere (see \glossref{Equinox} in
+Glossary).
+
+\Paragraph{Solstices.} About the time when the sun reaches its most
+\index{Solstices}%
+distant point from the celestial equator, for several days it
+seems neither to recede from it nor to approach it. The
+dates when the sun is at these two points are called the
+solstices (from \textit{sol}, sun; and \textit{stare}, to stand). June~21 is
+the summer solstice, and December~22 is the winter solstice;
+\textit{vice versa} for the southern hemisphere. The same terms
+are also applied to the two points in the ecliptic farthest
+from the equator; that is, the position of the sun on those
+dates.
+
+\Paragraph{At the Equator.} \emph{March~21.}\hspace{1em}Imagine you are at the
+\index{Equator@Equator \indexglossref{Equator}!terrestrial|(}%
+equator March~21. Bear in mind the fact that the North
+star (strictly speaking, the north pole of the celestial
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+sphere) is on the northern horizon, the South star on the
+\index{South, on map!star}%
+southern horizon, and the celestial equator extends from
+due east, through the zenith, to due west. It is sunrise of
+the vernal equinox. The sun is seen on the eastern horizon;
+the shadow it casts is due west and remains due west
+until noon, getting shorter and shorter as the sun rises
+higher.
+%% -----File: 148.png---Folio 149-------
+
+\includegraphicsmid{i148}{Fig.~45. Illumination of the earth in twelve positions, corresponding to months.
+  The north pole is turned toward us.}
+
+\Subparagraph{Shadows.} At noon the sun, being on the celestial
+equator, is directly overhead and casts no shadow, or the
+shadow is directly underneath. In the afternoon the
+shadow is due east, lengthening as the sun approaches
+the due west point in the horizon. At this time the sun's
+rays extend from pole to pole. The \emph{circle of illumination},
+\index{Circle of illumination, or day circle@Circle of illumination, or day circle\phantomsection\label{idx:coi}}%
+that great circle separating the lighted half of the earth
+from the half which is turned away from the sun, since it
+%% -----File: 149.png---Folio 150-------
+extends at this time from pole to pole, coincides with a
+meridian circle and bisects each parallel. Half of each
+parallel being in the light and half in the dark, during
+one rotation every point will be in the light half a day and
+away from the sun the other half, and day and night are
+equal everywhere on the globe.
+
+\emph{After March~21} the sun creeps back in its orbit, gradually,
+away from the celestial equator toward the North
+\index{Equator@Equator \indexglossref{Equator}!celestial}%
+\index{Celestial equator}%
+star. At the equator the sun thus rises more and more
+toward the north of the due east point on the horizon,
+and at noon casts a shadow toward the south. As the
+sun gets farther from the celestial equator, the south noon
+shadow lengthens, and the sun rises and sets farther
+toward the north of east and west.
+
+\emph{On June~21} the sun has reached the point in the ecliptic
+farthest from the celestial equator, about $23\frac{1}{2}°$~north.
+The vertical ray on the earth is at a corresponding distance
+from the equator. The sun is near the constellation
+Cancer, and the parallel marking the turning of the sun
+\index{Tropics}%
+\index{Cancer, constellation of!tropic of}%
+\index{Cancer, constellation of}%
+from his course toward the polestar is called the Tropic
+(from a Greek word meaning \emph{turning}) of Cancer. Our
+terrestrial parallel marking the southward turning of the
+vertical ray is also called the Tropic of Cancer. At this
+\index{Celestial latitude!tropics}%
+date the circle of illumination extends $23\frac{1}{2\extrafracspacing}°$~beyond the
+north pole, and all of the parallels north of~$66\frac{1}{2}°$ from the
+equator are entirely within this circle of illumination and
+have daylight during the entire rotation of the earth. At
+this time the circle of illumination cuts unequally parallels
+north of the equator so that more than half of them are in
+the lighted portion, and hence days are longer than nights
+in the northern hemisphere. South of the equator the
+conditions are reversed. The circle of illumination does
+not extend so far south as the south pole, but falls short
+%% -----File: 150.png---Folio 151-------
+of it~$23\frac{1}{2}°$, and consequently all parallels south of~$66\frac{1}{2}°$ are
+entirely in the dark portion of the earth, and it is continual
+night. Other circles south of the equator are so
+intersected by the circle of illumination that less than
+half of them are in the lighted side of the earth, and the
+days are shorter than the nights. It is midwinter there.
+
+\emph{After June~21} gradually the sun creeps along in its
+orbit away from this northern point in the celestial sphere
+toward the celestial equator. The circle of illumination
+again draws toward the poles, the days are more nearly
+of the same length as the nights, the noon sun is more
+nearly overhead at the equator again, until by September~23,
+the autumnal equinox, the sun is again on the celestial
+equator, and conditions are exactly as they were at the
+March equinox.
+\index{Circle of illumination, or day circle@Circle of illumination, or day circle\phantomsection\label{idx:coi}}%
+
+\emph{After September~23} the sun, passing toward the South
+star from the celestial equator, rises to the south of a due
+\index{South, on map!star}%
+east line on the equator, and at noon is to the south of the
+zenith, casting a north shadow. The circle of illumination
+withdraws from the north pole, leaving it in darkness,
+and extends beyond the south pole, spreading there the
+glad sunshine. Days grow shorter north of the equator, less
+than half of their parallels being in the lighted half, and
+south of the equator the days lengthen and summer comes.
+
+\emph{On December~22} the sun has reached the most distant
+point in the ecliptic from the celestial equator toward the
+South star, $23\frac{1}{2}°$~from the celestial equator and $66\frac{1}{2}°$~from
+the South star, the vertical ray on the earth being at corresponding
+distances from the equator and the south pole.
+The sun is now near the constellation Capricorn, and everywhere
+within the tropics the shadow is toward the north;
+\index{Tropics}%
+\index{Celestial latitude!tropics}%
+\index{Capricorn, constellation of!tropic of}%
+\index{Capricorn, constellation of}%
+on the tropic of Capricorn the sun is overhead at noon,
+and south of it the shadow is toward the south. Here
+%% -----File: 151.png---Folio 152-------
+\index{Circle of illumination, or day circle@Circle of illumination, or day circle\phantomsection\label{idx:coi}}%
+\index{Compass, magnetic, or mariner's}%
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+\index{Magnetic compass}%
+\index{North, line!pole}%
+\index{Orbit, of earth}%
+\index{Pole, celestial!terrestrial|(}%
+\index{Vertical ray of sun}%
+the vertical ray turns toward the equator again as the sun
+creeps in the ecliptic toward the celestial equator.
+
+Just as the tropics are the parallels which mark the
+farthest limit of the vertical ray from the equator, the
+polar circles are the parallels marking the farthest extent
+of the circle of illumination beyond the poles, and are the
+same distance from the poles that the tropics are from the
+equator.
+
+\ParagraphNoSpace{The Width of the Zones} is thus determined by the distance
+\index{Zones}%
+the vertical ray travels on the earth, and with the
+moving of the vertical ray, the shifting of the day circle.
+This distance is in turn determined by the angle which
+the earth's orbit forms with the plane of the equator. The
+planes of the equator and the orbit forming an angle of~$23\frac{1}{2}°$,
+the vertical ray travels that many degrees each side
+of the equator, and the torrid zone is $47°$~wide. The circle
+of illumination never extends more than~$23\frac{1}{2}°$ beyond each
+pole, and the frigid zones are thus $23\frac{1}{2}°$~wide. The remaining
+or temperate zones between the torrid and the frigid
+zones must each be $43°$~wide.
+
+\Paragraph{At the North Pole.} Imagine you are at the north pole.
+Bear in mind the fact that the North star is always almost
+exactly overhead and the celestial equator always on the
+horizon. On March~21 the sun is on the celestial equator
+and hence on the horizon.\footnote
+  {Speaking exactly, the sun is seen there before the spring equinox
+  and after the autumnal equinox, owing to refraction and the dip of the
+  horizon. See p.~\pageref{page:160}.}
+The sun now swings
+around the horizon once each rotation of the earth, casting
+long shadows in every direction, though, being at the
+north pole, they are always toward the south.\footnote
+  {The student should bear in mind the fact that directions on the
+  earth are determined solely by reference to the true geographical
+  pole, not the magnetic pole of the mariner's compass. At the north
+\index{Magnetic pole}%
+  pole the compass points due south, and at points between the magnetic
+  pole and the geographical pole it may point in any direction excepting
+  toward the north. Thus Admiral A.~H. Markham says, in the \textit{Youth's
+  Companion} for June~22, 1902:
+
+  ``When, in 1876, I was sledging over the frozen sea in my endeavor
+  to reach the north pole, and therefore traveling in a due north direction,
+  I was actually steering \emph{by compass} E.~S.~E., the variation of the
+  compass in that locality varying from ninety-eight degrees to one
+  hundred and two degrees westerly.''}
+After the
+\index{Equator@Equator \indexglossref{Equator}!terrestrial|)}%
+%% -----File: 152.png---Folio 153-------
+\index{Compass, magnetic, or mariner's}%
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+\index{Magnetic compass}%
+\index{Magnetic pole}%
+\index{Markham, A. H.}%
+\index{North, line!pole}%
+\index{Pole, celestial!magnetic}%
+\index{South, on map!pole}%
+\index{Youth's Companion}%
+spring equinox, the sun gradually rises higher and higher
+in a gently rising spiral until at the summer solstice, June~21,
+it is $23\frac{1}{2}°$~above the horizon. After this date it gradually
+approaches the horizon again until, September~23,
+the autumnal equinox, it is exactly on the horizon, and
+after this date is seen no more for six months. Now the
+stars come out and may be seen perpetually tracing their
+circular courses around the polestar. Because of the reflection
+and refraction of the rays of light in the air, twilight
+prevails when the sun is not more than about $18°$~below
+the horizon, so that for only a small portion of the six
+months' winter is it dark, and even then the long journeys
+of the moon above the celestial equator, the bright stars
+that never set, and the auroras, prevent total darkness
+(see p.~\pageref{page:164}). On December~22 the sun is $23\frac{1}{2}°$~below the
+horizon, after which it gradually approaches the horizon
+again, twilight soon setting in until March~21 again shows
+the welcome face of the sun.
+
+\ParagraphNoSpace{At the South Pole} the conditions are exactly reversed.
+There the sun swings around the horizon in the opposite
+direction; that is, in the direction opposite the hands of a
+watch when looked at from above. The other half of the
+celestial sphere from that seen at the north pole is always
+above one, and no stars seen at one pole are visible at the
+other pole, excepting the few in a very narrow belt around
+the celestial equator, lifted by refraction of light.
+%% -----File: 153.png---Folio 154-------
+\index{Axis, changes in position of!parallelism of}%
+\index{Gyroscope@Gyroscope (j\={\i}$'$r\={o}\;sk\={o}p)}%
+\index{Parallelism of earth's axis}%
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+
+\Paragraph{Parallelism of the Earth's Axis.} Another condition of
+the earth in its revolution should be borne in mind in
+explaining change of seasons. The earth might rotate on
+an axis and revolve around the sun with the axis inclined~$23\frac{1}{2}°$
+and still give us no change in seasons. This can
+easily be demonstrated by carrying a globe around a central
+object representing the sun, and by rotating the axis
+one can maintain the same inclination but keep the vertical
+ray continually at the equator or at any other circle
+within the tropics. In order to get the shifting of the
+vertical ray and change of seasons which now obtain, the
+axis must constantly point in the same direction, and its
+position at one time be parallel to its position at any other
+time. This is called the parallelism of the earth's axis.
+
+That the earth's axis has a very slow rotary motion, a
+slight periodic ``nodding'' which varies its inclination
+toward the plane of the ecliptic, and also irregular motions
+of diverse character, need not confuse us here, as they are
+either so minute as to require very delicate observations
+to determine them, or so slow as to require many years to
+show a change. These three motions of the axis are discussed
+in the Appendix under ``Precession of the Equinoxes,''
+``Nutation of the Poles,'' and ``Wandering of the
+Poles'' (p.~\pageref{page:286}).
+
+\Paragraph{\nbstretchyspace Experiments with the Gyroscope.} The \emph{gyroscope}, probably
+familiar to most persons, admirably illustrates the
+causes of the parallelism of the earth's axis. A disk, supported
+in a ring, is rapidly whirled, and the rotation tends
+to keep the axis of the disk always pointing in the same
+direction. If the ring be held in the hands and carried
+about, the disk rapidly rotating, it will be discovered that
+any attempt to change the direction of the axis will meet
+with resistance. This is shown in the simple fact that a
+\index{Pole, celestial!terrestrial|)}%
+%% -----File: 154.png---Folio 155-------
+\index{Circle of illumination, or day circle@Circle of illumination, or day circle\phantomsection\label{idx:coi}|(}%
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!length of|(}%
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+\index{Foucault@Foucault (foo\;ko$'$), experiment, with gyroscope}%
+\index{Gyroscope@Gyroscope (j\={\i}$'$r\={o}\;sk\={o}p)}%
+\index{Holway, R. S.}%
+\index{Proofs, form of earth!rotation of earth}%
+\index{Rotation, proofs of}%
+\index{Vertical ray of sun}%
+rapidly rotating top remains upright and is not easily
+tipped over; and, similarly, a bicycle running at a rapid
+rate remains erect, the rapid motion of the wheel (or
+top) giving the axis a tendency to remain in the same
+plane.
+
+The gyroscope shown in Figure~\figureref{i154}{46}\footnote
+  {Taken, by permission, from the \textit{Journal of Geography} for February,
+\index{Journal of Geography}%
+  1904.}
+is one used by
+Professor R.~S. Holway of the University of California.
+\index{California}%
+\index{University of California}%
+It was made by mounting a six-inch sewing machine wheel
+on ball bearings in the fork of an old bicycle. Its advantages
+over those commonly used are its simplicity, the
+ball bearings, and its greater weight.
+
+\includegraphicsmid{i154}{Fig.~46}
+
+\Paragraph{Foucault Experiment.} In 1852, the year after his
+famous pendulum experiment, demonstrating the rotation
+of the earth, M.~Leon Foucault demonstrated the same
+facts by means of a gyroscope so mounted that, although
+the earth turned, the axis of the rotating wheel remained
+constantly in the same direction.
+
+\Section{Comparative Length of Day and Night}
+\index{Length of day|(}%
+
+\Paragraph{Day's Length at the Equinoxes.} One half of the earth
+being always in the sunlight, the circle of illumination is a
+great circle. The vertical ray marks the center of the
+lighted half of the surface of the earth. At the equinoxes
+%% -----File: 155.png---Folio 156-------
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+\index{Vertical ray of sun}%
+the vertical ray is at the equator, and the circle of illumination
+extends from pole to pole bisecting every parallel.
+Since at this time any given parallel is cut into two equal
+parts by the circle of illumination, one half of it is in the
+sunlight, and one half of it is in darkness, and during one
+rotation a point on a parallel will have had twelve hours
+day and twelve hours night. (No allowance is made for
+refraction or twilight.)
+
+\Paragraph{Day's Length after the Equinoxes.} After the vernal
+equinox the vertical ray moves northward, and the circle
+of illumination extends beyond the north pole but falls
+short of the south pole. Then all parallels, save the
+equator, are unequally divided by the circle of illumination,
+for more than half of each parallel north of the equator
+is in the light, and more than half of each parallel south
+of the equator is in darkness. Consequently, while the
+vertical ray is north of the equator, or from March~21 to
+September~23, the days are longer than the nights north
+of the equator, but are shorter than the nights south of
+the equator.
+
+During the other half of the year, when the vertical ray
+is south of the equator, these conditions are exactly
+reversed. The farther the vertical ray is from the equator,
+the farther is the circle of illumination extended beyond
+one pole and away from the other pole, and the more
+unevenly are the parallels divided by it; hence the days
+are proportionally longer in the hemisphere where the
+vertical ray is, and the nights longer in the opposite hemisphere.
+The farther from the equator, too, the greater
+is the difference, as may be observed from Figure~\figureref{i161}{50},
+page~\pageref{fig:i161}. Parallels near the equator are always nearly
+bisected by the circle of illumination, and hence day
+nearly equals night there the year around.
+%% -----File: 156.png---Folio 157-------
+\index{Equator@Equator \indexglossref{Equator}!length of day at}%
+\index{Pole, celestial!terrestrial}%
+
+\Paragraph{Day's Length at the Equator.} How does the length of
+day at the equator compare with the length of night?
+When days are shorter south of the equator, if they are
+longer north of it and \textit{vice versa}, at the equator they must
+be of the same length. The equator is always bisected
+by the circle of illumination, consequently half of it is
+always in the sunlight. This proposition, simple though
+it is, often needs further demonstration to be seen clearly.
+It will be obvious if one sees:
+
+(\textit{a})~A point on a sphere $180°$ in any direction from a
+point in a great circle lies in the same circle.
+
+(\textit{b})~Two great circles on the same sphere must cross
+each other at least once.
+
+(\textit{c})~A point $180°$ from this point of intersection common
+to both great circles, will lie in each of them, and hence
+must be a point common to both and a point of intersection.
+Hence two great circles, extending in any
+direction, intersect each other a second time~$180°$ from
+the first point of crossing, or half way around. The circle
+of illumination and equator are both great circles and
+hence bisect each other. If the equator is always bisected
+by the circle of illumination, half of it must always be in
+the light and half in the dark.
+
+\Paragraph{Day's Length at the Poles.} The length of day at the
+north pole is a little more than six months, since it extends
+from March~21 until September~23, or $186$~days. At the
+north pole night extends from September~23 until March~21,
+and is thus $179$~days in length. It is just opposite at
+the south pole, $179$~days of sunshine and $186$~days of
+twilight and darkness. This is only roughly stated in full
+days, and makes no allowance for refraction of light or
+twilight.
+
+\Paragraph{Longest Days at Different Latitudes.} The length of the
+\index{Circle of illumination, or day circle@Circle of illumination, or day circle\phantomsection\label{idx:coi}|)}%
+%% -----File: 157.png---Folio 158-------
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+longest day, that is, from sunrise  to sunset, in  different
+latitudes is as follows:
+\begin{center}
+\smallsize\nblabel{page:158}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{@{}*{3}{l@{\quad}l|}l@{\quad}l@{}}
+\hline
+\tablespacertop
+\rlap{Lat.} & \PadTo{12~\text{h.}\ 99~\text{m.}}{\text{Day}} &
+\rlap{Lat.} & \PadTo{12~\text{h.}\ 99~\text{m.}}{\text{Day}} &
+\rlap{Lat.} & \PadTo{12~\text{h.}\ 99~\text{m.}}{\text{Day}} &
+\rlap{Lat.} & \PadTo{999~\text{days}}{\text{Day}}\tablespacerbot \\
+\hline
+\tablespacertop
+$\Z0°$ & $12$~h.         & $25°$ & $13$~h. $34$~m. & $50°$     & $16$~h. $\Z9$~m. & $70°$ & $\Z65$~days \\
+$\Z5°$ & $12$~h. $17$~m. & $30°$ & $13$~h. $56$~m. & $55°$     & $17$~h. $\Z7$~m. & $75°$ & $103$ \PadTo{\text{days}}{``} \\
+$10°$  & $12$~h. $35$~m. & $35°$ & $14$~h. $22$~m. & $60°$     & $18$~h. $30$~m.  & $80°$ & $134$ \PadTo{\text{days}}{``} \\
+$15°$  & $12$~h. $53$~m. & $40°$ & $14$~h. $51$~m. & $65°$     & $21$~h. $09$~m.  & $85°$ & $161$ \PadTo{\text{days}}{``} \\
+$20°$  & $13$~h. $13$~m. & $45°$ & $15$~h. $26$~m. & $66°\,33'$ & $24$~h. $00$~m.  & $90°$ & $\Z\Z6$~mos.\tablespacerbot \\
+ \hline
+\end{tabular}
+\end{center}
+
+The foregoing table makes no allowance for the fact
+that the vertical ray is north of the equator for a longer
+time than it is south of the equator, owing to the fact that
+we are farther from the sun then, and consequently the
+earth revolves more slowly in its orbit. No allowance is
+made for refraction, which lifts up the rays of the sun
+when it is near the horizon, thus lengthening days everywhere.
+
+\Section{Refraction of Light}
+\index{Refraction of light}%
+
+\includegraphicsmid{i157}{Fig.~47}
+
+The rays of light on entering the atmosphere are bent
+out of straight courses. Whenever a ray of light enters
+obliquely a medium of greater or of less density, the ray
+is bent out of its course (Fig.~\figureref{i157}{47}). Such a change in
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!length of|)}%
+\index{Length of day|)}%
+%% -----File: 158.png---Folio 159-------
+direction is called refraction. When a ray of light enters
+obliquely a medium of greater density, as in passing
+through from the upper rarer atmosphere to the lower
+denser layers, or from air into water, the rays are bent in
+the direction toward a perpendicular to the surface or less
+obliquely. This is called the first law of refraction. The
+second law of refraction is the converse of this; that is, on
+entering a rarer medium the ray is bent more obliquely
+or away from a perpendicular to the surface. When a
+ray of light from an object strikes the eye, we see the
+object in the direction taken by the ray as it enters the
+eye, and if the ray is refracted this will not be the real
+position of the object. Thus a fish in the water (Fig.~\figureref{i158}{48})
+would see the adjacent boy as though the boy were nearly
+above it, for the ray from the boy to the fish is bent
+downwards, and the ray as it enters the eye of the fish
+seems to be coming from a place higher up.
+
+\includegraphicsmid{i158}{Fig.~48}
+
+\includegraphicsleft{i159}{Fig.~49}
+
+\Paragraph{Amount of Refraction Varies.} The amount of refraction
+depends upon the difference in the density of the
+%% -----File: 159.png---Folio 160-------
+media and the obliqueness with which the rays enter.
+Rays entering perpendicularly are not refracted at all.
+The atmosphere differs very greatly in density at different
+altitudes owing to its weight and elasticity. About one
+half of it is compressed within three miles of the surface
+of the earth, and at a height of ten miles it is so rare that
+sound can scarcely be transmitted through it. A ray of
+light entering the atmosphere obliquely is thus obliged to
+traverse layers of air of increasing density, and is refracted
+more and more as it approaches the earth.
+
+\begin{center} %[**TN:Table moved back in text to fit on page]
+\smallsize
+\begin{tabular}{@{}c@{\hspace{1em}}c|c@{\hspace{1em}}c|c@{\hspace{1em}}c@{}}
+\multicolumn{6}{c}{\textsc{Mean Refraction Table}}\\
+\multicolumn{6}{c}{(\emph{For Temperature $50°$~Fahr., barometric pressure $30$~in.})\tablespacerbot}\\
+\hline
+\settowidth{\TmpLen}{Apparent}%
+\parbox[c]{\TmpLen}{\centering\tablespacertop Apparent\\Altitude.\tablespacerbot} &
+\settowidth{\TmpLen}{Refraction.}%
+\parbox[c]{\TmpLen}{\centering Mean\\Refraction.} &
+\settowidth{\TmpLen}{Apparent}%
+\parbox[c]{\TmpLen}{\centering Apparent\\Altitude.} &
+\settowidth{\TmpLen}{Refraction.}%
+\parbox[c]{\TmpLen}{\centering Mean\\Refraction.} &
+\settowidth{\TmpLen}{Apparent}%
+\parbox[c]{\TmpLen}{\centering Apparent\\Altitude.} &
+\settowidth{\TmpLen}{Refraction.}%
+\parbox[c]{\TmpLen}{\centering Mean\\Refraction.} \\
+\hline
+\tablespacertop
+$0\rlap{$°$}$ & $36\rlap{$'$}\quad29.4\rlap{$''$}$ &
+$\Z8\rlap{$°$}$ & $6\rlap{$'$}\quad33.3\rlap{$''$}$ &
+$26\rlap{$°$}$ & $1\rlap{$'$}\quad58.9\rlap{$''$}$ \\
+%
+$1$ &  $24\quad53.6$ & $\Z9$ & $5\quad52.6$ & $30$ & $1\quad40.6$ \\
+$2$ &  $18\quad25.5$ &  $10$ & $5\quad19.2$ & $40$ & $1\quad\Z9.4$\\
+$3$ &  $14\quad25.1$ &  $12$ & $4\quad27.5$ & $50$ & $0\quad48.9$ \\
+$4$ &  $11\quad44.4$ &  $14$ & $3\quad49.5$ & $60$ & $0\quad33.6$ \\
+$5$ & $\Z9\quad52.0$ &  $16$ & $3\quad20.5$ & $70$ & $0\quad21.2$ \\
+$6$ & $\Z8\quad28.0$ &  $18$ & $2\quad57.5$ & $80$ & $0\quad10.3$ \\
+$7$ & $\Z7\quad23.8$ &  $22$ & $2\quad23.3$ & $90$ & $0\quad00.0$\tablespacerbot\\
+\hline
+\end{tabular}
+\end{center}
+
+\Paragraph{Effect of Refraction on Celestial Altitudes.}\nblabel{page:160} Thus, refraction
+increases the apparent altitudes of all celestial objects
+excepting those at the
+zenith (Fig.~\figureref{i159}{49}). The
+amount of refraction at
+the horizon is ordinarily
+$36'\ 29''$; that is to say,
+a star seen on the horizon
+is in reality over
+one half a degree below
+the horizon. The actual
+amount of refraction
+varies with the temperature, humidity, and pressure
+of the air, all of which affect its density and which must
+be taken into consideration in accurate calculations.
+Since the width of the sun as seen from the earth is about~$32'$,
+when the sun is seen just above the horizon it actually
+is just below it, and since the sun passes one degree in
+about four minutes, the day is thus lengthened about four
+minutes in the latitudes of the United States and more in
+\index{United States}%
+higher latitudes. This accounts for the statement in almanacs
+as to the exact length of the day at the equinoxes.
+Theoretically the day is twelve hours long then, but practically
+%% -----File: 160.png---Folio 161-------
+\index{Barometer}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+it is a few minutes longer. Occasionally there is
+an eclipse of the moon observed just before the sun has
+\index{Eclipse}%
+\index{Sun}%
+gone down. The earth is exactly between the sun and the
+moon, but because of refraction, both sun and moon are
+seen above the horizon.
+
+The sun and moon often appear flattened when near
+the horizon, especially when seen through a haze. This
+apparent flattening is due to the fact that rays from the
+lower portion are more oblique than those from the upper
+portion, and hence it is apparently lifted up more than
+the upper portion.
+
+\Section{Twilight}
+\index{Twilight|(}%
+
+The atmosphere has the peculiar property of reflecting
+\index{Atmosphere|(}%
+and scattering the rays of light in every direction. Were
+not this the case, no object would be visible out of the
+direct sunshine, shadows would be perfectly black, our
+houses, excepting where the sun shone, would be perfectly
+dark, the blue sky would disappear and we could see the
+stars in the day time just as well as at night. Because
+of this diffusion of light, darkness does not immediately
+set in after sunset, for the rays shining in the upper air
+%% -----File: 161.png---Folio 162-------
+are broken up and reflected to the lower air. This, in
+brief, is the explanation of twilight. There being practically
+no atmosphere on the moon there is no twilight
+there. These and other consequences resulting from the
+lack of an atmospheric envelope on the moon are described
+on p.~\pageref{page:263}. %[**TN: 'pp. 263, 264' in original text]
+
+\Paragraph{Length of Twilight.} Twilight is considered to last while
+the sun is less than about $18°$ below the horizon, though
+the exact distance varies somewhat with the condition of
+the atmosphere, the latitude, and the season of the year.
+There is thus a
+twilight zone immediately
+beyond
+the circle of illumination,
+and outside
+of this zone is the
+true night. Figure~\figureref{i161}{50}
+represents these
+three portions: (1)~the
+hemisphere receiving
+direct rays (slightly more than a hemisphere owing
+to refraction), (2)~the belt $18°$ from the circle of illumination,
+and (3)~the segment in darkness---total save for
+starlight or moonlight. The height of the atmosphere is,
+of course, greatly exaggerated. The atmosphere above
+the line $AB$ receives direct rays of light and reflects
+and diffuses them to the lower layers of atmosphere.
+
+\includegraphicsleft{i161}{Fig.~50}
+
+\Paragraph{Twilight Period Varies with Season.} It will be seen from
+Figure~\figureref{i161}{50} that the fraction of a parallel in the twilight
+zone varies greatly with the latitude and the season. At
+the equator the sun drops down at right angles to the
+horizon, hence covers the $18°$ twilight zone in $\dfrac{18}{360}$ of a
+%% -----File: 162.png---Folio 163-------
+\index{Bailey, S.~I.}%
+\index{Harper's Weekly}%
+\index{Midnight sun}%
+\index{Quito@Quito (k\={e}$'$t\={o}), Equador}%
+\index{Young, C. A.}%
+day or one hour and twelve minutes. This remains practically
+the same the year around there. In latitudes of
+the United States, the twilight averages one and one-half
+hours long, being greater in midsummer. At the poles,
+twilight lasts about two and one-half months.
+
+\Paragraph{Twilight Long in High Latitudes.} The reason why the
+twilight lasts so long in high latitudes in the summer will
+be apparent if we remember that the sun, rising north of
+east, swinging slantingly around and setting to the north
+of west, passes through the twilight zone at the same
+oblique angle. At latitude $48°~33'$ the sun passes around
+so obliquely at the summer solstice that it does not sink $18°$
+below the horizon at midnight, and stays within the twilight
+zone from sunset to sunrise. At higher latitudes on
+that date the sun sinks even less distance below the
+horizon. For example, at St.~Petersburg, latitude $59°~56'~30''$,
+the sun is only $6°~36'~25''$ below the horizon at midnight
+June~21 and it is light enough to read without
+artificial light. From $66°$ to the pole the sun stays
+entirely above the horizon throughout the entire summer
+solstice, that being the boundary of the ``land of the midnight
+sun.''
+
+\Paragraph{Twilight Near the Equator.} ``Here comes science now
+taking from us another of our cherished beliefs---the wide
+superstition that in the tropics there is almost no twilight,
+and that the `sun goes down like thunder out o' China
+\index{China}%
+'crosst the bay.' Every boy's book of adventure tells of
+travelers overtaken by the sudden descent of night, and
+men of science used to bear out these tales. Young, in
+his `General Astronomy,' points out that `at Quito the
+twilight is said to be at best only twenty minutes.' In
+a monograph upon `The Duration of Twilight in the
+Tropics,' S.~I. Bailey points out, by carefully verified
+%% -----File: 163.png---Folio 164-------
+\index{Arequipa@Arequipa (ä\;r\={a}\;k\={e}$'$pä), Peru}%
+\index{Harper's Weekly}%
+\index{Harvard Astronomical Station (Peru)}%
+\index{Markham, A. H.}%
+\index{Vincocaya@Vincocaya (v\u{\i}n\;k\={o}\;kä$'$yä), Peru}%
+observation and experiments, that the tropics have their
+fair share of twilights. He says: `Twilight may be said
+to last until the last bit of illuminated sky disappears from
+the western horizon. In general it has been found that
+this occurs when the sun has sunk about eighteen degrees
+below the horizon\dots. Arequipa, Peru, lies within the
+tropics, and has an elevation of $8,000$~feet, and the air is
+especially pure and dry, and conditions appear to be
+exceptionally favorable for an extremely short twilight.
+On Sunday, June~25, 1899, the following observations
+were made at the Harvard Astronomical Station, which is
+situated here: The sun disappeared at 5:30~\PM, local
+mean time. At 6~\PM, thirty minutes after sunset, I
+could read ordinary print with perfect ease. At 6:30~\PM{}
+I could see the time readily by an ordinary watch. At
+6:40~\PM, seventy minutes after sunset, the illuminated
+western sky was still bright enough to cast a faint shadow
+of an opaque body on a white surface. At 6:50~\PM,
+one hour and twenty minutes after sunset, it had disappeared.
+On August~27, 1899, the following observations
+were made at Vincocaya. The latitude of this place
+is about sixteen degrees south and the altitude $14,360$
+feet. Here it was possible to read coarse print forty-seven
+minutes after sunset, and twilight could be seen for
+an hour and twelve minutes after the sun's disappearance.'
+So the common superstition about no twilight in the
+tropics goes to join the William Tell myth.''---\textit{Harper's
+\DPtypo{Weeekly}{Weekly}}, April~5, 1902.
+
+\Paragraph{Twilight Near the Pole.}\nblabel{page:164} ``It may be interesting to relate
+the exact amount of light and darkness experienced
+during a winter passed by me in the Arctic regions within
+four hundred and sixty miles of the Pole.
+
+``From the time of crossing the Arctic circle until we
+%% -----File: 164.png---Folio 165-------
+\index{Crepusculum, the}%
+\index{Markham, A. H.}%
+\index{Vertical ray of sun}%
+established ourselves in winter quarters on the~3d of
+September, we rejoiced in one long, continuous day. On
+that date the sun set below the northern horizon at midnight,
+and the daylight hours gradually decreased until
+the sun disappeared at noon below the southern horizon
+on the~13th of October.
+
+``From this date until the~1st of March, a period of one
+hundred and forty days, we never saw the sun; but it
+must not be supposed that because the sun was absent we
+were living in total darkness, for such was not the case.
+During the month following the disappearance of the sun,
+and for a month prior to its return, we enjoyed for an
+hour, more or less, on either side of noon, a glorious twilight;
+but for three months it may be said we lived in
+total darkness, although of course on fine days the stars
+shone out bright and clear, rendered all the more brilliant
+by the reflection from the snow and ice by which we were
+surrounded, while we also enjoyed the light from the moon
+in its regular lunations.
+
+``On the~21st of December, the shortest day in the year,
+the sun at our winter quarters was at noon twenty degrees
+below the horizon. I mention this because the twilight
+circle, or, to use its scientific name, the \emph{crepusculum}, when
+dawn begins and twilight ends, is determined when the
+\index{Twilight|)}%
+sun is eighteen degrees below the horizon.
+
+``On our darkest day it was not possible at noon to read
+even the largest-sized type.''---Admiral A.~H. Markham,
+R.~N., in the \textit{Youth's Companion}, June~22, 1899.
+\index{Youth's Companion}%
+
+\Section{Effect of the Shifting Rays of the Sun.}
+
+\includegraphicsmid{i165-1}{Fig.~51}
+
+\Paragraph{Vertical Rays and Insolation.} The more nearly vertical
+\index{Insolation|(}%
+the rays of the sun are the greater is the amount of heat
+imparted to the earth at a given place, not because a vertical
+%% -----File: 165.png---Folio 166-------
+\index{Vertical ray of sun}%
+ray is any warmer, but because more rays fall over
+a given area. In Figure~\figureref{i165-1}{51} we notice that more perpendicular
+rays extend over a given area than slanting ones.
+We observe the morning and evening rays of the sun,
+even when falling perpendicularly upon an object, say
+through a convex lens or burning glass, are not so
+warm as those at midday. The reason is apparent
+from Figure~\figureref{i165-2}{52}, the
+slanting rays traverse
+through more
+of the atmosphere.
+
+\includegraphicsright{i165-2}{Fig.~52}
+
+At the summer
+solstice the sun's
+rays are more nearly
+vertical over Europe
+\index{Europe}%
+and the United
+States than at other
+times. In addition to the greater amount of heat received
+because of the less oblique rays, the days are longer than
+%% -----File: 166.png---Folio 167-------
+\index{Solstices}%
+nights and consequently more heat is received during the
+day than is radiated off at night. This increasing length
+of day time greatly modifies the climate of regions far to
+the north. Here the long summer days accumulate enough
+heat to mature grain crops and forage plants. It is interesting
+to note that in many northern cities of the United
+States the maximum temperatures are as great as in some
+southern cities.
+
+\Paragraph{How the Atmosphere is Heated.} To understand how
+\index{Atmosphere!how heated}%
+the atmosphere gets its heat we may use as an illustration
+the peculiar heat-receiving and heat-transmitting properties
+of glass. We all know that glass permits heat rays
+from the sun to pass readily through it, and that the dark
+rays of heat from the stove or radiator do not readily pass
+through the glass. Were it not for this fact it would be
+no warmer in a room in the sunshine than in the shade,
+and if glass permitted heat to escape from a room as
+readily as it lets the sunshine in we should have to dispense
+with windows in cold weather. Stating this in
+more technical language, transparent glass is diathermanous
+to luminous heat rays but athermanous to dark rays.
+Dry air possesses this same peculiar property and permits
+the luminous rays from the sun to pass readily through to
+the earth, only about one fourth being absorbed as they
+pass through. About three fourths of the heat the atmosphere
+receives is that which is radiated back as dark rays
+from the earth. Being athermanous to these rays the heat
+is retained a considerable length of time before it at length
+escapes into space. It is for this reason that high altitudes
+are cold, the atmosphere being heated from the
+\index{Atmosphere|)}%
+bottom upwards.
+
+\Paragraph{Maximum Heat Follows Summer Solstice.} Because of
+these conditions and of the convecting currents of air, and,
+%% -----File: 167.png---Folio 168-------
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+to a very limited extent, of water, the heat is so distributed
+and accumulated that the hottest weather is in the
+month following the summer solstice (July in the northern
+hemisphere, and January in the southern); conversely, the
+coldest month is the one following the winter solstice.
+This seasonal variation is precisely parallel to the diurnal
+change. At noon the sun is highest in the sky and pours
+in heat most rapidly, but the point of maximum heat is
+not usually reached until the middle of the afternoon, when
+the accumulated heat in the atmosphere begins gradually
+to disappear.
+
+\Paragraph{Astronomical and Climatic Seasons.} Astronomically
+\index{Seasons}%
+there are four seasons each year: spring, from the vernal
+equinox to the summer solstice; summer, from the summer
+solstice to the autumnal equinox; autumn, from the
+autumnal equinox to the winter solstice; winter, from the
+winter solstice to the spring equinox. As treated in physical
+geography, seasons vary greatly in number and
+length with differing conditions of topography and position
+in relation to winds, mountains, and bodies of water.
+In most parts of continental United States and Europe
+\index{Europe}%
+\index{United States}%
+there are four fairly marked seasons: March, April, and
+May are called spring months; June, July, and August,
+summer months; September, October, and November,
+autumn months; and December, January, and February,
+winter months. In the southern states and in western
+Europe the seasons just named begin earlier. In California
+\index{California}%
+and in most tropical regions, there are two seasons,
+one wet and one dry. In northern South America there
+\index{South America}%
+are four seasons,---two wet and two dry.
+
+From the point of view of mathematical geography
+there are four seasons having the following lengths in the
+northern hemisphere:
+%% -----File: 168.png---Folio 169-------
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+\index{St.~Petersburg, Russia}%
+\index{Seasons}%
+\index{Unequal heating}%
+{\smallsize
+\settowidth{\TmpLen}{Autumnal equinox plus}
+\newlength{\RightLen}
+\settowidth{\RightLen}{Summer half}
+\begin{align*}%[**TN: Outer: Spring/Summer, Autumn/Winter]
+&
+\left.
+  \begin{aligned}%[**TN: Middle 1: Spring, Summer]
+  &\smash[t]{\left.
+  \begin{aligned}%[**TN: Inner 1]
+  \PadTo[l]{\textsc{Autumn:\ }}{\textsc{Spring:}}
+    & \parbox[c]{\TmpLen}{Vernal equinox\dotfill}\
+        \text{March}~21 \\
+    & \parbox[c]{\TmpLen}{Summer solstice\dotfill}\
+        \PadTo[l]{\text{March}}{\text{June}}~21
+  \end{aligned}\right\}% [**TN: End of Inner 1]
+  }\ 92~\text{days} \\ % [**TN: Middle 1]
+%
+  &\smash[b]{\left.
+  \begin{aligned}%[**TN: Inner 2]
+  \PadTo[l]{\textsc{Autumn:\ }}{\textsc{Summer:}}
+    & \parbox[c]{\TmpLen}{Summer solstice\dotfill}\
+       \PadTo[l]{\text{March}}{\text{June}}~21 \\ %[**TN: Inner 2]
+    & \parbox[c]{\TmpLen}{Autumnal equinox\dotfill}\
+       \PadTo[l]{\text{March}}{\text{Sept.}}~23
+  \end{aligned}\right\}% [**TN: End of Inner 2]
+  }\ 94~\text{days} \\
+  \end{aligned}\right\}\  % [**TN: End of Middle 1]
+\parbox[c]{\RightLen}{\centering Summer half\\$186$~days}&
+\\[5ex] %[**TN: Outer; we've lied to LaTeX about heights, must fudge space here]
+%%
+&
+\left.
+  \begin{aligned}%[**TN: Middle 2: Autumn, Winter]
+  &\smash[t]{\left.
+  \begin{aligned}%[**TN: Inner 3]
+  \textsc{Autumn:\ }
+    & \parbox[c]{\TmpLen}{Autumnal equinox\dotfill}\
+       \PadTo[l]{\text{March}}{\text{Sept.}}~23 \\ %[**TN: Inner 3]
+    & \parbox[c]{\TmpLen}{Winter solstice\dotfill}\
+       \PadTo[l]{\text{March}}{\text{Dec.}}~22
+  \end{aligned}\right\}% [**TN: End of Inner 3]
+  }\ 90~\text{days} \\ % [**TN: Middle 2]
+%
+  &\smash[b]{\left.
+  \begin{aligned}%[**TN: Inner 4]
+  \PadTo[l]{\textsc{Autumn:\ }}{\textsc{Winter:}}
+    & \parbox[c]{\TmpLen}{Winter solstice\dotfill}\
+       \PadTo[l]{\text{March}}{\text{Dec.}}~22 \\ %[**TN: Inner 4]
+    & \parbox[c]{\TmpLen}{Vernal equinox\dotfill}\
+       \PadTo[l]{\text{March}}{\text{March}}~21
+  \end{aligned}\right\}%[**TN: End of Inner 4]
+  }\ 89~\text{days} \\
+  \end{aligned}\right\}\ % [**TN: End of Middle 2]
+\parbox[c]{\RightLen}{\centering Winter half\\$179$~days}&
+\end{align*}
+}
+
+\Paragraph{\nbstretchyspace Hemispheres Unequally Heated.}\nblabel{page:169} For the southern
+\index{Hemispheres unequally heated}%
+hemisphere, spring should be substituted for autumn, and
+summer for winter. From the foregoing it will be seen
+that the northern hemisphere has longer summers and
+shorter winters than the southern hemisphere. Since the
+earth is in perihelion, nearest the sun, December~31, the
+earth as a whole then receives more heat than in the northern
+summer when the earth is farther from the sun.
+Though the earth as a whole must receive more heat in
+December than in July, the northern hemisphere is then
+turned away from the sun and has its winter, which is thus
+warmer than it would otherwise be. The converse is true
+of the northern summer. The earth then being in aphelion
+receives less heat each day, but the northern hemisphere
+being turned toward the sun then has its summer, cooler
+than it would be were this to occur when the earth is in
+perihelion. It is well to remember, however, that while
+the earth as a whole receives more heat in the half
+year of perihelion, there are only $179$~days in that
+portion, and in the cooler portion there are $186$~days,
+so that the total amount of heat received in each
+portion is exactly the same. (See Kepler's Second Law,
+p.~\pageref{page:284}.)
+\index{Insolation|)}%
+%% -----File: 169.png---Folio 170-------
+\index{Altitude, of noon sun|(}%
+\index{Altitude, of noon sun!of polestar or celestial pole|(}%
+\index{Celestial latitude!pole|(}%
+\index{Equator@Equator \indexglossref{Equator}!celestial|(}%
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by altitude of noon sun|(}%
+\index{Pole, celestial}%
+
+\Section{Determination of Latitude from Sun's Meridian
+Altitude.}\nblabel{page:170}
+
+In Chapter~\hyperref[chap:II]{II} we learned how latitude is determined by
+ascertaining the altitude of the celestial pole. We are now
+in a position to see how this is commonly determined by
+reference to the noon sun.
+
+\Paragraph{Relative Positions of Celestial Equator and Celestial Pole.}
+\index{Celestial equator|(}%
+The meridian altitude of the celestial equator at a given
+place and the altitude of the celestial pole at that place are
+complementary angles, that is, together they equal~$90°$.
+Though when understood this proposition is exceedingly
+simple, students sometimes only partially comprehend it,
+and the later conclusions are consequently hazy.
+
+\includegraphicsmid{i169}{Fig.~53}
+
+1. The celestial equator is always $90°$~from the celestial
+pole.
+
+2. An arc of the celestial sphere from the northern horizon
+through the zenith to the southern horizon comprises~$180°$.
+
+3. Since there are $90°$~from the pole to the equator,
+from the northern horizon to the pole and from the
+southern horizon to the equator must together equal~$90°$.
+%% -----File: 170.png---Folio 171-------
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!uses of|(}%
+\index{Declination@Declination \indexglossref{Declination}|(}%
+\index{Nautical almanac@Nautical almanac\phantomsection\label{idx:na}}%
+\index{Pole, celestial}%
+
+One of the following statements is incorrect. Find
+which one it is.
+
+\textit{a.} In latitude~$30°$ the altitude of the celestial pole is~$30°$
+and that of the celestial equator is~$60°$.
+
+\textit{b.} In latitude~$36°$ the altitude of the celestial equator
+is~$54°$.
+
+\textit{c.} In latitude $48°~20'$ the altitude of the celestial equator
+is $41°~40'$.
+
+\textit{d.} If the celestial equator is $51°$~above the southern
+horizon, the celestial pole is $39°$~above the northern horizon.
+
+\textit{e.} If the altitude of the celestial equator is~$49°~31'$, the
+latitude must be~$40°~29'$.
+
+\textit{f.} If the altitude of the celestial equator is~$21°~24'$, the
+latitude is~$69°~36'$.
+
+On March~21 the sun is on the celestial equator.\footnote
+  {Of course, the center of the sun is not on the celestial equator all
+  day, it is there but the moment of its crossing. The vernal equinox
+  is the point of crossing, but we commonly apply the term to the day
+  when the passage of the sun's center across the celestial equator
+  occurs. During this day the sun travels northward less than~$24'$,
+  and since its diameter is somewhat more than~$33'$ some portion of the
+  sun's disk is on the celestial equator the entire day.}
+If on
+\index{Sun!declination of|(}%
+this day the sun's noon shadow indicates an altitude of~$40°$,
+we know that is the altitude of the celestial equator,
+and this subtracted from~$90°$ equals~$50°$, the latitude of
+the place. On September~23 the sun is again on the celestial
+equator, and its noon altitude subtracted from~$90°$
+equals the latitude of the place where the observation is
+made.
+
+\Paragraph{Declination of the Sun.} The declination of the sun or of
+any other heavenly body is its distance north or south of
+the celestial equator. The analemma, shown on page~\pageref{fig:i126},
+gives the approximate declination of the sun for every day
+in the year. The Nautical Almanac, \hyperref[page:125]{Table~1}, for any %[**TN: not labelled 'Table 1' in original text]
+\index{Almanac}%
+%% -----File: 171.png---Folio 172-------
+\index{Greenwich@Greenwich (Am.\ pron., gr\u{e}n$'$\;w\u{\i}ch; Eng.\ pron., gr\u{\i}n$'$\u{\i}j; or gr\u{e}n$'$\u{\i}j), England}%
+month gives the declination very exactly (to the tenth of
+a second) at apparent sun noon at the meridian of Greenwich,
+and the difference in declination for every hour, so
+the student can get the declination at his own longitude
+for any given day very exactly from this table. Without
+good instruments, however, the proportion of error of
+observation is so great that the analemma will answer
+ordinary purposes.
+
+\includegraphicsleft{i171}{Fig.~54}
+
+\Paragraph{How to Determine the Latitude of Any Place.}\nblabel{page:172} By ascertaining
+the noon altitude of the sun, and referring to the
+analemma or a declination
+table, one can easily compute
+the latitude of a place.
+
+1. First determine when
+the sun will be on your meridian
+and its shadow strike
+a north-south line. This is
+discussed on p.~\pageref{page:128}. %[**TN: 'pp.128, 129' in original text]
+
+2. By some device measure
+the altitude of the sun at
+apparent noon; i.e., when the
+shadow is north. \nblabel{page:173}A cardboard
+placed level under a
+window shade, as illustrated
+in Figure~\figureref{i171}{54}, will give surprisingly
+accurate results; a
+carefully mounted quadrant
+(see Fig.~\figureref{i172-1}{55}), however, will
+give more uniformly successful measurements. Angle~$A$
+(Fig.~\figureref{i171}{54}), the shadow on the quadrant, is the altitude of
+the sun. This is apparent from Figure~\figureref{i172-2}{56}, since $xy$~is the
+line to the sun, and $\text{angle}~B = \text{angle}~A$.
+
+\includegraphicsright{i172-1}{Fig.~55}
+
+3. Consult the analemma and ascertain the declination
+%% -----File: 172.png---Folio 173-------
+\index{San Francisco, Calif.}%
+of the sun. Add this to the sun's altitude if south declination,
+and subtract it if north declination. If you are south
+of the equator you
+must subtract declination
+south and
+add declination
+north. (If the addition
+makes the
+altitude of the sun
+more than~$90°$, subtract~$90°$
+from it,
+as under such circumstances
+you are
+north of the equator
+if it is a south
+shadow, or south of
+the equator if it
+is a north shadow.
+This will occur only
+within the tropics.)
+\index{Tropics}%
+
+\includegraphicsleft{i172-2}{Fig.~56}
+
+4. Subtract the result of step three from~$90°$, and the
+remainder is your latitude.
+
+\Paragraph{Example.} For example,
+say you are at San Francisco,
+October~23, and wish
+to ascertain your latitude.
+
+1. Assume you have a
+north-south line. (The sun's
+shadow will cross it on that
+date at $11$~h.\ $54$~m.\ $33$~s.,~\AM,
+Pacific time.)
+
+2. The altitude of the
+sun when the shadow is north is found to be~$41°$.
+%% -----File: 173.png---Folio 174-------
+\index{Chicago, Ill.}%
+\index{Quito@Quito (k\={e}$'$t\={o}), Equador}%
+\index{St.~Petersburg, Russia}%
+
+3. The declination is $11°$~S\@. Adding we get~$52°$, the
+altitude of the celestial equator.
+
+4. $90° - 52°$ equals~$38°$, latitude of place of observer.
+
+Conversely, knowing the latitude of a place, one can
+ascertain the noon altitude of the sun at any given day.
+From the \hyperref[fig:i126]{ana\-lemma} and the \hyperref[page:88]{table of latitudes} many interesting
+problems will suggest themselves, as the following
+examples illustrate.
+
+\includegraphicsleft{i173}{Fig.~57. Taking the altitude of the sun at sea}
+
+\Paragraph{Problem.} 1.~How high above the horizon does the sun
+get at St.~Petersburg on December~22?
+
+\Paragraph{Solution.} The latitude of St.~Petersburg is $59°~56'$~N.,
+hence the altitude of the celestial equator is~$30°~4'$. The
+declination of the sun December~22 is $23°~27'$~S\@. Since
+south is below the celestial equator
+at St.~Petersburg, the altitude of the
+sun is $30°~4'$~less $23°~27'$, or~$6°~37'$.
+
+\Paragraph{Problem.} 2.~At which city is the
+noon sun higher on June~21, Chicago
+or Quito?
+
+\Paragraph{Solution.} The latitude of Chicago
+is~$41°~50'$, and the altitude of the
+celestial equator, $48°~10'$. The declination
+of the sun June~21 is $23°~27'$~N\@.
+North being higher than the
+celestial equator at Chicago, the
+noon altitude of the sun is $48°~10'$~plus
+$23°~27'$, or $71°~37'$.
+
+The latitude of Quito being~$0°$, the
+altitude of the celestial equator is~$90°$.
+\index{Celestial equator|)}%
+The declination of the sun being
+$23°~27'$ from this, the sun's noon altitude
+must be $90°$~less $23°~27'$, or~$66°~33'$. The sun is thus
+\index{Sun!declination of|)}%
+$5°~4'$~higher at Chicago than at the equator on June~21.\nblabel{page:174}
+\index{Altitude, of noon sun|)}%
+\index{Altitude, of noon sun!of polestar or celestial pole|)}%
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!uses of|)}%
+\index{Celestial latitude!pole|)}%
+\index{Equator@Equator \indexglossref{Equator}!celestial|)}%
+%% -----File: 174.png---Folio 175-------
+\index{Horizon@Horizon \indexglossref{Horizon}}%
+
+\Paragraph{Latitude from Moon or Stars.} With a more extended
+knowledge of astronomy and mathematics and with suitable
+instruments, we might ascertain the position of the celestial
+equator in the morning or evening from the moon,
+planets, or stars as well as from the sun. At sea the
+latitude is commonly ascertained by making measurements
+of the altitudes of the sun at apparent noon with the sextant.
+The declination tables are used, and allowances
+are made for refraction and for the ``dip'' of the horizon,
+and the resultant calculation usually gives the latitude
+within about half a mile. At observatories, where the
+latitude must be ascertained with the minutest precision
+possible, it is usually ascertained from star observations
+with a zenith telescope or a ``meridian circle'' telescope,
+and is verified in many ways.
+\index{Declination@Declination \indexglossref{Declination}|)}%
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geographical!determined by altitude of noon sun|)}%
+\index{Seasons|)}%
+%% -----File: 175.png---Folio 176-------
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|(}%
+
+%[**TN: force contents pagebreak and re-output heading for second page]
+\addtocontents{toc}{\protect\newpage}
+\contentspage
+
+\Chapter{IX}{Tides}
+\index{Tides|(}%
+
+\Paragraph{Tides and the Moon.} The regular rise and fall of the
+level of the sea and the accompanying inflows and outflows
+of streams, bays, and channels, are called tides. Since
+very ancient times this action of the water has been associated
+with the moon because of the regular interval
+elapsing between a tide and the passage of the moon over
+the meridian of the place, and a somewhat uniform increase
+in the height of the tide when the moon in its orbit around
+the earth is nearest the sun or is farthest from it. This
+unquestioned lunar influence on the ocean has doubtless
+been responsible as the basis for thousands of unwarranted
+associations of cause and effect of weather, vegetable
+growth, and even human temperament and disease with
+phases of the moon or planetary or astral conditions.
+
+\Paragraph{Other Periodic Ebbs and Flows.} Since there are other
+periodical ebbs and flows due to various causes, it may be
+well to remember that the term tide properly applies only
+to the periodic rise and fall of water due to unbalanced
+forces in the attraction of the sun and moon. Other conditions
+which give rise to more or less periodical ebbs and
+flows of the oceans, seas, and great lakes are:
+
+\textit{a.} Variation in atmospheric pressure; low barometer
+\index{Barometer}%
+gives an uplift to water and high barometer a depression.
+
+\textit{b.} Variability in evaporation, rainfall and melting snows
+produces changes in level of adjacent estuaries.
+
+\textit{c.} Variability in wind direction, especially strong and
+continuous seasonal winds like monsoons, lowers the
+%% -----File: 176.png---Folio 177-------
+\index{Month@Month \indexglossref{Month}!sidereal}%
+\index{Month@Month \indexglossref{Month}!synodic}%
+\index{Orbit, of earth!of moon}%
+\index{Sidereal, clock!month}%
+level on the leeward of coasts and piles it up on the windward
+side.
+
+\textit{d.} Earthquakes sometimes cause huge waves.
+
+A few preliminary facts to bear in mind when considering
+the causes of tides:
+
+\Section{The Moon}
+
+\Paragraph{Sidereal Month.} The moon revolves around the earth
+in the same direction that the earth revolves about the
+sun, from west to east. If the moon is observed near a
+given star on one night, twenty-four hours later it will be
+found, on the average, about $13.2°$~to the eastward. To
+reach the same star a second time it will require as many
+days as that distance is contained times in~$360°$ or about
+$27.3$~days. This is the sidereal month, the time required
+for one complete revolution of the moon.
+
+\Paragraph{Synodic Month.} Suppose the moon is near the sun at a
+given time, that is, in the same part of the celestial sphere.
+During the twenty-fours hours following, the moon will
+creep eastward~$13.2°$ and the sun~$1°$. The moon thus
+gains on the sun each day about~$12.2°$, and to get in conjunction
+with it a second time it will take as many days
+as $12.2°$~is contained in~$360°$ or about $29.5$~days. This is
+called a synodic (from a Greek word meaning ``meeting'')
+month, the time from conjunction with the sun---new
+moon---until the next conjunction or new moon. The
+term is also applied to the time from opposition or full
+\index{Opposition}%
+moon until the next opposition or full moon. If the
+phases of the moon are not clearly understood it would
+be well to follow the \hyperref[page:9]{suggestions} on this subject in the
+first chapter.
+
+\Paragraph{Moon's Orbit.} The moon's orbit is an ellipse, its
+%% -----File: 177.png---Folio 178-------
+\index{Apogee@Apogee \indexglossref{Apogee}}%
+\index{Orbit, of earth!of moon}%
+nearest point to the earth is called perigee (from \textit{peri},
+\index{Perigee}%
+around or near; and \textit{ge}, the earth) and is about $221,617$
+miles. Its most distant point is called apogee (from \textit{apo},
+from; and \textit{ge}, earth) and is about $252,972$ miles. The
+average distance of the moon from the earth is $238,840$
+miles. The moon's orbit is inclined to the ecliptic $5°~8'$
+and thus may be that distance farther north or south than
+the sun ever gets.
+
+The new moon is said to be in \emph{conjunction} with the sun,
+\index{Conjunction}%
+both being on the same side of the earth. If both are
+then in the plane of the ecliptic an eclipse of the sun must
+\index{Eclipse}%
+take place. The moon being so small, relatively (diameter
+$2,163$~miles), its shadow on the earth is small and
+thus the eclipse is visible along a relatively narrow path.
+
+The full moon is said to be in \emph{opposition} to the sun,
+\index{Opposition}%
+it being on the opposite side of the earth. If, when in
+opposition, the moon is in the plane of the ecliptic it will
+be eclipsed by the shadow of the earth. When the moon
+is in conjunction or in opposition it is said to be in \emph{syzygy}.
+\index{Syzygy}%
+
+\Section{Gravitation}
+\index{Gravitation}%
+
+\Paragraph{Laws Restated.} This force was discussed in the \hyperref[page:16]{first
+chapter} where the two laws of gravitation were explained
+and illustrated. The term gravity is applied to the force
+of gravitation exerted by the earth (see Appendix, p.~\pageref{sec:gravity}).
+Since the explanation of tides is simply the application of
+the laws of gravitation to the earth, sun, and moon, we
+may repeat the two laws:
+
+First law: The force of gravitation varies directly as
+the mass of the object.
+
+Second law: The force of gravitation varies inversely
+as the square of the distance of the object.
+%% -----File: 178.png---Folio 179-------
+
+\Paragraph{\nbstretchyspace Sun's Attraction Greater, but Moon's Tide-Produc\-ing
+Influence Greater.} There is a widely current notion that
+since the moon causes greater tides than the sun, in the
+ratio of $5$~to~$2$, the moon must have greater attractive
+influence for the earth than the sun has. Now this cannot
+be true, else the earth would swing around the moon as
+certainly as it does around the sun. Applying the laws of
+gravitation to the problem, we see that the sun's attraction
+\index{Gravitation}%
+for the earth is approximately $176$~times that of the
+moon.\footnote
+  {For the method of demonstration, see p.~\pageref{page:19}. The following data
+  are necessary: Earth's mass,~$1$; sun's mass, $330,000$; moon's mass,~$\frac{1}{81}$;
+  distance of earth to sun, $93,000,000$ miles; distance of earth to moon,
+  $239,000$ miles.}
+
+The reasoning which often leads to the erroneous conclusion
+just referred to, is probably something like this:
+
+\SubparagraphNoSpace{Major premise:} Lunar and solar attraction causes tides.
+
+\SubparagraphNoSpace{Minor premise:} Lunar tides are higher than solar tides.
+
+\SubparagraphNoSpace{Conclusion:} Lunar attraction is greater than solar
+attraction.
+
+We have just seen that the conclusion is in error. One
+or both of the premises must be in error also. A study
+of the causes of tides will set this matter right.
+
+\Section{Causes of Tides\protect\footnotemark}
+\footnotetext{A mathematical treatment will be found in the \hyperref[page:290]{Appendix}.}
+
+It is sometimes erroneously stated that wind is caused
+by heat. It would be more nearly correct to say that
+wind is caused by the unequal heating of the atmosphere.
+Similarly, it is not the attraction of the sun and moon
+for the earth that causes tides, it is the unequal attraction
+for different portions of the earth that gives rise to unbalanced
+forces which produce tides.
+%% -----File: 179.png---Folio 180-------
+
+\includegraphicsmid{i179}{Fig.~58}
+
+Portions of the earth toward the moon or sun are $8,000$
+miles nearer than portions on the side of the earth opposite
+the attracting body, hence the force of gravitation is
+slightly different at those points as compared with other
+points on the earth's surface. It is obvious, then, that at
+$A$~and~$B$ (Fig.~\figureref{i179}{58}) there are two unbalanced forces, that
+is, forces not having counterparts elsewhere to balance
+them. At these two sides, then, tides are produced,
+since the water of the oceans yields to the influence of
+these forces. That this may be made clear, let us examine
+these tides separately.
+
+\Paragraph{The Tide on the Side of the Earth Toward the Moon.} If $A$
+is $239,000$ miles from the moon, $B$~is $247,000$ miles away
+from it, the diameter of the earth being~$AB$ (Fig.~\figureref{i179}{58}).
+Now the attraction of the moon at $A$,~$C$, and~$D$, is away
+from the center of the earth and thus lessens the force of
+gravity at those points, lessening more at~$A$ since $A$~is
+nearer and the moon's attraction is exerted in a line
+%% -----File: 180.png---Folio 181-------
+\index{Establishment, the, of a port}%
+directly opposite to that of gravity. The water, being
+fluid and easily moved, yields to this lightening of its
+weight and tends to ``pile up under the moon.'' We thus
+have a tide on the side of the earth toward the moon.
+
+\Paragraph{Tidal Wave Sweeps Westward.} As the earth turns
+on its axis it brings successive portions of the earth toward
+the moon and this wave sweeps around the globe as nearly
+as possible under the moon. The tide is retarded somewhat
+by shallow water and the configuration of the coast
+and is not found at a given place when the moon is at
+meridian height but lags somewhat behind. The time
+between the passage of the moon and high tide is called
+the \emph{establishment of the port}. This time varies greatly at
+different places and varies somewhat at different times of
+the year for the same place.
+
+\Paragraph{Solar Tides Compared with Lunar Tides.} Solar tides
+are produced on the side of the earth toward the sun for
+exactly the same reason, but because the sun is so far
+away its attraction is more uniform upon different parts
+of the earth. If $A$~is $93,000,000$ miles from the sun, $B$~is
+$93,008,000$ miles from the sun. The ratio of the squares of
+these two numbers is much nearer unity than the ratio
+of the numbers representing the squares of the distances
+of $A$~and~$B$ from the moon. If the sun were as near as
+the moon, the attraction for~$A$ would be greater by an
+enormous amount as compared with its attraction for~$B$.
+Imagine a ball made of dough with lines connected to
+every particle. If we pull these lines uniformly the ball
+will not be pulled out of shape, however hard we pull. If,
+however, we pull some lines harder than others, although
+we pull gently, will not the ball be pulled out of shape?
+Now the pull of the sun, while greater than that of the
+moon, is exerted quite evenly throughout the earth and
+%% -----File: 181.png---Folio 182-------
+\index{Great Britain}%
+has but a slight tide-producing power. The attraction of
+the moon, while less than that of the sun, is exerted less
+evenly than that of the sun and hence produces greater
+tides.
+
+It has been demonstrated that the tide-producing force
+of a body varies inversely as the cube of its distance and
+directly as its mass. Applying this to the moon and sun
+we get:
+\begin{flalign*}
+          &&\text{Let } T &= \text{sun's tide-producing power}, \\
+\text{and}&&            t &= \text{moon's tide-producing power}.&\phantom{\text{and}}
+\end{flalign*}
+
+The sun's mass is $26,500,000$ times the moon's mass,
+\[
+\therefore T : t  \dblcolon 26,500,000 : 1.
+\]
+
+But the sun's distance from the earth is $390$~times the
+moon's distance,
+\[
+\therefore T : t \dblcolon \frac{1}{390^3} : 1.
+\]
+
+Combining the two proportions, we get,
+\[
+T : t \dblcolon 2 : 5.
+\]
+
+It has been shown that, owing to the very nearly equal
+attraction of the sun for different parts of the earth, a
+body's weight is decreased when the sun is overhead, as
+compared with the weight six hours from then, by only
+$\dfrac{1}{20,000,000}$; that is, an object weighing a ton varies in
+weight $\frac{3}{4}$~of a grain from sunrise to noon. In case of the
+moon this difference is about $2\frac{1}{2}$~times as great, or nearly
+$2$~grains.
+%% -----File: 182.png---Folio 183-------
+\index{Gravity@Gravity\phantomsection\label{idx:g}|(}%
+
+\Paragraph{Tides on the Moon.} It may be of interest to note that
+the effect of the earth's attraction on different sides of the
+moon must be twenty times as great as this, so it is
+thought that when the moon was warmer and had oceans\footnote
+  {The presence of oceans or an atmosphere is not essential to the
+  theory, indeed, is not usually taken into account. It seems most certain
+  that the earth is not perfectly rigid, and the theory assumes that
+  the planets and the moon have sufficient viscosity to produce body
+  tides.}
+the tremendous tidal waves swinging around in the opposite
+direction to its rotation caused a gradual retardation
+of its rotation until, as ages passed, it came to keep the
+same face toward the earth. The planets nearest the sun,
+Mercury and Venus, probably keep the same side toward
+\index{Mercury}%
+\index{Venus}%
+the sun for a similar reason. Applying the same reasoning
+to the earth, it is believed that the period of rotation must
+be gradually shortening, though the rate seems to be
+entirely inappreciable.
+
+\includegraphicsmid{i183}{Fig.~59}
+
+\nblabel{page:183}\Paragraph{The Tide on the Side of the Earth Opposite the Moon.} A
+planet revolving around the sun, or a moon about a planet,
+takes a rate which varies in a definite mathematical ratio
+to its distance (see p.~\pageref{page:285}). The sun pulls the earth toward
+itself about one ninth of an inch every second. If
+the earth were nearer, its revolutionary motion would be
+faster. In case of planets having several satellites it is
+observed that the nearer ones revolve about the planet
+faster than the outer ones (see p.~\pageref{page:255}). Now if the
+earth were divided into three separate portions, as in
+Figure~\figureref{i183}{59}, the ocean nearest the sun, the earth proper,
+and the ocean opposite the sun would have three separate
+motions somewhat as the dotted lines show. Ocean~$A$
+would revolve faster than earth~$C$ or ocean~$B$. If these
+three portions were connected by weak bands their stretching
+apart would cause them to separate entirely. The
+%% -----File: 183.png---Folio 184-------
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+tide-producing power at~$B$ is this tendency it has to fall
+away, or more strictly speaking, to fall toward the sun \emph{less
+rapidly than the rest of the earth}.
+
+\Paragraph{Moon and Earth Revolve About a Common Center of
+Gravity.}\nblabel{page:184} What has been said of the earth's annual revolution
+around the sun applies equally to the earth's
+monthly swing around the center of gravity common to
+the earth and the moon. We commonly say the earth
+revolves about the sun and the moon revolves about the
+earth. Now the earth attracts the sun, in its measure,
+just as truly as the sun attracts the earth; and the moon
+attracts the earth, in the ratio of its mass, as the earth
+attracts the moon. Strictly speaking, the earth and sun
+revolve around their common center of gravity and the
+moon and earth revolve around their center of gravity.
+%% -----File: 184.png---Folio 185-------
+\index{North America}%
+\index{Tidal wave, bore, etc.}%
+It is as if the earth were connected with the moon by
+a rigid bar of steel (that had no weight) and the two,
+thus firmly bound at the ends of this rod $239,000$~miles
+long, were set spinning. If both were of the same weight,
+they would revolve about a point equidistant from each.
+The weight of the moon being somewhat less than $\frac{1}{81}$ that
+of the earth, this center of gravity, or point of balance,
+is only about $1,000$~miles from the earth's center.
+
+\Paragraph{Spring Tides.} When the sun and moon are in conjunction,
+\index{Conjunction}%
+\index{Spring tides}%
+both on the same side of the earth, the unequal
+attraction of both for the side toward them produces an
+unusually high tide there, and the increased centrifugal
+force at the side opposite them also produces an unusual
+high tide there. Both solar tides and both lunar tides
+are also combined when the sun and moon are in opposition.
+\index{Opposition}%
+Since the sun and moon are in syzygy (opposition
+\index{Syzygy}%
+or conjunction) twice a month, high tides, called spring
+tides, occur at every new moon and at every full moon.
+If the moon should be in perigee, nearest the earth, at the
+same time it was new or full moon, spring tides would be
+unusually high.
+
+\Paragraph{Neap Tides.} When the moon is at first or last quarter---moon,
+\index{Neap tides}%
+earth, and sun forming a right angle---the solar
+tides occur in the trough of the lunar tides and they are
+not as low as usual, and lunar tides occurring in the trough
+of the solar tides are not so high as usual.
+
+\includegraphicsmid{i185}{Fig.~60. Co-tidal lines} %[**TN: hyphen added for consistency]
+
+\Paragraph{Course of the Tidal Wave.} While the tidal wave is generated
+at any point under or opposite the sun or moon, it
+is out in the southern Pacific Ocean that the absence of
+\index{Pacific Ocean}%
+shallow water and land areas offers least obstruction to its
+movement. Here a general lifting of the ocean occurs,
+and as the earth rotates the lifting progresses under or
+opposite the moon or sun from east to west. Thus a huge
+\index{Gravity@Gravity\phantomsection\label{idx:g}|)}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|)}%
+%% -----File: 185.png---Folio 186-------
+\index{Atlantic Ocean}%
+\index{Co-tidal lines}%
+wave with crest extending north and south starts twice a
+day off the western coast of South America. The general
+\index{South America}%
+position of this crest is shown on the co-tidal map, one line %[**TN: hyphen added for consistency]
+for every hour's difference in time. The tidal wave is
+retarded along its northern extremity, and as it sweeps
+along the coast of northern South America and North
+America, the wave assumes a northwesterly direction and
+sweeps down the coast of Asia at the rate of about $850$~miles
+\index{Asia}%
+per hour. The southern portion passes across the
+Indian Ocean, being retarded in the north so that the
+\index{Indian Ocean}%
+southern portion is south of Africa when the northern portion
+\index{Africa}%
+has just reached southern India. The time it has
+\index{India}%
+taken the crest to pass from South America to south Africa
+is about $30$~hours. Being retarded by the African coast,
+the northern portion of the wave assumes an almost northerly
+direction, sweeping up the Atlantic at the rate of about
+$700$~miles an hour. It moves so much faster northward
+in the central Atlantic than along the coasts that the crest
+%% -----File: 186.png---Folio 187-------
+\index{Bores, tidal}%
+bends rapidly northward in the center and strikes all points
+of the coast of the United States within two or three hours
+\index{United States}%
+of the same time. To reach France the wave must swing
+\index{France}%
+around Scotland and then southward across the North Sea,
+\index{North Sea}%
+\index{Scotland}%
+reaching the mouth of the Seine about $60$~hours after
+starting from South America. A new wave being formed
+\index{South America}%
+about every $12$~hours, there are thus several of these tidal
+waves following one another across the oceans, each
+slightly different from the others.
+
+While the term ``wave'' is correctly applied to this tidal
+movement it is very liable to leave a wrong impression
+upon the minds of those who have never seen the sea.
+When thinking of this tidal wave sweeping across the
+ocean at the rate of several hundred miles per hour, we
+should also bear in mind its height and length (by height
+is meant the vertical distance from the trough to the crest,
+and by length the distance from crest to crest). Out in
+midocean the height is only a foot or two and the length
+is hundreds of miles. Since the wave requires about three
+hours to pass from trough to crest, it is evident that a ship
+at sea is lifted up a foot or so during six hours and then
+as slowly lowered again, a motion not easily detected. On
+the shore the height is greater and the wave-length shorter,
+for about six hours the water gradually rises and then for
+about six hours it ebbs away again. Breakers, bores, and
+unusual tide phenomena are discussed on p.~\pageref{page:189}.
+
+\Paragraph{Time Between Successive Tides.} The time elapsing
+from the passage of the moon across a meridian until it
+\index{Meridian}%
+crosses the same meridian again is $24$~hours $51$~min.\footnote
+  {More precisely, $24$~h.~$50$~m.~$51$~s. This is
+  the mean lunar day, or interval between successive passages of the moon over a given meridian.
+  The apparent lunar day varies in length from $24$~h.~$38$~m.\ to $25$~h.~$5$~m.\
+  for causes somewhat similar to those producing a variation in the length
+  of the apparent solar day.}
+This,
+%% -----File: 187.png---Folio 188-------
+\index{Day@Day \indexglossref{Day}\phantomsection\label{idx:d}, astronomical!lunar}%
+\index{Month@Month \indexglossref{Month}!sidereal}%
+in contradistinction to the solar and sidereal day, may
+be termed a lunar day. It takes the moon $27.3$~solar days
+to revolve around the earth, a sidereal month. In one
+day it journeys $\frac{10}{273}$~of a day or $51$~minutes. So if the
+moon was on a given meridian at 10~\AM, on one day,
+\index{Meridian}%
+by 10~\AM{} the next day the moon would have moved
+$12.2°$ eastward, and to direct the same meridian a second
+time toward the moon it takes on the average $51$~minutes
+longer than $24$~hours, the actual time varying from $38$~m.\ to
+$1$~h.~$6$~m.\ for various reasons. The tides of one day, then,
+are later than the tides of the preceding day by an average
+interval of $51$~minutes.
+
+\includegraphicsmid{i187}{Fig.~61. Low tide}
+
+In studying the movement of the tidal wave, we observed
+that it is retarded by shallow water. The spring tides
+\index{Spring tides}%
+being higher and more powerful move faster than the
+neap tides, the interval on successive days averaging only
+\index{Neap tides}%
+$38$~minutes. Neap tides move slower, averaging somewhat
+over an hour later from day to day. The establishment
+of a port, as previously explained, is the average time
+%% -----File: 188.png---Folio 189-------
+\index{Amazon, bores of}%
+\index{Bores, tidal}%
+\index{Fundy, Bay of}%
+\index{La Condamine@La Condamine (lä\;kôn$'$dä\;m\={e}n)}%
+\index{Tidal wave, bore, etc.}%
+elapsing between the passage of the moon and the high
+tide following it. The establishment for Boston is $11$~hours,
+$27$~minutes, although this varies half an hour at different
+times of the year.
+
+\Paragraph{Height of Tides.}\nblabel{page:189} The height of the tide varies greatly
+in different places, being scarcely discernible out in midocean,
+averaging only $1\frac{1}{2}$~feet in the somewhat sheltered
+Gulf of Mexico, but averaging $37$~feet in the Bay of Fundy.
+\index{Gulf of Mexico}%
+\index{Mexico!Gulf of}%
+The shape and situation of some bays and mouths of
+rivers is such that as the tidal wave enters, the front part
+of the wave becomes so steep that huge breakers form
+and roll up the bay or river with great speed. These
+bores, as they are called, occur in the Bay of Fundy, in
+the Hoogly estuary of the Ganges, in that of the Dordogne,
+the Severn, the Elbe, the Weser, the Yangtze, the
+Amazon, etc.
+
+\Paragraph{Bore of the Amazon.} A description of the bore of the
+Amazon, given by La Condamine in the eighteenth century,
+gives a good idea of this phenomenon. ``During three
+days before the new and full moons, the period of the
+highest tides, the sea, instead of occupying six hours to
+\index{Tides|)}%
+reach its flood, swells to its highest limit in one or two
+minutes. The noise of this terrible flood is heard five or
+six miles, and increases as it approaches. Presently you
+see a liquid promontory, $12$~or $15$~feet high, followed by
+another, and another, and sometimes by a fourth. These
+watery mountains spread across the whole channel, and
+advance with a prodigious rapidity, rending and crushing
+everything in their way. Immense trees are instantly
+uprooted by it, and sometimes whole tracts of land are
+swept away.''
+%% -----File: 189.png---Folio 190-------
+\index{Calendar!Jewish}%
+\index{Meridian|(}%
+\index{Projections, map|(}%
+
+\Chapter{X}{Map Projections}
+\index{Map projections|(}%
+
+\includegraphicsleft[19]{i189}{Fig.~62}
+\quad\par%[**TN: Dummy paragraph to aid pagination]
+
+\First{To} represent the curved surface of the earth, or any
+portion of it, on the plane surface of a map, involves
+serious mathematical difficulties. Indeed, it is impossible
+to do so with perfect accuracy.
+The term projection,
+as applied to the
+representation on a plane
+of points corresponding
+to points on a globe, is
+not always used in
+geography in its strictly
+mathematical sense, but
+denotes any representation
+on a plane of parallels
+\index{Parallels|(}%
+and meridians of the
+earth.
+
+\Section{The Orthographic Projection}
+\index{Orthographic projection|(}%
+
+\sloppy
+This is, perhaps, the
+most readily understood
+projection, and is one of
+the oldest known, having
+been used by the ancient
+Greeks for celestial representation. The globe truly represents
+the relative positions of points on the earth's surface.
+%% -----File: 190.png---Folio 191-------
+It might seem that a photograph of a globe would
+correctly represent
+on a flat surface
+the curved surface
+of the earth. A
+glance at Figure~\figureref{i189}{62},
+from a photograph
+of a globe, shows
+the parallels near
+the equator to be
+farther apart than
+those  near  the
+poles. This is not
+the way they are
+on the globe. The
+orthographic projection
+is the representation of the globe as a photograph
+would show it from a great distance.
+
+\includegraphicsright{i190-1}{Fig.~63. Equatorial orthographic projection}
+
+\Paragraph{Parallels and Meridians Farther Apart in Center of Map.}
+Viewing a globe from a distance, we observe that parallels
+%% -----File: 191.png---Folio 192-------
+and meridians appear somewhat as represented in
+Figure~\figureref{i190-1}{63}, being farther apart toward the center and increasingly
+nearer toward the outer portion. Now it is
+obvious from Figure~\figureref{i190-2}{64} that the farther the eye is placed
+from the globe, the less will be the distortion, although a
+removal to an infinite distance will not obviate all distortion.
+Thus the eye at~$x$ sees lines to $E$~and~$F$ much
+nearer together than lines to $A$~and~$B$, but the eye at the
+greater distance sees less difference.
+
+\includegraphicsmid{i190-2}{Fig.~64}
+
+\fussy
+When the rays are perpendicular to the axis, as in Figure~\figureref{i191}{65},
+the parallels at $A$,~$B$, $C$, $D$, and~$E$ will be seen on the
+tangent plane~$XY$
+at $A'$,~$B'$, $C'$, $D'$,
+and~$E'$. While the
+distance from~$A$ to~$B$
+on the globe
+is practically the
+same as the distance
+from~$D$ to~$E$,
+to the distant eye
+$A'$~and~$B'$ will
+appear much nearer
+together than $D'$~and~$E'$.
+Since $A$
+(or~$A'$) represents a pole and $E$ (or~$E'$) the equator, line~$XY$
+is equivalent to a central meridian and points $A'$,~$B'$,
+etc., are where the parallels cross it.
+
+\Paragraph{How to Lay off an Equatorial Orthographic Projection.}
+If parallels and meridians are desired for every $15°$, divide
+the circle into twenty-four equal parts; any desired number
+of parallels and meridians, of course, may be drawn. Now
+connect opposite points with straight lines for parallels
+(as in Fig.~\figureref{i191}{65}). The reason why parallels are straight lines
+%% -----File: 192.png---Folio 193-------
+\index{Ellipse@Ellipse \indexglossref{Ellipse}}%
+\index{Pole, celestial!terrestrial|(}%
+in the equatorial orthographic projection is apparent if
+one remembers that if the eye is in the plane of the equator
+and is at an infinite distance, the parallels will lie in practically
+the same plane as the eye.
+
+\includegraphicsright{i191}{Fig.~65}
+
+\sloppy
+To lay off the meridians, mark on the equator points
+exactly as on the central meridian where parallels intersect
+it. The meridians may now be made as arcs of circles
+passing through the poles and these points. With one
+foot of the compasses in the equator, or equator extended,
+place the other so that
+it will pass through the
+poles and one of these
+points. After a little
+trial it will be easy to
+lay off each of the meridians
+in this way.
+
+\fussy
+\includegraphicsright[14]{i192}{Fig.~66. Western hemisphere, in equatorial orthographic projection}
+
+To be strictly correct
+the meridians should not
+be arcs of circles as just
+suggested but should be
+semi-ellipses with the
+central meridian as
+major axis as shown in
+Figure~\figureref{i192}{66}. While somewhat more difficult, the student
+should learn how thus to lay them off. To construct the
+ellipse, one must first locate the foci. This is done by taking
+half the major axis (central meridian) as radius and with
+the point on the equator through which the meridian is
+to be constructed as center, describe an arc cutting the
+center meridian on each side of the equator. These points
+of intersection on the central meridian are the foci of the
+ellipse, one half of which is a meridian. By placing a pin
+at each of the foci and also at the point in the equator
+%% -----File: 193.png---Folio 194-------
+where the meridian must cross and tying a string as a loop
+around these three pins, then withdrawing the one at the
+equator, the ellipse may be made as described in the \hyperref[page:22]{first chapter}.
+
+\includegraphicsright{i193}{Fig.~67. Polar orthographic projection}
+
+\Paragraph{How to Lay off a Polar Orthographic Projection.} This
+is laid off more easily than the former projection. Here
+the eye is conceived to be directly above a pole and the
+equator is the boundary
+of the hemisphere seen.
+It is apparent that
+from this position the
+equator and parallels
+will appear as circles
+and, since the planes
+of the meridians pass
+through the eye, each
+meridian must appear
+as a straight line.
+
+Lay off for the equator
+a circle the same
+size as the preceding
+one (Fig.~\figureref{i191}{65}), subdividing
+it into twenty-four parts, if meridians are desired
+for every~$15°$. Connect these points with the center,
+which represents the pole. On any diameter mark off
+distances as on the center meridian of the equatorial
+orthographic projection (Fig.~\figureref{i191}{65}). Through these points
+draw circles to represent parallels. You will then have
+the complete projection as in Figure~\figureref{i193}{67}.
+
+Projections may be made with any point on the globe as
+center, though the limits of this book will not permit the
+rather difficult explanation as to how it is done for latitudes
+other than $0°$ or~$90°$. With the parallels and
+%% -----File: 194.png---Folio 195-------
+meridians projected, the map may be drawn. The student
+should remember that all maps which make any claim to
+accuracy or correctness are made by locating points of
+an area to be represented according to their latitudes and
+longitudes; that is, in reference to parallels and meridians.
+It will be observed that the orthographic system of projection
+crowds together areas toward the outside of the map
+and the scale of miles suitable for the central portion will
+\index{Scale of miles}%
+not be correct for the outer portions. For this reason a
+scale of miles never appears upon a hemisphere made on
+this projection.
+
+\begin{SmallText}
+\Section{\smallsize SUMMARY}
+In the orthographic projection:
+\index{Orthographic projection|)}%
+
+\begin{slist}
+\item[1.] The eye is conceived to be at an infinite distance.
+
+\item[2.] Meridians and parallels are farther apart toward the center of
+the map.
+
+\item[3.] When a point in the equator is the center, parallels are straight
+lines.
+
+\item[4.] When a pole is at the center, meridians are straight lines. If the
+northern hemisphere is represented, north is not toward the top
+of the map but toward the center.
+\end{slist}
+
+\medskip %[**TN: to help later pagination]
+\end{SmallText}
+
+\Section{Stereographic Projection}
+\index{Stereographic projection|(}%
+
+In the stereographic projection the eye is conceived to be
+upon the surface of the globe, viewing the opposite hemisphere.
+Points on the opposite hemisphere are projected
+upon a plane tangent to it. Thus in Figure~\figureref{i195}{68} the eye is
+at~$E$ and sees $A$~at~$A'$, $B$~at~$B'$, $C$~at~$C'$, etc. If the earth
+were transparent, we should see objects on the opposite
+half of the globe from the view point of this projection.
+%% -----File: 195.png---Folio 196-------
+
+\includegraphicsmid{i195}{Fig.~68}
+
+\includegraphicsleft{i196-1}{Fig.~69. Equatorial stereographic projection}
+
+\Paragraph{\nbstretchyspace How to Lay off an Equatorial Stereographic Projection.}
+In Figure~\figureref{i195}{68}, $E$ represents the eye at the equator, $A$~and~$N$
+are the poles and $A'N'$~is the corresponding meridian of
+the projection with $B'$,~$C'$, etc., as the points where the
+parallels cross the meridian. Taking the line~$A'N'$ of Figure~\figureref{i195}{68}
+as diameter, construct upon it a circle (see Fig.~\figureref{i196-1}{69}).
+%% -----File: 196.png---Folio 197-------
+Divide the circumference into twenty-four equal parts
+and draw parallels as
+arcs of circles. Lay
+off the equator and
+subdivide it the same
+as the central meridian,
+that is, the same as
+$A'N'$ of Figure~\figureref{i195}{68}.
+Through the points in
+the equator, draw meridians
+as arcs of circles
+and the projection is
+complete.
+
+\smallskip
+\begin{figure}[!ht]% widths chosen to fit in textwidth, in proportion to original sizes
+  \centering%
+  \figurelabel{i196-2}%
+  \includegraphics[width=.42\textwidth]{./images/i196-2.jpg}%
+  \hspace{0.03\textwidth}%
+  \figurelabel{i196-3}%
+  \includegraphics[width=.55\textwidth]{./images/i196-3.jpg}%
+  % caption widths match image widths above
+  \caption*{\begin{tabular}{@{}p{.42\textwidth}@{\hspace{0.03\textwidth}}p{.55\textwidth}@{}}
+    \centering Fig.~70. Polar stereographic projection &
+    \centering Fig.~71. Northern hemisphere in polar stereographic projection
+  \end{tabular}}%
+\end{figure}
+
+\Paragraph{The Polar Stereographic
+Projection} is
+made on the same
+plan as the polar orthographic projection, excepting that
+the parallels have the
+distances from the pole
+that are represented by the points in $A'N'$ of Figure~\figureref{i195}{68}
+(see Figs.~\figureref{i196-2}{70},~\figureref{i196-3}{71}).
+%% -----File: 197.png---Folio 198-------
+
+Areas are crowded together toward the center of the
+map when made on the stereographic projection and a
+scale of miles suitable for the central portion would be too
+small for the outer portion. This projection is often used,
+however, because it \DPtypo{it}{is} so easily laid off.
+
+\includegraphicsmid{i197}{Fig.~72. Hemispheres in equatorial stereographic projection}
+
+%\begin{SmallText}
+{\smallsize
+\Section{\smallsize SUMMARY}
+In the stereographic projection:
+\begin{slist}
+\item[1.] The eye is conceived to be on the surface of the globe.
+
+\item[2.] Meridians and parallels are nearer together toward the center of
+the map.
+
+\item[3.] When a point in the equator is the center of the map, parallels and
+meridians are represented as arcs of circles.
+
+\item[4.] When a pole is the center, meridians are straight lines.
+\end{slist}
+}%\end{SmallText}
+
+\Section{Globular Projection.}
+\index{Globular projection|(}%
+
+\includegraphicsright{i198-1}{Fig.~73}
+
+With the eye at an infinite distance (as in the orthographic
+\index{Orthographic projection}%
+projection), parallels and meridians are nearer
+together toward the \emph{outside} of the map; with the eye on
+the surface (as in the stereographic projection), they are
+\index{Stereographic projection|)}%
+nearer together toward the \emph{center} of the map. It would
+seem reasonable to expect that with the eye at some point
+%% -----File: 198.png---Folio 199-------
+intermediate between an infinite distance from the surface
+and the surface itself that the parallels and meridians
+would be equidistant at different
+portions of the map. That point is the sine of an
+angle of~$45°$, or a little less
+than the length of a radius
+away from the surface.
+To find this distance at which
+the eye is conceived to be
+placed in the globular projection,
+make a circle of the same
+size as the one which is the
+basis of the map to be made,
+draw two radii at an angle of~$45°$ (one eighth of the circle)
+and draw a line,~$AB$,
+from the extremity
+of one radius
+perpendicular
+to the other radius.
+The length of this
+perpendicular is the
+distance sought ($AB$,
+Fig.~\figureref{i198-1}{73}).
+
+Thus with the eye
+at~$E$ (Fig.~\figureref{i198-2}{74}) the
+pole~$A$ is projected
+to the tangent plane
+at~$A'$, $B$~at~$B'$, etc.,
+and the distances
+$A'B'$, $B'C'$,~etc., are
+practically equal so that they are constructed as though
+they were equal in projecting parallels and meridians.
+%% -----File: 199.png---Folio 200-------
+
+\includegraphicsleft{i198-2}{Fig.~74}
+
+\sloppy
+\Paragraph{How to Lay off an Equatorial Globular Projection.} As in
+the orthographic or stereographic projections, a circle is
+\index{Orthographic projection}%
+\index{Stereographic projection}%
+divided into equal parts,
+according to the number
+of parallels desired, the
+central meridian and
+equator being subdivided
+into half as many
+equal parts. Parallels
+and meridians may be
+drawn as arcs of circles, being sufficiently accurate for
+ordinary purposes (see Fig.~\figureref{i199-1}{75}).
+
+\fussy
+\includegraphicsleft{i199-1}{Fig.~75. Hemispheres in equatorial globular projection}
+
+\ParagraphNoSpace{The polar globular projection} is laid off precisely
+like the orthographic and the stereographic projections
+having the pole as the center, excepting that the concentric
+circles representing
+parallels are equidistant (see
+Fig.~\figureref{i199-2}{76}).
+
+By means of starlike additions
+to the polar globular projection
+(see Fig.~\figureref{i200}{77}), the entire
+globe may be represented. If
+folded back, the rays of the
+star would meet at the south
+pole.
+\includegraphicsright{i199-2}{Fig.~76. Polar globular projection}
+It should be noticed
+\index{South, on map}%
+that ``south'' in this projection
+is in a line directly
+away from the center; that is, the top of the map is south,
+the bottom south, and the sides are also south. While
+portions of the southern hemisphere are thus spread out,
+proportional areas are well represented, South America
+\index{South America}%
+and Africa being shown with little distortion of area and
+\index{Africa}%
+outline.
+%% -----File: 200.png---Folio 201-------
+
+\quad\par%[**TN: Dummy paragraph to aid pagination]
+
+\includegraphicsleft{i200}{Fig.~77. World in polar globular projection}
+
+The globular projection is much used to represent
+hemispheres, or with the
+star map to represent
+the entire globe, because
+the parallels on a meridian
+or meridians on a
+parallel are equidistant
+and show little exaggeration
+of areas. For this
+reason it is sometimes
+called an equidistant
+projection, although
+there are other equidistant
+projections. It
+is also called the De~la~Hire projection from its discoverer
+\index{De la Hire, Phillippe@De la Hire, Phillippe (f\={e}\;l\={e}p$'$ d\.{e}\;l\.{a}\;\={e}r$'$)}%
+(1640--1718).
+
+%\begin{SmallText}
+{\smallsize
+\Section{\smallsize SUMMARY}
+In the globular projection:
+\index{Globular projection|)}%
+\begin{slist}
+\item[1.]  The eye is conceived to be at a certain distance from the globe
+(sine~$45°$).
+
+\item[2.]  Meridians are divided equidistantly by parallels, and parallels are
+divided equidistantly by meridians.
+
+\item[3.]  When a pole is the center of the map, meridians are straight lines.
+
+\item[4.]  There is little distortion of areas.
+\end{slist}
+}%\end{SmallText}
+
+\Section{The Gnomonic Projection}
+\index{Gnomonic projection|(}%
+
+\includegraphicsleft{i201}{Fig.~78}
+
+When we look up at the sky we see what appears to be
+a great dome in which the sun, moon, planets, and stars
+are located. We seem to be at the center of this celestial
+sphere, and were we to imagine stars and other heavenly
+bodies to be projected beyond the dome to an imaginary
+plane we should have a gnomonic projection. Because
+of its obvious convenience in thus showing the position
+%% -----File: 201.png---Folio 202-------
+of celestial bodies, this projection is a very old one, having
+often been used by the ancients for celestial maps.
+
+Since the eye is at the center for mapping the celestial
+sphere, it is conceived to be at the center of the earth in
+projecting parallels and meridians of the earth. As will
+be seen from Figure~\figureref{i201}{78},
+the distortion is very
+great away from the
+center of the map and
+an entire hemisphere
+cannot be shown.
+
+All great circles on
+this projection are represented
+as straight lines.
+This will be apparent if
+one imagines himself at
+the center of a transparent
+globe having parallels
+and meridians
+traced upon it. Since
+the plane of every great
+circle passes through the
+center of the globe, the
+eye at that point will
+see every portion of a
+great circle as in one
+plane and will project
+it as a straight line. As will be shown later, it is because
+of this fact that sailors frequently use maps made
+on this projection.
+
+\includegraphicsright{i202-1}{Fig.~79. Polar gnomonic projection}
+
+\Paragraph{To Lay off a Polar Gnomonic Projection.} Owing to the
+fact that parallels get so much farther apart away from
+the center of the map, the gnomonic projection is almost
+%% -----File: 202.png---Folio 203-------
+never made with any other point than the pole for center,
+and then only for latitudes about forty degrees from the
+pole. The polar gnomonic
+projection is
+made like the polar
+projections previously
+described, excepting
+that parallels intersect
+the meridians at the
+distances represented
+in Figure~\figureref{i201}{78}. The
+meridians, being great
+circles, are represented
+as straight lines and
+the parallels as concentric
+circles.
+
+\Paragraph{Great Circle Sailing.} It would seem at first thought
+\index{Great circle sailing}%
+that a ship sailing to a
+point due eastward,
+say from New York to
+Oporto, would follow
+the course of a parallel,
+that is, would sail
+due eastward. This,
+however, would not be
+its shortest course.
+The solution of the
+following little catch
+problem in mathematical
+geography will
+make clear the reason
+for this. ``A man was forty rods due east of a bear,
+his gun would carry only thirty rods, yet with no change
+%% -----File: 203.png---Folio 204-------
+of position he shot and killed the bear. Where on earth
+were they?'' Solution: This could occur only near the
+pole where parallels are very small circles. The bear was
+westward from the man and westward is along the course
+of a parallel. The bear was thus distant forty rods in a
+curved line from the man but the bullet flew in a straight
+line (see Fig.~\figureref{i202-2}{80}).
+
+\includegraphicsleft{i202-2}{Fig.~80}
+
+The shortest distance between two points on the earth
+is along the arc of a great circle. A great circle passing
+through New York and Oporto passes a little to the north
+\index{Oporto, Portugal}%
+\index{New York}%
+of the parallel on which both cities are located. Thus it
+is that the course of vessels plying between the United
+States and Europe curves, somewhat to the northward of
+parallels. This following of a great circle by navigators
+is called great circle sailing. The equator is a great circle
+\index{Great circle sailing}%
+and parallels near it are almost of the same length. In
+sailing within the tropics, therefore, there is little advantage
+in departing from the course of a parallel. Besides
+this, the trade winds and doldrums control the choice of
+routes in that region and the Mercator projection is always
+\index{Mercator projection}%
+used in sailing there. In higher latitudes the gnomonic
+projection is commonly used.
+
+Although the gnomonic projection is rarely used excepting
+by sailors, it is important that students understand
+the principles underlying its construction since the most
+important projections yet to be discussed are based upon it.
+
+%\begin{SmallText}
+{\smallsize
+\Section{\smallsize SUMMARY}
+In the gnomonic projection:
+\index{Gnomonic projection|)}%
+
+\begin{slist}
+\item[1.] The eye is conceived to be at the center of the earth.
+
+\item[2.] There is great distortion of distances away from the center of the map.
+
+\item[3.] A hemisphere cannot be shown.
+
+\item[4.] All great circles are shown as straight lines.
+\begin{ssublist}
+\item[\textit{a.}] Therefore it is used largely for great circle sailing.
+\end{ssublist}
+
+\item[5.] The pole is usually the center of the map.
+\end{slist}
+}%\end{SmallText}
+%% -----File: 204.png---Folio 205-------
+
+\Section{The Homolographic Projection}
+\index{Homolographic projection|(}%
+
+The projections thus far discussed will not permit the
+representation of the entire globe on one map, with the
+exception of the starlike extension of the polar globular
+projection. The homolographic projection is a most
+ingenious device which is used quite extensively to represent
+the entire globe without distortion of areas. It is a
+modification of the globular projection.
+
+\includegraphicsmid{i204}{Fig.~81. Homolographic projection}
+
+\Paragraph{How to Lay off a Homolographic Projection.} First lay
+off an equatorial globular projection, omitting the parallels.
+The meridians are semi-ellipses, although those which are
+no more than $90°$~from the center meridian may be drawn
+as arcs of circles.
+
+Having laid off the meridians as in the equatorial
+globular projection, double the length of the equator,
+extending it equally in both directions, and subdivide
+these extensions as the equator was subdivided. Through
+%% -----File: 205.png---Folio 206-------
+these points of subdivision and the poles, draw ellipses for
+meridians.
+
+\Subparagraph{To draw the outer elliptical meridians.} Set the points of
+the compasses at the distance from the point through
+which the meridian is to be drawn to the central meridian.
+Place one point of the compasses thus set at a pole and
+mark off points on the equator for foci of the ellipse.
+Drive pins in these foci and also one in a pole. Around
+these three pins form a loop with a string. Withdraw
+the pin at the pole and draw the ellipse as described on
+\index{Ellipse@Ellipse \indexglossref{Ellipse}}%
+page~\pageref{page:22}. This process must be repeated for each pair of
+meridians.
+
+\includegraphicsmid{i205}{Fig.~82. World in homolographic projection}
+
+The parallels are straight lines, as in the orthographic
+projection, somewhat nearer together toward the poles.
+If nine parallels are drawn on each side of the equator,
+they may be drawn in the following ratio of distances,
+beginning at the equator: $2$, $1\frac{8}{9}$, $1\frac{7}{9}$, $1\frac{6}{9}$, $1\frac{5}{9}$, $1\frac{4}{9}$, $1\frac{3}{9}$, $1\frac{2}{9}$,~$1\frac{1}{9}$.
+This will give an approximately correct representation.
+
+One of the recent books to make frequent use of this
+projection is the ``Commercial Geography'' by Gannett,
+\index{Gannett, Garrison and Houston's Commercial Geography}%
+Garrison, and Houston (see Fig.~\figureref{i205}{82}).
+%% -----File: 206.png---Folio 207-------
+
+\Paragraph{Equatorial Distances of Parallels.} The following table
+gives the exact relative distances of parallels from the
+equator. Thus if a map twenty inches wide is to be
+drawn, ten inches from equator to pole, the first parallel
+will be $.69$~of an inch from the equator, the second $1.37$~inches,~etc.
+\begin{center}
+\smallsize
+\setlength\tabcolsep{3pt}
+\settowidth{\TmpLen}{tance}%
+\begin{tabular}{@{}*{5}{c|c||}c|c@{}}
+\hline
+$\phi$ & \parbox[c]{\TmpLen}{\tablespacertop\centering Dis-\\tance\tablespacerbot} &
+$\phi$ & \parbox[c]{\TmpLen}{\centering Dis-\\tance} &
+$\phi$ & \parbox[c]{\TmpLen}{\centering Dis-\\tance} &
+$\phi$ & \parbox[c]{\TmpLen}{\centering Dis-\\tance} &
+$\phi$ & \parbox[c]{\TmpLen}{\centering Dis-\\tance} &
+$\phi$ & \parbox[c]{\TmpLen}{\centering Dis-\\tance} \\
+\hline
+\tablespacertop
+ $\Z5°$ & .069 &
+ $20°$ & .272 &
+ $35°$ & .468 &
+ $50°$ & .651 &
+ $65°$ & .814 &
+ $80°$ & \Z.945 \\
+10\phantom{°} & .137 & 25\phantom{°} & .339 & 40\phantom{°} & .531 &
+55\phantom{°} & .708 & 70\phantom{°} & .862 & 85\phantom{°} & \Z.978\\
+15\phantom{°} & .205 & 30\phantom{°} & .404 & 45\phantom{°} & .592 &
+60\phantom{°} & .762 & 75\phantom{°} & .906 & 90\phantom{°} &  1.000\tablespacerbot\\
+\hline
+\end{tabular}
+\end{center}
+
+The homolographic projection is sometimes called the
+Mollweide projection from its inventor (1805), and the
+\index{Mollweide projection}%
+Babinet, or Babinet-homolographic projection from a
+\index{Babinet}%
+noted cartographer who used it in an atlas (1857). From
+the fact that within any given section bounded by parallels
+and meridians, the area of the surface of the map is
+equal to the area within similar meridians and parallels
+of the globe, is it sometimes called the equal-surface projection.
+
+%\begin{SmallText}
+{\smallsize
+\Section{\smallsize SUMMARY}
+
+In the homolographic projection:
+\index{Homolographic projection|)}%
+
+\begin{itemize}
+\item[1.]  The meridians are semi-ellipses, drawn as in the globular projection,
+$360°$~of the equator being represented.
+
+\item[2.]  The parallels are straight lines as in the orthographic projection.
+
+\item[3.]  Areas of the map represent equal areas of the globe.
+
+\item[4.]  There is no distortion of area and not a very serious distortion
+of form of continents.
+
+\item[5.]  The globe is represented as though its surface covered half of
+an exceedingly oblate spheroid.
+\end{itemize}
+}%\end{SmallText}
+%% -----File: 207.png---Folio 208-------
+
+\Section{The Van~der Grinten Projection}
+
+The homolographic projection was invented early in the
+nineteenth century. At the close of the century Mr.~Alphons
+\index{Van der Grinten, Alphons}%
+Van~der Grinten of Chicago invented another projection
+\index{Chicago, Ill.}%
+by which the entire surface of the earth may be
+represented. This ingenious system reduces greatly the
+angular distortion incident to the homolographic projection
+and for the inhabitable portions of the globe there is
+very little exaggeration of areas.
+
+\includegraphicsmid{i207}{Fig.~83. World in Van~der Grinten projection}
+
+In the Van der Grinten projection the outer boundary
+is a meridian circle, the central meridian and equator are
+straight lines, and other parallels and meridians are arcs
+of circles. The area of the circle is equal to the surface
+of a globe of one half the diameter of this circle. The
+equator is divided into~$360°$, but the meridians are, of
+course, divided into~$180°$.
+%% -----File: 208.png---Folio 209-------
+
+\includegraphicsright[10]{i208-1}{Fig.~84. World in Van~der Grinten projection}
+\quad\par
+
+\bigskip
+
+A modification of
+this projection is
+shown in Figure~\figureref{i207}{83}.
+In this the
+central meridian is
+only one half the
+length of the equator,
+and parallels are
+at uniform distances
+along this meridian.
+
+\bigskip
+
+\Section{Cylindrical Projections}
+\index{Cylindrical projection|(}%
+
+\Paragraph{Gnomonic Cylindrical
+Projection.} In
+\index{Gnomonic@Gnomonic (n\={o}\;m\u{o}n$'$\u{\i}k), cylindrical projection|(}%
+this projection the sheet on which the map is to be made
+is conceived to be
+wrapped as a cylinder
+around the
+globe, touching the
+equator. The eye
+is conceived to be
+at the center of the
+globe, projecting the
+parallels and meridians
+upon the tangent
+cylinder. Figure~\figureref{i208-2}{85}
+shows the
+cylinder partly unwrapped
+with meridians
+as parallel
+straight lines and
+parallels also as parallel straight lines. As in the gnomonic
+%% -----File: 209.png---Folio 210-------
+projection, the parallels are increasingly farther apart away
+from the equator.
+
+\includegraphicsleft{i208-2}{Fig.~85}
+
+\sloppy
+An examination of Figure~\figureref{i209}{86} will show the necessity
+for the increasing distances of parallels in higher latitudes.
+The eye at the center~($E$) sees $A$~at~$A'$, $B$~at $B'$,~etc. Beyond
+$45°$~from the equator the distance between parallels
+becomes very great. $A'B'$ represents the same distance
+($15°$~of latitude) as~$G'H'$, but is over twice as long on the
+map. At~$A'$ ($60°$~north
+latitude) the
+meridians of the
+globe are only half
+as far apart as they
+are at the equator,
+but they are represented
+on the map
+as though they were
+just as far apart
+there as at the equator.
+Because of the
+rapidly increasing
+distances of parallels,
+to represent
+higher latitude than~$60°$
+would require a
+very large sheet, so
+the projection is usually
+modified for a map of the earth as a whole, sometimes
+arbitrarily.
+
+\fussy
+$G'H'$~is the distance from the equator to the first parallel,
+and since a degree of latitude is about equal to a
+degree of longitude there, this distance may be taken
+between meridians.
+%% -----File: 210.png---Folio 211-------
+
+\sloppy
+\Paragraph{Stereographic Cylindrical Projection.} For reasons just
+given, the gnomonic or central cylindrical projection needs
+\includegraphicsleft{i209}{Fig.~86} %[**TN: mid-paragraph figure placement]
+reduction to show the poles at all or any high latitudes
+without great distortion. Such a reduction is well shown
+in the stereographic projection. In this the eye is conceived
+\index{Stereographic projection}%
+to be on the equator, projecting each meridian from
+the view point of the meridian opposite to it. Figure~\figureref{i210}{87}
+shows the plan on which it is laid off, meridians being parallel
+straight lines
+and equidistant and
+parallels being parallel
+straight lines at
+increasing distances
+away from the equator.
+
+\fussy
+\Paragraph{The Mercator (Cylindrical)
+Projection.}
+\index{Mercator projection|(}%
+\index{Globular projection}%
+\index{Gnomonic projection}%
+\index{Homolographic projection}%
+\index{Orthographic projection}%
+In the orthographic,
+stereographic, globular,
+gnomonic, homolographic,
+and Van~der
+Grinten projections,
+parallels or
+meridians, or both,
+are represented as
+curved lines. It
+should be borne in
+mind that directions on the earth are determined from
+parallels and meridians. North and south are along a
+\index{North, line!on map}%
+\index{South, on map}%
+meridian and when a meridian
+\includegraphicsright{i210}{Fig.~87} %[**TN: mid-paragraph figure placement]
+is represented as a curved
+line, north and south are along that curved line. Thus the
+two arrows shown at the top of Figure~\figureref{i204}{81}, are pointing in
+almost exactly opposite directions and yet each is pointing
+\index{Gnomonic@Gnomonic (n\={o}\;m\u{o}n$'$\u{\i}k), cylindrical projection|)}%
+%% -----File: 211.png---Folio 212-------
+due north. The arrows at the bottom point opposite
+each other, yet both point due south. The arrows pointing
+to the right point the same way, yet one points north
+and the other points south. A line pointing toward the
+\index{North, line!on map}%
+\index{South, on map}%
+top of a map may or may not point north. Similarly,
+parallels lie in a due east-west direction and to the right
+on a map may or may not be to the east.
+\index{Pole, celestial!terrestrial|)}%
+
+It should be obvious by this time that the map projections
+studied thus far represent directions in a most unsatisfactory
+manner, however well they may represent areas.
+Now to the sailor the principal value of a chart is to show
+directions to steer his course by and if the direction is represented
+by a curved line it is a slow and difficult process
+for him to determine his course. We have seen that the
+gnomonic projection employs straight lines to represent
+arcs of great circles, and, consequently, this projection is
+used in great circle sailing. The Mercator projection shows
+\index{Great circle sailing}%
+all parallels and meridians as straight lines at proportional
+distances, hence directions as straight lines, and is another,
+and the only other, kind of map used by sailors in plotting
+their courses.
+
+\includegraphicsright{i214}{Fig.~89}
+
+\Subparagraph{Maps in Ancient Times.} Before the middle of the fifteenth
+century, sailors did not cover very great portions
+of the earth's surface in continuous journeys out of sight
+of land where they had to be guided almost wholly by the
+stars. Mathematical accuracy in maps was not of very
+great importance in navigation until long journeys had to
+be made with no opportunity for verification of calculations.
+Various roughly accurate map projections were
+made. The map sent to Columbus about the year 1474
+\index{Columbus, Christopher}%
+by the Italian astronomer Toscanelli, with which he suggested
+\index{Toscanelli}%
+sailing directions across the ``Sea of Darkness,'' is
+an interesting illustration of a common type of his day.
+%% -----File: 212.png---Folio 213-------
+
+\index{North America}%
+\index{South America}%
+\index{Toscanelli}%
+\includegraphicssideways{i212}{Fig.~88}
+%% -----File: 213.png---Folio 214-------
+
+The long journeys of the Portuguese along the coast of
+Africa and around to Asia and the many voyages across
+\index{Africa}%
+\index{Asia}%
+the Atlantic early in the sixteenth century, made accurate
+map projection necessary. About the middle of that century,
+Emperor Charles~V of Spain employed a Flemish
+\index{Charles V., Emperor of Spain}%
+\index{Spain}%
+mathematician named Gerhard Kramer to make maps for
+\index{Kramer, Gerhard}%
+the use of his sailors. The word Kramer means, in German,
+``retail merchant,'' and this translated into Latin,
+then the universal language of science, becomes Mercator,
+and his invention of a very valuable and now widely used
+map projection acquired his Latinized name.
+
+\Subparagraph{Plan of Mercator Chart.} The Mercator projection is
+made on the same plan as the other cylindrical projections,
+excepting as to the distances between parallels.
+The meridians are represented as parallel lines, whereas
+on the globe they converge. There is thus a distortion of
+longitudes, greater and greater, away from the equator.
+Now the Mercator projection makes the parallels farther
+apart away from the equator, exactly proportional to the
+meridional error. Thus at latitude~$60°$ the meridians on
+the earth are almost exactly half as far apart as at the
+equator, but being equidistant on the map, they are represented
+as twice as far apart as they should be. The
+parallels in that portion of the Mercator map are accordingly
+made twice as far apart as they are near the equator.
+Since the distortion in latitude exactly equals the distortion
+in longitude and parallels and meridians are straight
+lines, all directions are represented as straight lines. A
+navigator has simply to draw upon the map a line from
+the point where he is to the point to which he wishes to
+sail in a direct course, measure the angle which this line
+forms with a parallel or meridian, and steer his ship according
+to the bearings thus obtained.
+%% -----File: 214.png---Folio 215-------
+
+\Subparagraph{To Lay off a Mercator Projection.} Figure~\figureref{i214}{89} shows the
+simplest method of laying off this projection. From the
+extremity of each radius drop a line to the nearest radius,
+parallel to the tangent~$A'L$. The lengths of these lines,
+respectively, represent the distances\footnote
+  {Technically speaking, the distance is the tangent of the angle of
+  latitude and any \hyperref[page:312]{table of natural tangents} will answer nearly as well
+  as the \hyperref[page:217]{table of meridional parts}, although the latter is more accurate,
+  being corrected for the oblateness of the meridian.}
+between parallels.
+Thus $N'M$ equals $CP$, $K'N'$ equals $BN$, $A'K'$ equals $AK$.
+The meridians are
+equidistant and are
+the same distance
+apart as the first
+parallel is from the
+equator.
+
+\smallskip
+\includegraphicsmid{i215}{Fig.~90. World in mercator projection}
+
+The table of meridional
+parts on page~\pageref{page:217} gives the
+relative distances of
+parallels from the
+equator. By means
+of this table a more
+exact projection
+may be laid off than
+by the method just suggested. To illustrate: Suppose we
+wish a map about twenty inches wide to include the 70th~parallels.
+We find in the table that $5944.3$~is the distance
+to the equator. Then, since the map is to extend $10$~inches
+on each side of the equator, $\dfrac{10}{5944.3}$~is the scale to be used
+in making the map; that is $1$~inch on the map will be
+represented by $10~\text{inches} ÷ 5944.3$. Suppose we wish to
+%% -----File: 215.png---Folio 216-------
+lay off parallels ten degrees apart. The first parallel to be
+drawn north of the equator has, according to the table,
+$599.1$ for its meridional distance. This multiplied by
+$\dfrac{10}{5944.3}$ equals slightly more than~$1$. Hence the parallel~$10°$
+should be laid off $1$~inch from the equator. The 20th~parallel
+has for its meridional distance $1217.3$. This multiplied
+by the scale $\dfrac{10}{5944.3}$ gives $2.03$~inches from the
+equator. The 30th~parallel has a meridional distance
+$1876.9$, this multiplied by the scale gives $3.15$~inches. In
+like manner the other parallels are laid off. The meridians
+will be $\dfrac{10}{5944.3} × 60$ or $600~\text{inches} ÷ 5944.3$ for every degree,
+or for ten degrees $6000~\text{inches} ÷ 5944.3$, which equals
+$1.01$~inches. This makes the map $36.36$~inches long ($1.01~\text{inches}
+× 36 = 36.36~\text{inches}$).
+
+\begin{center}
+\smallsize\nblabel{page:217}
+\index{Meridional parts, table of}%
+$\begin{array}{*{9}{r|}r}
+\multicolumn{10}{c}{\textsc{Table of Meridional Parts\tablespacerbot\footnotemark}}\\
+\hline
+\tablespacertop
+ 1° &   59.6 & 18° & 1091.1 & 35° & 2231.1 & 52° & 3647.1 & 69° &  5773.1 \\
+ 2° &  119.2 & 19° & 1154.0 & 36° & 2304.5 & 53° & 3745.4 & 70° &  5944.3 \\
+ 3° &  178.9 & 20° & 1217.3 & 37° & 2378.8 & 54° & 3846.1 & 71° &  6124.0 \\
+ 4° &  238.6 & 21° & 1281.0 & 38° & 2454.1 & 55° & 3949.1 & 72° &  6313.0 \\
+ 5° &  298.4 & 22° & 1345.1 & 39° & 2530.5 & 56° & 4054.9 & 73° &  6512.4 \\
+ 6° &  358.3 & 23° & 1409.7 & 40° & 2607.9 & 57° & 4163.4 & 74° &  6723.6 \\
+ 7° &  418.3 & 24° & 1474.7 & 41° & 2686.5 & 58° & 4274.8 & 75° &  6948.1 \\
+ 8° &  478.4 & 25° & 1540.3 & 42° & 2766.3 & 59° & 4389.4 & 76° &  7187.8 \\
+ 9° &  538.6 & 26° & 1606.4 & 43° & 2847.4 & 60° & 4507.5 & 77° &  7444.8 \\
+10° &  599.1 & 27° & 1673.1 & 44° & 2929.9 & 61° & 4628.1 & 78° &  7722.1 \\
+11° &  659.7 & 28° & 1740.4 & 45° & 3013.7 & 62° & 4754.7 & 79° &  8023.1 \\
+12° &  720.6 & 29° & 1808.3 & 46° & 3099.0 & 63° & 4884.5 & 80° &  8352.6 \\
+13° &  781.6 & 30° & 1876.9 & 47° & 3185.9 & 64° & 5018.8 & 81° &  8716.4 \\
+14° &  842.9 & 31° & 1946.2 & 48° & 3274.5 & 65° & 5158.0 & 82° &  9122.7 \\
+15° &  904.5 & 32° & 2016.2 & 49° & 3364.7 & 66° & 5302.5 & 83° &  9583.0 \\
+16° &  966.4 & 33° & 2087.0 & 50° & 3456.9 & 67° & 5452.8 & 84° & 10114.0 \\
+17° & 1028.6 & 34° & 2158.6 & 51° & 3551.0 & 68° & 5609.5 & 85° & 10741.7\tablespacerbot\\
+\hline
+\end{array}$
+\footnotetext{From Bowditch's \textit{Practical Navigator}.}
+\index{American Practical Navigator}%
+\index{Practical Navigator}%
+\index{Bowditch, Nathaniel}%
+\end{center}
+
+We see, then, that the same scale of miles cannot be used
+\index{Scale of miles}%
+for different parts of the map, though within~$30°$ of the
+equator representations of areas will be in very nearly true
+proportions. The parallels in a map not wider than this,
+say for Africa, may be drawn equidistant and the same
+\index{Africa}%
+%% -----File: 216.png---Folio 217-------
+distance apart  as the meridians, the inaccuracy not being
+very great.
+
+\begin{SmallText}
+\Section{\smallsize SUMMARY}
+In the cylindrical projection:
+\begin{slist}
+\item[1.] A cylinder is conceived to be wrapped around the globe, tangent
+to the equator.
+
+\item[2.] All parallels and meridians are represented as straight lines, the
+former intersecting the latter at right angles.
+
+\item[3.] The parallels are made at increasing distances away from the
+equator:
+\begin{ssublist}
+\item[\textit{a.}] In the gnomonic projection, as though projected from
+the center of the earth to the tangent cylinder.
+
+\item[\textit{b.}] In the stereographic projection, as projected from the
+equator upon an opposite meridian, the projection point
+varying for each meridian.
+
+\item[\textit{c.}] In the Mercator projection, at distances proportional to
+the meridional excess.
+
+Directions are better represented in this projection than in
+any other. Here northward is directly toward the top
+\index{North, line!on map}%
+of the map, eastward directly toward the right, etc.
+For this reason it is the projection most commonly
+employed for navigators' charts.
+\end{ssublist}
+%% -----File: 217.png---Folio 218-------
+
+\item[4.] There is great distortion of areas and outlines of continents in
+high latitudes; Greenland appears larger than South America.
+\index{Greenland}%
+\index{South America}%
+
+\item[5.] The entire globe may be represented in one continuous map.
+
+\item[6.] The same scale of miles cannot be used for high latitudes that is
+used near the equator.
+\end{slist}
+\index{Cylindrical projection|)}%
+\end{SmallText}
+
+\Section{Conic Projection}
+\index{Conic projection|(}%
+
+The portion of a sphere between the
+planes of two parallels which are near
+together is very similar to the zone of a
+cone (see Fig.~\figureref{i217-1}{91}). Hence, if we imagine
+a paper in the form of a cone placed
+upon the globe and parallels and
+meridians projected upon this cone from
+the center of the globe, then this conical
+map unrolled, we can understand
+this system.
+
+\includegraphicsleft{i217-1}{Fig.~91}
+
+Along the parallel tangent to the
+cone, points on the map will correspond
+exactly to points upon the globe. Parallels
+which are near the line of tangency will be represented
+very much in the relative
+positions they occupy on the
+globe. In a narrow zone, therefore,
+near the tangent parallel,
+there will be very little distortion
+in latitudes and longitudes
+and an area mapped within the
+zone will be very similar in form
+and area to the form and area
+as it appears upon the globe
+itself. For this reason the conic
+projection, or some modification of it, is almost always
+employed in representing small areas of the earth's surface.
+%% -----File: 218.png---Folio 219-------
+
+\includegraphicsright{i217-2}{Fig.~92}
+
+\Paragraph{To Lay off a Conic Projection.} If the forty-fifth parallel
+\index{North America}%
+is the center of the
+area to be mapped,
+draw two straight
+lines tangent to the
+forty-fifth parallel
+of a circle (see Fig.~\figureref{i218-1}{93}).
+Project upon
+these lines points
+for parallels as in
+the gnomonic projection.
+With the
+apex as center,
+draw arcs of circles
+through these points for parallels. Meridians are straight
+lines meeting at the
+apex and are equidistant
+along any parallel.
+
+It will be observed
+that parallels are farther
+apart away from the
+tangent parallel ($45°$,
+in this case) as in
+the Mercator projection
+\index{Mercator projection|)}%
+they are farther apart
+away from the equator,
+which is tangent to the
+globe in that projection.
+There is also an exaggeration
+of longitudes
+away from the tangent
+parallel. Because of this
+lengthening of parallels, meridians are sometimes curved
+%% -----File: 219.png---Folio 220-------
+inwardly to prevent too much distortion of areas. The
+need for this will be apparent if one draws parallels beyond
+the equator, for he will find they are longer than
+the equator itself unless meridians curve inwardly there.
+
+\index{Europe}%
+\includegraphicsright{i218-1}{Fig.~93}
+
+\sloppy
+By taking the tangent
+parallel ten degrees
+north of the equator and
+reducing distances of
+parallels, a fan-shaped
+map of the world may
+be shown. In this map
+of the world on the
+conic projection, there
+is even greater distortion
+of parallels south of
+the equator, but since
+meridians converge somewhat north of the equator there
+is less distortion in northern latitudes. Since most of the
+land area of the globe is in the northern hemisphere, this
+%% -----File: 220.png---Folio 221-------
+projection is much better suited to represent the entire
+world than the Mercator projection.
+\index{Mercator projection}%
+
+\includegraphicsleft{i218-2}{Fig.~94. North America in conic projection}
+
+\Paragraph{Bonne's (Conic) Projection.} This is a modification of
+\index{Bonne's projection}%
+the conic projection as previously described to prevent
+exaggeration of areas away from the parallel which is conceived
+to be touching the globe. The central meridian is
+a straight line and parallels are concentric equidistant
+circles. The distance between parallels is the length
+of the arc of the circle which is used as a basis for the
+projection. For ordinary purposes, the distance~$AB$
+(Fig.~\figureref{i218-1}{93}) may be taken for each of the distances between
+parallels.
+
+\fussy
+\includegraphicsmid{i219-1}{Fig.~95. The world in conic projection}
+
+\includegraphicsright{i219-2}{Fig.~96. Europe in conic projection}
+
+Having laid off the central meridian and marked off the
+arcs for parallels, the true distance of the meridian on each
+parallel is laid off and the meridian
+is drawn through these
+points. This gives a gentle
+inward curve for meridians
+toward the outside of the map
+of continents. Instead of following
+Bonne's system with
+strict accuracy, the map maker
+sometimes makes the curve a
+little less in lower latitudes,
+allowing a slight exaggeration
+of areas to permit the putting
+in of more details where they
+are needed.
+
+\includegraphicsright{i220}{Fig.~97}
+
+\Paragraph{Intersecting Conic Projection.} Where a considerable
+\index{Intersecting conic projection}%
+extent in latitude is to be represented, the cone is sometimes
+conceived to cut into the sphere. In this case,
+each meridian intersects the sphere at two parallels (see
+Fig.~\figureref{i220}{97}) and since along and near the tangent parallels
+%% -----File: 221.png---Folio 222-------
+($A$~and~$B$) there is little distortion, this plan is better
+adapted for a map showing greater width north and south
+than is the conic projection.
+
+The map of Europe well illustrates this difference.
+\index{Europe}%
+Europe lies between $35°$~and~$75°$ north latitude. On a
+conic projection the tangent parallel would be~$55°$. Near
+this parallel there would be no exaggeration of areas
+but at the extreme north and south, $20°$~away from this
+parallel, there would be considerable distortion. If, instead,
+we make an intersecting conic projection, we should have
+\index{Intersecting conic projection}%
+the cone pass through parallels $45°$~and~$65°$ and along
+these parallels there would be no distortion and no part
+of the map being more than~$10°$ away from these lines,
+there would be very little exaggeration anywhere.
+
+\index{Africa}%
+\index{Europe}%
+\includegraphicsleft{i222}{Fig.~98. Africa and Europe in polyconic projection}
+\index{Polyconic projection|(}%
+
+It should be noticed that the region between the intersections
+of the meridians must be projected back toward
+the center of the sphere and thus be made smaller in the
+map than it appears on the globe. The central parallel
+would be too short in proportion to the rest. Since this
+area of Europe (between $45°$~and~$65°$) is the most important
+portion and should show most details, it would be a
+serious defect, from the practical map maker's point of
+view, to minify it.
+
+\Paragraph{Polyconic Projection.} This differs from the conic projection
+in that it is readjusted at each parallel which is
+drawn, so that each one is tangent to the sphere. This
+makes the circumscribing cone bent at each parallel, a
+series of conic sections. The word polyconic means
+``many cones.'' The map constructed on this projection
+is thus accurate along each parallel, instead of along but
+one as in the conic projection or along two as in the intersecting
+conic projection. For representing small areas
+this is decidedly the most accurate projection known.
+%% -----File: 222.png---Folio 223-------
+Since the zone along each parallel is projected on an
+independent cone, the point
+which is the apex for one cone
+will not be the same for any
+other (unless both north and
+south latitudes are shown in
+the same map). In the conic
+projection the parallels are all
+made from the apex of the
+cone as the center. In the
+polyconic projection each parallel
+has its own conical apex
+and hence its own center. This
+may easily be observed by a
+comparison of the parallels in
+Figure~\figureref{i218-2}{94} (conic projection,
+all made from one center) and
+those in Figure~\figureref{i222}{98} (polyconic projection, each made from
+a different center)\DPtypo{}{.}
+
+\begin{SmallText}
+\Section{\smallsize SUMMARY}
+In the conic projection:
+\begin{slist}
+\item[1.] A cone is conceived to be fitted about a portion of the globe,
+tangent to some parallel.
+
+\item[2.] The tangent parallel shows no distortion and portions near it have
+but little. This projection is therefore used extensively for
+mapping small areas.
+
+\begin{ssublist}
+\item[\textit{a.}] In the conic projection on the gnomonic or central plan,
+the eye is conceived to be at the center of the globe,
+parallels are crowded closer together toward the central
+parallel, and distant areas are exaggerated.
+
+The cone may be conceived to intersect the globe at two
+parallels, between which there is a diminution of areas and
+beyond which there is an exaggeration of areas.
+%% -----File: 223.png---Folio 224-------
+
+\item[\textit{b.}] In the Bonne projection parallels are drawn at equidistant
+\index{Bonne's projection}%
+intervals from a common center and meridians are slightly
+curved to prevent distortion in longitudes.
+
+\item[\textit{c.}] In the polyconic projection many short conic sections are
+\index{Polyconic projection|)}%
+conceived to be placed about the globe, one for each parallel
+represented. Parallels are drawn from the apexes of the
+cones.
+\end{ssublist}
+\end{slist}
+\end{SmallText}
+
+\Section{The Scale}
+\index{Scale of miles}%
+
+The area of any map bears some proportion to the actual
+area represented. If the map is so drawn that each mile
+shall be represented by one inch on the map, since one
+mile equals $63,360$ inches, the scale is said to be $1 : 63,360$.
+This is often written fractionally, $\dfrac{1}{63,360}$. A scale of two
+inches to the mile is $1 : 31,680$. These, of course, can be
+used only when small areas are mapped. The following
+scales with their equivalents are most commonly used in
+the United States Geological Survey, the first being the
+\index{United States}%
+scale employed in the valuable geological folios covering
+a large portion of the United States.
+\begin{center}
+\smallsize%
+\begin{tabular}{l@{\ }l}
+Scale $1:125,000$, & $1$~mile $= 0.50688$~inches. \\
+Scale $1:90,000$,  & $1$~mile $= 0.70400$~inches. \\
+Scale $1:62,500$,  & $1$~mile $= 1.01376$~inches. \\
+Scale $1:45,000$,  & $1$~mile $= 1.40800$~inches.
+\end{tabular}
+\end{center}
+
+\Section{Some Conclusions}
+
+The following generalizations from the discussion of
+map projections seem appropriate.
+
+1. In all maps north and south lie along meridians and
+\index{North, line!on map}%
+\index{South, on map}%
+east and west along parallels. The top of the map may or
+may not be north; indeed, the cylindrical projection is the
+\index{Cylindrical projection}%
+only one that represents meridians by perpendicular lines.
+\index{Conic projection|)}%
+%% -----File: 224.png---Folio 225-------
+
+2. Maps of the same country on different projections
+may show different shapes and yet each may be correct.
+To make maps based upon some arbitrary system of
+triangles or lines is not scientific and often is not even
+helpful.
+
+3. Owing to necessary distortions in projecting the
+parallels and meridians, a scale of miles can rarely be used
+\index{Parallels|)}%
+with accuracy on a map showing a large area.
+
+4. Straight lines on maps are not always the shortest
+distances between two points. This will be clear if we
+remember that the shortest distance between two points
+on the globe is along the arc of a great circle. Now great
+circles, such as meridians and the equator, are very often
+represented as curved lines on a map, yet along such a
+curved line is the shortest distance between any two places
+in the line on the globe which the map represents.
+
+5. To ascertain the scale of miles per inch used on any
+map, or verify the scale if given, measure the space along
+a meridian for one inch and ascertain as correctly as possible
+\index{Meridian|)}%
+the number of degrees of latitude contained in the inch.
+Multiply this by the number of miles in one degree of
+latitude,~$69$, and you have the number of miles on the
+earth represented by one inch on the map.
+\index{Map projections|)}%
+\index{Projections, map|)}%
+%% -----File: 225.png---Folio 226-------
+
+\Chapter{XI}{The United States Government Land Survey}
+\index{Survey}%
+\index{United States|(}%
+\index{United States Government Land Survey|(}%
+
+\Paragraph{Allowance for Curvature.} One of the best proofs that
+\index{Allowance for curvature of earth's surface}%
+\index{Curvature of surface of earth, rate of}%
+the earth is a sphere is the fact that in all careful measurements
+over any considerable area, allowance must be made
+for the curvature of the surface. If two lines be drawn
+due northward for one mile in the northern part of the
+United States or in central Europe, say from the 48th
+\index{Europe}%
+parallel, they will be found nearer together at the northern
+extremities than they are at the southern ends.
+
+\Paragraph{Origin of Geometry.} One of the greatest of the practical
+\index{Geometry, origin of}%
+\index{Origin of geometry}%
+problems of mathematics and astronomy has been
+the systematic location of lines and points and the measurement
+of surfaces of the earth by something more definite,
+more easily described and relocated than metes and bounds.
+\index{Metes and bounds}%
+Indeed, geometry is believed to have had its origin in the
+need of the ancient Egyptians for surveying and relocating
+the boundaries of their lands after the Nile floods.
+\index{Nile}%
+
+\Paragraph{Locating by Metes and Bounds.} The system of locating
+lands by metes and bounds prevails extensively over the
+world and, naturally enough, was followed in this country
+by the early settlers from Europe. To locate an area by
+landmarks, some point of beginning is established and the
+\index{Landmarks, use of, in surveys|(}%
+boundary lines are described by means of natural objects
+such as streams, trees, well established highways, and
+stakes, piles of stone, etc., are placed for the purpose. The
+directions are usually indicated by reference to the magnetic
+compass and distances as ascertained by surveyors' chains.
+\index{Compass, magnetic, or mariner's}%
+\index{Magnetic compass}%
+\index{Surveyor's chain}%
+But landmarks decay and change, and rivers change their
+%% -----File: 226.png---Folio 227-------
+courses.\footnote
+  {Where a meandering river constitutes the boundary of a nation
+  or state, changes in the course of the stream give rise to problems in
+  civil government, as the following incident illustrates. A minister in
+  the southern part of South Dakota was called upon to officiate at a
+\index{South Dakota}%
+  wedding in a home in a bend of the Missouri River. During the high
+\index{Missouri!River}%
+  water of the preceding spring, the river had burst over the narrow
+  neck at the bend and at the time of the wedding it was flowing on
+  both sides of the cut-off so that there was a doubt as to whether the
+  main channel of the stream, the interstate boundary line, was north
+  of them and they were in Nebraska, or south and they were still in
+\index{Nebraska}%
+  South Dakota. To be assured of the legality of the marriage rite,
+  the bridal couple, minister, and witnesses rowed to the north bank,
+  and up on the South Dakota bluff the marriage service was performed,
+  the bridal party returning---they cared not to which state,
+  for the festivities.}
+The magnetic needle of the compass does not
+\index{Compass, magnetic, or mariner's}%
+\index{Magnetic compass}%
+\index{Isogonal@Isogonal (\={\i}\;s\u{o}g$'$\={o}n\;al) line}%
+point due north (excepting along two or three isogonal
+lines, called agones), and varies from year to year. This
+gives rise to endless confusion, uncertainty, and litigation.
+
+\includegraphicsleft{i227}{Fig.~99}
+
+Variation almost without limit occurs in such descriptions,
+and farms assume innumerable forms, sometimes
+having a score of angles. The transitory character of such
+platting of land is illustrated in the following excerpt from
+a deed to a piece of property in Massachusetts Bay Colony,
+\index{Massachusetts}%
+bearing the date: ``Anno Domini one thousand seven hundred
+and thirty-six and in the tenth year of the reign of
+our sovereign Lord George the Second, King.'' In this,
+\index{George II., King of England}%
+Emma Blowers deeds to William Stanley, ``A certain parcel
+of Upland and Swamp Ground Situate and lying in the
+Township of Manchester being the thirty-first lot into the
+Westerly Division of Common Rights made in said Manchester
+by the proprietors thereof in the year of our Lord
+one thousand six hundred ninety-nine, Said lot containing
+Ten Acres, more or less, being cutted and bounded as
+followeth Viz: At the Northeast Corner with a maple tree
+between Sowest and Abraham Master's, from that Southeasterly
+%% -----File: 227.png---Folio 228-------
+thirty-nine poles to Morgan's Stump, so called,
+from that Southeasterly fourty-four poles upon said west
+Farm Line to a black Oak tree, from that Sixty-six poles
+Northward to the first bounds, or however Otherwise the
+Said Lot is or ought to have been bounded.''
+\index{Metes and bounds}%
+
+\includegraphicsright{i228-1}{Fig.~100}
+
+\Paragraph{Survey of Northwest Territory.} When, in 1785, practically
+\index{Northwest Territory, survey of|(}%
+all of the territory north and west of the Ohio River
+\index{Ohio!River}%
+had been ceded to the United States by the withdrawal of
+state claims, Congress
+provided for its survey,
+profiting from the
+experiences resulting
+from hastily marked
+boundaries. Thomas
+Hutchins was appointed
+\index{Hutchins, Thomas}%
+Geographer of
+the United States, and
+after the selection of
+thirteen assistants, he
+was instructed to begin
+its survey. Starting in
+1786 from the southwest
+corner of Pennsylvania, he laid off a line due north
+\index{Pennsylvania}%
+to a point on the north bank of the Ohio River. From
+this point he started a line westward.
+According to the
+directions of Congress, every six miles along this east-west
+``geographer's line,'' meridians were to be laid off
+and parallels to it at intervals of six miles, each of the
+six miles square to be divided into thirty-six square
+miles and these divided into ``quarters,'' thus spreading a
+huge ``gridiron'' over the land. The larger squares were
+\index{Congressional township}%
+\index{Township|(}%
+called ``townships,'' an adaptation of the New England
+``town.'' They are commonly called ``Congressional
+\index{Landmarks, use of, in surveys|)}%
+%% -----File: 228.png---Folio 229-------
+townships'' in most parts of the United States, to distinguish
+them from the political subdivision of the county
+called the ``civil township''
+or the ``municipal
+township.''
+
+\includegraphicsleft{i228-2}{Fig.~101}
+
+\sloppy
+Jefferson is believed
+\index{Jefferson, Thomas}%
+to have suggested this
+general plan which with
+some variations has
+been continued over
+the major portion of
+the United States and
+the western portion of
+Canada. Hutchins and
+\index{Hutchins, Thomas}%
+\index{Canada}%
+his crew laid off the
+``geographer's line''
+only forty-two miles, making seven ranges of townships
+\index{Seven ranges of Ohio}%
+west of the Pennsylvania
+\index{Pennsylvania}%
+state boundary,
+when they were frightened
+away by the
+Indians. The work
+was continued, however,
+on the same general
+plan one exception
+being the method of
+numbering the sections.
+In these first
+``seven ranges'' the
+sections are numbered
+as in Figure~\figureref{i227}{99}, elsewhere
+in the United States they are numbered as in
+Figure~\figureref{i228-1}{100}, and in western Canada as in Figure~\figureref{i228-2}{101}.
+%% -----File: 229.png---Folio 230-------
+Each of the square miles is commonly called a ``section.''
+
+\fussy
+The law passed by Congress May~20, 1785, provided that,
+``The surveyors~\dots\ shall proceed to divide the said territory
+into townships of six miles square, by lines running
+due north and south, and others crossing these at right
+angles, as near as may be.'' Owing to the convergence of
+\index{Convergence of meridians}%
+\index{Allowance for curvature of earth's surface}%
+the meridians this, of course, was a mathematical impossibility;
+``as near as may be,'' however, has been broadly
+interpreted. According to the provisions of this act and
+the acts of May~18, 1796, May~10, 1800, and Feb.~11, 1805,
+and to rules of commissioners of the general land office, a
+complete system has been evolved, the main features of
+which are as follows:
+
+\Paragraph{Principal Meridians.} These are run due north, south,
+or north and south from some initial point selected
+with great care and located in latitude and longitude by
+astronomical means. Thirty-two or more of these principal
+meridians have been surveyed at irregular intervals
+and of varying lengths. Some of these are known by
+numbers and some by names. The first principal meridian
+\index{Meridian!principal, for surveys|(}%
+\index{Principal meridian|(}%
+is the boundary line between Indiana and Ohio;
+\index{Indiana}%
+\index{Ohio}%
+the second is west of the center of Indiana, extending the
+entire length of the state; the third is in the center of
+Illinois, extending the entire length of the state; the Tallahassee
+\index{Tallahassee, Fla.}%
+\index{Illinois}%
+principal meridian passes directly through that
+city and is only about twenty-three miles long; other
+principal meridians are named Black Hills, New Mexico,
+\index{Black Hills Meridian}%
+\index{Mount Diablo meridian}%
+\index{New Mexico}%
+\index{Louisiana}%
+\index{Indian principal meridian}%
+\index{San Bernardino, Calif.}%
+\index{Washington, D. C.}%
+\index{Map}%
+Indian, Louisiana, Mount Diablo, San Bernardino,\footnote
+  {The entire platting of the portions of the United States to which
+  this discussion refers is clearly shown on the large and excellent maps
+  of the United States, published by the Government and obtainable,
+  at the actual cost, eighty cents, from the Commissioner of the General
+  Land office, Washington,~D.~C.}
+etc.
+\index{Northwest Territory, survey of|)}%
+%% -----File: 230.png---Folio 231-------
+To the east, west, or east and west of principal meridians,
+\index{Ranges of townships|(}%
+north and south rows of townships called ranges are laid
+off. Each principal meridian, together with the system of
+townships based upon it, is independent of every other
+principal meridian and where two systems come together
+irregularities are found.
+
+\Paragraph{Base Lines.} Through the initial point selected from
+which to run the principal meridian, an east-west base line
+\index{Base line|(}%
+is run, at right angles to it, and corresponds to a true geographic
+parallel. As in case of the principal meridian,
+this line is laid off with great care since the accuracy of
+these controlling lines determines the accuracy of the
+measurements based upon them.
+
+Tiers of townships are laid off and numbered north and
+\index{Tiers of townships}%
+south of these base lines. In locating a township the word
+tier is usually omitted; township number~4 north, range~2
+west of the Michigan principal meridian, means the township
+\index{Michigan}%
+in tier 4~north of the base line and in the second range
+west of the Michigan principal meridian. This is the
+township in which Lansing, Michigan, is located.
+\index{Lansing, Mich.}%
+
+The fourth principal meridian in western Illinois and
+\index{Illinois}%
+Wisconsin has two base lines, one at its southern extremity
+\index{Wisconsin}%
+extending westward to the Mississippi River and the other
+\index{Mississippi!River}%
+constituting the interstate boundary line between Wisconsin
+and Illinois. The townships of western Illinois are
+numbered from the southern base line, and all of those in
+Wisconsin and northeastern Minnesota are numbered from
+\index{Minnesota}%
+the northern base line. The fourth principal meridian is
+in three sections, being divided by an eastern bend of the
+Mississippi River and by the western portion of Lake
+\index{Lake Superior}%
+Superior.
+
+\includegraphicssideways{i231}{Fig.~102.}
+
+The largest area embraced within one system is that
+based upon the fifth principal meridian. This meridian
+%% -----File: 231.png---Folio 232-------
+%% -----File: 232.png---Folio 233-------
+extends northward from the mouth of the Arkansas River
+\index{Arkansas River}%
+until it again intersects the Mississippi River in northeastern
+Missouri and then again it appears in the big eastern
+bend of the Mississippi River in eastern Iowa. Its
+base line passes a few miles south of Little Rock, Arkansas,
+\index{Little Rock, Ark.}%
+\index{Arkansas@Arkansas (\phonArkansas)}%
+from which fact it is sometimes called the Little Rock
+base line. From this meridian and base line all of Arkansas,
+\index{Meridian!rate for convergence}%
+Missouri, Iowa, North Dakota, and the major portions
+of Minnesota and South Dakota have been surveyed, an
+\index{Minnesota}%
+\index{South Dakota}%
+area considerably larger than that of Germany and Great
+\index{Great Britain}%
+\index{Germany}%
+Britain and Ireland combined. The most northern tier
+\index{Ireland}%
+from this base lies about a mile south of the forty-ninth
+parallel, the boundary line between the United States and
+Canada, and is numbered~163. The southern row of sections
+\index{Canada}%
+of tier~164 with odd lottings lies between tier~163 and
+Canada. Its most northern township is in the extreme
+northern portion of Minnesota, west of the Lake of the
+\index{Lake of the Woods}%
+Woods, and is numbered~168. It thus lies somewhat
+more than a thousand miles north of the base from which
+it was surveyed. There are nineteen tiers south of the
+base line in Arkansas, making the extreme length of this
+area about $1122$~miles. The most eastern range from the
+fifth principal meridian is numbered~17 and its most
+western,~104, making an extent in longitude of $726$~miles.
+\index{Ranges of townships|)}%
+
+\includegraphicsleft{i233}{Fig.~103.}
+
+\Paragraph{Standard Parallels.} The eastern and western boundaries
+\index{Standard parallel}%
+of townships are, as nearly as may be, true meridians, and
+when they have been extended northward through several
+\index{Allowance for curvature of earth's surface}%
+\index{Convergence of meridians}%
+\index{Curvature of surface of earth, rate of}%
+tiers, their convergence becomes considerable. At latitude~$40°$
+the convergence is about $6.7$~feet per mile or somewhat
+more than $40$~feet to each township. To prevent this
+diminution in size of townships to the north of the base
+line, standard parallels are run, along which six-mile
+%% -----File: 233.png---Folio 234-------
+measurements are made for a new set of townships. These
+lines are also called \emph{correction lines} for obvious reasons.
+
+\Paragraph{Division of Dakotas.} When Dakota Territory was
+\index{North Dakota}%
+\index{South Dakota}%
+\index{Dakotas, division of}%
+\index{Division of Dakotas}%
+divided and permitted to enter the Union as two states,
+the dividing line agreed upon was the \emph{seventh standard parallel}
+\index{Standard parallel}%
+from the base line of the fifth principal meridian.
+This line is about four miles south of the parallel $46°$ from
+the equator and was chosen in preference to the geographic
+parallel because it was the boundary line between
+farms, sections, townships,
+and, to a considerable
+extent, counties.
+The boundary line between
+Minnesota and
+Iowa is what is called
+a secondary base line
+and corresponds to a
+standard parallel between
+\index{Tiers of townships}%
+tiers 100~and~101
+north of the base line
+\index{Base line|)}%
+of the fifth principal
+meridian.
+
+The standard parallels
+have been run at varying intervals, the present distance
+being $24$~miles. None at all were used in the earlier
+surveys. Since public roads are usually built on section
+and quarter section lines, wherever a north-south road
+crosses a correction line, there is a ``jog'' in the road, as a
+\index{Correction line}%
+glance at Figure~\figureref{i233}{103} will show.
+
+\includegraphicsmid{i234-1}{Fig.~104.}
+
+\Paragraph{Townships Surveyed Northward and Westward.} The
+practice in surveying is to begin at the southeast corner of
+a township and measure off to the north and west. Thus
+the sections in the north and west are liable to be larger
+%% -----File: 234.png---Folio 235-------
+or smaller than $640$~acres, depending upon the accuracy of
+the survey. In case of a fractional township, made by the
+intervention of large bodies of water or the meeting of
+another system of survey or a state line, the sections bear
+the same numbers they would have if the township were
+full. Irregular surveys and other causes sometimes make
+the townships or sections
+considerably
+larger than the desired
+area. In such cases $40$~acre
+lots, or as near
+that size as possible,
+appear in the northern
+row of sections, the
+other half section remaining
+\index{Section}%
+as it would
+otherwise be. These
+lots may also appear
+in the western part of
+a township, and the
+discrepancy should appear in the western half of each
+section. This is illustrated in Figure~\figureref{i234-1}{104}.
+
+\includegraphicsleft{i234-2}{Fig.~105.}
+
+\Paragraph{Legal Subdivisions of a Section.} The legal subdivisions
+%% -----File: 235.png---Folio 236-------
+of a section are by halves, quarters, and half quarters. The
+\index{Section}%
+designation of the portions of a section is marked in Figure~\figureref{i234-2}{105}.
+The abbreviations look more unintelligible than they
+really are. Thus N.~E.~$\frac{1}{4}$ of S.~E.~$\frac{1}{4}$ of Sec.~24, T.~123~N. R.~64
+W. 5~\PM{} means the northeast quarter of the southeast
+quarter of section~24, in tier of townships number~123 north,
+\index{Ranges of townships}%
+\index{Tiers of townships}%
+and in range~64 west of the fifth principal meridian. Any
+\index{Meridian!principal, for surveys|)}%
+\index{Principal meridian|)}%
+such description can easily be located on the United States
+\index{United States|)}%
+map issued by the General Land Office.
+\index{Map}%
+\index{Township|)}%
+\index{United States Government Land Survey|)}%
+%% -----File: 236.png---Folio 237-------
+
+\Chapter{XII}{Triangulation in Measurement and Survey}
+\index{Triangulation}%
+
+\includegraphicsright{i236-1}{Fig.~106}
+
+\First{The} ability to measure the distance and size of objects
+\index{Measuring distances of objects}%
+without so much as touching them seems to the child or
+uneducated person to be a great mystery, if not an impossibility.
+Uninformed persons sometimes contend that
+astronomers only guess at the distances and dimensions
+of the sun, moon, or a planet. The principle of such measurement
+is very simple and may easily be applied.
+
+\includegraphicsleft{i236-2}{Fig.~107}
+
+\Paragraph{\nbstretchyspace To Measure the Width of a Stream.} Suppose we wish to
+measure the width of a river,
+yard, or field without actually
+crossing it. First make a
+triangle having two equal
+sides and one right angle
+(Fig.~\figureref{i236-1}{106}). Select some easily
+distinguished point on the
+farther side, as~$X$ (Fig.~\figureref{i236-2}{107}), and find a convenient point
+opposite it, as~$B$. Now carry the triangle to the right or
+left of~$B$ until by sighting
+you see that the
+long side is in line with~$B$
+when the short side
+is in line with~$X$. You
+will then form the triangle
+$BAX$~or~$BCX$.
+It is apparent (by similar
+triangles) that $AB$~or~$CB$ equals~$BX$. Measure off $AB$~or~$BC$
+and you will have~$BX$, the distance sought. If
+%% -----File: 237.png---Folio 238-------
+\index{Measuring distances of objects!heights of objects}%
+you measure both to the right and to the left and take the
+average of the two you will get a more nearly correct
+result.
+
+\includegraphicsleft{i237}{Fig.~108}
+
+\Paragraph{To Measure the Height of an Object.} In a similar manner
+one may measure the height of a flagstaff or building.
+Let~$X$ represent the highest point in the flagstaff (Fig.~\figureref{i237}{108})
+and place the triangle on or near the ground, with the
+short side toward~$X$ and long side level. The distance to
+the foot of the pole is its height. It is easy to see from
+this that if we did not have a triangle just as described,
+say the angle at the
+point of sighting was
+less, by measuring
+that angle and looking
+up the value of
+its tangent in a trigonometrical
+table, one
+could as easily calculate
+the height or
+distance. The angle
+of the triangle from
+which sighting was done is~$45°$, its tangent is~$1.0000$, that is,
+$XB$~equals $1.0000$~times~$BC$. If the angle used were~$20°$, instead
+of~$45°$, its tangent would be~$.3640$; that is, $XB$~would
+equal $.3640$~times~$BC$. If the angle were~$60°$, the tangent
+would be~$1.7321$, that is, $XB$~would equal that number
+times~$BC$. A complete \hyperref[page:312]{list of tangents} for whole degrees
+is given in the Appendix. With the graduated quadrant
+the student can get the noon altitude of the sun (though
+for this purpose it need not be noon), and by getting the
+length of shadow and multiplying this by its natural tangent
+get the height of the object. If it is a building that
+is thus measured, the distance should be measured from
+%% -----File: 238.png---Folio 239-------
+the end of the shadow to the place directly under the point
+casting the longest shadow measured.
+
+Two examples may suffice to illustrate how this may
+be done.
+
+1. Say an object casts a shadow $100$~feet from its base
+when the altitude of the sun is observed to be~$58°$. The
+\hyperref[page:312]{table} shows the tangent of~$58°$ to be~$1.6003$. The height
+of the object, then, must be $1.6003$~times $100$~feet or $160.03$~feet.
+
+2. Suppose an object casts a shadow $100$~feet when the
+sun's height is observed to be $68°~12'$. Now the \hyperref[page:312]{table} does
+not give the tangent for fractions of degrees, so we must
+add to~$\tan 68°$ $\frac{1}{5}$~of the difference between the values of
+$\tan 68°$~and~$\tan 69°$ ($12' = \frac{1}{5}°$).
+
+The \hyperref[page:312]{table} shows that
+\begin{align*}
+\tan 69° & = 2.6051,\ \text{and} \\
+\tan 68° & = 2.4751,\ \text{hence the} \\
+\text{difference} & = \smash{\overline{\rule{0pt}{2ex}0.1300.}} \\
+\tfrac{1}{5}\ \text{of}\ .1300 & = 0.0260,\ \text{and since} \\
+\tan 68° & = 2.4751,\ \text{and we have found that} \\
+\tan 12' & =  0.0260,\ \text{it follows that} \\
+\tan 68°~12' & = 2.5011.
+\end{align*}
+
+Multiplying $100$~feet by this number representing the
+value of~$\tan 68°\ 12'$
+\[
+100~\text{feet} × 2.5011 = 250.11~\text{feet, answer}.
+\]
+
+By simple proportion one may also measure the height
+of an object by the length of the shadow it casts. Let $XB$~represent
+a flagstaff and $BC$~its shadow on the ground
+(Fig.~\figureref{i237}{108}). Place a ten-foot pole (any other length will
+do) perpendicularly and measure the length of the shadow
+%% -----File: 239.png---Folio 240-------
+it casts and immediately mark the limit of the shadow
+of the flagstaff and measure its length in a level line.
+Now the length of the flagstaff will bear the same ratio to
+the length of the pole that the length of the shadow of
+the flagstaff bears to the length of the shadow of the
+pole. If the length of the flagstaff's shadow is $60$~feet and
+that of the pole is $6$~feet, it is obvious that the former is
+ten times as high as the latter, or $100$~feet high. In formal
+proportion
+\[
+BX : B'X' \dblcolon BC : B'C'.
+\]
+
+\includegraphicsmid{i239}{Fig.~109}
+
+\Paragraph{To Measure the Width of the Moon.} To measure the
+\index{Measuring diameter of moon}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+width of the moon if its distance is known. Cut from a
+piece of paper a circle one inch in diameter and paste it
+high up on a window in view of the full moon. Find how
+far the eye must be placed from the disk that the face of
+the moon may be just covered by the disk. To get this
+distance it is well to have one person hold the end of a
+tapeline against the window near the disk and the observer
+%% -----File: 240.png---Folio 241-------
+hold the line even with his eye. You then have three elements
+of the following proportion:
+\[
+\text{Dist.\ to disk} : \text{dist.\ to moon} \dblcolon \text{width of disk} : \text{width of moon}.
+\]
+From these elements, multiplying extremes and means
+\index{Measuring diameter of moon}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+and dividing, it is not difficult to get the unknown element,
+the diameter of the moon. If the student is careful in his
+measurement and does not forget to reduce all dimensions
+to the same denomination, either feet or inches, he will be
+surprised at the accuracy of his measurement, crude though
+it is.
+
+\Paragraph{How Astronomers Measure Sizes and Distances.} It is by
+\index{Measuring distances of objects}%
+the aid of these principles and the use of powerful and
+accurate instruments that the distances and dimensions of
+celestial bodies are determined, more accurately, in some
+instances, than would be likely to be done with rod and
+chain, were such measurement possible.
+
+In measuring the distance of the moon from the earth
+two observations may be made at the same moment from
+widely distant points on the earth. Thus a triangle is
+formed from station~A and station~B to the moon. The
+base and included angles being known, the distance can
+be calculated to the apex of the triangle, the moon. There
+are several other methods based upon the same general
+principles, such as two observations from the same point
+twelve hours apart. Since the calculations are based upon
+lines conceived to extend to the center of the earth, this is
+called the geocentric parallax (see \glossref{Parallax} in Glossary).
+\index{Parallax}%
+It is impossible to get the geocentric parallax of other
+stars than the sun because they are so far away that lines
+sighted to one from opposite sides of the earth are apparently
+parallel. It is only by making observations six
+months apart, the diameter of the earth's orbit forming the
+%% -----File: 241.png---Folio 242-------
+base of the triangle, that the parallaxes of about forty stars
+have been determined and even then the departure from
+the parallel is so exceedingly slight that the distance can
+be given only approximately. The parallax of stars is
+called heliocentric, since the base passes through the center
+of the sun.
+
+\Section{Survey by Triangulation}
+
+A method very extensively employed for exact measurement
+of land surfaces is by laying off imaginary triangles
+across the surface, and by measuring the length of one side
+and the included angles all other dimensions may be accurately
+computed. Immense areas in India, Russia, and
+\index{India}%
+\index{Russia}%
+North America have been thus surveyed. The triangulation
+\index{North America}%
+surveys of the United States comprise nearly a
+million square miles extending from the Atlantic to the
+\index{Atlantic Ocean}%
+\index{Pacific Ocean}%
+Pacific. This work has been carried on by the United
+\index{United States Geological Survey}%
+States Geological Survey for the purpose of mapping the
+topography and making geological maps, and by the United
+\index{United States Coast and Geodetic Survey}%
+States Coast and Geodetic Survey.
+
+\includegraphicsmid{i241}{Fig.~110}
+%% -----File: 242.png---Folio 243-------
+
+\Paragraph{Determination of Base Line.} The surveyor selects two
+\index{Base line}%
+points a few miles apart where the intervening surface is
+level. The distance between these points is ascertained,
+great care being used to make it as correct as possible, for
+this is the base line and all calculations rest for their accuracy
+upon this distance as it is the only line measured.
+The following extracts from the Bulletin of the United
+\index{Bulletin, U. S. G. S.}%
+States Geological Survey on Triangulation, No.~122, illustrate
+\index{United States Geological Survey}%
+the methods employed. ``The Albany base line (in
+\index{Albany, Tex.}%
+central Texas) is about nine miles in length and was measured
+\index{Texas}%
+twice with a $300$-foot steel tape stretched under a
+tension of $20$~pounds. The tape was supported by stakes
+at intervals of $50$~feet, which were aligned and brought to
+the grade established by more substantial supports, the
+latter having been previously set in the ground $300$~feet
+apart, and upon which markings of the extremities of the
+tape were made. The two direct measurements differed
+by $0.167$~foot, but when temperature corrections were
+applied the resulting discrepancy was somewhat greater,
+owing possibly to difficulty experienced at the time of
+measurements in obtaining the true temperature of the
+tape. The adopted length of the line after applying the
+corrections for temperature, length of tape, difference on
+posts, inclination, sag, and sea level, was $45,793.652$ feet.''
+``The base line (near Rapid City, South Dakota) was
+\index{Rapid City, S. D.}%
+\index{South Dakota}%
+measured three times with a $300$-foot steel tape; temperature
+was taken at each tape length; the line was supported
+at each $50$~feet and was under a uniform tension of $20$~pounds.
+The adopted length of the line after making corrections
+for slope, temperature, reduction to sea level,~etc.,
+is $25,796.115$ feet (nearly $5$~miles), and the probable error
+of the three measurements is $0.84$~inch.'' ``The Gunnison
+\index{Gunnison, Utah}%
+line (Utah) was measured under the direction of Prof.\
+\index{Utah}%
+%% -----File: 243.png---Folio 244-------
+A.~H. Thompson, in 1875, the measurement being made
+\index{Thompson, A. H.}%
+by wooden rods carried in a trussed wooden case. These
+rods were oiled and varnished to prevent absorption of
+moisture, and their length was carefully determined by
+comparisons with standard steel rods furnished by the
+United States Coast and Geodetic Surveys.''
+\index{United States Coast and Geodetic Survey}%
+
+\Paragraph{\nbstretchyspace Completion of Triangle.} From each extremity of the
+base line a third point is sighted and with an instrument
+\index{Base line}%
+the angle this line forms with the base line is determined.
+Thus suppose $AB$ (Fig.~\figureref{i243}{111}) represents the base line. At~$A$
+the angle~$CAB$ is determined and at~$B$ the angle~$CBA$
+is determined. Then by trigonometrical
+tables the lengths
+of lines $CA$~and~$BC$ are exactly
+determined. Any one
+of these lines may now be
+used as a base for another
+triangle as with base~$AB$.
+If the first base line is correct,
+and the angles are determined
+accurately, and
+proper allowances are made for elevations and the curvature
+of the earth, the measurement is very accurate and
+easily obtained, whatever the intervening obstacles between
+the points. In some places in the western part of the
+United States, long lines, sometimes many miles in length,
+are laid off from one high elevation to another. The
+longest side thus laid off in the Rocky Mountain region
+is $183$~miles long.
+
+\includegraphicsleft{i243}{Fig.~111}
+
+``On the recent primary triangulation much of the
+observing has been done at night upon acetylene lamps;
+directions to the distant light keepers have been sent by
+the telegraphic alphabet and flashes of light, and the
+%% -----File: 244.png---Folio 245-------
+necessary observing towers have been built by a party
+expert in that kind of work in advance of the observing
+\index{Hayford, J. F.}%
+\index{United States Coast and Geodetic Survey}%
+party.''\footnote
+  {John~F. Hayford, Inspector of Geodetic Work, United States
+  Coast and Geodetic Survey, in a paper relating to Primary Triangulation
+  before the Eighth International Geographic Congress, 1904.}
+
+\Paragraph{Survey of Indian Territory.} In March, 1895, Congress
+\index{Indian Territory, survey of}%
+provided for the survey of the lands of Indian Territory
+and the work was placed in charge of the Director of the
+Geological Survey instead of being let out on contract as
+had been previously done. The system of running principal
+and guide meridians, base and correction parallels,
+and township and section lines was adopted as usual and
+since the topographic map was made under the same direction,
+a survey by triangulation was made at the same time.
+The generally level character of the country made it possible
+to make triangles wherever desired, so the ``checkerboard''
+system of townships has superimposed upon it
+triangles diagonally across the townships. In this way the
+accurate system of triangulation was used to correct the
+errors incident to a survey by the chain. Since so many
+lines were thus laid off and all were made with extreme
+accuracy, the work of making the contour map was rendered
+comparatively simple.
+%% -----File: 245.png---Folio 246-------
+
+\Chapter{XIII}{The Earth in Space}\nblabel{page:246}
+\index{Earth in Space|(}%
+
+\Paragraph{The Solar System.} The group of heavenly bodies to
+\index{Solar system|(}%
+which the earth belongs is called, after its great central
+sun, the solar system. The members of the solar system
+\index{Sun|(}%
+are the sun; eight large planets, some having attendant
+\index{Planets}%
+satellites or moons; several hundred smaller planets called
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+asteroids, or planetoids; and occasional comets and meteors.
+\index{Asteroids}%
+\index{Comets}%
+The planets with their satellites, and the asteroids all
+revolve around the sun in the same direction in elliptical
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+orbits not far from a common plane. Those visible to the
+naked eye may be seen not far from the ecliptic, the path
+of the sun in its apparent revolution. The comets and
+swarms of meteors also revolve around the sun in greatly
+elongated orbits.
+
+The solar system is \emph{widely separated} from any of the
+stars, with which the planets should not be confused. If
+one could fly from the earth to the sun, $93,000,000$ miles,
+in a single day, it would take him only a month to reach
+the orbit of the most distant planet, Neptune, but at that
+same terrific rate, it would take over seven hundred years
+\index{Distances, of planets!of stars}%
+\index{Star, distance of a}%
+to reach the very nearest of the distant stars. If a circle
+three feet in diameter be made to represent the orbit of
+the earth, an object over seventy miles away would represent
+the nearest of the distant stars.
+
+The earth's orbit as seen from the nearest star is as a
+\index{Orbit, of earth}%
+circle a trifle over half an inch in diameter seen at a distance
+of a mile. Do not imagine that the brightest stars
+are nearest.
+%% -----File: 246.png---Folio 247-------
+
+From the foregoing one should not fail to appreciate the
+immensity of the earth's orbit. It is small only in a relative
+sense. The earth's orbit is so large that in traveling
+eighteen and one half miles the earth departs from a
+perfectly straight line only about \emph{one ninth of an inch}; it
+is nearly $584,000,000$ miles in length and the average
+orbital velocity of the earth is $66,600$ miles per~hour.
+
+\Paragraph{Sun's Onward Motion.}\nblabel{page:247} It has been demonstrated that
+many of the so-called fixed stars are not fixed in relation
+to each other but have ``proper'' motions of their own.
+It is altogether probable that each star has its own motion
+in the universe. Now the sun is simply one of the stars
+(see p.~\pageref{page:265}), and it has been demonstrated that with its
+system of planets it is moving rapidly, perhaps $40,000$
+miles per~hour, toward the constellation Hercules. Many
+\index{Hercules@Hercules (h\~{e}r$'$c\={u}\;l\={e}z), constellation}%
+speculations are current as to whether our sun is controlled
+by some other sun somewhat as it controls the planets,
+and also as to general star systems. Any statement of
+such conditions with present knowledge is little, if any,
+more than a guess.
+
+\Paragraph{Nebular Hypothesis.} Time was when it was considered
+\index{Nebular hypothesis|(}%
+impious to endeavour to ascertain the processes by which
+God works ``in His mysterious way, His wonders to perform;''
+and to assign to natural causes and conditions
+what had been attributed to God's fiat was thought sacrilegious.
+It is hoped that day has forever passed.
+
+This great theory as to the successive stages and conditions
+in the development of the solar system, while
+doubtless faulty in some details, is at present almost the
+only working hypothesis advanced and ``forms the foundation
+of all the current speculations on the subject.'' It
+gives the facts of the solar system a unity and significance
+scarcely otherwise obtainable.
+%% -----File: 247.png---Folio 248-------
+
+A theory or a hypothesis, if worthy of serious attention,
+is always based upon facts. Some of the facts upon
+which the nebular theory is based are as follows:
+
+1. All of the planets are not far from a common
+plane.
+
+2. They all revolve around the sun in the same direction.
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+
+3. Planetary rotation and revolution are in the same
+direction, excepting, perhaps, in case of Uranus and
+Neptune.
+
+4. The satellites revolve around their respective planets
+in the direction of their rotation and not far from the
+plane of revolution.
+
+5. All the members seem to be made up of the same
+kinds of material.
+
+6. Analogy.
+
+\textit{a.} The nebulæ we see in the heavens have the same
+\index{Nebulae}%
+general appearances this theory assumes the solar system
+to have had.
+
+\textit{b.} The swarms of meteorites making the rings of Saturn
+\index{Meteors}%
+\index{Saturn}%
+are startlingly suggestive of the theory.
+
+\textit{c.} The gaseous condition of the sun with its corona
+suggests possible earlier extensions of it. The fact that
+the sun rotates faster at its equator than at other parts
+also points toward the nebular theory. The contraction
+theory of the source of the sun's heat, so generally accepted,
+\index{Sun|)}%
+is a corollary of the nebular theory.
+
+\textit{d.} The heated interior of the earth and the characteristics
+of the geological periods suggest this theory as
+the explanation.
+
+\Subparagraph{The Theory.} These facts reveal a system intimately
+related and pointing to a common physical cause. According
+to the theory, at one time, countless ages ago, all
+%% -----File: 248.png---Folio 249-------
+the matter now making up the solar system was in one
+great cloudlike mass extending beyond the orbit of the
+most distant planet. This matter was not distributed with
+uniform density. The greater attraction of the denser
+portions gave rise to the collection of more matter around
+them, and just as meteors striking our atmosphere generate
+\index{Meteors}%
+by friction the flash of light, sometimes called falling
+or shooting stars, so the clashing of particles in this nebulous
+mass generated intense heat.
+
+\Subparagraph{Rotary Motion.} Gradually the whole mass balanced
+about its center of gravity and a well-defined rotary
+motion developed. As the great nebulous mass condensed
+and contracted, it rotated faster and faster. The
+centrifugal force at the axis of rotation was, of course,
+zero and increased rapidly toward the equator. The force
+of gravitation thus being partially counteracted by centrifugal
+force at the equator, and less and less so at other
+points toward the axis, the mass flattened at the poles.
+The matter being so extremely thin and tenuous and acted
+upon by intense heat, also a centrifugal force, it flattened
+out more and more into a disklike form.
+
+As the heat escaped, the mass contracted and rotated
+faster than ever, the centrifugal force in the outer portion
+thus increased at a greater rate than did the power of
+gravitation due to its lessening diameter. Hence, a time
+came when the centrifugal force of the outer portions
+exactly balanced the attractive power of gravitation and
+the rim or outer fragments ceased to contract toward the
+central mass; and the rest, being nearer the center of
+gravity, shrank away from these outer portions. The
+outer ring or ringlike series of fragments, thus left off,
+continued a rotary motion around the central mass,
+remaining in essentially the same plane.
+%% -----File: 249.png---Folio 250-------
+
+\Subparagraph{Planets Formed from Outlying Portions.} Since the
+matter in the outlying portions, as in the whole mass, was
+somewhat unevenly distributed, the parts of it consolidated.
+The greater masses in the outer series hastened
+by their attraction the lesser particles back of them,
+retarded those ahead of them, and thus one mass was
+formed which revolved around the parent mass and
+rotated on its axis. If this body was not too dense it
+might collect into the satellites or moons revolving around
+it. This process continued until nine such rings or lumps
+had been thrown off, or, rather, \emph{left off}. The many small
+planets around the sun between the orbit of Mars and
+\index{Sun}%
+that of Jupiter were probably formed from one whose parts
+\index{Jupiter}%
+were so nearly of the same mass that no one by its preponderating
+attraction could gather up all into a planet.
+The explanation of the rings of Saturn is essentially the
+same.
+
+\Subparagraph{Conclusion as to the Nebular Hypothesis.} This theory,
+with modifications in detail, forms the basis for much of
+scientific speculation in subjects having to do with the
+earth. That it is the ultimate explanation, few will be so
+hardy as to affirm. Many questions and doubts have been
+thrown on certain phases recently but it is, in a sense,
+the point of departure for other theories which may displace
+it. Perhaps even the best of recent theories to
+receive the thoughtful attention of the scientific world,
+the ``planetesimal hypothesis,'' can best be understood
+\index{Planetesimal hypothesis}%
+in general outline, in terms of the nebular theory.
+
+\Paragraph{The Planetesimal Hypothesis.} This is a new explanation
+of the genesis of our solar system which has been
+worked out by Professors Chamberlin and Moulton of
+\index{Chamberlin, T. C.}%
+\index{Moulton, F. R.}%
+the University of Chicago, and is based upon a very
+\index{University of Chicago}%
+careful study of astronomical facts in the light of mathematics
+%% -----File: 250.png---Folio 251-------
+and astrophysics. It assumes the systems to have
+been evolved from a spiral nebula, similar to the most
+\index{Nebulae}%
+common form of nebulæ observed in the heavens. It is
+supposed that the nebulous condition may have been
+caused by our sun passing so near a star that the tremendous
+\index{Sun}%
+tidal strain caused the eruptive prominences (which
+the sun shoots out at frequent intervals) to be much
+larger and more vigorous than usual, and that these, when
+projected far out, were pulled forward by the passing star
+and given a revolutionary course about the sun. The arms
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+of spiral nebulæ have knots of denser matter at intervals
+which are supposed to be due to special explosive impulses
+and to become the centers of accretion later. The material
+thus shot out was very hot at first, but soon cooled
+into discrete bodies or particles which moved independently
+about the sun like planets (hence the term \emph{planetesimal}).
+\index{Orbit, of earth}%
+When their orbits crossed or approached each other,
+the smaller particles were gathered into the knots, and
+these ultimately grew into planets. Less than one seven-hundredth
+of the sun was necessary to form the planets
+and satellites.
+
+This hypothesis differs from the nebular hypothesis in a
+number of important particulars. The latter assumes the
+earth to have been originally in a highly heated condition,
+while under the planetesimal hypothesis the earth may
+have been measurably cool at the surface at all times, the
+interior heat being due to the compression caused by
+gravity. The nebular hypothesis views the atmosphere as
+\index{Atmosphere!origin of}%
+the thin remnant of voluminous original gases, whereas
+the new hypothesis conceives the atmosphere to have been
+gathered gradually about as fast as consumed, and to have
+come in part from the heated interior, chiefly by volcanic
+action, and in part from outer space. The oceans, according
+%% -----File: 251.png---Folio 252-------
+to the old theory, were condensed from the great
+masses of original aqueous vapors surrounding the earth;
+according to the new theory the water was derived from
+the same sources as the atmosphere. According to the
+\index{Atmosphere!origin of}%
+planetesimal hypothesis the earth, as a whole, has been
+solid throughout its history, and never in the molten state
+assumed in the nebular hypothesis.
+\index{Nebular hypothesis|)}%
+
+\Paragraph{Solar System not Eternal.} Of one thing we may be
+reasonably certain, the solar system is not an eternal one.
+When we endeavor to extend our thought and imagination
+backward toward ``the beginning,'' it is only \emph{toward}
+creation; when forward, it is only \emph{toward} eternity.
+
+\begin{verse}\smallsize
+``Thy kingdom is an everlasting kingdom,\\
+And thy dominion endureth throughout all generations.''\\
+\hfill---\textsc{Psalms}, 145, 13.
+\index{Psalms}%
+\end{verse}
+
+\Section{The Mathematical Geography of the Planets, Moon,
+and Sun}
+
+The following brief sketches of the mathematical geography
+of the planets give their conditions in terms corresponding
+to those applied to the earth. The data and
+comparisons with the earth are only approximate. The
+more exact figures are found in the \hyperref[page:266]{table} at the end of
+the chapter.
+
+Striving for vividness of description occasionally results
+in language which implies the possibility of human inhabitancy
+on other celestial bodies than the earth, or suggests
+interplanetary locomotion (see p.~\pageref{page:305}). Such conditions
+\emph{exist only in the imagination}. An attempt to exclude
+astronomical facts not bearing upon the topic in hand and
+not consistent with the purpose of the study, makes necessary
+the omission of some of the most interesting facts.
+%% -----File: 252.png---Folio 253-------
+For such information the student should consult an astronomy.
+The beginner should learn the names of the planets
+in the order of their nearness to the sun. Three minutes
+repetition, with an occasional review, will fix the order:
+\begin{center}
+\begin{tabular}{l}
+Mercury, Venus, Earth, Mars, Asteroids,\\
+\index{Asteroids}%
+\index{Mars|(}%
+\index{Mercury}%
+\index{Venus}%
+Jupiter, Saturn, Uranus, Neptune.
+\index{Jupiter}%
+\index{Neptune}%
+\index{Uranus@Uranus (\={u}$'$ra\;nus)}%
+\index{Saturn}%
+\end{tabular}
+\end{center}
+There are obvious advantages in the following discussion
+in not observing this sequence, taking Mars first, then
+Venus, etc.
+
+\Section{Mars}
+
+\Paragraph{Form and Dimensions.} In form Mars is very similar
+to the earth, being slightly more flattened toward the
+poles. Its mean diameter is $4,200$~miles, a little more
+than half the earth's. A degree of latitude near the
+equator is $36.6$~miles long, getting somewhat longer toward
+the poles as in case of terrestrial latitudes.
+
+Mars has a little less than one third the surface of the
+earth, has one seventh the volume, weighs but one ninth
+as much, is three fourths as dense, and an object on its
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Mars}%
+surface weighs about two fifths as much as it would here.
+A man weighing one hundred and fifty pounds on the
+earth would weigh only fifty-seven pounds on Mars, could
+jump two and one half times as high or far, and could
+throw a stone two and one half times the distance he could
+here.\footnote
+  {He could not throw the stone any swifter on Mars than he could
+  on the earth; gravity there being so much weaker, the stone would move
+  farther before falling to the surface.}
+A pendulum clock taken from the earth to Mars
+would lose nearly nine hours in a day as the pendulum
+would tick only about seven elevenths as fast there. A
+%% -----File: 253.png---Folio 254-------
+watch, however, would run essentially the same there as
+here. As we shall see presently, either instrument would
+have to be adjusted in order to keep Martian time as the
+day there is longer than ours.
+
+\Paragraph{Rotation.} Because of its well-marked surface it has
+been possible to ascertain the period of rotation of Mars
+with very great precision. Its sidereal day is $24$~h.\ $37$~m.\
+$22.7$~s. The solar day is $39$~minutes longer than our solar
+day and owing to the greater ellipticity of its orbit the
+solar days vary more in length than do ours.
+
+\Paragraph{Revolution and Seasons.} A year on Mars has $668$~Martian
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+\index{Lowell, Percival}%
+days,\footnote
+  {\textit{Mars}, by Percival Lowell.}
+and is nearly twice as long as ours. The
+orbit is much more elliptical than that of the earth, perihelion
+being $26,000,000$~miles nearer the sun than aphelion.
+For this reason there is a marked change in the amount of
+heat received when Mars is at those two points, being
+almost one and one half times as much when in perihelion
+as when in aphelion. The northern summers occur when
+Mars is in aphelion, so that hemisphere has longer, cooler
+summers and shorter and warmer winters than the southern
+hemisphere.
+
+\begin{center}
+\smallsize
+\begin{tabular}{@{}p{0.45\textwidth}@{\hspace{0.1\textwidth}}p{0.45\textwidth}@{}}
+\multicolumn{1}{@{}c@{\hspace{0.1\textwidth}}}{\textsc{Northern Hemisphere}} &
+  \multicolumn{1}{@{}c@{}}{\textsc{Southern Hemisphere}} \\[1ex]
+Spring \dotfill 191 days & Spring \dotfill 149 days \\
+Summer \dotfill 181 days & Summer \dotfill 147 days \\
+Autumn \dotfill 149 days & Autumn \dotfill 191 days \\
+Winter \dotfill 147 days & Winter \dotfill 181 days \\
+\end{tabular}
+\end{center}
+
+
+\Paragraph{Zones.} The equator makes an angle of $24°~50'$ with the
+\index{Zones|(}%
+planet's ecliptic (instead of $23°~27'$ as with us) so the change
+in seasons and zones is very similar to ours, the climate,
+of course, being vastly different, probably \emph{very cold} because
+of the rarity of the atmosphere (about the same as on our
+\index{Atmosphere!on Mars}%
+%% -----File: 254.png---Folio 255-------
+highest mountains) and absence of oceans. The distance
+from the sun, too, makes a great difference in climate.
+Being about one and one half times as far from the earth,
+the sun has an apparent diameter only two thirds as
+great and only four ninths as much heat is received over
+a similar area.
+
+\Paragraph{Satellites.}\nblabel{page:255} Mars has two satellites or moons. Since
+\index{Deimos@Deimos (d\u{\i}$'$mus)}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+\index{Phobos@Phobos (f\={o}$'$b\u{u}s)}%
+Mars was the god of war of the Greeks these two satellites
+have been given the Greek names of Deimos and Phobos,
+meaning ``dread'' and ``terror,'' appropriate for ``dogs
+of war.'' They are very small, only six or seven miles in
+diameter. Phobos is so near to Mars ($3,750$~miles from the
+surface) that it looks almost as large to a Martian as our
+moon does to us, although not nearly so bright. Phobos,
+being so near to Mars, has a very swift motion around the
+\index{Mars|)}%
+planet, making more than three revolutions around it
+during a single Martian day. Now our moon travels
+around the earth from west to east but only about $13°$ in
+a day, so because of the earth's rotation the moon rises
+in the east and sets in the west. In case of Phobos, it
+revolves faster than the planet rotates and thus rises in
+the west and sets in the east. Thus if Phobos rose in the
+west at sunset in less than three hours it would be at
+meridian height and show first quarter, in five and one
+half hours it would set in the east somewhat past the
+full, and before sunrise would rise again in the west almost
+at the full again. Deimos has a sidereal period of $30.3$~hours
+and thus rises in the east and sets in the west, the
+period from rising to setting being $61$~hours.
+
+\Section{Venus}
+\index{Venus}%
+
+\Paragraph{Form and Dimensions.} Venus is very nearly spherical
+and has a diameter of $7,700$~miles, very nearly that of the
+%% -----File: 255.png---Folio 256-------
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Venus}%
+earth, so its latitude and longitude are very similar to ours.
+Its surface gravity is about $\frac{9}{10}$ that of the earth. A man
+weighing $150$~pounds here would weigh $135$~pounds there.
+
+\Paragraph{Revolution.} Venus revolves around the sun in a period
+of $225$ of our days, probably rotating once on the journey,
+thus keeping essentially the same face toward the sun.
+The day, therefore, is practically the same as the year, and
+the zones are two, one of perpetual sunshine and heat and
+the other of perpetual darkness and cold. Its atmosphere
+\index{Atmosphere!on Venus}%
+is of nearly the same density as that of the earth. Being
+a little more than seven tenths the distance of the earth
+from the sun, that blazing orb seems to have a diameter
+nearly one and one half times as great and pours nearly
+twice as much light and heat over a similar area. Its
+orbit is more nearly circular than that of any other planet.
+
+\Section{Jupiter}
+\index{Jupiter}%
+
+\Paragraph{Form and Dimensions.} After Venus, this is the brightest
+of the heavenly bodies, being immensely large and
+having very high reflecting power. Jupiter is decidedly
+oblate. Its equatorial diameter is $90,000$~miles and its
+polar diameter is $84,200$~miles. Degrees of latitude near
+the equator are thus nearly $785$~miles long, increasing to
+over $800$~miles near the pole. The area of the surface is
+$122$~times that of the earth, its volume~$1,355$, its mass or
+weight~$317$, and its density about one fourth.
+
+\Paragraph{Surface Gravity.} The weight of an object on the surface
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Jupiter}%
+of Jupiter is about two and two thirds times its weight
+here. A man weighing $150$~pounds here would weigh $400$~pounds
+there but would find he weighed nearly $80$~pounds
+more near the pole than at the equator, gravity being so
+much more powerful there. A pendulum clock taken from
+%% -----File: 256.png---Folio 257-------
+the earth to Jupiter would gain over nine hours in a day
+\index{Jupiter}%
+and would gain or lose appreciably in changing a single
+degree of latitude because of the oblateness of the planet.
+
+\Paragraph{Rotation.} The rotation of this planet is very rapid,
+occupying a little less than ten hours, and some portions
+seem to rotate faster than others. It seems to be in a
+molten or liquid state with an extensive envelope of gases,
+\index{Atmosphere!on Jupiter}%
+eddies and currents of which move with terrific speed.
+The day there is very short as compared with ours and a
+difference of one hour in time makes a difference of over
+$36°$~in longitude, instead of~$15°$ as with us. Their year
+being about $10,484$~of their days, their solar day is only a
+few seconds longer than their sidereal day.
+
+\Paragraph{Revolution.} The orbit of Jupiter is elliptical, perihelion
+\index{Revolution@Revolution \indexglossref{Revolution}|(}%
+being about $42,000,000$ miles nearer the sun than aphelion.
+Its mean distance from the sun is $483,000,000$ miles, about
+five times that of the earth. The angle its equator forms
+with its ecliptic is only~$3°$, so there is little change in
+seasons. The vertical ray of the sun never gets more
+than $3°$~from the equator, and the torrid zone is $6°$~wide.
+The circle of illumination is never more than $3°$~from or
+beyond a pole so the frigid zone is only $3°$~wide. The
+temperate\footnote
+  {These terms are purely relative, meaning, simply, the zone on
+  Jupiter corresponding in position to the temperate zone on the earth.
+  The inappropriateness of the term may be seen in the fact that Jupiter
+  is intensely heated, so that its surface beneath the massive hot vapors
+  surrounding it is probably molten.}
+zone is $84°$~wide.
+
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|(}%
+Jupiter has seven moons.
+
+\Section{Saturn}\nblabel{page:257}
+\index{Saturn}%
+
+\Paragraph{Form and Dimensions.} The oblateness of this planet
+is even greater than that of Jupiter, being the greatest of
+%% -----File: 257.png---Folio 258-------
+the planets. Its mean diameter is about $73,000$ miles. It,
+therefore, has $768$~times the volume of the earth and $84$~times
+the surface. Its density is the lowest of the planets,
+only about one eighth as dense as the earth. Its surface
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Saturn}%
+gravity is only slightly more than that of the earth, varying,
+however, $25$~per~cent from pole to equator.
+
+\Paragraph{Rotation.} Its sidereal period of rotation is about $10$~h.\
+$14$~m., varying slightly for different portions as in case
+of Jupiter. The solar day is only a few seconds longer
+than the sidereal day.
+
+\sloppy
+\Paragraph{Revolution.} Its average distance from the sun is
+$866,000,000$ miles, varying considerably because of its
+ellipticity. It revolves about the sun in $29.46$~of our
+years, thus the annual calendar must comprise $322,777$
+of the planet's days. %[**TN: Calculation error: 29.46 years is roughly 25,000 days of 10h 14m]
+
+\fussy
+The inclination of Saturn's axis makes an angle of~$27°$
+\index{Saturn}%
+between the planes of its equator and its ecliptic. Thus
+the vertical ray sweeps over~$54°$ giving that width to its
+torrid zone, $27°$~to the frigid, and $36°$~to the temperate.
+Its ecliptic and our ecliptic form an angle of~$2.5°$, so we
+always see the planet very near the sun's apparent path.
+
+Saturn has surrounding its equator immense disks, of
+thin, gauzelike rings, extending out nearly $50,000$ miles
+from the surface. These are swarms of meteors or tiny
+moons, swinging around the planet in very nearly the
+same plane, the inner ones moving faster than the outer
+ones and being so very minute that they exert no appreciable
+attractive influence upon the planet.
+
+In addition to the rings, Saturn has ten moons.
+
+\Section{Uranus}
+\index{Uranus@Uranus (\={u}$'$ra\;nus)}%
+
+\Paragraph{Form and Dimensions.} This planet, which is barely
+visible to the unaided eye, is also decidedly oblate, nearly
+\index{Zones|)}%
+%% -----File: 258.png---Folio 259-------
+as much so as Saturn. Its mean diameter is given as
+from $34,900$ miles to $28,500$ miles. Its volume, on basis
+of the latter (and latest) figures, is $47$~times that of the
+earth. Its density is very low, about three tenths that of
+the earth, and its surface gravity is about the same as
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Uranus}%
+ours at the equator, increasing somewhat toward the
+pole.
+
+Nothing certain is known concerning its rotation as it
+has no distinct markings upon its surface. Consequently
+we know nothing as to the axis, equator, days, calendar,
+or seasons.
+
+Its mean distance from the sun is $19.2$~times that of the
+earth and its sidereal year $84.02$~of our years.
+
+Uranus has four satellites swinging around the planet
+\index{Uranus@Uranus (\={u}$'$ra\;nus)}%
+in very nearly the same plane at an angle of~$82.2°$ to the
+plane of the orbit. They move from west to east around
+the planet, not for the same reason Phobos does about
+Mars, but probably because the axis of the planet, the
+plane of its equator, and the plane of these moons has
+been tipped~$97.8°$ from the plane of the orbit and the
+north pole has been tipped down below or south of the
+ecliptic, becoming the south pole, and giving a backward
+rotation to the planet and to its moons.
+
+\Section{Neptune}
+\index{Neptune}%
+
+Neptune is the most distant planet from the sun, is
+probably somewhat larger than Uranus, and has about
+the same density and slightly greater surface gravity.
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Neptune}%
+
+Owing to the absence of definite markings nothing is
+known as to its rotation. Its one moon, like those of
+Uranus, moves about the planet from west to east in a
+plane at an angle of $34°~48'$ to its ecliptic, and its backward
+motion suggests a similar explanation, the inclination
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|)}%
+%% -----File: 259.png---Folio 260-------
+of its axis is more than~$90°$ from the plane of its
+\index{Neptune}%
+ecliptic.
+
+\Section{Mercury}
+\index{Mercury}%
+
+This is the nearest of the planets to the sun, and as it
+never gets away from the sun more than about the width
+of forty suns (as seen from the earth), it is rarely visible
+and then only after sunset in March and April or before
+sunrise in September and October.
+
+\Paragraph{Form and Dimensions.} Mercury has about three
+eighths the diameter of the earth, one seventh of the surface,
+and one eighteenth of the volume. It probably has
+one twentieth of the mass, nine tenths of the density,
+and a little less than one third of the surface gravity.
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on Mercury}%
+
+\Paragraph{Rotation and Revolution.} It is believed that Mercury
+rotates once on its axis during one revolution. Owing to
+its elliptical orbit it moves much more rapidly when near
+perihelion than when near aphelion, and thus the sun
+loses as compared with the average position, just as it
+does in the case of the earth, and sweeps eastward about~$23\frac{1}{2}°$
+from its average position. When in aphelion it gains
+and sweeps westward a similar amount. This shifting
+eastward making the sun ``slow'' and westward making
+the sun ``fast'' is called libration.
+
+Thus there are four zones on Mercury, vastly different
+\index{Zones}%
+from ours, indeed, they are not zones (belts) in a terrestrial
+sense.
+
+\textit{a.} An elliptical central zone of perpetual sunshine,
+extending from pole to pole and $133°$~in longitude. In
+this zone the vertical ray shifts eastward~$23 \frac{1}{2}°$ and back
+again in the short summer of about $30$~days, and westward
+a similar extent during the longer winter of about $58$~days.
+Two and one half times as much heat is received
+%% -----File: 260.png---Folio 261-------
+in the summer, when in perihelion, as is received in the
+winter, when in aphelion. Thus the eastward half of
+this zone has hotter summers and cooler winters than
+does the western half. Places along the eastern and
+western margin of this zone of perpetual sunshine see the
+sun on the horizon in winter and only $23 \frac{1}{2}°$~high in the
+summer.
+
+\textit{b.} An elliptical zone of perpetual darkness, extending
+from pole to pole and $133°$~wide from east to west.
+
+\textit{c.} Two elliptical zones of alternating sunshine and
+darkness (there being practically no atmosphere on Mercury,
+\index{Atmosphere!on Mercury}%
+\index{Mercury}%
+there is no twilight there), each extending from
+pole to pole and $47°$~wide. The eastern of these zones
+has hotter summers and cooler winters than the western
+one has.
+
+\Section{The Moon}
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|(}%
+
+\Paragraph{Form and Dimensions.} The moon is very nearly
+spherical and has a diameter of $2,163$~miles, a little over
+one fourth that of the earth, its volume one forty-fourth,
+its density three fifths, its mass~$\frac{10}{815}$, and its surface
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on moon}%
+gravity one sixth that upon the earth. A pendulum
+clock taken there from the earth would tick so slowly
+that it would require about sixty hours to register one of
+our days. A degree of latitude (or longitude at its
+equator) is a little less than nineteen miles long.
+
+\Paragraph{Rotation.} The moon rotates exactly once in one revolution
+around the earth, that is, keeps the same face
+toward the earth, but turns different sides toward the
+sun once each month.
+
+Thus what we call a sidereal month is for the moon
+itself a sidereal day, and a synodic month is its solar
+day. The latter is $29.5306$~of our days, which makes the
+%% -----File: 261.png---Folio 262-------
+\index{Orbit, of earth!of moon}%
+moon's solar day have $708$~h.\ $44$~m.\ $3.8$~s. If its day were
+divided into twenty-four parts as is ours, each one would
+be longer than a whole day with us.
+
+\Paragraph{Revolution and Seasons.} The moon's orbit around the
+sun has essentially the same characteristics as to perihelion,
+aphelion, longer and shorter days,~etc., as that of
+the earth. The fact that the moon goes around the earth
+does not materially affect it from the sun's view point.
+To illustrate the moon's orbit about the sun, draw a circle
+$78$~inches in diameter. Make $26$~equidistant dots in
+this circle to represent the earth for each new and full
+moon of the year. Now for each new moon make a dot
+one twentieth of an inch toward the center (sun) from
+every other dot representing the earth, and for every full
+moon make a dot one twentieth of an inch beyond the
+alternate ones. These dots representing the moon, if
+connected, being never more than about one twentieth
+of an inch from the circle, will not vary materially from
+the circle representing the orbit of the earth, and the
+moon's orbit around the sun will be seen to have in every
+part a concave side toward the sun.
+
+The solar day of the moon being $29.53$~of our days, its
+tropical year must contain as many of those days as that
+number is contained times in $365.25$~days or about $12.4$~days.
+The calendar for the moon does not have anything
+\index{Calendar!on moon}%
+corresponding to our month, unless each day be
+treated as a month, but has a year of $12.4$~long days of
+nearly $709$~hours each. The exact length of the moon's
+solar year being $12.3689$~d., its calendar would have the
+peculiarity of having one leap year in every three, that is,
+two years of $12$~days each and then one of $13$~days,
+with an extra leap year every $28$~years.
+
+The earth as seen from the moon is much like the moon
+\index{Revolution@Revolution \indexglossref{Revolution}|)}%
+%% -----File: 262.png---Folio 263-------
+as seen from the earth, though very much larger, about
+four times as broad. Because the moon keeps the same
+face constantly toward the earth, the latter is visible to
+only a little over half of the moon. On this earthward
+side our planet would be always visible, passing through
+precisely the same phases as the moon does for us, though
+\index{Phases of the moon}%
+in the opposite order, the time of our new moon being
+``full earth'' for the moon. So brightly does our earth
+then illuminate the moon that when only the faint crescent
+of the sunshine is visible to us on the rim of the
+moon, we can plainly see the ``earth shine'' on the rest
+of the moon's surface which is toward us.
+
+\Paragraph{Zones.} The inclination of the plane of the moon's
+\index{Zones}%
+equator to the plane of the ecliptic is $1°~32'$ (instead of
+$23°~27'$ as in the case of the earth). Thus its zone corresponding
+to our torrid\footnote
+  {Again we remind the reader that these terms are not appropriate
+  in case of other celestial bodies than the earth. The moon has almost
+  no atmosphere to retain the sun's heat during its long night of nearly
+\index{Atmosphere!absence of, on moon}%
+  $354$~hours and its dark surface must get exceedingly cold, probably
+  several hundred degrees below zero.}
+zone is $3°~4'$ wide, the frigid zone
+$1°~32'$, and the temperate zones $86°~56'$.
+
+\Paragraph{Absence of Atmosphere.}\nblabel{page:263} The absence of an atmosphere
+on the moon makes conditions there vastly different from
+those to which we are accustomed. Sunrise and sunset
+show no crimson tints nor beautiful coloring and there
+is no twilight. Owing to the very slow rotation of the
+moon, $709$~hours from sun-noon to sun-noon, it takes
+nearly an hour for the disk of the sun to get entirely above
+the horizon on the equator, from the time the first glint
+of light appears, and the time of sunset is equally prolonged;
+as on the earth, the time occupied in rising or
+setting is longer toward the poles of the moon. The stars
+%% -----File: 263.png---Folio 264-------
+do not twinkle, but shine with a clear, penetrating light.
+They may be seen as easily in the daytime as at night,
+even those very near the sun. Mercury is thus visible
+\index{Sun|(}%
+the most of the time during the long daytime of $354$~hours,
+and Venus as well. Out of the direct rays of the
+sun, pitch darkness prevails. Thus craters of the volcanoes
+are very dark and also cold. In the tropical portion
+the temperature probably varies from two or three hundred
+degrees below zero at night to exceedingly high temperatures
+in the middle of the day. During what is to the
+moon an eclipse of the sun, which occurs whenever we see
+the moon eclipsed, the sun's light shining through our
+atmosphere makes the most beautiful of coloring as
+\index{Atmosphere!absence of, on moon}%
+viewed from the moon. The moon's atmosphere is so
+rare that it is incapable of transmitting sound, so that a
+deathlike silence prevails there. Oral conversation is
+utterly impossible and the telephone and telegraph as we
+have them would be of no use whatever. Not a drop of
+water exists on that cold and cheerless satellite.
+
+Perhaps it is worth noting, in conclusion, that it is
+believed that our own atmosphere is but the thin remnant
+of dense gases, and that in ages to come it will get more
+and more rarified, until at length the earth will have the
+same conditions as to temperature, silence,~etc., which
+now prevail on the moon.
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}|)}%
+
+\Section{The Sun}
+
+\Paragraph{Dimensions.} The diameter is $866,500$ miles, nearly
+four times the distance of the moon from the earth. Its
+surface area is about $12,000$~times that of the earth, and
+its volume over a million times. Its density is about
+one fourth that of the earth, its mass $332,000$ times, and
+its surface gravity is $27.6$~times our earth's. A man
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on sun}%
+%% -----File: 264.png---Folio 265-------
+weighing $150$~pounds here would weigh over two tons
+there, his arm would be so heavy he could not raise it
+and his bony framework could not possibly support his
+\index{Gravity@Gravity\phantomsection\label{idx:g}!on sun}%
+body. A pendulum clock there would gain over a hundred
+hours in a day, so fast would the attraction of the
+sun draw the pendulum.
+\index{Sun!a star|(}%
+
+\Paragraph{Rotation.} The sun rotates on its axis in about $25\frac{1}{3\extrafracspacing}$ of
+our days, showing the same portion to the earth every
+$27\frac{1}{4}$~days. This rate varies for different portions of the
+sun, its equator rotating considerably faster than higher
+latitudes. The direction of its rotation is from west to
+east from the sun's point of view, though as viewed from
+the earth the direction is from our east to our west. The
+plane of the equator forms an angle of about~$26°$ with the
+plane of our equator, though only about~$7\frac{1}{4}°$ with the
+plane of the ecliptic.
+
+When we realize that the earth, as viewed from the sun,
+is so tiny that it receives not more than one billionth of
+its light and heat, we may form some idea of the immense
+flood of energy it constantly pours forth.
+
+\Paragraph{The Sun a Star.}\nblabel{page:265} ``The word `star' should be omitted
+\index{Star, distance of a!sun a|(}%
+from astronomical literature. It has no astronomic meaning.
+Every star visible in the most penetrating telescope
+is a hot sun. They are at all degrees of heat, from dull
+red to the most terrific white heat to which matter can be
+subjected. Leaves in a forest, from swelling bud to the
+`sere and yellow,' do not present more stages of evolution.
+A few suns that have been weighed, contain less matter
+than our own; some of equal mass; others are from ten
+to twenty and thirty times more massive, while a few are
+so immensely more massive that all hopes of comparison
+fail.
+
+\nblabel{page:265b}``Every sun is in motion at great speed, due to the attraction
+\index{Larkin, E. L.|(}%
+\index{Fixed stars}%
+\index{Star, distance of a!motions of}%
+%% -----File: 265.png---Folio 266-------
+and counter attraction of all the others. They go in
+every direction. Imagine the space occupied by a swarm
+of bees to be magnified so that the distance between each
+bee and its neighbor should equal one hundred miles. The
+insects would fly in every possible direction of their own
+%% -----File: 266.png---Folio 267-------
+volition. Suns move in every conceivable direction, not
+\index{Fixed stars}%
+\index{Star, distance of a!motions of}%
+as they will, but in abject servitude to gravitation. They
+must obey the omnipresent force, and do so with mathematical
+accuracy.'' From ``New Conceptions in Astronomy,''
+by Edgar~L. Larkin, in \textit{Scientific American}, February~3,
+\index{Scientific American}%
+\index{Larkin, E. L.|)}%
+\index{Earth in Space|)}%
+\index{Star, distance of a!sun a|)}%
+1906.
+
+%[**TN: table moved to end of chapter to fit on page]
+%[**TN: table is full of space/alignment tweaks which will need adjustment if layout is changed]
+\begin{table}[ht]
+\begin{minipage}{\textwidth}
+\begin{center}
+\index{Distances, of planets}%
+\index{Jupiter}%
+\index{Mars}%
+\index{Mercury}%
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+\index{Neptune}%
+\index{Saturn}%
+\index{Solar system!table}%
+\index{Uranus@Uranus (\={u}$'$ra\;nus)}%
+\index{Venus}%
+\renewcommand{\thempfootnote}{\fnsymbol{mpfootnote}} % for asterisk footnotemark
+\scriptsize\nblabel{page:266}
+\setlength\tabcolsep{2pt}
+\renewcommand{\arraystretch}{2}
+\begin{tabular}{|l|c|*{8}{r|}}%
+\multicolumn{10}{c}{\smallsize\textsc{Solar System Table}\tablespacerbot}\\\hline
+\index{Solar system|)}%
+\settowidth{\TmpLen}{Neptune}%
+\multirow{2}{\TmpLen}{\centering\rotatebox{90}{\parbox[c]{11ex}{\centering Object}\hspace{2em}}} &
+\multirow{2}{12pt}{\centering\rotatebox{90}{\parbox[c]{11ex}{\centering Symbol}\hspace{2em}}} &
+\settowidth{\TmpLen}{$866,400$}%
+\multirow{2}{\TmpLen}{\centering\rotatebox{90}{\parbox[c]{11ex}{\centering Mean\\Diameter\\(miles)}\hspace{2em}}} &
+\settowidth{\TmpLen}{$24$h~$37$m~$22.7$s}%
+\multirow{2}{\TmpLen}{\centering\rotatebox{90}{\parbox[c]{11ex}{\medskip\centering Sidereal\\Day}\hspace{2em}}} &
+\multicolumn{6}{c|}{As compared with the earth\mpfootnotemark}\\
+\cline{5-10}
+&&&&
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Heat per\\Unit Area}\hspace{1em}}} &
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Density}}} &
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Mass}}} &
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Surface\\Gravity}}} &
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Sidereal\\Year}}}   &
+\multicolumn{1}{c|}{\rotatebox{90}{\parbox[c]{11ex}{\centering Dist.\\from $\astrosun$}}} \\
+\hline
+Mercury & \smallsize$\mercury$ &  $3,000$ & \multicolumn{1}{c|}{$\Z88$~days}
+    & $6.800$ & $0.85$ &       $0.048$ &  $0.330$ &   $0.24$ &  $0.4$ \\
+\hline
+Venus   & \smallsize$\venus$   &  $7,700$ & \multicolumn{1}{c|}{$225$~days}
+    & $1.900$ & $0.94$ &       $0.820$ &  $0.900$ &   $0.62$ &  $0.7$ \\
+\hline
+Earth   & \smallsize$\earth$   &  $7,918$ & \multicolumn{1}{c|}{*}
+    & $1.000$ & $1.00$ &       $1.000$ &  $1.000$ &   $1.00$ &  $1.0$ \\
+\hline
+Mars    & \smallsize$\mars$    &  $4,230$ & $24$h~$37$m~$22.7$s
+    & $0.440$ & $0.73$ &       $0.110$ &  $0.380$ &   $1.88$ &  $1.5$ \\
+\hline
+Jupiter & \smallsize$\jupiter$ & $88,000$ &  $9$h~$55$m~\phantom{22.7s}
+    & $0.040$ & $0.23$ &     $317.000$ &  $2.650$ &  $11.86$ &  $5.2$ \\
+\hline
+Saturn  & \smallsize$\saturn$  & $73,000$ & $10$h~$14$m~\phantom{22.7s}
+    & $0.010$ & $0.13$ &      $95.000$ &  $1.180$ &  $29.46$ &  $9.5$ \\
+\hline
+Uranus  & \smallsize$\uranus$  & $31,700$ & \hfill?\hfill{}
+    & $0.003$ & $0.31$ &      $14.600$ &  $1.110$ &  $84.02$ & $19.2$ \\
+\hline
+Neptune & \smallsize$\neptune$ & $32,000$ & \hfill?\hfill{}
+    & $0.001$ & $0.34$ &      $17.000$ &  $1.250$ & $164.78$ & $30.1$ \\
+\hline
+Sun     & \smallsize$\astrosun$&$866,400$ & $25$d~$7$h~$48$m$\Z\Z$
+\index{Sun|)}%
+\index{Sun!a star|)}%
+    &         & $0.25$ & $332,000.000$ & $27.650$ &          &        \\
+\hline
+Moon    & \smallsize$\leftmoon$&  $2,163$ & $27$d~$7$h~$43$m$\Z\Z$
+    &         & $0.61$ &       $0.012$ &  $0.166$ &          &        \\
+\hline
+\end{tabular}
+\footnotetext{The dimensions of the earth and other data are given in the
+table of geographical constants p.~\pageref{page:310}.}
+\end{center}
+\end{minipage}
+\end{table}
+%% -----File: 267.png---Folio 268-------
+
+\Chapter{XIV}{Historical Sketch}
+\index{Historical sketch|(}%
+
+\Section{The Form of the Earth}
+
+\First{While} various views have been held regarding the form
+of the earth, those worthy of attention\footnote
+  {As for modern, not to say recent, pseudo-scientists and alleged
+  divine revealers who contend for earths of divers forms, the reader
+  is referred to the entertaining chapter entitled ``Some Cranks and
+  their Crotchets'' in John Fiske's \textit{A Century of Science}, also the footnote
+\index{Fiske, John}%
+  on pp.~267--268, Vol.~I, of his \textit{Discovery of America}.}
+may be grouped
+under four general divisions.
+
+\Paragraph{{\mdseries I.} The Earth Flat.} Doubtless the universal belief of
+primitive man was that, save for the irregularities of mountain,
+hill, and valley, the surface of the earth is flat. In all
+the earliest literature that condition seems to be assumed.
+The ancient navigators could hardly have failed to observe
+the apparent convex surface of the sea and very ancient
+literature as that of Homer alludes to the bended sea.
+\index{Homer}%
+This, however, does not necessarily indicate a belief in the
+spherical form of the earth.
+
+Although previous to his time the doctrine of the spherical
+form of the earth had been advanced, Herodotus
+\index{Herodotus@Herodotus (he\;r\u{o}d$'$\;o\;tus)}%
+(born about 484~\BC, died about 425~\BC)\ did not believe
+in it and scouted whatever evidence was advanced in its
+favor. Thus in giving the history of the Ptolemys, kings
+\index{Ptolemy Necho, of Egypt}%
+of Egypt, he relates the incident of Ptolemy Necho (about
+\index{Egypt}%
+610--595~\BC)\ sending Ph{\oe}nician sailors on a voyage
+\index{Phoenicians}%
+around Africa, and after giving the sailors' report that
+\index{Africa}%
+they saw the \emph{sun to the northward} of them, he says, ``I,
+%% -----File: 268.png---Folio 269-------
+for my part, do not believe them.'' Now seeing the sun
+to the northward is the most logical result if the earth be
+a sphere and the sailors went south of the equator or south
+of the tropic of Cancer in the northern summer.
+\index{Cancer, constellation of!tropic of}%
+\index{Tropics}%
+
+Ancient travelers often remarked the apparent sinking
+of southern stars and rising of northern stars as they
+traveled northward, and the opposite shifting of the heavens
+as they traveled southward again. In traveling eastward
+or westward there was no displacement of the heavens
+and travel was so slow that the difference in time of
+sunrise or star-rise could not be observed. To infer that
+the earth is curved, at least in a north-south direction, was
+most simple and logical. It is not strange that some began
+to teach that the earth is a cylinder. Anaximander (about
+\index{Anaximander@Anaximander (\u{a}n\;\u{a}x\;\u{\i}\;m\u{a}n$'$der)}%
+611--547~\BC), indeed, did teach that it is a cylinder\footnote
+  {According to some authorities he taught that the earth is a
+  sphere and made terrestrial and celestial globes. See Ball's \textit{History of
+  Mathematics}, p.~18.}
+\index{Ball's History of Mathematics}%
+and
+thus prepared the way for the more nearly correct theory.
+
+\Paragraph{{\mdseries II.} The Earth a Sphere.} The fact that the Chaldeans
+\index{Chaldeans}%
+had determined the length of the tropical year within less
+than a minute of its actual value, had discovered the precession
+of the equinoxes, and could predict eclipses over
+two thousand years before the Christian era and that in
+China similar facts were known, possibly at an earlier
+\index{China}%
+period, would indicate that doubtless many of the astronomers
+of those very ancient times had correct theories as
+to the form and motions of the earth. So far as history
+has left any positive record, however, Pythagoras (about
+\index{Pythagoras@Pythagoras (p\u{\i}\;th\u{a}g$'$\={o}\;ras)}%
+582--507~\BC), a Greek\footnote
+  {Sometimes called a Ph{\oe}nician.}
+philosopher, seems to have been
+the first to advance the idea that the earth is a sphere.
+His theory being based largely upon philosophy, nothing
+%% -----File: 269.png---Folio 270-------
+but a perfect sphere would have answered for his conception.
+He was also the first to teach that the earth
+rotates\footnote
+  {Strictly speaking, Pythagoras seems to have taught that both
+  sun and earth revolved about a central fire and an opposite earth
+  revolved about the earth as a shield from the central fire. This rather
+  complicated machinery offered so many difficulties that his followers
+  abandoned the idea of the central fire and ``opposite earth'' and had
+  the earth rotate on its own axis.}
+on its axis and revolves about the sun.
+
+Before the time of Pythagoras, Thales (about 640--546~\BC),
+\index{Pythagoras@Pythagoras (p\u{\i}\;th\u{a}g$'$\={o}\;ras)}%
+\index{Thales@Thales (th\={a}$'$l\={e}z)}%
+and other Greek philosophers had divided the earth
+into five zones, the torrid zone being usually considered
+so fiery hot that it could not be crossed, much less inhabited.
+Thales is quoted by Plutarch as believing that the
+\index{Plutarch}%
+earth is a sphere, but it seems to have been proved that
+Plutarch was in error. Many of the ancient philosophers
+did not dare to teach publicly doctrines not commonly
+accepted, for fear of punishment for impiety. It is
+possible that his private teaching was different from his
+public utterances, and that after all Plutarch was right.
+
+Heraclitus, Plato, Eudoxus, Aristotle and many others
+\index{Aristotle@Aristotle (\u{a}r$'$\u{\i}s\;tot\;l)}%
+\index{Eratosthenes@Eratosthenes (\~{e}r\;\.{a}\;t\u{o}s$'$\;th\={e}\;n\={e}z)}%
+\index{Heraclitus@Heraclitus (h\u{e}r\;a\;kl\={\i}$'$tus)}%
+\index{Eudoxus}%
+\index{Plato}%
+in the next two centuries taught the spherical form of the
+earth, and, perhaps, some of them its rotation. Most of
+them, however, thought it not in harmony with a perfect
+universe, or that it was impious, to consider the sun as
+predominant and so taught the geocentric theory.
+
+The first really scientific attempt to calculate the size
+of the earth was by Eratosthenes (about 275--195~\BC).
+He was the keeper of the royal library at Alexandria, and
+made many astronomical measurements and calculations
+of very great value, not only for his own day but for ours
+as well. Syene, the most southerly city of the Egypt of
+\index{Syene, Egypt}%
+his day, was situated where the sundial cast no shadow
+at the summer solstice. Measuring carefully at Alexandria,
+\index{Alexandria, Egypt}%
+%% -----File: 270.png---Folio 271-------
+he found the noon sun to be one fiftieth of the circumference
+to the south of overhead. He then multiplied
+the distance between Syene and Alexandria, $5,000$~stadia
+\index{Stadium@Stadium (st\={a}$'$\;d\u{\i}\;um)}%
+\index{Alexandria, Egypt}%
+by~$50$ and got the whole circumference of the earth to be
+$250,000$ stadia. The distance between the cities was not
+known very accurately and his calculation probably contained
+a large margin of error, but the exact length of the
+Greek stadium of his day is not known\footnote
+  {The most reliable data seem to indicate the length of the stadium
+  was $606\frac{3}{4}$~feet.}
+and we cannot
+tell how near the truth he came.
+
+Any sketch of ancient geography would be incomplete
+without mention of Strabo (about 54~\BC--21~\AD) who is
+\index{Strabo@Strabo (str\={a}$'$b\={o})}%
+sometimes called the ``father of geography.'' He believed
+the earth to be a sphere at the center of the universe.
+He continued the idea of the five zones, used such circles
+as had commonly been employed by astronomers and
+geographers before him, such as the equator, tropics, and
+polar circles. His work was a standard authority for
+many centuries.
+
+About a century after the time of Eratosthenes, Posidonius,
+\index{Eratosthenes@Eratosthenes (\~{e}r\;\.{a}\;t\u{o}s$'$\;th\={e}\;n\={e}z)}%
+\index{Posidonius@Posidonius (p\u{o}s$'$\u{\i}\;d\={o}\;n\u{\i}\;us)}%
+a contemporary of Strabo, made another measurement,
+basing his calculations upon observations of a star
+instead of the sun, and getting a smaller circumference,
+though that of Eratosthenes was probably too small.
+Strabo, Hipparchus, Ptolemy and many others made estimates
+\index{Hipparchus@Hipparchus (h\u{\i}p\;ar$'$kus)}%
+\index{Ptolemy, Claudius}%
+as to the size of the earth, but we have no record of
+any further measurements with a view to exact calculation
+until about 814~\AD{} when the Arabian caliph Al-Mamoum
+\index{Al-Mamoum}%
+sent astronomers and surveyors northward and southward,
+carefully measuring the distance until each party found a
+star to have shifted to the south or north one degree.
+%% -----File: 271.png---Folio 272-------
+This distance of two degrees was then multiplied by~$180$
+and the whole circumference obtained.
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+
+The period of the dark ages was marked by a decline in
+learning and to some extent a reversion to primitive conceptions
+concerning the size, form, or mathematical properties
+of the earth. Almost no additional knowledge
+was acquired until early in the seventeenth century.
+Perhaps this statement may appear strange to some
+readers, for this was long after the discovery of America
+by Columbus. It should be borne in mind that his voyage
+\index{Columbus, Christopher}%
+and the resulting discoveries and explorations contributed
+nothing directly to the knowledge of the form or size of
+the earth. That the earth is a sphere was generally
+believed by practically all educated people for centuries
+before the days of Columbus. The Greek astronomer
+Cleomedes, writing over a thousand years before Columbus
+\index{Cleomedes@Cleomedes (kl\={e}\;\u{o}m$'$\={e}\;d\={e}z)}%
+was born, said that all competent persons excepting
+the Epicureans accepted the doctrine of the spherical
+\index{Epicureans}%
+form of the earth.
+
+In 1615 Willebrord Snell, professor of mathematics at
+\index{Snell, Willebrord}%
+the University of Leyden, made a careful triangular survey
+\index{Leyden, Holland}%
+\index{Survey}%
+of the level surfaces about Leyden and calculated
+the length of a degree of latitude to be $66.73$~miles. A
+recalculation of his data with corrections which he suggested
+gives the much more accurate measurement of $69.07$~miles.
+About twenty years later, an Englishman named
+Richard Norwood made measurements and calculations
+\index{Norwood, Richard}%
+in southern England and gave $69.5$ as the length of a
+degree of latitude, the most accurate measurement up to
+that time.
+
+It was about 1660 when Isaac Newton (1642--1727)
+\index{Newton, Isaac}%
+discovered the laws of gravitation, but when he applied
+\index{Gravitation}%
+the laws to the motions of the moon his calculations did
+%% -----File: 272.png---Folio 273-------
+not harmonize with what he assumed to be the size
+of the earth. About 1671 the French astronomer, Jean
+\index{Picard@Picard (p\={e}\;kär$'$), Jean}%
+Picard, by the use of the telescope, made very careful
+measurements of a little over a degree of longitude and
+obtained a close approximation to its length. Newton,
+learning of the measurement of Picard, recalculated the
+mass of the earth and motions of the moon and found his
+law of gravitation as the satisfactory explanation of all the
+conditions. Then, in 1682, after having patiently waited
+over twenty years for this confirmation, he announced
+the laws of gravitation, one of the greatest discoveries
+in the history of mankind. We find in this an excellent
+instance of the interdependence of the sciences. The
+careful measurement of the size of the earth has contributed
+immensely to the sciences of astronomy and physics.
+
+\Paragraph{{\mdseries III.} The Earth an Oblate Spheroid.}\nblabel{page:273} From the many
+\index{Oblateness of earth|(}%
+calculations which Newton's fertile brain could now make,
+he soon was enabled to announce that the earth must be,
+not a true sphere, but an oblate spheroid. Christian
+Huygens, a celebrated contemporary of Newton, also contended
+\index{Huygens@Huygens (h\={\i}$'$gens), Christian}%
+for the oblate form of the earth, although not on
+the same grounds as those advanced by Newton.
+
+In about 1672 the trip of the astronomer Richer to
+\index{Richer@Richer (re\;sh\={a}y$'$), John}%
+French Guiana, South America, and his discovery that
+\index{Guiana, French}%
+\index{South America}%
+pendulums swing more slowly there (see the discussion
+under the topic The Earth an Oblate Spheroid, p.~\pageref{page:28}),
+and the resulting conclusion that the earth is not a true
+sphere, but is flattened toward the poles, gave a new
+impetus to the study of the size of the earth and other
+mathematical properties of it.
+
+Over half a century had to pass, however, before the
+true significance of Richer's discovery was apparent to
+all or generally accepted. An instance of a commonly
+%% -----File: 273.png---Folio 274-------
+accepted reason assigned for the shorter equatorial pendulum
+is the following explanation which was given to
+James~II of England when he made a visit to the Paris
+\index{Paris, France}%
+\index{James II., King of England}%
+\index{England}%
+Observatory in 1697. ``While Jupiter at times appears
+\index{Jupiter}%
+to be not perfectly spherical, we may bear in mind the
+fact that the theory of the earth being flattened is sufficiently
+disproven by the circular shadow which the earth
+throws on the moon. The apparent necessary shortening
+of the pendulum toward the south is really only a correction
+for the expansion of the pendulum in consequence of
+the higher temperature.'' It is interesting to note that if
+this explanation were the true one, the average temperature
+at Cayenne would have to be $43°$~above the boiling
+point.
+
+\index{Proofs, form of earth}%
+Early in the eighteenth century Giovanni Cassini, the
+astronomer in charge of the Paris Observatory, assisted by
+his son, continued the measurement begun by Picard and
+\index{Picard@Picard (p\={e}\;kär$'$), Jean}%
+came to the conclusion that the earth is a prolate spheroid.
+A warm discussion arose and the Paris Academy of
+Sciences decided to settle the matter by careful measurements
+in polar and equatorial regions.
+
+In 1735 two expeditions were sent out, one into Lapland
+\index{Lapland}%
+and the other into Peru. Their measurements, while
+\index{Peru}%
+not without appreciable errors, showed the decided difference
+of over half a mile for one degree and demonstrated
+conclusively the oblateness of a meridian and, as Voltaire
+\index{Voltaire}%
+wittily remarked at the time, ``flattened the poles and
+the Cassinis.''
+\index{Cassini@Cassini (käs\;s\={e}$'$n\={e}), G. D., and J.}%
+
+The calculation of the oblateness of the earth has occupied
+the attention of many since the time of Newton. His
+calculation was~$\frac{1}{230}$; that is, the polar diameter was $\frac{1}{230}$
+shorter than the equatorial. Huygens estimated the flattening
+\index{Huygens@Huygens (h\={\i}$'$gens), Christian}%
+to be about~$\frac{1}{500}$. The most commonly accepted
+%% -----File: 274.png---Folio 275-------
+spheroid representing the earth is the one calculated in
+1866 by A.~R. Clarke, for a long time at the head of the
+\index{Clarke, A. R.}%
+English Ordnance Survey (see p.~\pageref{page:30}). Purely astronomical
+calculations, based upon the effect of the bulging of the
+equator upon the motion of the moon, seem to indicate
+slightly less oblateness than that of General Clarke. Professor
+William Harkness, formerly astronomical director
+\index{Harkness, William}%
+of the United States Naval Observatory, calculated it to
+be very nearly~$\frac{1}{300}$.\nblabel{page:275}
+
+\Paragraph{{\mdseries IV.} The Earth a Geoid.} During recent years many
+\index{Geoid@Geoid (j\={e}$'$oid)}%
+\index{Geodesy \indexglossref{Geodesy}}%
+careful measurements have been made on various portions
+of the globe and extensive pendulum tests given to ascertain
+the force of gravity. These measurements demonstrate
+that the earth is not a true sphere; is not an oblate
+spheroid; indeed, its figure does not correspond to that of
+any regular or symmetrical geometric form. As explained
+in Chapter~\hyperref[chap:II]{II}, the equator, parallels, and meridians are
+not true circles, but are more or less elliptical and wavy
+in outline. The extensive triangulation surveys and the
+\index{Triangulation}%
+application of astrophysics to astronomy and geodesy
+make possible, and at the same time make imperative, a
+careful determination of the exact form of the geoid.
+\index{Oblateness of earth|)}%
+
+\Section{The Motions of the Earth}
+
+The Pythagoreans maintained as a principle in their
+\index{Pythagoras@Pythagoras (p\u{\i}\;th\u{a}g$'$\={o}\;ras)}%
+philosophy that the earth rotates on its axis and revolves
+about the sun. Basing their theory upon \textit{a~priori} reasoning,
+they had little better grounds for their belief than
+those who thought otherwise. Aristarchus (about 310--250~\BC),
+\index{Aristarchus@Aristarchus (\u{a}r\;\u{\i}s\;tär$'$k\u{u}s)}%
+a Greek astronomer, seems to have been the
+first to advance the heliocentric theory in a systematic
+manner and one based upon careful observations and calculations.
+From this time, however, until the time of
+%% -----File: 275.png---Folio 276-------
+Copernicus, the geocentric theory was almost universally
+\index{Copernicus@Copernicus (k\={o}\;per$'$n\u{\i}\;k\u{u}s)|(}%
+adopted.
+
+\sloppy
+The geocentric theory is often called the Ptolemaic system
+\index{Ptolemaic system}%
+from Claudius Ptolemy (not to be confused with
+ancient Egyptian kings of the same name), an Alexandrian
+astronomer and mathematician, who seems to have done
+most of his work about the middle of the second century,~\AD.
+He seems to have adopted, in general, the valuable
+astronomical calculations of \nblabel{page:276}Hipparchus (about 180--110~\BC).
+The system is called after him because he compiled
+so much of the observations of other astronomers
+who had preceded him and invented a most ingenious
+system of ``cycles,'' ``epicycles,'' ``deferents,'' ``centrics,''
+and ``eccentrics'' (now happily swept away by the Copernican
+system) by which practically all of the known facts
+of the celestial bodies and their movements could be
+accounted for and yet assume the earth to be at the center
+of the universe.
+
+\fussy
+Among Ptolemy's contributions to mathematical geography
+were his employment of the latitude and longitude
+of places to represent their positions on the globe (a scheme
+probably invented by Hipparchus), and he was the first
+to use the terms ``meridians of longitude'' and ``parallels
+of latitude.'' It is from the Latin translation of his subdivisions
+of degrees that we get the terms ``minutes'' and
+``seconds'' (for centuries the division had been followed,
+originating with the Chaldeans. See p.\pageref{page:141}). The sixty
+subdivisions he called first small parts; in Latin, ``\textit{minutæ
+primæ},'' whence our term ``minute.'' The sixty subdivisions
+of the minute he called second small parts; in
+Latin, ``\textit{minutæ secundæ},'' whence our term ``second.''
+
+The Copernican theory of the solar system, which has
+\index{Copernican system@Copernican system \indexglossref{Copernican system}|(}%
+universally displaced all others, gets its name from the
+%% -----File: 276.png---Folio 277-------
+Polish astronomer Nicolas Copernicus (1473--1543). He
+revived the theory of Aristarchus, and contended that the
+\index{Aristarchus@Aristarchus (\u{a}r\;\u{\i}s\;tär$'$k\u{u}s)}%
+earth is not at the center of the solar system, but that the
+sun is, and planets all revolve around the sun. He had
+\index{Proofs, form of earth!revolution of earth}%
+no more reasons for this conception than for the geocentric
+theory, excepting that it violated no laws or principles,
+was in harmony with the known facts, and was simpler.
+
+Contemporaries and successors of Copernicus were far
+from unanimous in accepting the heliocentric theory. One
+\index{Geocentric, latitude!theory,@theory, \indexglossref{Geocentric, Theory}}%
+\index{Heliocentric theory@Heliocentric theory \indexglossref{Heliocentric, Theory}}%
+of the dissenters of the succeeding generation is worthy of
+note for his logical though erroneous argument against it.
+\index{Brahe (brä), Tycho}%
+Tycho Brahe\footnote
+  {Tycho Brahe (1546--1601) a famous Swedish astronomer, was born
+  at Knudstrup, near Lund, in the south of Sweden, but spent most of
+\index{Sweden}%
+  his life in Denmark.}
+contended that the Copernican theory was
+impossible, because if the earth revolved around the sun,
+and at one season was at one side of its orbit, and at
+another was on the opposite side, the stars would apparently
+change their positions in relation to the earth (technically,
+there would be an annual parallax), and he could
+\index{Parallax}%
+detect no such change. His reasoning was perfectly sound,
+but was based upon an erroneous conception of the distances
+of the stars. The powerful instruments of the past
+fifty years have made these parallactic motions of many of
+the stars a determinable, though a very minute, angle, and
+constitute an excellent proof of the heliocentric theory
+(see p.~\pageref{page:109}).
+
+Nine years after the death of Brahe, Galileo Galilei
+\index{Galilei, Galileo@Galilei, Galileo (g\u{a}l\;\u{\i}\;l\={e}$'$\={o}\;g\u{a}l\;\u{\i}\;l\={a}$'$\={e})}%
+(1564--1642) by the use of his recently invented telescope
+discovered that there were moons revolving about Jupiter,
+\index{Jupiter}%
+indicating by analogy the truth of the Copernican theory.
+Following upon the heels of this came his discovery that
+Venus in its swing back and forth near the sun plainly
+\index{Venus}%
+%% -----File: 277.png---Folio 278-------
+shows phases just as our moon does, and appears larger
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+when in the crescent than when in the full. The only
+logical conclusion was that it revolves around the sun,
+\index{Proofs, form of earth!revolution of earth}%
+\index{Revolution@Revolution \indexglossref{Revolution}}%
+again confirming by analogy the Copernican theory. Galilei
+\index{Heliocentric theory@Heliocentric theory \indexglossref{Heliocentric, Theory}}%
+was a thorough-going Copernican in private belief, but
+was not permitted to teach the doctrine, as it was considered
+unscriptural.
+
+\index{Galilei, Galileo@Galilei, Galileo (g\u{a}l\;\u{\i}\;l\={e}$'$\={o}\;g\u{a}l\;\u{\i}\;l\={a}$'$\={e})}%
+As an illustration of the humiliating subterfuges to
+which he was compelled to resort in order to present an
+argument based upon the heretical theory, the following
+is a quotation from an argument he entered into concerning
+three comets which appeared in 1618. He based
+\index{Comets}%
+his argument as to their motions upon the Copernican
+system, professing to repudiate that theory at the same
+time.
+
+``Since the motion attributed to the earth, which I as
+a pious and Christian person consider most false, and not
+to exist, accommodates itself so well to explain so many and
+such different phenomena, I shall not feel sure that, false
+as it is, it may not just as deludingly correspond with the
+phenomena of comets.''
+
+One of the best supporters of this theory in the next
+generation was Kepler (1571--1630), the German astronomer,
+\index{Kepler, Johann}%
+and friend and successor of Brahe. His laws of
+\index{Brahe (brä), Tycho}%
+planetary motion (see p.~\pageref{page:284}) were, of course, based upon
+the Copernican theory, and led to Newton's discovery of
+the laws of gravitation.
+
+\nblabel{page:278}James Bradley (1693--1762) discovered in 1727 the
+\index{Bradley, James}%
+aberration of light (see p.~\pageref{page:104}), and the supporters of the
+\index{Aberration of light@Aberration of light \indexglossref{Aberration}}%
+\index{Geocentric, latitude!theory,@theory, \indexglossref{Geocentric, Theory}}%
+Ptolemaic system were routed, logically, though more
+than a century had to pass before the heliocentric theory
+became universally accepted.
+\index{Copernican system@Copernican system \indexglossref{Copernican system}|)}%
+\index{Copernicus@Copernicus (k\={o}\;per$'$n\u{\i}\;k\u{u}s)|)}%
+\index{Historical sketch|)}%
+%% -----File: 278.png---Folio 279-------
+
+\addtocontents{toc}{\vspace{1.5ex}\protect\begin{center}\protect\thoughtbreak\protect\end{center}\vspace{1.5ex}}
+
+\SpecialChapter{Appendix}
+\addcontentsline{toc}{section}{\textsc{Appendix}}
+\addtocontents{toc}{\vspace{2ex}}
+
+\AppendixSection{GRAVITY}\nblabel{sec:gravity}
+\index{Gravity@Gravity\phantomsection\label{idx:g}|(}%
+
+\First{Gravity} is frequently defined as the earth's attractive
+influence for an object. Since the attractive influence
+of the mass of the earth for an object on or near its surface
+is lessened by centrifugal force (see p.~\pageref{page:14b}) and in
+other ways (see p.~\pageref{page:183}), it is more accurate to say that
+the force of gravity is the resultant of
+
+\textit{a.} The attractive force mutually existing between the
+earth and the object, and
+
+\textit{b.} The lessening influence of centrifugal force due to
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}|(}%
+the earth's rotation.
+
+Let us consider these two factors separately, bearing
+in mind the laws of gravitation (see p.~\pageref{page:16}).
+
+\textit{a.} Every particle of matter attracts every other
+particle.
+
+(1) Hence the point of gravity for any given object
+on the surface of the earth is determined by the mass of
+the object itself as well as the mass of the earth. The
+object pulls the earth as truly and as much as the earth
+attracts the object. The common center of gravity of the
+earth and this object lies somewhere between the center
+of the earth's mass and the center of the mass of the
+object. Each object on the earth's surface, then, must
+have its own independent common center of gravity between
+it and the center of the earth's mass. The position
+of this common center will vary---
+
+(\textit{a}) As the object varies in amount of matter (first
+law), and
+%% -----File: 279.png---Folio 280-------
+
+(\textit{b}) As the distance of the object from the center of
+the earth's mass varies (inversely as the square of the
+distance).
+
+(2) Because of this principle, the position of the sun
+or moon slightly modifies the exact position of the center
+of gravity just explained. It was shown in the discussion
+of tides that, although the tidal lessening of
+\index{Tides}%
+the weight of an object is as yet an immeasurable
+quantity, it is a calculable one and produces tides (see
+p.~\pageref{page:183}).
+
+\textit{b.}\nblabel{page:280} The rotation of the earth gives a centrifugal force
+to every object on its surface, save at the poles.
+
+(1) Centrifugal force thus exerts a slight lifting influence
+on objects, increasing toward the equator. This
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+lightening influence is sufficient to decrease the weight
+of an object at the equator by $\frac{1}{289}$~of the whole. That
+is to say, an object which weighs $288$~pounds at the
+equator would weigh a pound more if the earth did not
+rotate. Do not infer from this that the centrifugal force
+at the pole being zero, a body weighing $288$~pounds at the
+equator would weigh $289$~pounds at the pole, not being
+\index{Pole, celestial!terrestrial}%
+lightened by centrifugal force. This would be true \emph{if the
+earth were a sphere}. The bulging at the equator decreases
+a body's weight there by~$\frac{1}{599}$ as compared with the weight
+at the poles. Thus a body at the equator has its weight
+lessened by~$\frac{1}{289}$ because of rotation and by~$\frac{1}{599}$ because
+of greater distance from the center, or a total of~$\frac{1}{195}$ of
+its weight as compared with its weight at the pole. A
+body weighing $195$~pounds at the pole, therefore, weighs
+but $194$~pounds at the equator. Manifestly the rate of
+the earth's rotation determines the amount of this centrifugal
+force. If the earth rotated seventeen times as
+fast, this force at the equator would exactly equal the
+%% -----File: 280.png---Folio 281-------
+earth's attraction,\footnote
+  {Other things equal, centrifugal force varies with the square of
+  the velocity (see p.~\pageref{page:14}), and since centrifugal force at the equator equals
+  $289$~times gravity, if the velocity of rotation were increased $17$~times,
+  centrifugal force would equal gravity ($17^2 = 289$).}
+objects there would have no weight;
+that is, gravity would be zero. In such a case the plumb
+line at all latitudes would point directly toward the nearest
+celestial pole. A clock at the 45th~parallel with a pendulum
+beating seconds would gain one beat every $19 \frac{1}{2}$ minutes
+if the earth were at rest, but would lose three beats in the
+same time if the earth rotated twice as fast.
+
+\nblabel{page:281}(2) Centrifugal force due to the rotation of the earth
+not only affects the amount of gravity, but modifies the
+direction in which it is exerted. Centrifugal force acts
+in a direction at right angles to the axis, not directly
+opposite the earth's attraction excepting at the equator.
+Thus plumb lines, excepting at the equator and poles,
+are slightly tilted toward the poles.
+
+\includegraphicsright{i280}{Fig.~112}
+
+If the earth were at rest a plumb line at latitude~$45°$
+\index{Deviation, of pendulum!of plumb line|(}%
+\index{Plumb line}%
+would be in the direction toward the center of the mass
+of the earth at~$C$ (Fig.~\figureref{i280}{112}).
+The plumb line
+would then be~$PC$. But
+centrifugal force is exerted
+toward~$CF$, and the
+resultant of the attraction
+toward~$C$ and centrifugal
+force toward~$CF$
+makes the line deviate
+to a point between those
+directions, as~$CG$, the
+true center of gravity, and
+the plumb line becomes~$P'CG$. The amount of the centrifugal
+%% -----File: 281.png---Folio 282-------
+force is so small as compared with the earth's
+attraction that this deviation is not great. It is greatest
+at the 45th~parallel where it amounts to $5'~57''$, or nearly
+one tenth of a degree. There is an almost equal deviation
+due to the oblateness of the earth. At latitude~$45°$
+the total deviation of the plumb line from a line drawn
+\index{Plumb line}%
+to the center of the earth is \DPtypo{$11'~30.65.''$}{$11'~30.65''$.}
+\index{Gravity@Gravity\phantomsection\label{idx:g}|)}%
+
+\AppendixSection{LATITUDE}\nblabel{page:282}
+
+In Chapter~\hyperref[chap:II]{II} the latitude of a place was simply defined
+as the arc of a meridian intercepted between that place
+and the equator. This is true geographical latitude, but
+the discussion of \emph{gravity} places us in a position to understand
+astronomical and geocentric latitude, and how geographic
+latitude is determined from astronomical latitude.
+
+Owing to the elliptical form of a meridian ``circle,'' the
+vertex of the angle constituting the latitude of a place is
+not at the center of the globe. A portion of a meridian
+circle near the equator is an arc of a smaller circle than
+a portion of the same \DPtypo{meridan}{meridian} near the pole (see p.~\pageref{fig:i042}
+and Fig.~\figureref{i042}{18}).
+
+\Paragraph{Geocentric Latitude.} It is sometimes of value to speak
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!geocentric}%
+of the angle formed at the center of the earth by two
+lines, one drawn to the place whose latitude is sought,
+and the other to the equator on the same meridian. This
+is called the geocentric latitude of the place.
+
+\Paragraph{Astronomical Latitude.} The astronomer ascertains latitude
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!astronomical}%
+from celestial measurements by reference to a level
+line or a plumb line. Astronomical latitude, then, is the
+angle formed between the plumb line and the plane of
+the equator.
+
+In the discussion of gravity, the last effect of centrifugal
+%% -----File: 282.png---Folio 283-------
+force noted was on the direction of the plumb line.
+It was shown that this line, excepting at the equator and
+poles, is deviated slightly toward the pole. The effect of
+this is to increase correspondingly the astronomical latitude
+of a place. Thus at latitude~$45°$, astronomical latitude
+is increased by $5'~57''$, the amount of this deviation.
+If there were no rotation of the earth, there would be no
+deviation of the plumb line, and what we call latitude~$60°$
+would become $59°~54'~51''$. Were the earth to rotate twice
+as fast, this latitude, as determined by the same astronomical
+instruments, would become $60°~15'~27''$.
+
+If adjacent to a mountain, the plumb line deviates
+toward the mountain because of its attractive influence on
+the plumb bob; and other deviations are also observed,
+such as with the ebb and flow of a near by tidal wave.
+These deviations are called ``station errors,'' and allowance
+must be made for them in making all calculations based
+upon the plumb line.
+
+\Paragraph{Geographical latitude} is simply the astronomical latitude,
+\emph{corrected} for the deviation of the plumb line. Were it not
+for these deviations the latitude of a place would be determined
+within a few feet of perfect accuracy. As it is,
+errors of a few hundred feet sometimes may occur (see
+p.~\pageref{page:289}).
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}|)}%
+\index{Deviation, of pendulum!of plumb line|)}%
+
+\sloppy
+\Paragraph{Celestial Latitude.} In the discussion of the celestial
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!celestial}%
+\index{Celestial latitude}%
+\index{Celestial latitude!meridians}%
+sphere many circles of the celestial sphere were described
+in the same terms as circles of the earth. The celestial
+equator, Tropic of Cancer, etc., are imaginary circles which
+\index{Equator@Equator \indexglossref{Equator}!celestial}%
+\index{Celestial equator}%
+correspond to the terrestrial equator, Tropic of Cancer, etc.
+Now as terrestrial latitude is distance in degrees of a meridian
+\index{Meridian}%
+\index{Meridian!celestial}%
+north or south of the equator of the earth, one would
+infer that celestial latitude is the corresponding distance
+along a celestial meridian from the celestial equator, but
+%% -----File: 283.png---Folio 284-------
+this \emph{is not the case}. Astronomers reckon celestial latitude
+from the \emph{ecliptic} instead of from the celestial equator. As
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}}%
+\index{Celestial equator}%
+\index{Equator@Equator \indexglossref{Equator}!celestial}%
+previously explained, the distance in degrees from the
+celestial equator is called \emph{declination}.
+
+\fussy
+\Paragraph{Celestial Longitude} is measured in degrees along the
+\index{Longitude@Longitude \indexglossref{Longitude}!celestial}%
+\index{Celestial latitude!longitude}%
+ecliptic from the vernal equinox as the initial point, measured
+always eastward the $360°$~of the ecliptic.
+
+In addition to the celestial pole $90°$~from the celestial
+equator, there is a pole of the ecliptic, $90°$~from the ecliptic.
+\index{Pole, celestial}%
+A celestial body is thus located by reference to two sets of
+circles and two poles.
+
+(\textit{a}) Its declination from the celestial equator and position
+\index{Declination@Declination \indexglossref{Declination}}%
+in relation to hour circles, as celestial meridians are
+\index{Celestial latitude!meridians}%
+\index{Meridian!celestial}%
+commonly called (see \glossref[Hour-circles]{Glossary}).
+
+(\textit{b}) Its celestial latitude from the ecliptic and celestial
+\index{Latitude@Latitude \indexglossref{Latitude}\phantomsection\label{idx:lt}!celestial}%
+\index{Celestial latitude}%
+longitude from ``ecliptic meridians.''
+
+\AppendixSection{KEPLER'S LAWS}\nblabel{page:284}
+\index{Kepler, Johann!laws of|(}%
+
+These three laws find their explanation in the laws of
+gravitation, although Kepler discovered them before Newton
+made the discovery which has immortalized his name.
+
+First Law. The orbit of each planet is an ellipse, having
+the sun as a focus.
+
+Second Law. The planet moves about the sun at such
+rates that the straight line connecting the center of the
+sun with the center of the planet (this line is called the
+planet's radius vector) sweeps over equal areas in equal
+\index{Radius vector}%
+times (see Fig.~\figureref{i284}{113}).
+
+\index{Hemispheres unequally heated}%
+\index{Unequal heating}%
+The distance of the earth's journey for each of the
+\index{Orbit, of earth}%
+\index{Revolution@Revolution \indexglossref{Revolution}|(}%
+twelve months is such that the ellipse is divided into
+twelve equal areas. In the discussion of seasons we
+observed (p.~\pageref{page:169}) that when in perihelion, in January, the
+\index{Perihelion}%
+%% -----File: 284.png---Folio 285-------
+earth receives more heat each day than it does when in
+aphelion, in July. The northern hemisphere, being turned
+\index{Aphelion@Aphelion \indexglossref{Aphelion}}%
+away from the sun in January, thus has warmer winters
+than it would otherwise have, and being toward the sun
+in July, has cooler summers. This is true only for corresponding
+days, not for the seasons as a whole. According
+to Kepler's second law the earth must receive exactly the
+same \emph{total amount} of heat from the vernal equinox (March~21)
+to the autumnal equinox (Sept.~23), when farther from
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}}%
+the sun, as from the autumnal to the vernal equinox, when
+nearer the sun. During the former period, the northern
+summer, the earth receives less heat day by day, but
+there are more days.
+
+\includegraphicsmid{i284}{Fig.~113}
+
+\nblabel{page:285}Third Law. The squares of the lengths of the times (sidereal
+years) of planets are proportional to the cubes of their
+\index{Planets}%
+distances from the sun. Thus,
+\begin{multline*} %[**TN: layout altered slightly to fit page width]
+  (\text{Earth's year})^2 : (\text{Mars' year})^2 \dblcolon \\
+\index{Mars}%
+  (\text{Earth's distance})^3 : (\text{Mars' distance})^3.
+\end{multline*}
+Knowing the distance of the earth to
+%% -----File: 285.png---Folio 286-------
+the sun and the distance of a planet to the sun, we have
+three of the quantities for our proportion, calling the
+earth's year~$1$, and can find the year of the planet; or,
+knowing the time of the planet, we can find its distance.
+\index{Kepler, Johann!laws of|)}%
+
+\AppendixSection{MOTIONS OF THE EARTH'S AXIS}\nblabel{page:286a}
+\index{Motions of the earth's axis|(}%
+
+In the \hyperref[chap:VIII]{chapter} on seasons it was stated that excepting
+for exceedingly slow or minute changes the earth's axis
+at one time is parallel to itself at other times. There are
+three such motions of the axis.
+
+\Paragraph{Precession of the Equinoxes.}\nblabel{page:286} Since the earth is slightly
+\index{Precession of equinoxes|(}%
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}!precession of|(}%
+oblate and the bulging equator is tipped at an angle
+of~$23\frac{1}{2}°$ to the ecliptic, the sun's attraction on this rim
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}}%
+tends to draw the axis over at right angles to the equator.
+The rotation of the earth, however, tends to keep the
+axis parallel to itself, and the effect of the additional acceleration
+of the equator is to cause the axis to rotate slowly,
+keeping the same angle to the ecliptic, however.
+
+At the time of Hipparchus (see p.~\pageref{page:276}), who discovered
+\index{Hipparchus@Hipparchus (h\u{\i}p\;ar$'$kus)}%
+this rotation of the axis, the present North star, Alpha
+Ursa Minoris, was about $12°$~from the true pole of the
+\index{Pole, celestial}%
+\index{Pole, celestial!of the ecliptic}%
+\index{Pole, celestial!terrestrial}%
+celestial sphere, toward which the axis points. The course
+which the pole is taking is bringing it somewhat nearer
+the polestar; it is now about $1°~15'$~away, but a hundred
+\index{North, line!star@star\phantomsection\label{idx:ns}}%
+\index{Polestar@Polestar\phantomsection\label{idx:p}, (\emph{see} \hyperref[idx:ns]{North star})}%
+years hence will be only half a degree from it. The period
+of this rotation is very long, about $25,000$ years, or $50.2''$
+each year. Ninety degrees from the ecliptic is the pole
+of the ecliptic about which the pole of the celestial equator
+rotates, and from which it is distant~$23\frac{1}{2}°$.
+
+As the axis rotates about the pole of the ecliptic, the
+point where the plane of the equator intersects the plane
+%% -----File: 286.png---Folio 287-------
+of the ecliptic, that is, the equinox, gradually shifts around
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}}%
+westward. Since the vernal equinox is at a given point
+in the earth's orbit one year, and the next year is reached
+\index{Year}%
+a little ahead of where it was the year before, the term
+\emph{precession of the equinoxes} is appropriate. The sidereal
+\index{Sidereal, clock!year}%
+year (see p.~\pageref{page:132}) is the time required for the earth to
+make a complete revolution in its orbit. A solar or tropical
+year is the interval from one vernal equinox to the
+next vernal equinox, and since the equinoxes ``precede,''
+a tropical year ends about twenty minutes before the
+earth reaches the same point in its orbit a second time.
+
+\sloppy
+As is shown in the discussion of the earth's revolution
+(p.~\pageref{page:169}), the earth is in perihelion December~31, making
+the northern summer longer and cooler, day by day, than
+it would otherwise be, and the winter shorter and warmer.
+The traveling of the vernal equinox around the orbit,
+however, is gradually shifting the date of perihelion, so
+that in ages yet to come perihelion will be reached in July,
+and thus terrestrial climate is gradually changing. This
+perihelion point (and with it, aphelion) has a slight westward
+\index{Aphelion@Aphelion \indexglossref{Aphelion}}%
+motion of its own of $11.25''$ each year, making, with
+the addition of the precession of the equinoxes of~$50.2''$, a
+total shifting of the perihelion point (see ``\glossref{Apsides}'' in
+\index{Apsides@Apsides \indexglossref{Apsides}}%
+the Glossary) of~$1'~1.45''$. At this slow rate, $10,545$ years
+must pass before perihelion will be reached July~1. The
+amount of the ellipticity of the earth's orbit is gradually
+decreasing, so that by the time this shifting has taken
+place the orbit will be so nearly circular that there may be
+but slight climatic effects of this shift of perihelion. It
+may be of interest to note that some have reasoned that
+ages ago the earth's orbit was so elliptical that the
+northern winter, occurring in aphelion, was so long and
+cold that great glaciers were formed in northern North
+%% -----File: 287.png---Folio 288-------
+America and Europe which the short, hot summers could
+\index{North America}%
+\index{Europe}%
+not melt. The fact of the glacial age cannot be disputed,
+but this explanation is not generally accepted as satisfactory.
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}!precession of|)}%
+\index{Precession of equinoxes|)}%
+
+\fussy
+\Paragraph{Nutation of the Poles.}\nblabel{page:288} Several sets of gravitative influences
+\index{Nutation of poles}%
+\index{Axis, changes in position of}%
+cause a slight periodic motion of the earth's axis
+toward and from the pole of the ecliptic. Instead of
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}!obliquity of}%
+``preceding'' around the circle $47°$ in diameter, the axis
+makes a slight wavelike motion, a ``nodding,'' as it is
+called. The principal nutatory motion of the axis is
+due to the fact that the moon's orbit about the earth
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+\index{Orbit, of earth!of moon}%
+(inclined $5°~8'$ to the ecliptic) glides about the ecliptic in
+$18$~years, $220$~days, just as the earth's equator glides about
+the ecliptic once in $25,800$ years. Thus through periods
+of nearly nineteen years each the obliquity of the ecliptic
+\index{Obliquity of the ecliptic@Obliquity of the ecliptic\phantomsection\label{idx:ooe}}%
+(see pp.~\pageref{page:118},~\pageref{page:147}) gradually increases and decreases again.
+The rate of this nutation varies somewhat and is always
+very slight; at present it is $0.47''$~in a year.
+
+\Paragraph{Wandering of the Poles.} In the discussion of gravity
+\index{Wandering of the poles}%
+\index{Pole, celestial!nutation of}%
+\index{Pole, celestial!of the ecliptic}%
+\index{Pole, celestial!terrestrial}%
+(p.~\pageref{sec:gravity}), it was shown that any change in the position of
+particles of matter effects a change in the point of gravity
+common to them. Slight changes in the crust of the earth
+are constantly taking place, not simply the gradational
+changes of wearing down mountains and building up of
+depositional features, but great diastrophic changes in
+mountain structure and continental changes of level.
+Besides these physiographic changes, meteorological conditions
+must be factors in displacement of masses, the
+accumulation of snow, the fluctuation in the level of great
+rivers,~etc. For these reasons minute changes in the
+position of the axis of rotation must take place within the
+earth. Since 1890 such changes in the position of the axis
+within the globe have been observed and recorded. The
+%% -----File: 288.png---Folio 289-------
+``wandering of the poles,'' as this slight shifting of the
+\index{Axis, changes in position of}%
+axis is called, has been demonstrated by the variation in
+the latitudes of places. \nblabel{page:289}A slight increase in the latitude
+of an observatory is noticed, and at the same time a corresponding
+decrease is observed in the latitude of an
+observatory on the opposite side of the globe. ``So
+definite are the processes of practical astronomy that the
+\index{North, line!pole}%
+position of the north pole can be located with no greater
+\index{Todd, David}%
+uncertainty than the area of a large Eskimo hut.''\footnote
+  {Todd's \textit{New Astronomy}, p.~95.}
+
+In 1899 the International Geodetic Association took
+\index{Geodetic Association, International}%
+\index{International Geodetic Association}%
+steps looking to systematic and careful observations and
+records of this wandering of the poles. Four stations
+not far from the thirty-ninth parallel but widely separated
+in longitude were selected, two in the United States, one
+\index{United States}%
+in Sicily, and the other in Japan.
+\index{Japan}%
+\index{Sicily}%
+
+All of the variations since 1889 have been within an
+area less than sixty feet in diameter.
+
+\Paragraph{Seven Motions of the Earth.} Seven of the well-defined
+\index{Seven motions of earth}%
+\index{Motions of the earth}%
+motions of the earth have been described in this book:
+
+1. Diurnal Rotation.
+
+2. Annual Revolution in relation to the sun.
+\index{Revolution@Revolution \indexglossref{Revolution}|)}%
+
+3. Monthly Revolution in relation to the moon (see
+p.~\pageref{page:184}).
+
+4. Precessional Rotation of Axis about the pole of the
+ecliptic.
+
+5. Nutation of the poles, an elliptical or wavelike motion
+in the precessional orbit of the axis.
+
+6. Shifting on one axis of rotation, then on another,
+leading to a ``wandering of the poles.''
+
+7. Onward motion with the whole solar system (see
+``Sun's Onward Motion,'' p.~\pageref{page:247}).
+\index{Motions of the earth's axis|)}%
+%% -----File: 289.png---Folio 290-------
+
+\AppendixSection{MATHEMATICAL TREATMENT OF TIDES}\nblabel{page:290}
+\index{Tides|(}%
+
+The explanation of the cause of tides in the \hyperref[chap:IX]{chapter}
+on that subject may be relied upon in every particular,
+although mathematical details are omitted. The mathematical
+treatment is difficult to make plain to those who
+have not studied higher mathematics and physics. Simplified
+as much as possible, it is as follows:
+
+Let it be borne in mind that to find the cause of tides
+we must find \emph{unbalanced forces which change their positions}.
+Surface gravity over the globe varies slightly in different
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+places, being less at the equator and greater toward the
+poles. As shown elsewhere, the force of gravity at the
+\index{Pole, celestial!terrestrial}%
+equator is less for two reasons:
+
+\textit{a.} Because of greater centrifugal force.
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}}%
+
+\textit{b.} Because of the oblateness of the earth.
+
+(\textit{a})  Centrifugal force being greater at the equator than
+elsewhere, there is an unbalanced force which must cause
+the waters to pile up to some extent in the equatorial
+region. If centrifugal force were sometimes greater at the
+equator and sometimes at the poles, there would be a corresponding
+shifting of the accumulated waters and we
+should have a tide---and it would be an immense one.
+But we know that this unbalanced force does not change
+its position, and hence it cannot produce a tide.
+
+(\textit{b}) Exactly the same course of reasoning applies to the
+unbalanced force of gravity at the equator due to its
+greater distance from the center of gravity. The position
+of this unbalanced force does not shift, and no tide results.
+
+Since the earth turns on its axis under the sun and
+moon, any unbalanced forces they may produce will necessarily
+shift as different portions of the earth are successively
+turned toward or from them. Our problem, then,
+%% -----File: 290.png---Folio 291-------
+is to find the cause and direction of the unbalanced forces
+produced by the moon or sun.
+
+\includegraphicsmid{i290}{Fig.~114}
+
+In Figure~\figureref{i290}{114}, let $CA$~be the acceleration toward the
+\index{Acceleration@Acceleration \indexglossref{Acceleration}|(}%
+moon at~$C$, due to the moon's attraction. Let $BD$~be
+the acceleration at~$B$. Now $B$~is nearer the moon than~$C$,
+so $BD$~will be greater than~$CA$, since the attraction
+varies inversely as the square of the distance.
+
+From $B$ construct~$BE$ equal to~$CA$. Comparing forces
+$BE$ and~$BD$, the latter is greater. Completing the parallelogram,
+we have~$BFDE$. Now it is a simple demonstration
+in physics that if two forces act upon~$B$, one to~$F$ and
+the other to~$E$, the resultant of the two forces will be the
+diagonal~$BD$. Since $BE$ and~$BF$ combined result in~$BD$,
+it follows that $BF$~represents the unbalanced force at~$B$.
+
+At $B$, then, there is an unbalanced force as compared
+with~$C$ as represented by~$BF$. At~$B'$ the unbalanced
+force is represented by~$B'F'$. Note the \emph{pulling direction}
+in which these unbalanced forces are exerted.
+
+\begin{SmallText}
+\textsc{Note.}---For purposes of illustration the distance of the moon
+represented in the figures is greatly diminished. The distance~$CA$ is
+taken arbitrarily, likewise the distance~$BD$. If~$CA$ were longer,
+however, $BD$~would be still longer; and while giving $CA$ a different
+length, would modify the form of the diagram, the mathematical relations
+would remain unchanged. Because of the short distance given~$CM$
+in the figures, the difference between the $BF$ in Figure~\figureref{i290}{114} and $BF$
+in Figure~\figureref{i291-1}{115} is greatly exaggerated. The difference between the
+unbalanced or tide-producing force on the side toward the moon and
+that on the opposite side is approximately $.0467\,BF$ (Fig.~\figureref{i290}{114}).
+\end{SmallText}
+%% -----File: 291.png---Folio 292-------
+
+\includegraphicsmid{i291-1}{Fig.~115}
+
+In Figure~\figureref{i291-1}{115}, $B$~is farther from the moon than~$C$, hence
+$BE$ (equal to~$CA$) is greater than~$BD$, and the unbalanced
+force at~$B$ is~$BF$, directed away from the moon. A study
+of Figures \figureref{i290}{114}~and~\figureref{i291-1}{115} will show that the unbalanced force
+on the side towards the moon ($BF$~in Fig.~\figureref{i290}{114}) is slightly
+greater than the unbalanced force on the side opposite the
+moon ($BF$~in Fig.~\figureref{i291-1}{115}). The difference, however, is exceedingly
+slight, and the tide on the opposite side is practically
+equal to the tide on the side toward the attracting
+body.
+
+\includegraphicsmid{i291-2}{Fig.~116}
+
+Combining the arrows showing the directions of the unbalanced
+forces in the two figures, we have the arrows shown
+in Figure~\figureref{i291-2}{116}. The distribution and direction of the unbalanced
+forces may be thus summarized: ``The disturbing
+\index{Barlow and Bryan's Mathematical Astronomy}%
+force produces a pull along~$AA'$ and a squeeze along~$BB'$.''\footnote
+  {\textit{Mathematical Astronomy}, Barlow and Bryan, p.~377.}
+\index{Acceleration@Acceleration \indexglossref{Acceleration}|)}%
+\index{Tides|)}%
+%% -----File: 292.png---Folio 293-------
+
+\AppendixSection{THE ZODIAC}\nblabel{page:293}
+\index{Zodiac}%
+
+This belt in the celestial sphere is $16°$~wide with the
+ecliptic as the center. The width is purely arbitrary. It
+could have been wider or narrower just as well, but was
+adopted by the ancients because the sun, moon, and planets
+known to them were always seen within $8°$ of the pathway
+of the sun. We know now that several asteroids, as
+\index{Asteroids}%
+truly planets as the earth, are considerably farther from
+the ecliptic than~$8°$; indeed, Pallas is sometimes $34°$~from
+\index{Pallas}%
+the ecliptic---to the north of overhead to people of northern
+United States or central Europe.
+\index{Europe}%
+\index{United States}%
+
+\includegraphicsmid{i293}{Fig.~117}
+
+\Paragraph{Signs.} As the sun ``creeps backward'' in the center of
+the zodiac, one revolution each year, the ancients divided
+its pathway into twelve parts, one for each month. To
+each of these sections of thirty degrees ($360°÷12 = 30°$)
+names were assigned, all but one after animals, each one
+being considered appropriate as a ``sign'' of an annual
+recurrence (see p.~\pageref{page:117}). Aries seems commonly to have
+been taken as the first in the series, the beginning of
+spring. Even yet the astronomer counts the tropical year
+from the ``First point of Aries,'' the moment the center
+of the sun crosses the celestial equator on its journey
+northward.
+
+As explained in the discussion of the precession of the
+equinoxes (p.~\pageref{page:286}), the point in the celestial equator where
+the center of the sun crosses it shifts westward one degree
+in about seventy years. In ancient days the First point of
+Aries was in the constellation of that name but now it is
+in the constellation to the west, Pisces. The sign Aries
+\index{Pisces@Pisces (p\u{\i}s$'$s\={e}z)}%
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation!first point of}%
+begins with the First point of Aries, and thus with the westward
+travel of this point all the signs have moved back
+into a constellation of a different name. Another difference
+%% -----File: 293.png---Folio 294-------
+between the signs and the constellations of the zodiac
+\index{Signs of zodiac}%
+\index{Celestial equator}%
+\index{Equator@Equator \indexglossref{Equator}!celestial}%
+is that the star clusters are of unequal length, some more
+than~$30°$ and some less, whereas the signs are of uniform
+length. The positions and widths of the signs and constellations
+with the date when the sun enters each are
+\index{Sun!apparent motions of}%
+shown in Figure~\figureref{i293}{117}.
+
+\ParagraphNoSpace{Aries,} the first sign, was named after the ram, probably
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation}%
+because to the ancient Chaldeans, where the name seems
+\index{Chaldeans}%
+to have originated, this was the month of sacrifice. The
+sun is in Aries from March~21 until April~20. It is represented
+%% -----File: 294.png---Folio 295-------
+by a small picture of a ram~\includegraphicssymbol{i294-1} or by a hieroglyphic~(\includegraphicssymbol{i294-2}).
+
+\ParagraphNoSpace{Taurus,} the second sign~(\includegraphicssymbol{i294-3}), was dedicated to the
+\index{Taurus}%
+bull. In ancient times this was the first of the signs,
+the vernal equinox being at the beginning of this sign.
+According to very ancient mythology it was the bull that
+drew the sun along its ``furrow'' in the sky. There
+are, however, many other theories as to the origin of the
+designation. The sun is in Taurus from April~20 until
+May~21.
+
+\ParagraphNoSpace{Gemini,} the third sign, signifies twins~(\includegraphicssymbol{i294-4}) and gets its
+\index{Gemini}%
+name from two bright stars, Castor and Pollux, which used
+to be in this sign, but are now in the sign Cancer. The
+sun is in Gemini from May~21 until June~22.
+
+\ParagraphNoSpace{Cancer,} the fourth sign~(\includegraphicssymbol{i294-5}), was named after the
+\index{Cancer, constellation of!sign of zodiac}%
+crab, probably from the fact that when in this sign the
+sun retreats back again, crablike, toward the south. The
+sun is in Cancer from June~22 until July~23.
+
+\ParagraphNoSpace{Leo,} signifying lion, is the fifth sign~(\includegraphicssymbol{i294-6}) and seems
+\index{Leo}%
+to have been adopted because the lion usually was used
+as a symbol for fire, and when the sun was in Leo the
+hottest weather occurred. The sun is in this sign from
+July~23 until August~23.
+
+\ParagraphNoSpace{Virgo,} the virgin~(\includegraphicssymbol{i294-7}), refers to the Chaldean myth of
+\index{Virgo}%
+the descent of Ishtar into hades in search of her husband.
+The sun is in Virgo from August~23 until September~23.
+
+The foregoing are the summer signs and, consequently,
+the corresponding constellations are our winter constellations.
+It must be remembered that the sign is always
+about $30°$ (the extreme length of the ``Dipper'') to the
+\index{Big Dipper}%
+west of the constellation of the same name.
+
+\ParagraphNoSpace{Libra,} the balances~(\includegraphicssymbol{i294-8}), appropriately got its name
+\index{Libra@Libra (li$'$bra)}%
+from the fact that the autumnal equinox, or equal balancing
+%% -----File: 295.png---Folio 296-------
+of day and night, occurred when the sun was in the
+constellation thus named the Balances. The sun is now
+in Libra from September~23 until October~24.
+\index{Libra@Libra (li$'$bra)}%
+
+\ParagraphNoSpace{Scorpio} is the eighth sign~(\includegraphicssymbol{i295-1}). The scorpion was a
+\index{Scorpio}%
+symbol of darkness, and was probably used to represent
+the shortening of days and lengthening of nights. The
+sun is now in Scorpio from October~24 until November~23.
+
+\begin{wrapfigure}[2]{r}{0pt}%
+  \includegraphics[width=0.6in]{./images/i295-2.pdf}%
+\end{wrapfigure}
+\ParagraphNoSpace{Sagittarius,} meaning an archer or bowman, is
+\index{Sagittarius@Sagittarius (s\u{a}g\;\u{\i}t\;t\={a}$'$r\u{\i}\;\u{u}s)}%
+sometimes represented as a Centaur with a
+bow and arrow. The sun is in this sign from November~23
+until December~22.
+
+\ParagraphNoSpace{Capricorn,} signifying goat, is often represented as having
+\index{Capricorn, constellation of!sign of zodiac}%
+the tail of a fish~(\includegraphicssymbol{i295-3}). It probably has its origin
+as the mythological nurse of the young solar god. The
+sun is in Capricorn from December~22 until January~20.
+
+\ParagraphNoSpace{Aquarius,} the water-bearer~(\includegraphicssymbol{i295-4}), is the eleventh sign
+\index{Aquarius@Aquarius (ä\;kw\={a}$'$r\u{\i}\;\u{u}s)}%
+and probably has a meteorological origin, being associated
+as the cause of the winter rains of Mediterranean countries.
+The sun is in this sign from January~20 until
+February~19.
+
+\ParagraphNoSpace{Pisces} is the last of the twelve signs. In accordance
+\index{Pisces@Pisces (p\u{\i}s$'$s\={e}z)}%
+with the meaning of the term, it is represented as two
+fishes~(\includegraphicssymbol{i295-5}). Its significance was probably the same as
+the water-bearer. The sun is in this sign from February~19
+until the vernal equinox, March~21, when it has completed
+the ``labors'' of its circuit, only to begin over
+again.
+
+The twelve signs of the ancient Chinese zodiac were
+\index{Chinese calendar!zodiac}%
+dedicated to a quite different set of animals; being, in
+order, the Rat, the Ox, the Tiger, the Hare, the Dragon,
+the Serpent, the Horse, the Sheep, the Monkey, the Hen,
+the Dog, and the Pig. The Egyptians adopted with a few
+changes the signs of the Greeks.
+%% -----File: 296.png---Folio 297-------
+
+\Section{Myths and Superstitions as to the Relation of
+the Zodiac to the Earth}
+\index{Myths and superstitions of the zodiac}%
+
+When one looks at the wonders of the heavens it does
+not seem at all strange that in the early dawn of history,
+ignorance and superstition should clothe the mysterious
+luminaries of the sky with occult influences upon the
+earth, the weather, and upon human affairs. The ancients,
+observing the apparent fixity of all the stars excepting the
+seven changing ones of the zodiac---the sun, moon, and
+five planets known to them---endowed this belt and its
+seven presiding deities with special guardianship of the
+earth, giving us seasons, with varying length of day and
+change of weather; bringing forth at its will the sprouting
+of plants and fruitage and harvest in their season; counting
+off inevitably the years that span human life; bringing
+days of prosperity to some and of adversity to others;
+and marking the wars and struggles, the growth and
+decay of nations. With such a background of belief, at
+once their science and their religion, it is not strange that
+when a child was born the parents hastened to the astrologer
+to learn what planet or star was in the ascendancy,
+that is, most prominent during the night, and thus learn
+in advance what his destiny would be as determined from
+the character of the star that would rule his life.
+
+The moon in its monthly path around the earth must
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+pass through the twelve signs of the zodiac in $29\frac{1}{2}$~days or
+spend about $2\frac{1}{2}$~days to each sign. During the blight of
+intelligence of the dark ages, some mediæval astrologer
+conceived the simple method of subdividing the human
+body into twelve parts to correspond to the twelve constellations
+of the zodiac. Beginning with the sign Aries,
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation!sign of zodiac}%
+he dedicated that to the head, the neck he assigned to
+%% -----File: 297.png---Folio 298-------
+Taurus, the arms were given over to Gemini, the stars of
+\index{Gemini}%
+\index{Taurus}%
+Cancer were to rule the breast, the heart was presided
+over by Leo, and so on down to Pisces which was to rule
+\index{Leo}%
+the feet. Now anyone who was born when the moon was in
+Aries would be strong in the head, intellectual; if in Taurus,
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation!sign of zodiac}%
+he would be strong in the neck and self-willed, etc. Moreover,
+since the moon makes a circuit of the signs of the
+zodiac in a month, according to his simple scheme when
+the moon is in Aries the head is especially affected; then
+diseases of the head rage (or is it then that the head
+is stronger to resist disease?), and during the next few days
+when the moon is in Taurus, beware of affections of the
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+neck, and so on down the list. The very simplicity of this
+scheme and ease by which it could be remembered led to
+its speedy adoption by the masses who from time immemorial
+have sought explanations of various phenomena
+by reference to celestial bodies.
+
+Now there is no astronomical or geographical necessity
+\index{Myths and superstitions of the zodiac}%
+for considering Aries as the first sign of the zodiac. Our
+year begins practically with the advent of the sun into
+Capricorn---the beginning of the year was made January~1
+for this very purpose. The moon is not in any peculiar
+position in relation to the earth March~21 any more than
+it is December~23. If when the calendar was revised the
+numbering of the signs of the zodiac had been changed
+also, then Capricorn, the divinities of which now rule the
+\index{Capricorn, constellation of!sign of zodiac}%
+\emph{knees}, would have been made to rule the \emph{head}, and the
+whole artificial scheme would have been changed! Besides,
+the sign Capricorn does not include the \emph{constellation} Capricorn,
+so with the precession of the equinoxes the subtle
+influences once assigned to the heavenly bodies of one
+constellation have been shifted to an entirely different set
+of stars! The association of storms with the sun's crossing
+%% -----File: 298.png---Folio 299-------
+the equinox and with the angle the cusps of the moon
+show to the observer (a purely geometric position varying
+with the position of the observer) is in the same class as
+bad luck attending the taking up of the ashes after the sun
+has gone down or the wearing of charms against rheumatism
+or the ``evil'' eye.
+
+\begin{verse}\smallsize
+``The fault, dear Brutus, is not in our stars,\\
+But in ourselves, that we are underlings.''\\
+\hfill---\textsc{Shakespeare.}
+\index{Shakespeare}%
+\end{verse}
+%% -----File: 299.png---Folio 300-------
+
+\clearpage
+\AppendixSection{PRACTICAL WORK IN MATHEMATICAL
+\index{Practical work|(}%
+GEOGRAPHY}
+
+Concrete work in this subject has been suggested directly,
+by implication, or by suggestive queries and problems
+throughout the book. No instruments of specific character
+have been suggested for use excepting such as are
+easily provided, as a graduated quadrant, compasses, an
+isosceles right triangle, etc. Interest in the subject will
+be greatly augmented if the following simple instruments,
+or similar devices, are made or purchased and \emph{used}.
+
+\Section{To Make a Sundial}
+\index{Sundial|(}%
+
+\includegraphicsleft{i299}{Fig.~118}
+
+\sloppy
+This is not especially
+difficult and may be accomplished
+in several
+ways. A simple
+plan is shown in Figure~\figureref{i299}{118}. Angle~$BAC$ should be the
+co-latitude of the place, that is, the latitude subtracted
+from~$90°$, though this is not at all essential. The hour
+lines may be marked off according to two systems, for
+standard time or for local time.
+
+\fussy
+\Paragraph{Standard Time Dial.} If you wish your dial to indicate
+clock time as correctly as possible, it will be necessary to
+consult the analemma or an almanac to ascertain the equation
+of time when the hour lines are drawn. Since the sun
+is neither fast nor slow April~14, June~15, September~1, or
+December~25, those are the easiest days on which to lay
+off the hours. On one of those dates you can lay them off
+according to a reliable timepiece.
+%% -----File: 300.png---Folio 301-------
+
+If you mark the hour lines at any other date; ascertain
+the equation of time (see p.~\pageref{fig:i126}) and make allowances
+accordingly. Suppose the date is October~27. The analemma
+\index{Analemma@Analemma \indexglossref{Analemma}, description of!uses of}%
+shows the sun to be $16$~minutes fast. You should
+mark the hour lines that many minutes before the hour as
+indicated by your timepiece, that is, the noon line when
+your watch says 11:44~o'clock, the 1~o'clock line when
+the watch indicates 12:44,~etc. If the equation is slow,
+say five minutes, add that time to your clock time, marking
+the noon line when your watch indicates 12:05, the
+next hour line at 1:05,~etc. It is well to begin at the hour
+for solar noon, at that time placing the board so that the
+sun's shadow is on the XII~mark and after marking off the
+afternoon hours measure from the XII~mark westward
+corresponding distances for the forenoon. Unless you
+chance to live upon the meridian which gives standard
+time to the belt in which you are, the noon line will be
+somewhat to the east or west of north.
+
+This sundial will record the apparent solar time of the
+meridian upon which the clock time is based. The difference
+in the time indicated by the sundial and your watch
+at any time is the equation of time. Test the accuracy
+of your sundial by noticing the time by your watch when
+the sundial indicates noon and comparing this difference
+with the equation of time for that day. If your sundial
+is accurate, you can set your watch any clear day by looking
+up the equation of time and making allowances accordingly.
+Thus the analemma shows that on May~28 the sun
+is three minutes fast. When the sundial indicates noon
+you know it is three minutes before twelve by the clock.
+
+\Paragraph{Local Time Dial.} To mark the hour lines which show
+the local mean solar time (see p.~\pageref{page:64}), set the XII~hour
+line due north. Note accurately the clock time when the
+%% -----File: 301.png---Folio 302-------
+shadow is north. One hour later mark the shadow line
+for the I~hour line, two hours later mark the II~hour line,
+etc. This dial will indicate the apparent solar time of
+your meridian. You can set your watch by it by first
+\index{Meridian!standard time}%
+converting it into mean solar time and then into standard
+time. (This is explained on p.~\pageref{page:129}) %[**TN: 'pp. 128, 129' in original text]
+
+It should be noted that these two sundials are exactly
+the same for persons who use local time, or, living on the
+standard time meridian, use standard time.
+
+\Section{The Sun Board}
+\index{Sun Board}%
+
+The uses of the mounted quadrant in determining latitude
+were shown in the chapter on seasons (see p.~\pageref{page:173}).
+Dr.~J.~Paul Goode, of the University of Chicago, has
+\index{Goode, J. Paul}%
+\index{University of Chicago}%
+designed a very convenient little instrument which answers
+well for this and other purposes.
+
+\includegraphicsmid{i301}{Fig.~119}
+
+A vertically placed quadrant enables one to ascertain
+\index{Altitude, of noon sun}%
+\index{Sundial|)}%
+%% -----File: 302.png---Folio 303-------
+the altitude of the sun for determining latitude and calculating
+\index{Altitude, of noon sun}%
+the heights of objects.
+By means of a graduated circle
+placed horizontally the azimuth
+\index{Azimuth}%
+of the sun (see \glossref[Azimuth]{Glossary}) may
+be ascertained. A simple vernier
+gives the azimuth readings to
+quarter degrees. It also has a
+device for showing the area covered
+by a sunbeam of a given
+size, and hence its heating power.
+\index{Sun Board}%
+
+\Section{The Heliodon}
+\index{Heliodon@Heliodon (h\={e}$'$\;l\u{\i}\;o\;don)}%
+
+\includegraphicsmid{i302}{Fig.~120}
+
+This appliance was designed by
+Mr.~J.~F. Morse, of the Medill
+\index{Morse, J. F.}%
+High School, Chicago. It vividly
+illustrates the apparent path of
+the sun at the equinoxes and solstices
+\index{Equinox@Equinox \phantomsection\label{idx:e}\indexglossref{Equinox}!precession of}%
+\index{Solstices}%
+at any latitude. The points
+of sunrise and sunset can also be shown and hence the
+length of the longest day or night can be calculated.
+\index{Practical work|)}%
+%% -----File: 303.png---Folio 304-------
+
+\clearpage
+\AppendixSection{WHAT KEEPS THE MEMBERS OF THE SOLAR
+SYSTEM IN THEIR ORBITS?}
+
+\index{What keeps the members of the solar system in their orbits?|(}%
+\index{Orbit, of earth|(}%
+\index{Projectiles|(}%
+When a body is thrown in a direction parallel to the
+horizon, as the bullet from a level gun, it is acted upon by
+two forces:
+
+(\textit{a}) The projectile force of the gun,~$AB$. (Fig.~\figureref{i303}{121}.)
+
+(\textit{b}) The attractive force of the earth,~$AC$.
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+
+The course it will actually take from point~$A$ is the
+diagonal~$AA'$. When it reaches~$A'$ the force~$AB$ still
+acts (not considering the friction of the air), impelling it
+in the line~$A'B'$. Gravity continues to pull it in the line~$A'C'$,
+and the projectile takes the diagonal direction~$A'A''$
+and makes the curve (not a broken line as in the figure)
+$AA'A''$. It is obvious from this diagram that if the impelling
+force be sufficiently great, line~$AB$ will be so long in
+relation to line~$AC$ that the bullet will be drawn to the
+earth just enough to keep it at the same distance from
+the surface as that of its starting point.
+
+\includegraphicsmid{i303}{Fig.~121}
+
+The amount of such a projectile force near the surface
+of the earth at the equator as would thus keep an object
+%% -----File: 304.png---Folio 305-------
+at an unvarying distance from the earth is $26,100$ feet per
+second. Fired in a horizontal direction from a tower (not
+allowing for the friction of the air) such a bullet would
+forever circle around the earth. Dividing the circumference
+of the earth (in feet) by this number we find that
+such a bullet would return to its starting point in about
+$5,000$ seconds, or $1$~h.\ $23$~m., making many revolutions
+around the earth during one day. Since our greatest guns,
+throwing a ton of steel a distance of twenty-one miles,
+give their projectiles a speed of only about $2,600$ feet
+per second, it will be seen that the rate we have given
+is a terrific one. If this speed were increased to $37,000$ feet
+per second, the bullet would never return to the earth.
+\nblabel{page:305}One is tempted here to digress and demonstrate the utter
+impossibility of human beings even ``making a trip to the
+moon,'' to say nothing of one to a much more distant
+planet. The terrific force with which we should have to
+be hurled to get away from the earth, fourteen times the
+speed of the swiftest cannon ball, is in itself an insuperable
+difficulty. Besides this, there would have to be the most
+exact calculation of the force and direction, allowing for
+(\textit{a})~the curve given a projectile by gravity, (\textit{b})~the centrifugal
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+%% -----File: 305.png---Folio 306-------
+force of rotation, (\textit{c})~the revolution of the earth,
+(\textit{d})~the revolution of the moon, (\textit{e})~the friction of the air,
+a variable quantity, impossible of calculation with absolute
+accuracy, (\textit{f})~the inevitable swerving in the air by
+reason of its currents and varying density, and (\textit{g})~the
+influence on the course by the attraction of the sun and
+planets. In addition to these mathematical calculations
+\index{Planets}%
+as to direction and projectile force, there would be the
+problem of (\textit{h})~supply of air, (\textit{i})~air pressure, to which our
+bodies through the evolution of ages have become adapted,
+(\textit{j})~the momentum with which we would strike into the
+moon if we did ``aim'' right,~etc.
+
+\index{Scientific American}%
+\includegraphicsmid{i304}{Fig.~122. Paths of Projectiles of Different Velocities (Scientific American
+Supplement, Sept.~22, 1906. Reproduced by permission)}
+
+Returning to our original problem, we may notice that
+if the bullet were fired horizontally at a distance of $4,000$
+miles from the surface of the earth, the pull of gravity would
+be only one fourth as great (second law of gravitation),
+and the projectile would not need to take so terrific a speed
+to revolve around the earth. As we noticed in the discussion
+of Mars (see p.~\pageref{page:255}), the satellite Phobos is so near
+\index{Phobos@Phobos (f\={o}$'$b\u{u}s)}%
+\index{Mars}%
+its primary, $1,600$ miles from the surface, that it revolves
+at just about the rate of a cannon ball, making about three
+revolutions while the planet rotates once.
+
+While allusion has been made only to a bullet or a moon,
+in noticing the application of the law of projectiles, the
+\index{Projectiles|)}%
+principle applies equally to the planets. Governed by the
+law here illustrated, a planet will revolve about its primary
+in an orbit varying from a circle to an elongated ellipse.
+Hence we conclude that a combination of projectile and
+attractive forces keeps the members of the solar system
+in their orbits.
+\index{Orbit, of earth|)}%
+\index{What keeps the members of the solar system in their orbits?|)}%
+%% -----File: 306.png---Folio 307-------
+
+\clearpage
+
+\AppendixSection{FORMULAS AND TABLES}
+\index{Formulas|(}%
+
+\Section{Symbols Commonly Employed}\nblabel{page:307}
+\index{Symbols}%
+
+There are several symbols which are generally used in
+works dealing with the earth, its orbit or some of its other
+properties. To the following brief list of these are added
+a few mathematical symbols employed in this book,
+which may not be familiar to many who will use it. The
+general plan of using arbitrary symbols is shown on page~\pageref{page:14},
+where $G$~represents universal gravitation and $g$~represents
+gravity; $C$~represents centrifugal force and $c$~centrifugal
+force due to the rotation of the earth.
+
+\begin{flist}
+\item $\phi$ (Phi), latitude.
+
+\item $\varepsilon$ (Epsilon), obliquity of the ecliptic, also eccentricity of
+an ellipse.
+
+\item $\pi$ (Pi), the number which when multiplied by the diameter
+of a circle equals the circumference; it is
+$3.14159265$, nearly $3.1416$, nearly~$3\frac{1}{7}$. $\pi^2 =9.8696044$.
+
+\item $\delta$ (Delta), declination, or distance in degrees from the
+celestial equator.
+
+\item $\propto$, ``varies as;'' $x \propto y$ means $x$~varies as~$y$.
+
+\item $<$, ``is less than;'' $x < y$ means $x$~is less than~$y$.
+
+\item $>$, ``is greater than;'' $x > y$ means $x$~is greater than~$y$.
+\end{flist}
+
+\Section{Formulas}
+
+\Subsection{The Circle and Sphere}
+
+\begin{flist}
+\item
+\begin{tabular}{@{}p{.5\linewidth}@{}p{.5\linewidth}@{}}
+$r$ = radius.   & $c$ = circumference.\\
+$d$ = diameter. & $a$ = area.
+\end{tabular}
+%% -----File: 307.png---Folio 308-------
+\item $\pi d = c$.
+\item $\dfrac{\rule{0pt}{2ex}c}{\pi} = d$.
+\item $\pi r^2$ = area.
+\item $4\pi r^2$ = surface of sphere.
+\item $\frac{4}{3} \pi r^3$ = volume of sphere $= 4.1888 r^3$ (nearly).
+\end{flist}
+
+\Subsection{The Ellipse}
+\index{Ellipse@Ellipse \indexglossref{Ellipse}}%
+
+\begin{flist}
+\item
+\begin{tabular}{@{}p{.5\linewidth}@{}p{.5\linewidth}@{}}
+$a = \frac{1}{2\extrafracspacing}$ major axis. & $o = $ oblateness.\\
+$b = \frac{1}{2}$ minor axis. & $e = $ eccentricity.\\
+\hspace*{.25\textwidth}\rlap{$\pi ab = $ area of ellipse.}
+\end{tabular}
+\end{flist}
+\begin{align*}
+o &= \frac{a-b}{a} \\
+e &= \sqrt{\frac{a^2 - b^2}{a^2}}
+\end{align*}
+
+\Subsection{The Earth Compared with Other Bodies}
+
+\begin{flist}
+\item $P =$ the radius of the body as compared with the
+radius of the earth. Thus in case of the moon, the
+\index{Moon or satellite@Moon or satellite\phantomsection\label{idx:m}}%
+moon's radius~$= 1081$, the earth's radius~$= 3959$,
+and $P = \frac{1081}{3959}$.
+\item $P^2 =$ surface of body as compared with that of the
+earth.
+\item $P^3 =$ volume of body as compared with that of the
+earth.
+\item $\dfrac{\rule{0pt}{1.5ex}\text{mass}}{P^2} =$ surface gravity as compared with that of the
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+earth.
+\end{flist}
+%% -----File: 308.png---Folio 309-------
+
+\Subsection{Centrifugal Force}
+\index{Centrifugal force@Centrifugal force \indexglossref{Centrifugal force}}%
+
+\begin{flist}
+\item
+\begin{tabular}{@{}p{.5\linewidth}@{}p{.5\linewidth}@{}}
+$c =$ centrifugal force. & $r =$ radius.\\
+$v =$ velocity.          & $m =$ mass.\\
+                         & $c = \dfrac{mv^2}{r}$.
+\end{tabular}
+\end{flist}
+
+Lessening of surface gravity at any latitude by reason
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+of the centrifugal force due to rotation.
+
+$g = \text{surface gravity}$.
+
+$c\ \text{at any latitude} = \dfrac{g\strut}{289\strut} × \cos^2 \phi$.
+
+Deviation of the plumb line from true vertical by reason
+of centrifugal force due to rotation.
+
+$d = \text{deviation}$.
+
+$d = 357'' × \sin 2\phi$.
+
+\Subsection{Miscellaneous}
+
+Rate of swing of pendulum varies inversely as the
+\index{Pendulum clock}%
+square root of the surface gravity. $r = \dfrac{1}{\sqrt{g}}$.
+
+Density of a body~$=\dfrac{\strut\text{mass}}{\strut\text{vol.}}$.
+\index{Density, formula for}%
+
+Hourly deviation of the plane of a pendulum due to
+the rotation of the earth~$= \sin \text{latitude} × 15°$ ($d = \sin \phi
+× 15°$).
+
+Weight of bodies above the surface of the earth.
+
+$w = \text{weight}$,
+
+$d =$~distance from the center of the earth.
+
+$w \propto \dfrac{1\strut}{d^2\strut}$.
+
+Weight of bodies below the surface of the earth.
+$w \propto d$.
+\index{Formulas|)}%
+%% -----File: 309.png---Folio 310-------
+
+\AppendixSection{GEOGRAPHICAL CONSTANTS\protect\footnotemark}\nblabel{page:310}%
+\index{Geographical constants}%
+\index{Clarke, A. R.}%
+  \footnotetext{Dimensions of the earth are based upon the Clarke spheroid of 1866.}
+
+\index{Dimensions of earth}%
+\index{Earth's dimensions}%
+\noindent Equatorial semi-axis: \\
+\index{Equator@Equator \indexglossref{Equator}!terrestrial}%
+\DotRow{\qquad in feet}{$20,926,062$.}
+\DotRow{\qquad in meters}{$6,378,206.4$}
+\DotRow{\qquad in miles}{$3,963.307$}
+
+\medskip%[**TN: to aid pagination]
+\index{Diameter of earth}%
+\index{Polar diameter of earth}%
+\noindent Polar semi-axis: \\
+\DotRow{\qquad in feet}{$20,855,121$.}
+\DotRow{\qquad in meters}{$6,356,583.8$}
+\DotRow{\qquad in miles}{$3,949.871$}
+\DotRow{Oblateness of earth}{$1 ÷ 294.9784$}
+\DotRow{Circumference of equator (in miles)}{$24,901.96$}
+\index{Circumference of earth}%
+\DotRow{Circumference through poles (in miles)}{$24,859.76$}
+\DotRow{Area of earth's surface, square miles}{$196,971,984$.}
+\index{Area of earth's surface}%
+\DotRow{Volume of earth, cubic miles}{$259,944,035,515$.}
+\index{Volume of earth}%
+\DotRow{Mean density (Harkness)}{$5.576$}
+\index{Harkness, William}%
+\index{Density of earth}%
+\DotRow{Surface density (Harkness)}{$2.56$}
+\DotRow{Obliquity of ecliptic (see page~\pageref{page:118})}{$23° 27' 4.98$~s.}
+\index{Ecliptic@Ecliptic \indexglossref{Ecliptic}!obliquity of}%
+\index{Obliquity of the ecliptic@Obliquity of the ecliptic\phantomsection\label{idx:ooe}}%
+\DotRow{Sidereal year}{$365$~d.\ $6$~h.\ $9$~m.\ $8.97$~s.\ or $365.25636$~d.}
+\index{Sidereal, clock!year}%
+\index{Year}%
+\DotRow{Tropical year}{$365$~d.\ $5$~h.\ $48$~m.\ $45.51$~s.\ or $365.24219$~d.}
+\DotRow{Sidereal day}{$23$~h.\ $56$~m.\ $4.09$~s.\ of mean solar time.}
+\DotRow{Distance of earth to sun, mean (in miles)}{$92,800,000$.}
+\DotRow{Distance of earth to moon, mean (in miles)}{$238,840$.}
+\index{Distances, of planets}%
+
+\vspace*{-\baselineskip}%[**TN: to aid pagination]
+\AppendixSection{MEASURES OF LENGTH}\nblabel{page:310b}
+\index{Measures of length}%
+
+\vspace*{-0.5\baselineskip}%[**TN: to aid pagination]
+\noindent\DotRow{Statute mile}{$5,280.00$~feet}
+\index{Mile, in various countries}%
+\DotRow{Nautical mile,\footnotemark\ or knot}{$6,080.27$~\PadTo{\text{feet}}{``}}
+\footnotetext{As defined by the United States Coast and Geodetic Survey.}%
+\index{United States Coast and Geodetic Survey}%
+\DotRow{German sea mile}{$6,076.22$~\PadTo{\text{feet}}{``}}
+\DotRow{Prussian mile, law of 1868}{$24,604.80$~\PadTo{\text{feet}}{``}}
+\DotRow{Norwegian and Swedish mile}{$36,000.00$~\PadTo{\text{feet}}{``}}
+\DotRow{Danish mile}{$24,712.51$~\PadTo{\text{feet}}{``}}
+\DotRow{Russian werst, or versta}{$3,500.00$~\PadTo{\text{feet}}{``}}
+\DotRow{Meter}{$3.28$~\PadTo{\text{feet}}{``}}
+\index{Meter, length of}%
+\DotRow{Fathom}{$6.00$~\PadTo{\text{feet}}{``}}
+\index{Fathom, length of}%
+\DotRow{Link of surveyor's chain}{$0.66$~\PadTo{\text{feet}}{``}}
+\index{Link of surveyor's chain}%
+\index{Surveyor's chain}%
+%% -----File: 310.png---Folio 311-------
+\pagebreak
+\vfill
+\begin{SmallText}
+\index{Cosines, natural, table of}%
+\index{Sines, natural, table of}%
+\[
+\begin{array}{@{}c|>{\ }c<{\ }|c||c|>{\ }c<{\ }|c||c|>{\ }c<{\ }|c@{}}
+\multicolumn{9}{c}{\nblabel{page:311}\text{TABLE OF NATURAL SINES AND COSINES}\tablespacerbot}\\
+\hline
+\tablespacertop
+\text{Sin} & & \text{Cos} &
+\text{Sin} & & \text{Cos} &
+\text{Sin} & & \text{Cos}\tablespacerbot\\
+\hline
+\tablespacertop
+\Z0\rlap{°}& .0000 & 90\rlap{°}& 31\rlap{°}& .5150 & 59\rlap{°}& 61\rlap{°}& .8746 & 29\rlap{°} \\
+\Z1 & .0175 & 89 & 32 & .5299 & 58 & 62 & .8829 & 28 \\
+\Z2 & .0349 & 88 & 33 & .5446 & 57 & 63 & .8910 & 27 \\
+\Z3 & .0523 & 87 & 34 & .5592 & 56 & 64 & .8988 & 26 \\
+\Z4 & .0698 & 86 & 35 & .5736 & 55 & 65 & .9063 & 25 \\
+\Z5 & .0872 & 85 & 36 & .5878 & 54 & 66 & .9135 & 24 \\
+\Z6 & .1045 & 84 & 37 & .6018 & 53 & 67 & .9205 & 23 \\
+\Z7 & .1219 & 83 & 38 & .6157 & 52 & 68 & .9272 & 22 \\
+\Z8 & .1392 & 82 & 39 & .6293 & 51 & 69 & .9336 & 21 \\
+\Z9 & .1564 & 81 & 40 & .6424 & 50 & 70 & .9397 & 20 \\
+ 10 & .1736 & 80 & 41 & .6561 & 49 & 71 & .9455 & 19 \\
+ 11 & .1908 & 79 & 42 & .6691 & 48 & 72 & .9511 & 18 \\
+ 12 & .2079 & 78 & 43 & .6820 & 47 & 73 & .9563 & 17 \\
+ 13 & .2250 & 77 & 44 & .6947 & 46 & 74 & .9613 & 16 \\
+ 14 & .2419 & 76 & 45 & .7071 & 45 & 75 & .9659 & 15 \\
+ 15 & .2588 & 75 & 46 & .7193 & 44 & 76 & .9703 & 14 \\
+ 16 & .2756 & 74 & 47 & .7314 & 43 & 77 & .9744 & 13 \\
+ 17 & .2924 & 73 & 48 & .7431 & 42 & 78 & .9781 & 12 \\
+ 18 & .3090 & 72 & 49 & .7547 & 41 & 79 & .9816 & 11 \\
+ 19 & .3256 & 71 & 50 & .7660 & 40 & 80 & .9848 & 10 \\
+ 20 & .3420 & 70 & 51 & .7771 & 39 & 81 & .9877 & \Z9 \\
+ 21 & .3584 & 69 & 52 & .7880 & 38 & 82 & .9903 & \Z8 \\
+ 22 & .3746 & 68 & 53 & .7986 & 37 & 83 & .9925 & \Z7 \\
+ 23 & .3907 & 67 & 54 & .8090 & 36 & 84 & .9945 & \Z6 \\
+ 24 & .4067 & 66 & 55 & .8192 & 35 & 85 & .9962 & \Z5 \\
+ 25 & .4226 & 65 & 56 & .8290 & 34 & 86 & .9976 & \Z4 \\
+ 26 & .4384 & 64 & 57 & .8387 & 33 & 87 & .9986 & \Z3 \\
+ 27 & .4540 & 63 & 58 & .8480 & 32 & 88 & .9994 & \Z2 \\
+ 28 & .4695 & 62 & 59 & .8572 & 31 & 89 & .9998 & \Z1 \\
+ 29 & .4848 & 61 & 60 & .8660 & 30 & 90 & \llap{1}.0000 & \Z0 \\
+ 30 & .5000 & 60 & & & & & & \tablespacerbot\\
+\hline
+\end{array}
+\]
+%% -----File: 311.png---Folio 312-------
+\clearpage
+\index{Cotangents, natural, table of}%
+\index{Tangents, natural, table of}%
+\[
+\begin{array}{@{}c|>{\ }c<{\ }|c||c|>{\ }c<{\ }|c||c|>{\ }c<{\ }|c@{}}
+\multicolumn{9}{c}{\nblabel{page:312}\text{TABLE OF NATURAL TANGENTS AND COTANGENTS}\tablespacerbot}\\
+\hline
+\tablespacertop
+\text{Tan} & & \text{Cot} &
+\text{Tan} & & \text{Cot} &
+\text{Tan} & & \text{Cot}\tablespacerbot\\
+\hline
+\tablespacertop
+\Z0\rlap{°} & .0000 & 90\rlap{°} & 31\rlap{°} & \Z.6009 & 59\rlap{°} & 61\rlap{°} & 1.8040 & 29\rlap{°} \\
+\Z1 & .0175 & 89 & 32 & \Z.6249 & 58 & 62 & 1.8807 & 28 \\
+\Z2 & .0349 & 88 & 33 & \Z.6494 & 57 & 63 & 1.9626 & 27 \\
+\Z3 & .0524 & 87 & 34 & \Z.6745 & 56 & 64 & 2.0503 & 26 \\
+\Z4 & .0699 & 86 & 35 & \Z.7002 & 55 & 65 & 2.1445 & 25 \\
+\Z5 & .0875 & 85 & 36 & \Z.7265 & 54 & 66 & 2.2460 & 24 \\
+\Z6 & .1051 & 84 & 37 & \Z.7536 & 53 & 67 & 2.3559 & 23 \\
+\Z7 & .1228 & 83 & 38 & \Z.7813 & 52 & 68 & 2.4751 & 22 \\
+\Z8 & .1405 & 82 & 39 & \Z.8098 & 51 & 69 & 2.6051 & 21 \\
+\Z9 & .1584 & 81 & 40 & \Z.8391 & 50 & 70 & 2.7475 & 20 \\
+ 10 & .1763 & 80 & 41 & \Z.8693 & 49 & 71 & 2.9042 & 19 \\
+ 11 & .1944 & 79 & 42 & \Z.9004 & 48 & 72 & 3.0777 & 18 \\
+ 12 & .2126 & 78 & 43 & \Z.9325 & 47 & 73 & 3.2709 & 17 \\
+ 13 & .2309 & 77 & 44 & \Z.9657 & 46 & 74 & 3.4874 & 16 \\
+ 14 & .2493 & 76 & 45 &  1.0000 & 45 & 75 & 3.7321 & 15 \\
+ 15 & .2679 & 75 & 46 &  1.0355 & 44 & 76 & 4.0108 & 14 \\
+ 16 & .2867 & 74 & 47 &  1.0724 & 43 & 77 & 4.3315 & 13 \\
+ 17 & .3057 & 73 & 48 &  1.1106 & 42 & 78 & 4.7046 & 12 \\
+ 18 & .3249 & 72 & 49 &  1.1504 & 41 & 79 & 5.1446 & 11 \\
+ 19 & .3443 & 71 & 50 &  1.1918 & 40 & 80 & 5.6713 & 10 \\
+ 20 & .3640 & 70 & 51 &  1.2349 & 39 & 81 & 6.1338 & \Z9 \\
+ 21 & .3839 & 69 & 52 &  1.2794 & 38 & 82 & 7.1154 & \Z8 \\
+ 22 & .4040 & 68 & 53 &  1.3270 & 37 & 83 & 8.1443 & \Z7 \\
+ 23 & .4245 & 67 & 54 &  1.3764 & 36 & 84 & 9.5144 & \Z6 \\
+ 24 & .4452 & 66 & 55 &  1.4281 & 35 & 85 & \llap{1}1.43\Z\Z & \Z5 \\
+ 25 & .4663 & 65 & 56 &  1.4826 & 34 & 86 & \llap{1}4.30\Z\Z & \Z4 \\
+ 26 & .4877 & 64 & 57 &  1.5399 & 33 & 87 & \llap{1}9.08\Z\Z & \Z3 \\
+ 27 & .5095 & 63 & 58 &  1.6003 & 32 & 88 & \llap{2}4.64\Z\Z & \Z2 \\
+ 28 & .5317 & 62 & 59 &  1.6643 & 31 & 89 & \llap{5}7.29\Z\Z & \Z1 \\
+ 29 & .5543 & 61 & 60 &  1.7321 & 30 & 90 & 0.0000 & \Z0 \\
+ 30 & .5774 & 60 & & & & & &\tablespacerbot \\
+\hline
+\end{array}
+\]
+\end{SmallText}
+
+%% -----File: 312.png---Folio 313-------
+\clearpage
+\Section{LIST OF TABLES GIVEN IN THIS BOOK}
+\index{Tables, list of}%
+\begin{center}
+\smallsize
+\begin{tabular}{@{}p{\textwidth}@{}}
+\hfill\scriptsize\textsc{page} \\
+Curvature of earth's surface \dotfill \pageref{page:28a} \\
+Cosines \dotfill \pageref{page:311} \\
+Cotangents \dotfill \pageref{page:312} \\
+Day, length of longest day at different latitudes \dotfill \pageref{page:158} \\
+Declination of the sun, see analemma \dotfill \pageref{fig:i126} \\
+Deviation of freely swinging pendulum due to earth's rotation \dotfill \pageref{page:57} \\
+Distances, etc., of planets \dotfill \pageref{page:266} \\
+Equation of time, see analemma \dotfill \pageref{fig:i126} \\
+Earth's dimensions, etc. \dotfill \pageref{page:310} \\
+Latitudes, lengths of degrees \dotfill \pageref{page:44} \\
+\qquad of principal cities of the world \dotfill \pageref{page:88} \\
+Longitudes, lengths of degrees \dotfill \pageref{page:44} \\
+\qquad of principal cities of the world \dotfill \pageref{page:88} \\
+Measures of length \dotfill \pageref{page:310b} \\
+Meridional parts \dotfill \pageref{page:217} \\
+Sines, natural \dotfill \pageref{page:311} \\
+Solar system table \dotfill \pageref{page:266} \\
+Standard time adoptions \dotfill \pageref{page:81} \\
+Tangents, natural \dotfill \pageref{page:312} \\
+Time used in various countries \dotfill \pageref{page:81} \\
+Velocity of earth's rotation at different latitudes \dotfill \pageref{page:58} \\
+Vertical ray of sun, position on earth, see analemma \dotfill \pageref{fig:i126}%
+\index{Vertical ray of sun}
+\end{tabular}
+\end{center}
+%% -----File: 313.png---Folio 314-------
+
+\SpecialChapter{Glossary}
+\index{Glossary|(}%
+\addcontentsline{toc}{section}{\textsc{Glossary}}
+
+\addtocontents{toc}{\vspace{2ex}}
+
+\begin{SmallText}
+\Gloss{Aberration}, the apparent displacement of sun, moon, planet, or star produced
+as a resultant of (\textit{a})~the orbital velocity of the earth, and (\textit{b})~the
+velocity of light from the heavenly body.
+
+\Gloss{Acceleration}, increase or excess of mean motion or velocity.
+
+\Gloss{Altitude}, elevation in degrees (or angle of elevation) of an object above
+the horizon.
+
+\Gloss{Analemma}, a scale showing (\textit{a})~the mean equation of time and (\textit{b})~the
+mean declination of the sun for each day of the year.
+
+\Gloss{Aphelion} (\u a f\=e$'$ li on), the point in a planet's orbit which is farthest
+from the sun.
+
+\Gloss{Apogee} (\u ap$'$ o je), the point farthest from the earth in any orbit;
+usually applied to the point in the moon's orbit farthest from the
+earth.
+
+\Gloss{Apparent solar day}, see \glossref{Day}.
+
+\Gloss{Apparent (solar) time}, see \glossref{Time}.
+
+\Gloss{Apsides} (\u ap$'$ si d\=ez), line of, a line connecting perihelion and aphelion
+of a planet's orbit, or perigee and apogee of a moon's orbit.
+Apsides is plural for apsis, which means the point in an orbit
+nearest to the primary or farthest from it.
+
+\Gloss{Arc}, part of a circle; in geography, part of the circumference of a
+circle.
+
+\Gloss{Asteroids}, very small planets. A large number of asteroids revolve
+\index{Asteroids}%
+around the sun between the orbits of Mars and Jupiter.
+
+\Gloss{Autumnal equinox}, see \glossref{Equinox}.
+
+\Gloss{Axis}, the line about which an object rotates.
+\index{Axis, changes in position of!defined}%
+
+\Gloss{Azimuth} (\u az$'$ {\u \i} m\u uth) the angular distance of an object from the celestial
+\index{Azimuth}%
+meridian of the place of the observer to the celestial meridian of
+the object. The azimuth of the sun is the distance in degrees from
+its point of rising or setting to a south point on the horizon.
+
+\Gloss{Celestial sphere}, the apparent hollow sphere in which the sun, moon,
+planets, comets, and stars seem to be located.
+\index{Celestial latitude!sphere}%
+
+\Gloss{Center of gravity} the point about which a body (or group of
+bodies) balances.
+
+\Gloss{Centrifugal force} (sen trif$'$ u gal), a force tending away from a center.
+
+\Gloss{Centripetal force} (sen trip$'$ e tal), a force tending toward a center.
+
+\Gloss{Colures} (k\=o l\=urz$'$), the four principal meridians of the celestial sphere,
+two passing through the equinoxes and two through the solstices.
+
+\Gloss{Conjunction}, see \glossref{Syzygy}.
+%% -----File: 314.png---Folio 315-------
+
+\Gloss{Copernican system} (k\=o per$'$ ni can), the theory of the solar system
+advanced by Copernicus (1473--1543) that the sun is the center of
+the solar system, the planets rotating on their axes and revolving
+around the sun. See \glossref[Heliocentric]{Heliocentric theory}.
+
+\Gloss{Co-tidal lines}, lines passing through places that have high tide at the
+\index{Co-tidal lines}%
+same time.
+
+\Gloss{Day}.\\
+\Subgloss{Astronomical day}, a period equal to a mean solar day, reckoned
+\index{Astronomical day}%
+from noon and divided into twenty-four hours, usually numbered
+from one to twenty-four.
+
+\Subgloss{Civil day}, the same as an astronomical day excepting that it is
+\index{Civil day}%
+reckoned from midnight. It is also divided into twenty-four
+hours, usually numbered in two series, from one to twelve.
+
+\Subgloss{Sidereal day}, the interval between two successive passages of a
+\index{Sidereal, clock!day}%
+celestial meridian over a given terrestrial meridian. The zero
+meridian from which the sidereal day is reckoned is the one
+passing through the First point of Aries. The length of the
+sidereal day is $23$~h.\ $56$~m.\ $4.09$~s. The sidereal day is divided
+into twenty-four hours, each shorter than those of the civil or
+astronomical day; they are numbered from one to twenty-four.
+
+\Subgloss{Solar day}. \\
+\textit{Apparent solar day}, the interval between two successive passages
+of the sun's center over the meridian of a place; that is, from
+sun noon to the next sun noon; this varies in length from $23$~h.\ $59$~m.\ $38.8$~s.\
+to $24$~h.\ $0$~m.\ $30$~s. \\
+\textit{Mean solar day}, the average interval between successive passages
+of the sun's center over the meridian of a place; that is, the average
+of the lengths of all the solar days of the year; this average
+is $24$~h.\ as we commonly reckon civil or clock time.
+
+\Gloss{Declination} is the distance in degrees of a celestial body from the
+celestial equator. Declination in the celestial sphere corresponds
+to latitude on the earth.
+
+\Gloss{Eccentricity} (\u ek s\u en tr{\u \i}s$'$ {\u \i} ty), see \glossref{Ellipse}.
+
+\Gloss{Ecliptic} (\=e kl{\u \i}p$'$ t{\u \i}k), the path of the center of the sun in its apparent
+orbit in the celestial sphere. A great circle of the celestial sphere
+whose plane forms an angle of~$23°~27'$ with the plane of the equator.
+This inclination of the plane of the ecliptic to the plane of the
+equator is called the \emph{obliquity} of the ecliptic. The points~$90°$
+from the ecliptic are called the \emph{poles} of the ecliptic. Celestial
+latitude is measured from the ecliptic.
+\index{Obliquity of the ecliptic@Obliquity of the ecliptic\phantomsection\label{idx:ooe}}%
+
+\Gloss{Ellipse}, a plane figure bounded by a curved line, every point of which
+is at such distances from two points within called the foci (pronounced
+f\=o$'$ s\=\i; singular, focus) that the sum of the distances is
+constant.
+%% -----File: 315.png---Folio 316-------
+
+\Subgloss{Eccentricity} (\u{e}k s\u{e}n tris$'$ \u{\i} ty) is the fraction obtained by dividing
+the distance of a focus to the center of the major axis by one half
+the major axis.
+
+\Subgloss{Oblateness} or ellipticity is the deviation of an ellipse from a circle
+and is the fraction obtained by dividing the difference between
+the major and minor axes by the major axis.
+
+\Gloss{Ellipticity} (\u{e}l l\u{\i}p tis$'$ \u{\i} ty), see \glossref{Ellipse}.
+
+\Gloss{Equation of time} (\={e} kw\={a}$'$ shun), the difference between apparent
+solar time, or time as actually indicated by the sun, and the mean
+solar time, or the average time indicated by the sun. It is usually
+indicated by the minus sign when the apparent sun is faster than
+the mean sun and with the plus sign when the apparent time is
+slow. The apparent sun time combined with the equation of time
+gives the mean time; \textit{e.g.}, by the apparent sun it is $10$~h.\ $30$~m., the
+equation is $- 2$~m.\ (sun fast $2$~m.), combined we get $10$~h.\ $28$~m.,
+the mean sun time. See \glossref{Day}.
+
+\Gloss{Equator} (\={e} kw\={a}$'$ ter), when not otherwise qualified means terrestrial
+equator.
+
+\Subgloss{Celestial equator}, the great circle of the celestial sphere in the
+\index{Celestial equator}%
+plane of the earth's equator. Declination is measured from the
+celestial equator.
+
+\Subgloss{Terrestrial equator}, the great circle of the earth $90°$~from the
+poles or ends of the axis of rotation. Latitude is measured from
+the equator.
+
+\Gloss{Equinox}, one of the two points where the ecliptic intersects the celestial
+equator. Also the time when the sun is at this point.
+
+\Subgloss{Autumnal equinox}, the equinox which the sun reaches in autumn.
+Also the time when the sun is at that point, September~23.
+
+\Subgloss{Vernal equinox}, the equinox which the sun reaches in spring.
+This point is called the First point of Aries, since that sign of
+\index{Aries@Aries (\u{a}$'$r\u{\i}\;\={e}z), constellation!first point of}%
+the zodiac begins with this point, the sign extending eastward
+from it~$30°$. The celestial meridian (see \glossref[Colures]{Colure}) passing through %[**TN 'colure' in original]
+this point is the zero meridian of the celestial sphere, from which
+celestial longitude is reckoned. The vernal equinox is also the
+time when the sun is at this point, about March~21, the beginning
+of the astronomical year. See \glossref{Year}.
+
+\Gloss{Geocentric} (j\={e} \={o} s\u{e}n$'$ trik; from \textit{ge}, earth; \textit{centrum}, center),
+
+\Subgloss{Theory} of the solar system assumes the earth to be at the center
+of the solar system; see \glossref{Ptolemaic system}.
+
+\Subgloss{Latitude}, see \glossref{Latitude}.
+
+\Subgloss{Parallax}, see \glossref{Parallax}.
+
+\Gloss{Geodesy} (j\={e} \u{o}d$'$ \u{e} sy), a branch of mathematics or surveying which
+is applied to the determination, measuring, and mapping of lines or
+areas on the surface of the earth.
+%% -----File: 316.png---Folio 317-------
+
+\Gloss{Gravitation}, the attractive force by which all particles of matter tend
+\index{Gravitation}%
+to approach one another.
+
+\Gloss{Gravity}, the resultant of (\emph{a})~the earth's attraction for any portion of
+\index{Gravity@Gravity\phantomsection\label{idx:g}}%
+matter rotating with the earth and (\emph{b})~the centrifugal force due to
+its rotation. The latter force~(\emph{b}) is so small that it is usually
+ignored and we commonly speak of gravity as the earth's attraction
+for an object. Gravity is still more accurately defined in the
+Appendix.
+
+\Gloss{Heliocentric} (h\={e} l\u{\i} \={o} s\u{e}n$'$\DPtypo{}{\ }trik; from \emph{helios}, sun; \emph{centrum}, center).
+
+\Subgloss{Theory} of the solar system assumes the sun to be at the center of
+the solar system; also called the Copernican system (see \glossref{Copernican
+system}).
+
+\Subgloss{Parallax}, see \glossref{Parallax}.
+
+\Gloss{Horizon} (h\={o} r\={\i}$'$ zon), the great circle of the celestial sphere cut by a
+plane passing through the eye of the observer at right angles to
+the plumb line.
+
+\Subgloss{Dip of horizon}. If the eye is above the surface, the curvature of
+the earth makes it possible to see beyond the true horizon. The
+angle formed, because of the curvature of the earth, between the
+true horizon and the visible horizon is called the \emph{dip} of the
+horizon.
+
+\Subgloss{Visible horizon}, the place where the earth and sky seem to meet.
+At sea if the eye is near the surface of the water the true horizon
+and the visible horizon are the same, since water levels and forms
+a right angle to the plumb line.
+
+\Gloss{Hour-circles}, great circles of the celestial sphere extending from pole
+to pole, so called because they are usually drawn every $15°$ or one
+for each of the twenty-four hours of the day. While hour-circles
+correspond to meridians on the earth, celestial longitude (see
+\glossref{Longitude}) is not reckoned from them as they change with the
+rotation of the earth.
+
+\Gloss{Latitude}, when not otherwise qualified, geographical latitude is
+meant.
+
+\Subgloss{Astronomical latitude}, the distance in degrees between the
+plumb line at a given point on the earth and the plane of the
+equator.
+
+\Subgloss{Celestial latitude}, the distance in degrees between a celestial
+body and the ecliptic.
+
+\Subgloss{Geocentric latitude}, the angle formed by a line from a given
+point on the earth to the center of the earth (nearly the same
+as the plumb line) and the plane of the equator.
+
+\Subgloss{Geographical latitude}, the distance in degrees of a given point
+on the earth from the equator. Astronomical, geocentric, and
+%% -----File: 317.png---Folio 318-------
+geographical latitude are nearly the same (see discussion of \hyperref[page:282]{Latitude}
+in Appendix).
+
+\Gloss{Local time}, see \glossref{Time}.
+
+\Gloss{Longitude}.\\
+\Subgloss{Celestial longitude}, the distance in degrees of a celestial body
+\index{Celestial latitude!longitude}%
+from lines passing through the poles of the ecliptic (see \glossref{Ecliptic}),
+called ecliptic meridians; the zero meridian, from which celestial
+\index{Meridian}%
+\index{Meridian!celestial}%
+longitude is reckoned, is the one passing through the First point
+of Aries (see \glossref{Equinox}).
+
+\Subgloss{Terrestrial longitude}, the distance in degrees of a point on the
+earth from some meridian, called the prime meridian.
+
+\Gloss{Mass}, the amount of matter in a body, regardless of its volume or
+size.
+
+\Gloss{Mean solar time}, see \glossref{Time}.
+
+\Gloss{Meridian}.\\
+\sloppy
+\Subgloss{Celestial meridian}, a great circle of the celestial sphere passing
+through the celestial poles and the zenith of the observer. The
+celestial meridian passing through the zenith of a given place
+constantly changes with the rotation of the earth.
+
+\fussy
+\Subgloss{Terrestrial meridian}, an imaginary line on the earth passing
+from pole to pole. A meridian circle is a great circle passing
+through the poles.
+
+\Gloss{Month}.\\
+\Subgloss{Calendar month}, the time elapsing from a given day of one month
+to the same numbered day of the next month; \textit{e.g}., January~3
+to February~3. This is the civil or legal month.
+
+\Subgloss{Sidereal month}, the time it takes the moon to revolve about the
+\index{Sidereal, clock!month}%
+earth in relation to the stars; one exact revolution of the moon
+about the earth; it varies about three hours in length but averages
+$27.32166$~d.
+
+\Subgloss{Synodic month}, the time between two successive new moons or
+full moons. This is what is commonly meant by the lunar
+month, reckoned from new moon to new moon; its length varies
+about thirteen hours but averages $29.53059$~d. There are several
+other kinds of lunar months important in astronomical
+calculations.
+
+\Subgloss{Solar month}, the time occupied by the sun in passing through a
+sign of the zodiac; mean length, $30.4368$~d.
+
+\Gloss{Nadir} (n\={a}$'$ d\~{e}r), the point of the celestial sphere directly under the
+place on which one stands; the point $180°$~from the zenith.
+
+\Gloss{Neap tides}, see \hyperref[page:290]{Tides}.
+
+\Gloss{Nutation}, a small periodic elliptical motion of the earth's axis, due
+\index{Nutation of poles}%
+principally to the fact that the plane of the moon's orbit is not the
+same as the plane of the ecliptic, so that when the moon is on one
+%% -----File: 318.png---Folio 319-------
+side of the plane of the ecliptic there is a tilting tendency given the
+bulging equatorial region. The inclination of the earth's axis, or
+the obliquity of the ecliptic, is thus slightly changed through a
+period of $18.6$~years, varying each year from $0''$~to~$2''$\DPtypo{}{.} (See
+\hyperref[page:286a]{Motions of the Axis} in the Appendix.)
+
+\Gloss{Oblateness}, the same as ellipticity; see \glossref{Ellipse}.
+
+\Gloss{Oblate spheroid}, see \glossref{Spheroid}.
+
+\Gloss{Obliquity} (\u{o}b l\u{\i}k$'$ w\u{\i} ty), of the ecliptic, see \glossref{Ecliptic}.
+
+\Gloss{Opposition}, see \glossref{Syzygy}.
+
+\Gloss{Orbit}, the path described by a heavenly body in its revolution about
+another heavenly body.
+
+\Gloss{Parallax}, the apparent displacement, or difference of position, of an
+\index{Parallax}%
+object as seen from two different stations or points of view.
+
+\Subgloss{Annual or heliocentric parallax} of a star is the difference in
+the star's direction as seen from the earth and from the sun.
+The base of the triangle thus formed is based upon half the major
+axis of the earth's orbit.
+
+\Subgloss{Diurnal or geocentric parallax} of the sun, moon, or a planet is
+the difference in its direction as seen from the observers' station
+and the center of the earth. The base of the triangle thus formed
+is half the diameter of the equator.
+
+\Gloss{Perigee} (p\u{e}r$'$ \u{\i} je), the point in the orbit of the moon which is nearest
+\index{Perigee}%
+to the earth. The term is sometimes applied to the nearest point
+of a planet's orbit.
+
+\Gloss{Perihelion} (p\u{e}r \u{\i} h\={e}$'$ l\u{\i} \u{o}n), the point in a planet's orbit which is nearest
+\index{Perihelion}%
+to the sun.
+
+\Gloss{Poles}.\\
+\Subgloss{Celestial}, the two points of the celestial sphere which coincide
+\index{Pole, celestial}%
+with the earth's axis produced, and about which the celestial
+sphere appears to rotate.
+
+\Subgloss{Of the ecliptic}, the two points of the celestial sphere which are $90°$ from
+the ecliptic.
+
+\Subgloss{Terrestrial}, the ends of the earth's axis.
+
+\Gloss{Ptolemaic system} (t\u{o}l \={e} m\={a}$'$ \u{\i}k), the theory of the solar system advanced
+\index{Ptolemaic system}%
+by Claudius Ptolemy (100--170~\AD)\ that the earth is the center of
+the universe, the heavenly bodies daily circling around it at different
+rates. Called also the geocentric theory (see \glossref{Geocentric}).
+
+\Gloss{Radius} (plural, radii, r\={a}$'$ d\u{\i} \={\i}), half of a diameter.
+
+\Gloss{Radius Vector}, a line from the focus of an ellipse to a point in the
+\index{Radius vector}%
+boundary line. Thus a line from the sun to any planet is a radius
+vector of the planet's orbit.
+
+\Gloss{Refraction of light}, in general, the change in direction of a ray of
+\index{Refraction of light}%
+light when it enters obliquely a medium of different density. As
+%% -----File: 319.png---Folio 320-------
+used in astronomy and in this work, refraction is the change in
+direction of a ray of light from a celestial body as it enters the
+atmosphere and passes to the eye of the observer. The effect is to
+cause it to seem higher than it really is, the amount varying with the
+altitude, being zero at the zenith and about $36'$ at the horizon.
+
+\Gloss{Revolution}, the motion of a planet in its orbit about the sun, or of a
+satellite about its planet.
+
+\Gloss{Rotation}\DPtypo{}{,} the motion of a body on its axis.
+\index{Rotation of earth@Rotation of earth\phantomsection\label{idx:r}}%
+
+\Gloss{Satellite}, a moon.
+
+\Gloss{Sidereal day}, see \glossref{Day}.
+
+\Gloss{Sidereal year}, see \glossref{Year}.
+
+\Gloss{Sidereal month}, see \glossref{Month}.
+
+\Gloss{Sidereal time}, see \glossref{Time}.
+
+\Gloss{Signs of the zodiac}, its division of $30°$ each, beginning with the vernal
+\index{Signs of zodiac}%
+equinox or First point of Aries.
+
+\Gloss{Solar times}, see \glossref{Time}.
+
+\Gloss{Solstices} (s\u{o}l$'$ st\u{\i}s es; \emph{sol}, sun; \emph{stare}, to stand), the points in the
+\index{Solstices}%
+ecliptic farthest from the celestial equator, also the dates when the
+sun is at these points; June~21, the summer solstice; December~22,
+the winter solstice.
+
+\Gloss{Spheroid} (sf\={e}$'$ roid), a body nearly spherical in form, usually referring
+\index{Spheroid}%
+to the mathematical form produced by rotating an ellipse about
+one of its axes; called also an ellipsoid or spheroid of revolution
+(in this book, a spheroid of rotation).
+
+\Subgloss{Oblate spheroid}, a mathematical solid produced by rotating an
+ellipse on its minor axis (see \glossref{Ellipse}).
+
+\Subgloss{Prolate spheroid}, a mathematical solid produced by rotating an
+ellipse on its major axis (see \glossref{Ellipse}).
+
+\Gloss{Syzygy} (s\u{\i}z$'$ \u{\i} jy; plural, syzygies), the point of the orbit of the moon
+\index{Syzygy}%
+(planet or comet) nearest to the earth or farthest from it. When
+in the syzygy nearest the earth, the moon (planet or comet) is said
+to be in conjunction; when in the syzygy farthest from the earth it
+\index{Conjunction}%
+is said to be in opposition.
+
+\Gloss{Time}.\\
+\Subgloss{Apparent solar time}, the time according to the actual position
+of the sun, so that twelve o'clock is the moment when the
+sun's center passes the meridian of the place (see \glossref[Day, Solar day]{Day, apparent
+solar}).
+
+\Subgloss{Astronomical time}, the mean solar time reckoned by hours numbered
+up to twenty-four, beginning with mean solar noon (see
+\glossref[Day, Astronomical day]{Day, astronomical}).
+
+\Subgloss{Civil time}, legally accepted time; usually the same as astronomical
+time except that it is reckoned from midnight. It is commonly
+numbered in two series of twelve hours each day, from midnight
+%% -----File: 320.png---Folio 321-------
+and from noon, and is based upon a meridian prescribed by law
+or accepted as legal (see \glossref[Day, Civil day]{Day, civil}).
+
+\Subgloss{Equation of time}, see \glossref{Equation of time}.
+
+\Subgloss{Sidereal time}, the time as determined from the apparent rotation
+of the celestial sphere and reckoned from the passage of the
+vernal equinox over a given place. It is reckoned in sidereal
+days (see \glossref[Day, Sidereal day]{Day, sidereal}).
+
+\Subgloss{Solar time} is either apparent solar time or mean solar time,
+reckoned from the mean or average position of the sun (see
+\glossref[Day, Solar day]{Day, solar day}).
+
+\Subgloss{Standard time}, the civil time that is adopted, either by law or
+usage, in any given region; thus practically all of the people of
+the United States use time which is five, six, seven, or eight hours
+earlier than mean Greenwich time, being based upon the mean
+solar time of~$75°$, $90°$, $105°$, or~$120°$ west of Greenwich.
+
+\Gloss{Tropical year}, see \glossref{Year}.
+
+\Gloss{Tropics}.\index{Tropics}\\
+\Subgloss{Astronomical}, the two small circles of the celestial sphere parallel
+\index{Celestial latitude!tropics}%
+to the celestial equator and $23°~27'$ from it, marking the northward
+and southward limits of the sun's center in its annual
+(apparent) journey in the ecliptic; the northern one is called the
+tropic of Cancer and the southern one the tropic of Capricorn,
+from the signs of the zodiac in which the sun is when it reaches
+the tropics.
+
+\Subgloss{Geographical}, the two parallels corresponding to the astronomical
+tropics, and called by the same names.
+
+\Gloss{Vernal equinox}, see \glossref[Equinox, Vernal equinox]{Equinox, vernal}.
+
+\Gloss{Year}.\index{Year}\\
+\Subgloss{Anomalistic year} (a nom a l\u{\i}s$'$ tik), the time of the earth's revolution
+from perihelion to perihelion again; length $365$~d., $6$~h.,
+$13$~m., $48$~s.
+
+\Subgloss{Civil year}, the year adopted by law, reckoned by all Christian
+countries to begin January~1st. The civil year adopted by
+Protestants and Roman Catholics is almost exactly the true
+length of the tropical year, $365.2422$~d., and that adopted by Greek
+Catholics is $365.25$~d. The civil year of non-Christian countries
+varies as to time of beginning and length, thus the Turkish civil
+year has $354$~d.
+
+\Subgloss{Lunar year}, the period of twelve lunar synodical months (twelve
+new moons); length, $354$~d.
+
+\Subgloss{Sidereal year}, the time of the earth's revolution around the sun
+\index{Sidereal, clock!year}%
+in relation to a star; one exact revolution about the sun; length,
+$365.2564$~d.
+%% -----File: 321.png---Folio 322-------
+
+\Subgloss{Tropical year}, the period occupied by the sun in passing from one
+tropic or one equinox to the same again, having a mean length of
+$365$~d.\ $5$~h.\ $48$~m.\ $45.51$~s.\ or $365.2422$~d. A tropical year is shorter
+than a sidereal year because of the precession of the equinoxes.
+
+\Gloss{Zenith} (z\={e}$'$ n\u{\i}th), the point of the celestial sphere directly overhead;
+$180°$ from the nadir.
+
+\Gloss{Zodiac} (z\={o}$'$ d\u{\i} ak), an imaginary belt of the celestial sphere extending
+\index{Zodiac}%
+about eight degrees on each side of the ecliptic. It is divided into
+twelve equal parts ($30°$ each) called signs, each sign being somewhat
+to the west of a constellation of the same name. The ecliptic being
+the central line of the zodiac, the sun is always in the center of it,
+apparently traveling eastward through it, about a month in each
+sign. The moon being only about $5°$ from the ecliptic is always in
+the zodiac, traveling eastward through its signs about $13°$ a day.
+\end{SmallText}
+\index{Glossary|)}%
+%% -----File: 322.png---Folio 323-------
+
+\printindex
+
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+
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
+%                                                                         %
+% End of Project Gutenberg's Mathematical Geography, by Willis E. Johnson %
+%                                                                         %
+% *** END OF THIS PROJECT GUTENBERG EBOOK MATHEMATICAL GEOGRAPHY ***      %
+%                                                                         %
+% ***** This file should be named 31344-t.tex or 31344-t.zip *****        %
+% This and all associated files of various formats will be found in:      %
+%         http://www.gutenberg.org/3/1/3/4/31344/                         %
+%                                                                         %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
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diff --git a/LICENSE.txt b/LICENSE.txt
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+This eBook, including all associated images, markup, improvements,
+metadata, and any other content or labor, has been confirmed to be
+in the PUBLIC DOMAIN IN THE UNITED STATES.
+
+Procedures for determining public domain status are described in
+the "Copyright How-To" at https://www.gutenberg.org.
+
+No investigation has been made concerning possible copyrights in
+jurisdictions other than the United States. Anyone seeking to utilize
+this eBook outside of the United States should confirm copyright
+status under the laws that apply to them.
diff --git a/README.md b/README.md
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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #31344 (https://www.gutenberg.org/ebooks/31344)