THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES 2i 'K AN ANGULAR TOUR OF THE WORLD OR THE CURIOSITIES OF Latitude and Longitude A BOOK FOR TEACHERS BY EDWARD R. E. COWELL Member of the Chicago Academy of Sciences PUBLISHED BY THOMAS CHARLES CO CHICAGO COPYRIGHTED 1894 BY E. R. E. COWELL Engineering $ Mathematical Sciences & 3 / "*"> C33 TO THE TEACHER. ^ I A HE object of this little work is to make the sub- A. ject clear, so that it may be intelligently pre- sented to your classes. A clear understanding of the earth's motions and the relation of the earth to the other heavenly bodies is necessary in teaching mathe- matical geography. Facts belong to the physical world and truths to the moral and spiritual world. A teacher who has the best and highest development of the scholar in view will combine facts and truths in teaching. L/et me explain. ' ' The world rotates on its axis once in twenty-four hours." That is a physical fact. ' ' We must always have a cause adequate to produce an effect." That is a moral truth. "The earth's axis is inclined sixty-six and one-half degrees to the sun's path." That is a fact. " The wisdom of this arrangement is evident. ' ' That is a truth. I believe in the concrete idea in teaching. In order to present a fact so that it may be readily seen, it should be given in a concrete form. I believe the 4 TO THE TEACHER. truth can be arrived at without wasting the mental powers in mere mathematical gymnastics. We must understand the principles involved in a problem, get a bird's-eye view of it, get down to the roots of it and out to the twigs of it grasp it. It is of no use to work out a problem by rule unless the student understands the reason for the rule. I believe in fulness of explanation and in variety of illustration, and in arriving at knowledge by inductive reasoning; and let us forever bear in mind this truth, that " we must always have a cause ade- quate to produce an effect. ' ' STATE NORMAL SCHOOL, ItOS AfiCEIlES, GRU. CONTENTS. PAGK. Accurate Clocks 45 Altitude , .,... 25 Angle of Night Shadow 28 Angular Distances 41 Angular Tour of the World. ., 10 Antipodal Meridian 20-5(5 Antipodes 20 Apparent Sun Time 64 Apparition ... 18 Astronomical Geography & A Wonderful Clock 45 Axis of Rotation 14 Belts (Zone) 15 Beginning of a Day 51 Celestial Pole 36 Center of Gravity 34 Changes in Appearance of the Heavens 37 Circumnavigating the Globe 60 Climate 22 Clocks Agree 21 Clocks Differ 21 Clock The Earth 42-44 Co-Latitude 25 Co-Incident Phenomena :'> - J Compensation Balance 30 Concentric Zone Boundaries.... .. 14 CONTENTS. Concrete Teaching 3 Cone of Rotation 43 Date Line 53 Dawn and Twilight 36 Day 42 Declination 25 Direction of Rotation and Revolution. ... 13 Diurnal Rotation 34 East and West 35 Equator 39 Equinoxes 12 Facts and Truths 3 Gain or Loss of Time; 57 Gravity 39 Greenland 17 Greenwich Mean Time 63 Gyroscope 43 Heat 31 Inclination of Axis 12 International Date Line 53 Land of the Midnight Sun 17 Latitude and the Sun's Meridian Altitude 23 Defined 33 How to Obtain 26 Of Cities 76 Law of Compensation 30 London 51 Longest Day 18 Longitude Defined 41 How Obtained at Sea 63 Of Cities.... 76 CONTENTS. 7 Longitude Proof of Earth's Rotundity '. 10 'Longitudinal Quadrants of the Earth 54 Magnetic Pole 34 Making of a Zone 13 Mathematical Geography 40 Mean Sun Titne 65 Meridian 180 53 Meridians 41 Midnight 56 Motions of a Steam Engine 11 Mountain-top Temperatures 22 Night 23 Night Shadow 19-30 Noon 22 North Polar Star 33 Norway 17 Occupation 18 Parallels 15 Parallelism of the Axis 12 Pendulum , 39 Phenomena of Day and Night 29 Place of Sun's Rising and Setting 28 Polaris 43 Poles 36 Precession 43 Proofs of Earth's Rotundity 10 Revolution 13 Rising and Setting Stars 39 Rotation 13 Sidereal Time 44 Sidereal Clock.... .. 44 8 CONTENTS. Sea Level Temperatures . 22 Seasons. 1* Sextant 64 Shape of the Earth 32-72 Standard Time 67 Succession of Days 49 Sun's Declination 19 Sun's Meridian Altitude 23 Sun-DialTime 23 Telegrams from Distant Points ... 10 The Midnight Sun 17 Time .". 42 Value of a Degree Latitude 72 Longitude 70 Watches ., 45 Where does the Day Begin? .'., 51 Width of the Zones 15 Yesterday and Today 55 Zones How Made t 18 ILLUSTRATIONS. 1. The Earth 6ti 2. Rotation of the Northern Heavens 35 3. Twilight Projection 37 4. The Hour Angle 47 5. Longitudinal Quadrants 54 6. Direction of Rotation, etc 13 7. Sunrise and Sunset Points .'. 28 8. Sun's Meridian Altitude 24 9. Angle of the Sun's Rays ... 25 AN ANGULAR TOUR OF THE WORLD; The Curiosities of Latitude and Longitude LATITUDE BREADTH. LONGITUDE... ...LENGTH. HT^HERE is no latitude at the equator and no longi- -* tude at London (or Greenwich), these being the initial or starting-points from which latitude and longitude are measured. We may define the position of any place on the earth very accurately by giving its latitude and longitude. The City Hall. New York, for instance, is 40 42' 44" north latitude and 74 o' 24" west longitude. Yale College, New Haven, is 41 18' 28" north latitude and 72 55' 45" west longitude. The State House, Boston, is 42 21' 28" north latitude and 71 3' 50" west longitude. The Auditorium, Chicago, 1541 53' north latitude and 87 37' west longitude. 10 CURIOSITIES OF LATITUDE AND LONGITUDE. One of the simplest and most self-evident proofs of the rotundity or sphericity of our earth is in con- nection with longitude. If the earth were flat, the sun at rising would appear at the same instant to every one west of it, say at Yokohama, Athens, London, New York, Chicago and San Francisco. Now the fact is, that when the sun is rising in Australia it is setting in England, and it is on the meridian of (or noon at) Chicago, all at the same instant. If we were to send a telegram from Melbourne in the early morning (sunrise) of Sunday, July i, it would reach Chicago Saturday noon, June 30, the previous day. L/et me take you on a personally conducted tour around the world. We will travel around the earth obliquely, at an angle of 66^ degrees to the equator, crossing every meridian and every parallel as far as the two circles. This might be called "An Angular Tour of the World. ' ' We shall witness some very interesting phenomena. The curiosities of latitude and longitude are simply those phenomena we experience by change of posi- tion. If a person living on the equator and used to seeing the sun rise and set at six o'clock every day CURIOSITIES OF LATITUDE AND LONGITUDE. II throughout the year were to go to latitude 66^3 north (on June 21), he would see the sun at midnight. This to him would be a curiosity; it is a phenomenon of latitude. Suppose a person living, say, at San Francisco, saw the sun set at 5 p. M., and could travel rapidly around the earth on that parallel, the sun would set at 5 P. M. for him at Pekin, China, and every other place on the parallel, provided he had adjusted his watch to the local time of the place. That is a phe- nomenon of longitude and latitude. Now, suppose a person lived at the Arctic Circle, on, say, meridian 75 west longitude, another at the Equator, and another at the Antarctic Circle, on the same meridian ; all three would have exactly the same time their clocks would all agree. L/et me give you an analysis of the strange and complex phenomena which I call the " Curiosities of Latitude and Longitude.'' Three causes combine to produce these results: First The axial rotation of the earth (diurnal). Second The inclination of the axis of rotation. Third The earth's yearly revolution around the sun. Did you ever watch the motions of the separate parts of a steam engine valve, piston and valve- 12 CURIOSITIES OF LATITUDE AND LONGITUDE. gear? The motion of each is simple; each part works in harmony with, and in relation to, the other parts; the result looks complex. Just so in regard to the several motions of the earth. Note, now, the effect of the inclination of the earth's axis, 66^ degrees, to the plane of its orbit, or 23^* to a perpendicular to the plane of the earth's orbit. The equator is inclined 23 ^ degrees to the apparent path of the sun, or the ecliptic. The par- 'allelism of the axis to itself in the yearly journey is strictly maintained. The rotation of the seasons spring, summer, autumn and winter is one result of this inclina- tion, and the belting of the earth with zones is another. In the rotation of seasons it will be observed that in both spring and fall (or autumn) seasons days and nights are equal\ all over the globe. The night shadow is then perpendicular, whereas in the summer and winter seasons the greatest possible variation takes place in the length of day and night and in the ' position of the night shadow. The plane of the ecliptic, or sun's path, is the the plane of the earth's orbit. This crosses the equator at an angle of * 23-28 / . f Equinox Vernal March 21, and Autumnal Sept. 21 . CURIOSITIE ES OF LA TITUDE AND LONGITUDE. 13 The inclination of the axis to the plane of the earth's orbit is 66^ or 23^ to a perpendicular to the plane. The following diagram shows the direc- tion of revolution and rotation, also the fixed axis of rotation : ZONES HOW MADE. What makes a zone ? Did you ever watch a wood-turner at his lathe? Let him touch any point on a revolving cylinder or globe with the point of his instrument and instantly that point becomes a circle by the rotation of the cylinder on its axis, and the fixed position of the axis. Now, if the rays of the sun touch a point north or south, say, for instance, the Arctic Circle, the diurnal 14 CURIOSITIES OF LATITUDE AND LONGITUDE. rotation of our globe makes that point a circle. As compared to the (apparent) moving sun in his yearly path, the earth's rotation is rapid. Here is another point, say 23 28' nortri of the equator, over which the sun is vertical; the daily rotation makes this a circle again, and that circle is the Tropic of Cancer. Now, if the sun is vertical (in the zenith) at any point on the Tropic of Cancer, he is vertical at every point on that parallel; for the time being the "sun stands still," while the earth keeps on rotating, and, as the Tropic of Cancer is the limit of the sun's path north of the equator, of course it is the limit of verticality, hence marks the northern boundary of the Torrid Zone. Observe that these circles are all concentric, paral- lel to each other, because of the fixed position of the axis of rotation. No matter how many points may be touched by the wood-turner in his work, these all become concentric circles, because of the fixed axis of rotation. This explains why the same series of phenomena takes place at all points "on a parallel. It is due to the stationary sun (for the time) and the rapidly rotating earth. Were the rotation slower (say a month), there would be quite an appreciable difference in the phenomena at different places on, a parallel. CURIOSITIES OF LATITUDE AND LONGITUDE. 15 A parallel is a circle running around the earth, east and west, smaller than the equator, all points of which are equally distant from the equator. It is a circle parallel to the equator. From what has been said, it will readily be seen that the zones are made practically by the sun, in combination with the rotating earth and the fixed axis of rotation. There are five zones, as there are five races of men, and five great continents and five large oceans. As the Arctic and Antarctic, or Frigid Zones, bound the limit of the sun's rays at the winter solstice, so the Torrid Zone bounds the limit of his verticality at the summer solstice. The width of the zones, therefore, corresponds with the apparent movements of the sun, the inclina- tion of the earth's axis to a perpendicular to the ecliptic, or sun's path, being 23 degrees and 28 min- utes. So we have the widths of the zones as follows: Arctic 23 28' North Temperate 43 04' Torrid 46 56', or twice 23 28' South Temperate 43 04' Antarctic 23 28' 1 80 oo' 1 6 CURIOSITIES OF LATITUDE AND LONGITUDE. It will be observed by this arrangement that the greatest possible width is given to that portion of the earth best adapted to man and his needs, /. e. , best adapted for his occupation, namely, the two temperate s zones a belt 86 8' wide, or nearly half of the total of 1 80 degrees. The proportion is very much larger than this when we consider the area of this belt. The value of a degree of longitude rapidly diminishes as we approach the poles so that the area of the Frigid Zones is much smaller in proportion to their width than the Temper- ate or Torrid Zones. If the earth's equator were not inclined 23 28' to the ecliptic or sun's path, that is, if the sun moved in the equator instead of the ecliptic, eternal cold and darkness would prevail at some places, and eter- nal heat and light at others. It is the inclination of the axis plus the rotation of that axis, together with the yearly path of the sun, that produces the compen- satory balance of the alternate and equal distribution of heat and cold, light and darkness for the whole earth. I believe the earth is adapted to man and his needs. The wisdom of the inclination, rotation and revolution is evident; nothing in Nature is accidental. When the " Heavens and the Earth were finished" they were finished in the sense of perfection and completeness. CURIOSITIES OF LATITUDE AND LONGITUDE. IJ Suppose the axis of the earth were inclined 56^ instead of 66 y> to the plane of its orbit. New Orleans would then be in the Torrid Zone, and Edinburgh would be in the Arctic Zone. Suppose the inclination were 76^, Greenland would then be in the North Temperate Zone, and Bombay, which is now in the Torrid, would be in the North Temperate Zone. Now suppose the angle of the ecliptic to the equa- tor was 30 instead of 23 28'. The width of the zones would be as follows: Torrid, 60; the two Frigid Zones, 30 each; the Temperate Zones, 30 each, and England would then be in the Arctic Zone and in winter would have no sun at all. Travelers call Norway the land of the midnight sun, but this is true of any land beyond the 665^ par- allel of latitude. On the 2ist of June the sun does not set at all from the Arctic Circle to the North Pole, and on the 2ist of December he does not set from the Antarctic Circle to the South Pole. I suppose that the reason why Norway is especially designated as the " Land of the Midnight Sun" is, that Norway is accessible to travelers and is in the regular route of excursion travel, but Greenland, being within the Arctic regions, is getting to be quite as accessible, and is just as much the 1 8 CURIOSITIES OF LATITUDE AND LONGITUDE. "Land of the Midnight Sun" as are Sweden and Norway. The two polar circles are the farthest limits north and south where a day can consist of just twenty-four hours (on June 21 and December 21) with no night. Less than these two points the day can never be twenty-four hours long. Beyond these circles the day may be anywhere from 24 hours to six months long. The two circles, therefore, mark the maximum twenty- four-hour day, or a period of twenty-four hours when the sun is above the horizon. Let me explain this phenomenon of latitude. The greatest length of the day for all latitudes north of the equator, occurs on June 21. The night shadow then extends in a diagonal line from one edge of the Arctic Circle, to the opposite edge of the Ant- arctic Circle, thus uncovering (or exposing to the sun's rays) the northern Frigid Zone, and completely cov- ering the southern. The cut on page 28 shows the position of the night shadow for June 21. This diagonal line cuts the equator at an angle of 66 ]/ 2 and is 23}^ from the meridian or perpendicular. At the equator the day would be just 12 hours long, the sun would rise at 6 and set at 6; at the 55th parallel the day would be 18 hours long; sun rises at 3 and sets at 9; at the 66 ^< parallel, the day is 24 CURIOSITIES OF LATITUDE AND LONGITUDE. 19 hours long and the sun neither rises nor sets, but at noon he is 47 high and at midnight on the horizon, and due north. At the 55th parallel south, the day would be now, only six hours long; sun rises at 9 and sets at 3. At the 66^4 parallel south, there would be no day; sun does not rise at all. The night is 24 hours long. Now as the line of the night shadow forms an angle with the meridian, equal to the angle of the sun with the equator, the greater the angle the greater will be the difference in lengths of the day and night at vari- ous latitudes, and, as the greatest angle is 23^ and the greatest difference 12 hours (at the Polar Circles) each degree would represent about 30 minutes. If, therefore, the sun were 4 north declination, there would be a difference of about two hours between the length of the day at the equator and at the Polar Cir- cles; that is, the day would be two hours in excess of 12 at the Arctic Circle, and two hours less than 12 at the Antarctic Circle. Four degrees south declination would reverse this. Of course, at the very poles themselves a very slight angle would produce a day of 24 hours long and as the angle increased, the region of perpetual sunshine would increase in the one Polar Zone and correspondingly decrease in the other. People who live on opposite sides of the earth, or 20 CURIOSITIES OF LATITUDE AND LONGITUDE. the Antipodes, have opposite latitudes, longitudes, days, nights and seasons. The Antipodal Meridian is the one removed 12 hours from your own your Antipodes, the point on that meridian in opposite lat- itude to your own. People living in the same longitude have the same NOON, and, in fact, all hours of the day alike. Their clocks will all agree, but the times of their sunrise and sunset depends on the declination of the sun and their latitude. People living on the same parallel of latitude have sunrise and sunset at the same hours rel- atively, but their clocks will all differ. The relative time of sunrise, for instance, on the 42d parallel, would be the same to all places on that parallel, although in absolute time they might be hours apart. Sunrise would be at about the same hour to people living in Boston, Albany, Buffalo, Chicago, Omaha> Pekin, Constantinople, Rome and Madrid, although these places are widely apart in absolute time. CURIOSITIES OF LATITUDE AND LONGITUDE. 21 CLOCKS ALL AGREE. CLOCKS ALL DIFFER. \\ ^ 'd ~ j i. A Parallel of Latitude. Longitude is measured on this line east and west. On this line the lengths of the day, time of sunrise and sunset all differ (ex- cept twice a year). The time at any point on this line agrees with the time at any other point If it is XII (noon) at 66}^ north, it is XII (noon) at 66^ south. On this line the lengths of the day and time of sun- rise arid sunset are the same at all points, On this line time differs at every point. No two points have the same time, but the relative time of sunrise and sunset would be the same at every point. I have stated that all places in the same latitude have the same seasons, length of day and night, hours of sunrise and sunset, etc., but they may not have the same climatic conditions, on account of 22 CURIOSITIES OF LATITUDE AND LONGITUDE. various physical causes, mountain ranges, ocean cur- rents, etc. For instance, England and Labrador are nearly in the same latitude, but the equatorial cur- rents that reach England make a mild and soft cli- mate, while Labrador is cold and sterile. Sea level temperatures are quite different from those of mountain tops. A mountain 15,000 feet high, even at the equator, would have a temperature about equal to that of the sea level at the Arctic Circle. There is a great difference in the United States in the climate of the Pacific slope and that of the inte- rior of the same latitude. So that, although the zones are bounded by mathe- matically concentric circles, made practically by the sun's path, the isothermal or heat lines curve accord- ing to the modifying conditions mentioned. NOON. When the sun is on the meridian of a place (i.e., when it has attained its highest altitude), it is NOON at that meridian, and at that meridian only. Only one meridian can have noon at the same instant; all others are either in A. M. or p. M. Bear in mind that a meridian runs from pole to pole, or half around the CURIOSITIES OF LATITUDE AND LONGITUDE. 23 earth; consequently the antipodal or opposite meridian must be a midnight meridian. Now, noon is a point exactly half way (sun-dial time) between sunrise and sunset, and midnight a point exactly opposite noon. Of course, in average or mean sun time the fore- noon may be longer or shorter than the afternoon. The earth turns uniformly on its axis. Noon is marching around the world with measured tread. One meridian after another is brought opposite the sun. The period of the rotation is twenty-four hours, not a second more or less. LATITUDE AND THE SUN'S MERIDIAN ALTITUDE. Latitude will, of course, affect the sun's meridian altitude. Note the height of the sun in the diagram on page 24. It is arranged for March and September; the sun is vertical on the equator; the angle diminishes from this (90) to zero at either pole. At the two tropics the altitude is 66>< and at the two circles 23^ at noon. The angle for June, the highest limit north, when the sun is vertical on the Tropic of Cancer, will 24 CURIOSITIES OF LATITUDE AND LONGITUDE. extend 23^ beyond the North Pole, so that at the North Pole the meridian altitude would be 23^. The angle for December would just touch the Arctic SI LATITUDE NORTH. > 66(4 23', : w j: | ! ! i! L rl % i LATITUDE SOUTH. P&Vi 90 > ^ \ / \ / \ , \ / : \ / / S \ 2 ^ V, X 2 r \ v s. ff v ^ 53 '] t . ^ \ \ J X s, ) y ^ . J s, s i \ / N. 2 ' S, ! ! OS 1 I 1 September 21. Circle; consequently the sun would not appear above the horizon from that point to the North Pole. March 21 and September 21 the angle would just CURIOSITIES OF LATITUDE AND LONGITUDE. 25 touch either pole. The sun would, therefore, be on the horizon at midday at those points. The sun's declination- is its distance north or south of the equator. To find the sun's meridian altitude, add its declina- tion for that day to the . co-latitude of the place (the co-latitude of a place is its latitude deducted from 90); that is, if the latitude and declination are both of the same name; but if one is north and the other south, it must be deducted instead of added. For instance, we have stated that the sun's meridian alti- tude for the Arctic Circle (66>< north) for the 2ist of June would be 47. ' The declination of the sun for this da}- is 23^2 north, and the co-latitude of 66^ would be 23><; this added to the declination equals 47, which is the meridian altitude of the sun for that date. When the sun is at a meridian alti- tude of 45, his rays would fall perpendicularly on the side of a hill facing the south at an angle of 45. 26 CURIOSITIES OF LATITUDE A;ND LONGITUDE. Latitude does not affect TIME, except, as we have stated, the times of sunrise and sunset. I have explained how the meridian altitude of the sun can be found from the latitude and the sun's declination. Here is a simple rule for finding latitude: LATITUDE HOW OBTAINED. From 90 (corrected 89 48') deduct the sun's ob- served altitude, which will equal the zenith distance (make Z. D. north if sun bears south, or south if the sun bears north). Add to zenith distance the sun's declination, if both same name, and the sum will be the latitude. If one is north and the other is south, deduct; the latitude will then be the same name as the greater number. June 2ist the sun's meridian alti- tude at the Arctic Circle is 47; 90 47 43 (its Z. D.) added to 23^ (Sun's N. Dec.) = 66}^, or the latitude. On the 2ist of December the conditions we have stated for June in regard to meridian altitude north "and south would be reversed. The sun is vertical on the earth only at places between the tropics. The mer- idian altitude of the sun is therefore never 90 or vertical (in the zenith) at any place outside of the Torrid Zone. (Never vertical in the United States. ) CURIOSITIES OF LATITUDE AND LONGITUDE. 27 The sun is vertical on the equator only on the 2ist of March and 2ist of September; on the Tropic of Cancer on the 2ist of June and on the Tropic of Capricorn on the 2ist of December. On March 21 and September 21 the sun's meridian altitude equals the co-latitude of a place; for instance, the latitude of Chicago is 42 N. ; the co-latitude is 90 42= 48, the meridian altitude at that date. 90 minus the altitude of a heavenly body equals its zenith distance. 90 minus the latitude of a place, equals its co-lati- tude or complement. 90 minus the sun's declination equals its polar distance. > Latitude affects the apparent place of the rising and setting of the sun. In March and September, or at the two equinoxes, the sun rises due east and sets due west, but as he advances northward or southward his rising and setting points advance northward or southward. On the 2ist of June the sun rises 23^ degrees north of east, but for all places north of the Tropic of Cancer the sun will be south of the observer at noon. If the sun is due south at noon, he will be due north at midnight. In summer, in the higher latitudes, the sun rises 28 CURIOSITIES OF LATITUDE AND LONGITUDE. and sets farther and farther from the east and west points until it is due north. MIDNIGHT DIAGRAM SHOWING THE POINTS OF SUN'S RISING AND SETTING JUNE 21. CURIOSITIES OF LATITUDE AND LONGITUDE. 29 'THE PHENOMENA OF DAY AND NIGHT. The phenomena of day and night are phenomena belonging to both latitude and longitude. On the 2ist of June, two-thirds of the night shadow on the earth is below the equator and one-third of the night shadow is above it. On the 2ist of December these conditions are reversed. The shadow of night on the earth and the illuminated portions are always exactly half and half (the shadow, however, includes dawn and twilight), but the position of the shadow is depen- dent upon the time of year and latitude. The shadow is always pivoted at the equator, consequently day and night at this place are always equal. Twice a year, March and September, the shadow is perpen- dicular to the equator; that is, the line of the shadow is co-incident with the meridian line to which it may be pivoted. The shadow is always at a right angle to the sun, so that if the sun is north the shadow is south; and if the sun is south the shadow is north. Whatever angle the sun makes with the equator, a corresponding angle of the night shadow is made with the meridian. On the 2ist of June and the 2ist of December the line of the shadow cuts the Arctic Circle on the one hand and the Antarctic Circle on the other, and the angle is 23^. At all other times 30 CURIOSITIES OF LATITUDE AND LONGITUDE. of the year the shadow encroaches upon the polar regions until the shadow becomes perpendicular, as stated, March 21 and September 21; so that every portion of the earth has an equal amount of shadow and sunshine at some time of the year from pole to pole. There is a wonderful compensation balance in the earth. There is not a spot on its surface that does not enjoy, at some time, its equal share of the oppo- sites of night and day, or sunshine and shadow, heat and cold, summer and winter, etc. This is especially true of sunshine. All parts of the earth have an equal amount of sunshine in the yearly distribution of sunshine. Take, for instance, the latitude of New York at the summer solstice, June 21; New York has fifteen hours of sunshine and nine hours of shadow. The opposite latitude south, say a place in New Zealand, has nine hours of sunshine and fifteen hours of shadow. Now, take December 21; the winter solstice: New York has nine hours of sunshine and fifteen of shadow, while New Zealand has fifteen of sunshine and nine of shadow. The law ol compensation is exemplified in the distribution of heat and cold. The greatest heat is of course in the Torrid Zone, where the rays of the CURIOSITIES OF LATITUDE AND LONGITUDE. 31 sun fall perpendicularly, and the greatest cold is in the Frigid Zones, where the rays of the sun fall obliquely upon the earth. But here comes in the wonderful compensator}- balance of unequal day and night, thus in a measure equalizing the heat. Heat is cumulative. If more heat is received by day than can be radiated away at night, it grows and accumulates. Thus, in the Northern Hemisphere, though the longest day is reached in June, the hottest days are in July and August. At the equator, or in the hot-belt, days and nights are about equal in length, so that when the sun sets at b o'clock the earth begins to cool and the heat gathered during the day is radiated away during the twelve hours of the night. Travelers who go to southern states in summer re- mark upon the coolness of the nights, notwithstand- ing the hot days. Thus, this law of compensation (owing to the diur- nal rotation and the inclination of the axis of rota- tion), makes all parts of our earth habitable and adapted to the needs of man. Day and night must always together equal 24 hours. If the day exceeds 12 hours, the night is less than 12 hours in exact proportion. Day and night 32 CURIOSITIES OF LATITUDE AND LONGITUDE. are differential for all latitudes and 24 hours is trie total. Knowing the length of either the day or night (by day and night I mean the time between the rising and setting, or the setting and the rising sun) it is easy to get the hours of sunrise or sunset; or, know- ing the hours of sunrise and sunset, it is easy to get the length of the day or night. Double the hour of sunrise for the length of the night, And double the hour of sunset for the length of the day; Or take half the length of the day for the hour of sunset, And half the length of the night for the hour of sunrise. CO-INCIDENT PHENOMENA. The same latitude phenomena occurs in the co-iu- cident months as follows: May and July, April and August, February and October, January and November. In shape the earth is an oblate spheroid, i. e., a sphere slightly flattened at the poles, with an excess CURIOSITIES OF LATITUDE AND LONGITUDE. 33 of matter at the equator. Its polar diameter is 7,899 and its equatorial diameter 7,925 statute miles; the value of a degree therefore at the poles is 0.7 of a mile greater than at the equator. Its circumference is 24,897 statute miles. Latitude is measured north and south from the equator, and the latitude of a place is its distance in degrees north or south of the equator. Probably sea levels in corresponding lati- tudes north or south of the equator are equi-distant from the earth's center. THE NORTH POLAR STAR. Latitude affects the height of the Pole Star, which is always at an altitude equal to the observer's latitude. The farther we go north, the higher the Pole Star appears above our horizon. To an observer at the equator, the Pole Star will be on his horizon. Standing at the North Pole this star would be in his zenith. At any latitude between these two places the star will appear at a correspond- ing altitude. At New York, for instance, the star will appear about 41 degrees above the horizon. At the latitude of Chicago, 42 degrees. At London it would be 52, and at Christiania, Nor- 34 CURIOSITIES OF LATITUDE AND LONGITUDE. way, the star would appear about 60 degrees above the horizon. Every degree we move north, the North Star moves a degree higher in the heavens. It is easy to find the value of a degree of latitude, for if a ship sails about 69 miles north or south the Pole Star would move a degree north or south ; hence 69 miles must be about the value of a degree of latitude. Note the table on pp. 72-73. This will show the exact value of a degree of latitude; it varies from 68.698 to 69.392, i. e., expressed in English statute miles. The diurnal (daily) rotation (apparent) of the north- ern heavens is contrary to the hands of a watch. The earth is our observatory, but bear in mind it is a movable observatory. The apparent movements of the celestial bodies are due solely to the movements of our earth. The center of gravity possibly may not lie in the center of our earth. The greater land por- tion of the earth is in the Northern Hemisphere, and the greater part of this land portion is in the eastern half, between 15 W. and 160 E. Long. The magnetic pole is not the North pole, but is in about 105 West Long, and 75 North Lat.; the com- pass will not therefore always point North. The variation must be known and corrected by the navi- gator. CURIOSITIES OF LATITUDE AND LONGITUDE. 35 As regards the moving circle of rotation, East and West are arbitrary terms. There is no East or West in a circle. DIRECTION OF DIURNAL ROTATION. The diurnal rotation of the earth causes an appar- ent diurnal rotation of the heavens. In the northern 36 CURIOSITIES OF LATITUDE AND LONGITUDE. hemisphere it will be seen that the north celestial pole is the point about which the heavens revolve. Here a star has no diurnal motion. The north celes- tial pole is in a line with the axis of the earth. A prolonged exposure photograph of the circumpolar stars (i. e., those stars which are above the observer's horizon) show concentric rings of light. Even the Pole Star itself leaves a little trail of light as it revolves around the true pole, about a degree and a half from it. The true celestial pole is that point in the heav- ens where the axis of the earth, if prolonged, would pierce the heavens. Although the diurnal rotation of the earth is unvary- ing, this great clock having kept time through all the ages without the loss of a second, yet the axis of the earth is not (according to recent investiga- tions and experiments) a rigid or fixed line in the earth; i. e., the North Pole does not maintain an absolutely fixed position. This, of course, affects lat- itudes. CURIOSITIES OF LATITUDE AND LONGITUDE. 37 DAWN AND TWILIGHT. Latitude affects the amount and duration of twi- light; the duration varies with the season and the latitude, the longer twilights existing in the north- TWILIGHT PROJECTION. 38 CURIOSITIES OF LATITUDE AND LONGITUDE. ern latitudes (in summer), and in the southern latitudes (in winter).* The reason for this is that the greater the distance from the equator north and south, the more oblique is the line of the setting or rising sun with the horizon; consequently the greater length of time occupied in reaching the 18 limit of reflection. The sun ap- proaching the horizon vertically, reflection would dis- appear much sooner than if he approached it at an oblique angle. Dawn and twilight are of equal duration. They are both included between the setting and rising of the sun. Twilight continues until the sun is 18 be- low the horizon. Dawn begins when the sun is 18 from rising. CHANGES IN THE APPEARANCE OF THE HEAVENS. Another curiosity of latitude is the change in the appearance of the heavens at different points. *It should be borne in mind that in speaking of summer and winter, we mean that portion of the year representing the summer and winter of the Northern Hemisphere. December is the sum- mer of the Southern Hemisphere and June the winter season. CURIOSITIES OF LATITUDE AND LONGITUDE. 39 On the equator at latitude zero, stars will rise and set vertically, cutting the horizon at right angles. At the poles or latitude 90, the stars would neither rise nor set, but would revolve around the pole in concentric circles at altitudes corresponding to their declinations. The moon would be visible for about two weeks, and the sun for six months at a time. At any latitude between the equator and the poles, the stars would rise and set obliquely. LATITUDE AFFECTS GRAVITY. A body would weigh more at the poles than at the equator, but if weighed with ordinary weight balances the difference would not show, as the weights them- selves would be affected as well as that which is weighed. A pendulum swings faster at the poles than at the equator. A pendulum clock that would keep accu- rate time at the equator, would gain 3 y z minutes a day at the poles; moreover, as a pendulum would swing in a true plane, the rotation of the earth would cause it to form a star marked upon the surface of the globe could it swing about the pole. Such are some of the curiosities of latitude. We might recapitulate some of the effects, as follows: 40 CURIOSITIES OF LATITUDE AND LONGITUDE. 1. Varying lengths of day and night. 2. The hours of sunrise and sunset. 3. The angle of the sun. 4. The place of the sun's rising and setting. 5. The peculiar angles of the rising and setting of stars. 6. The position of the night shadow. 7. Variation in length of degrees. 8. Height of the Pole Star. 9. The circles of perpetual apparition and occul- tation. 10. Twilight and dawn. 11. Gravity. 12. The pendulum. The curiosities of latitude mentioned are those which are due solely to the motions of the earth. I have not touched on the physical aspects of latitude except incidentally. The work is intended to show those phenomena which come within the reach and scope of Mathemat- ical Geography. CURIOSITIES OF LATITUDE AND LONGITUDE. 41 LONGITUDE AND TIME. LONGITUDE is the angular distance between any two meridians. It is reckoned, east or west, from any given meridian, called a first or prime meridian. Meridian circles run around the earth north and south, and a meridian reaches from pole to pole. Meridian lines all con- verge at the poles, and cut the equator at right angles. The greatest longitude any place can have is 1 80, or half around the globe. Longitude is ex- pressed in degrees, minutes and seconds. WHAT IS TIME ? A part of duration. The system of those relations which any event has to any other, past, present or future; an arc cut out of the circle of eternity. Time is personified as an old man, bald-headed, but having a forelock, and carrying a scythe and hour-glass. 42 CURIOSITIES OF LATITUDE AND LONGITUDE. Tempus (L.), Temps (P.), Tempo (P. I.), whence temporal, temporary, etc. Cent. Die. Chronos Time. Chronology Reckoning of time. Time has been compared to a stream, or the flow of a river; the part that goes by now will never pass again. Time is a procession of seconds, minutes, hours and days, months, years and centuries, ever march- ing on. How is time measured ? What is our chronometric register? What is the standard unit? THE EARTH OUR CLOCK. The axial rotation of the earth once in 24 hours, or one day, gives us our exact standard of measure- ment. By the word day, we mean the whole 24 hours, or the period of one rotation of the earth upon its axis. From dial, dies, come diary, diurnal, day. Cent. Die. Day and night must always equal 24. 60 seconds i minute. 60 miriutes=i hour. 24 hours =i day, or period of the Earth's rotation. 24 hours=i44o minutes, or 86,400 seconds. CURIOSITIES OF LATITUDE AND LONGITUDE. 4.3 The earth, in its rotation, obeys an original im- pulse. This movement of the earth does not come under the law of universal gravitation. When a body turns upon a true and symmetrical axis and gravity is not brought into play, the axis will maintain its unvarying position. A gyroscope top illustrates this. When set in motion, the axis always maintains the direction in which it is placed. There may be two movements of the gyroscope top the one a rapid rotation on its axis, the other a slow, conical movement of its axis, owing to a rotation of the top, frame and all. The earth was set spinning with the northern end of its axis pointing to the north celestial pole, and that position it still maintains. It is true there is a slow circular motion of the pole of the earth around the pole of the ecliptic, causing the precession of the equinoxes, i.e., the zenith of the poles change about 20" annually. In time, therefore, Polaris will cease to be the Pole Star. There is also a slight oscillation of the pole itself, but practically the axis maintains its true position. Polaris, the bright polar star, is the jewel in which the axis is pivoted, though at present Polaris, strictly speaking, is i 16' from the true north celestial pole. The earth turns upon its axis, or polar diameter, in 44 CURIOSITIES OF LATITUDE AND LONGITUDE. an inclined position of 23^, in exactly 23 hours, 56 minutes, 4^ seconds, expressed in mean solar time, from west to east, as do all the planets. A SIDEREAL DAY. This is a sidereal day. It is the length of time that elapses between two successive transits of the same fixed star across a meridian. Let not the student be confused because a sidereal day is shorter than a mean solar day. There are exactly 24 sidereal hours in a sidereal day, and exactly 24 mean solar hours in a mean solar day, but a sidereal day expressed in mean solar time is 4 minutes shorter than a mean solar day. As regards the earth, the sun moves, while the stars do not. The gain of mean solar over a sidereal day of 4 min- utes a day, amounts to 2 hours a month, or i day a year. A sidereal clock (such as are used in observa- tories) and a mean solar clock, therefore, do not coincide, except on the 2ist of March. The hands would then agree. The difference of 24 hours would not appear. Like the hands of a watch, they are not together at any hour except 12 o'clock. The earth, in its diurnal rotation sweeps the entire circle of the heavens. All circles contain exactly CURIOSITIES OF LATITUDE AND LONGITUDE. 45 360. The 360 of this circle are traversed in exactly 24 hours, and as 360-^24=15, it is evident that each hour of the 24, the earth passes through just 15. Now the day contains 24 hours, 1440 minutes or 86,400 seconds, and the 360 contains 21,600 minutes or i, 296,000 seconds ; hence the earth will pass through 15 in one hour, 15' in one minute, and 15" of arc in one second. The accuracy and steadiness of the turning of the earth are so remarkable that each fractional part of the 24 hours will show an exact proportionate num- ber of degrees, minutes and seconds of arc passed over; in fact, when the last second of the 24 hours is passed, the last second of the 1,296,000 seconds of arc is also finished. A WONDERFUL CLOCK. The next beat of the clock begins the first 15" of the circle again, and every beat of the pendulum thereafter carries the earth through 15" of arc. When we consider the accuracy of this magnificent clock, we are astonished. The best time-keepers are lever escapements and chronometer balances; watches of high-class makes, with care in wearing, will run within one second per week. Tiffany of New York 46 CURIOSITIES OF LATITUDE AND LONGITUDE. has records of watches running ten months with a variation of only seven seconds. Full chronometers are not in use for pocket wear; they are liable to be affected by any sudden motion of the wearer. Our chronometer is liable to no accidents; it needs no oiling or cleaning; it never runs down. No clock that was ever constructed can ' ' keep time' ' with the earth. This clock is adjusted to heat, cold and posi- tion. It is self-winding, never gets out of order, and is synchronized -to beat with the stars. It has not lost a beat through all the ages; that is, the time of its rotation has not varied in thousands of years. The star that is cut in two by the line in the field of the transit telescope at 8 o'clock, sidereal time, tonight, will be cut in two by the same line at pre- cisely 8 o'clock, sidereal time, tomorrow night, and the next night, and so on through the years and ages. The figures on p. 47 represent two sections cut from a globe and a Mercator map, respectively. The space represents one hour or 15. It will be seen that all the parallel horizontal lines and spaces have the same value, both in time and degrees. Time and longitude are synonymous. It will be observed that a point at u ^4" moves very slowly compared with a point at "/)," yet the time CURIOSITIES OF LATITUDE AND LONGITUDE. 47 occupied will be precisely the same. "Z>" represents the equator. POLE EQUATOR A point on the earth's surface at the equator moves toward the east at the rate of about 1,000 miles an hour, because the earth's equatorial circumference is about 25,000 miles, and as it takes 24 hours for one complete rotation, a point here would move, in one hour, one twenty-fourth of the circumference, or about 1,000 miles. This motion is reduced to noth- ing at the poles. 48 CURIOSITIES OF LATITUDE AND LONGITUDE. At the latitude of New York, the motion is about 800 miles per hour, and at the latitude of Christiania, it is reduced to 500 miles per hour; but a point on the equator passes over 15 in one hour; so does a point at the 6oth parallel. The hare at the equator will arrive at his destina- tion at the same instant as the tortoise at the 6oth parallel. All hour circles have the same value, whether they contain 60 miles or one mile to a degree. Longitude is not synonymous with miles. It is not measured in miles, but in degrees. An hour angle contains 15, whether it contains 900 miles (as at the equator), or one mile (as at the 8gih parallel). See table on page 70. CURIOSITIES OF LATITUDE AND LONGITUDE. 49 THE SUCCESSION OF DAYS. Now let us see how the days follow each other. When and where does a day begin? Where does Saturday or Sunday begin? Is Sunday universal over the earth, or is it partly Sunday and partly Saturday or Monday or some other day? Is today the same day of the month at New York and New Zealand, at Bombay and at San Francisco? Let me say that there is always day and night on the globe that is to say, somewhere it is always per- petual day and somewhere perpetual night around the world. The sun is always waking up the morn- ing and chasing away the shadows of night. "Somewhere the glorious morning hues, The eastern sky's adorning; Somewhere upon this earth of ours You'll find 'tis always morning." And night is always following up the day. Where, then, does the day begin? Now suppose we begin our investigation of this subject at Chicago, near the 50 CURIOSITIES OF LATITUDE AND LONGITUDE. 9oth meridian of west longitude, on, say Saturday morning at 6 o'clock, we shall find the local time of New York to be 7 o'clock A. M.; 10 A. M. at the Azores in mid- Atlantic, noon at London, 7.30 P. M. at Pekin, China, while at New Zealand the day is drawing to a close. Thus it is early morning at Chicago, breakfast time in New York, dinner time in London, and supper time in Pekin all in the same day. Suppose now we take a step to the westward of Chicago. It is 4 A. M. at San Francisco, and 1.30 A. M. at Honolulu. But all this is Saturday, a civil day twenty-four hours long, and as the civil day begins at midnight, it is evident that this particular day was born a little to the west of Honolulu. Civil days are divided into periods of twelve hours each; hence all clock dials are divided into twelve spaces of one hour each. To a person living at Honolulu, then, Saturday has just begun; to one living in London it is noon of Saturday; to one living in New Zealand Saturday is nearly over and he is sleeping into Sunday morning; to a resident of Chicago, Sunday is eighteen hours away, while to a Londoner, it is but twelve hours away. Now it is clear that by the time Sunday gets to Honolulu, it is Monday morning at "New Zealand. CURIOSITIES OF LATITUDE AND LONGITUDE. 51 Though Honolulu and New Zealand are not far apart in longitude, they are widely apart as regards lati- tude, the one being in north and the other in south latitude. But latitude does not affect time. People who live on the opposite side of the earth, or Antipodes, have opposite latitudes, longitudes, days, nights and seasons. The people of Europe have observed their Sunday while the people of the United States are sleeping, and while the people of the United States are observ- ing their Sunday, the people of Europe are sleeping into Monday morning. It is evident, therefore, that for purposes of commerce and navigation, there must be a beginning somewhere of a day, at some point on the earth a day must begin and end, that is, the com- mercial civil day; Saturday, for instance, the day we have just been describing. WHERE DOES THE DAY BEGIN? The point opposite noon would evidently be the best TIME point, and a point farthest removed from land and civilization, the best GEOGRAPHICAL point with which to begin a new day. I/mdon being the metropolitan city of the earth, the geographical center of the land portion and the commercial center, it is 52 CURIOSITIES OF LATITUDE AND LONGITUDE. fitting also that it be the time center, and that the meridian of London should be the first meridian. A point opposite London in the Pacific ocean is a point farthest removed from this center of the world's civilization; it is therefore the best point to begin the day. The maritime powers of the world have agreed to regard this iSoth degree of longitude from London (or Greenwich) as the point where the day changes. This meridian therefore leads the day. Its passage under the iSoth or midnight celestial meridian marks the beginning of a new day for the earth ; here today becomes tomorrow. We have a new date for the month, and a new day for. the week in the transition. It is here that Saturday ends and Sunday begins. It is here, then, that Sunday was born, just to the west of Honolulu, but bear in mind that the day travels westward, therefore this new born day does not visit Honolulu until it has made the circuit of the round globe. Sunday travels west via New Zealand. Honolulu and New Zealand are only about 30 apart in longitude, but they are a whole day apart as regards any particular day, because the point at which the day changes lies between them. Again, it is CURIOSITIES OF LATITUDE AND LONGITUDE. 53 evident that Sunday is a long way off from Honolulu, because that place has only just passed out of Friday into Saturday, whereas New Zealand is passing out of Saturday into Sunday. Sunday travels west, because the earth travels east. Sunday must visit China, Russia, India and all of Europe, must cross the Atlantic and the United States before it can reach the Pacific and Honolulu, and no sooner does Honolulu get out of Saturday into Sunday, than Monday morning appears at New Zea- land. THE INTERNATIONAL DATE LINE. The international date line, though practically the iSoth meridian, is a line drawn irregularly through the Pacific ocean, south through Behring- sea; south- west past the Aleutian islands; south from Attu island on meridian 172 south, to parallel 15 north; east on 1 5th parallel to i5Oth meridian west; south on i5Oth meridian to parallel 15 south; west, clearing Society islands, to meridian 155 west; south to Tropic of Capricorn; southwest by south indefinitely. The day begins here, at the iSoth meridian and travels west, because the earth travels east. When it arrives at London it is about 12 hours old, at New 54 CURIOSITIES OF LATITUDE AND LONGITUDE. York about 17 hours old, and at San Francisco about 20 hours old. When the day arrives here at the iSoth meridian, it is 24 hours old; it gradually grows less and less, with the new day following, the old day diminishes and the new day increases. When noon arrives here, the end of the day is at London, with the new day following close. The preceding day is west of the line, the succeed- ing day is east of it. The longitudinal quadrants of the earth are as follows : XII NOON The initial meridian London. VI A.M. The goth meridian of W. L. Chicaj CURIOSITIES OF LATITUDE AND LONGITUDE. 55 MIDNIGHT The iSoth meridian Pacific Oceaff. VI P.M. Tr^oth meridian of E. L. Calcutta. These are the four cardinal points of the circle. In studying the above diagram, it is necessary to bear in mind the point of view, which is the iSoth meridian, looking through the globe to London. It does not represent the plane of any parallel, but is designed to show longitude. When XII (noon) is at London, one day and date prevail over the entire earth. If' noon is either east or west of London, parts of two days are in operation. When noon is at London, there is only "a today" upon the earth. When noon leaves London, there is "a today," "a yesterday" and "a tomorrow" in operation. Suppose, for instance, noon had arrived at Chicago- Chicago's antipodal meridian is the meridian which passes through Calcutta. Therefore, if it is noon at Chicago it is midnight at Calcutta. All of that portion of the earth east of Calcutta is therefore in tomorrow, and there people could say of that portion of the earth west of Calcutta (which would include of course Chi- cago) "that is in yesterday,"- and everyone has "a today. ' ' When it is noon at London only one day occu- pies the earth simply because there are 1 2 hours either side of noon, and 12 hours in either direction would 56 CURIOSITIES OF LATITUDE AND LONGITUDE. produce midnight. The opposite meridian from Lon- don being the iSoth degree, of course, there it would be midnight. The antipodal meridian of any place is the one removed from it by 12 hours, or 180 degrees. To find your antipodal meridian, deduct from 180 your meridian. This will give your opposite meridian in opposite longitude. For instance, what is the opposite (or antipodal) meridian to New York (75th W. L.) 180 75=105; 105 E. L. is the antipodal meri- dian to New York. When noon leaves London on its travels west (every- thing goes west) and arrives at the i5th degree of west longitude, or, in other words, has advanced one hour to the west, the new day starting at the iSoth meridian is one hour old and has advanced to the i65th degree of east longitude. We have explained how the two places, Honolulu and New Zealand, are near together and yet practic- ally a whole day apart, Honolulu being, just east of the line and New Zealand just to the west of it We have explained that the day travels west, so New Zealand is the first to see the new-born day. It is clear, then, if it is Friday (near midnight) at Hono- lulu to the east of the line and Sunday (near i A. M.) to the west of it, that a ship which sails from Honolulu to New Zealand, or from east to west, must sail out of CURIOSITIES OF LATITUDE AND LOXGITUDE. 57 Friday into Sunday, and thereby skips the interven- ing day of Saturday, and gains a day, while vice versa, a ship which sails from New Zealand (where Sunday has begun) to Honolulu, where Friday has just ended and Saturday begun, or from west to east, must lose a day, because it has to go back into Friday. Now this change of date at the i8oth meridian must npt be confounded with the gain or loss of time in trawling east or west with or against the rotation of the Barth. To gain or lose on the sun we must move our noon point. The moment we leave our position, i. e. , our meridian, we gain or lose, just in proportion to the number of degrees passed over. GAIN OR LOSS OF TIME. For instance, if we leave New York at the 75th meridian and sail east to London, we have gained as many hours as fifteen is contained in seventy-five, or five hours, i. e., our noon in New York is five hours back of the noon we are now experiencing; or, in other words, noon of London is 7 A. M. at New York, and noon of New York is 5 p. M. of London. Here we gain absolute time, and this time is in exact pro- portion to the number of degrees passed over. In the other case an arbitrary line changed our date and put 58 CURIOSITIES OF LATITUDE AND LONGITUDE. us backward or forward in our dates. Moreover the crossing of this iSoth meridian makes us gain the day as we go west and lose as we go east. In sailing, as regards the sun, just the reverse of this is true. We gain time in sailing east and lose time in sailing west, and in the latter case the time bears an exact proportion to the number of degrees passed over, while in the former we jump a whole day. Every 15 passed over east or west is one hour of time, and as there are 360 in the entire circuit we should gain or lose in making the entire circuit just twenty-four hours, or one day, because 360 -f- 15= 24. Now we may creep over the 15 or fly over them the result is just the same. With Jules Verne we may circumnavigate the globe in eighty days, or we may take eighty years to do it. We shall in either case lose or gain but twenty-four hours. How shall we reconcile this gain in traveling east- ward with the loss in covering the i Both meridian? Now in sailing, say from 30 west of New Zealand to 30 east of Honolulu (for purpose of illustration let us imagine these two places to be on the iSoth meri- dian), we have passed to the east 60, a four hours' &ain in time, but in doing this we crossed the line going east, so we lost a day. What have we lost or gained? Well, we have lost a day and gained CURIOSITIES OF LATITUDE AND LONGITUDE. 59 four hours. In other words we have lost twenty hours. Suppose it was 10 A. M. of Sunday 30 west of the line, 30 east of it is 2 P. M. of Saturday. If Sunday was July 31, then we shall find our date to be Satur- day, July 30, at 2 P. M., because we count back twenty hours from 10 A. M. Sunday. So a ship which sails east from London around the world crossing this meridian, will lose a day and gain half a day. That is to say if it is noon Saturday, July 31, at London, it is midnight of Saturday, July 31, at this meridian. Now at this arbitrary line or the iSoth meridian, we have practically parts of two days in operation, while at all other places on the Earth there is but one day. On the line we have the midnight hours of Friday and the early hours of Sunday, the rest of the globe being occupied by Saturday. Saturday is flanked on the one side by Friday and on the other by Sunday/ I have stated that Honolulu and New Zealand were a whole day apart practically they are yet this is not strictly correct. The difference is not exactly a whole day, by putting it thus the student at once grasps the idea that one place is in one day of the week and the other in another day of the week. 60 CURIOSITIES OF LATITUDE AND LONGITUDE. The aim is to make it perfectly clear why it is Saturday in one place and Sunday in another on the earth. CIRCUMNAVIGATING THE GLOBE. If a ship were to circumnavigate the globe on the equator, at the rate of 900 geographical miles a day, it would take just twenty-four days to do it, because 15 multiplied by sixty, the number of miles in a degree at the equator, would produce 900, and as 15 is one twenty-fourth of the circumference it would take just twenty-four days to sail the 360. Now as the meridians converge at the poles, the number of miles to a degree grows less and less as we approach the poles. At 60 north latitude, for instance, there are only thirty miles to a degree, consequently a ship sailing 900 miles a day will take but twelve days to circumnavigate the globe on this parallel. Time and longitude are synonymous, but not time and distance. We cannot measure miles east or west without knowing on what parallel they are to be measured. There is no time and longitude at the absolute poles. Nor is it needed. We cannot sail much nearer than 10 of the poles. The moment, however, we leave CURIOSITIES OF LATITUDE AND LONGITUDE. 6 1 the pole, the meridian lines have an appreciable angle, therefore, longitude can be computed. Now the earth performs a complete rotation on its axis in exactly twenty-four hours, and in doing this goes through exactly 360, and each fractional part of the twenty-four hours will show an exact correspond- ing number of degrees (of arc) passed over. It is evident from this that degrees of longitude and hours of time are convertible and interchangeable terms. Longitude means length as latitude means breadth, though latitude has nothing to do with time. There are 21,600 minutes, or 1,296,000 seconds of arc in 360. Also there are 1440 minutes, or 86,400 seconds of time in twenty-four hours. Now by divid- ing degrees by hours, or minutes by minutes, or seconds by seconds, we shall see that fifteen degrees of longitude will equal one hour of time, fifteen minutes of longitude one minute of time, and fifteen seconds of longitude one second of time. The difference in longitude between any two places is the angular distance between their meridians, and is expressed in degrees and fractions. Now if we knew the local time of two places, we could easily reduce this time to degrees of longitude by multiplying the number of hours by fifteen, which 62 CURIOSITIES OF LATITUDE AND LONGITUDE. would give degrees, or by adding four minutes for each degree. On land it is easy to get simultaneous times by telegraph, but at sea this could not be done, except in some instances, as, for instance, when the Atlantic cable was laid, the time was transmitted daily from the land to the ship. Knowing the difference in time, and consequently the longitude, it is easy to get the distance, i. e. , taking into account the number of miles to a degree on a given parallel. With each degree of latitude, however, the miles in a degree of longitude decrease from the equator to the pole. This is easily understood by observing how the meridian lines converge towards one another at the poles, on a globe, as we have ex- plained. The greatest longitude a place can have, east or west, is 1 80, though sometimes it is reckoned clear around the globe from a given meridian. CURIOSITIES OF LATITUDE AND LONGITUDE. 63 THE FINDING OF LONGITUDE, London (or Greenwich) time is the standard for navigators all over the world. It is the universal time meridian. Every ship, therefore, carries a chronom- eter, a finely made and nicely adjusted watch, with a compensation balance, hung and balanced so as to be affected as little as possible by the motion of the ship, and this chronometer is set to Greenwich Mean Time. To find his longitude, the navigator must know the mean time of the ship, and Greenwich mean time. This latter should be kept by the ship's chronom- eter (and the error of rate known, to be cor- rected in calculation). His own observations must be corrected for dip (distance from the sea level), re- fraction, parallax, and also for the semi-diameter of the sun (if he observes the sun). In other words, the navigator must know the hour angle of the sun. In order to get this he must know 64 CURIOSTTIES OF LATITUDE AND LONGITUDE. 1. His Tatitude. 2. The ?tm's altitude, and 3. The sun's declination for that day. And when he has found apparent sun time, it must be corrected (by equation) to mean sun time; then having found the mean sun time of the ship, and noted the difference between it and Greenwich mean time, longitude is easily ascertained by converting the difference in time found into longitude. Latitude is taken at noon, when the sun is near the meridian, but longitude observations are taken morn- ing or evening when the sun is a few degrees above the horizon. The instrument used is called a sextant, because it represents the sixth part of a circle. If the navigator finds the local time of the ship to be later in the day, then he is in east longitude. If he finds it to be earlier in the day, he is in west longitude, because as the earth travels towards the east, places to the east of us will be later in the day, while those west of us will be earlier in the day. For instance, if the time of the ship be noon, and the captain finds that his chronometer says 8 A. M., then he is in 60 east longitude. But if his chronometer says 4 p. M., then he is in 60 west longitude. We have shown how time is kept by the rotation of CURIOSITIES OF LATITUDE AND LONGITUDE. 65 the earth. Now the solar or sun day is variable, but bear in mind that it is the length of the day, plus the length of the night, that makes the whole day. The solar day is variable. Not so the rotation of the earth. That is forever the same. It is the mean sun, or average sun, that makes the true day. The time as kept by clocks is mean sun time. It is the time representing the 24 hours of the earth's ro- tation. Sidereal time is time as referred to the stars. A sidereal day, expressed in sidereal hours, is the same as a mean solar day expressed in mean solar hours. The sun travels in the ecliptic or obliquely across the earth; if he traveled in the equater, he would move uniformly, and his path could be divided into 24 equal parts, but as he moves obliquely we are obliged to make an average sun (or mean sun). Apparent, or real sun time, therefore, is not the same as mean sun time. The difference varies from o to 15 minutes. In speaking of noon being exactly half way be- tween sunrise and sunset, we mean apparent noon. In closing let me say that a great many cobwebs will be brushed away by bearing in mind two facts: First, that the earth rotates in exactly twenty-four hours. Second, that it sweeps through the grand circle of 360 in just that period. And when we 66 CURIOSITIES OF LATITUDE AND LONGITUDE. come to understand that it has done this for ages without appreciable loss, we are simply astonished at the accuracy of this magnificent clock, and the wis- dom that planned it. CURIOSITIES OF LATITUDE AND LONGITUDE. 69 Not only would they cut through cities, but streets and even houses, so that possibly it might be six o'clock in the parlor and seven o'clock in the kitchen of a house. Moreover, as Captain Parker states in his ' ' Fa- miliar Talks on Astronomy," "standard time is not natural, and it would produce in some instances curious anomalies ; for instance, suppose standard time was 30 minutes later than real sun time at a given place. On March 2ist the sun would then rise at 6:30 standard time, and set at 6:30 standard time at that place; that would make the morning 5^ hours long and the afternoon 6^ hours long." Nevertheless, I am an advocate for a system of universal standard time for the earth, because it is of great benefit to travelers. And I hope all the nations of the earth will soon adopt it for all railway and steamer lines. 70 CURIOSITIES OF LATITUDE AND LONGITUDE. LONGITUDE. The following table gives the number of miles in a degree at each parallel from the equator to the pole: LENGTH OF A DEGREE OF LONGITUDE AT EACH PARALLEL OF LATITUDE. STATUTE NAUT. STATUTE NAUT. LAT. MILE. MILE. LAT. MILE. MILE. O 69.160 60.000 45 48. 986 42.498 I 69.150 59-991 46 48.126 4I-752 2 69.119 59-964 47 47-25I 40.992 3 69.066 59-9I9 48 46.362 40.223 4 68.992 59.855 49 45-459 39-439 5 68.898 59-773 50 44.542 38-643 6 68. 783 59-673 5 1 43.611 37-835 7 68. 647 59-555 52 42.667 37.016 8 68.491 59-4I9 53 41.710 36.186 9 68.314 59-265 54 40.740 35-344 10 68.116 59-093 55 39-758 34-491 ii 67.898 58.904 56 38.763 33.628 12 67.659 58.697 57 37-756 32.755 13 67.400 58.472 58 36.737 31.872 H 67.120 58.229 59 35-707 30.979 15 66.820 57.968 60 34-666 30.076 16 66.499 57.690 61 33-6i5 29.164 17 66.158 57-394 62 32.553 28.242 18 65.797 57.081 63 31.481 27.311 19 65.416 56.751 64 30-399 26.372 20 65-015 56.404 65 29.308 25-425 CURIOSITIES OF LATITUDE AND LONGITUDE. 7 I STATUTE NAUT. STATUTE NAUT. LAT. MILE. MILE. LAT. MILE. MILE. 21 64.594 56.039 66 28. 208 24.471 22 64.154 55-657 67 27.100 23-509 23 63-695 55.258 68 25-983 22.540 24 63.216 54-843 69 24-857 21.564 25 62.718 54'4H 70 23.723 20.582 26 62.201 53-962 7i 22.582 19-593 27 61.665 53-497 72 21-435 18.598 28 61. no 53-oi6 73 20.282 17-597 2 9 60.536 52.518 74 19.122 16.590 30 59-944 52.005 75 !7-95 6 I5-578 3 1 59-334 5*-476 76 16.784 14.561 32 58.706 50-931 77 15.607 13-539 33 58.060 50-370 78 14.425 12.513 34 57-396 49-794 79 13-238 11.484 35 56.715 49-203 80 12.047 10.452 36 56.016 48.597 81 10.853 9.417 37 55- 3 47.976 82 9-656 8-379 38 54-568 47-340 83 8.456 7-338 39 53- 8l 9 46.690 84 7-253 6.294 40 53-053 46.026 85 6.048 5.248 4i 52.271 45-348 86 4.841 4-200 42 51-473 44-656 87 3-632 3-!5i 43 50-659 43-950 88 2.422 2. 101 44 49.830 43-231 89 1. 211 1.050 72 CURIOSITIES OF LATITUDE AND LONGITUDE. LATITUDE. The earth is an oblate spheroid, i. e. , its Polar diameter is about 26^/2 miles shorter than its Equa- torial diameter. Were the earth a perfect sphere, the miles in a degree of latitude would be the same at each parallel. They do not vary much, however, as the following table will show: LENGTH OF A DEGREE OF LATITUDE AT EACH PARALLEL. STATUTE NAUT. LAT. MILE. MILE. O 68.698 59.600 I 68.698 59.600 2 68.699 59.601 3 68.700 59.602 4 68. 702 59-603 5 68. 704 59-605 6 68.706 59.607 7 68. 709 59.609 8 68.712 59.612 9 68.715 59-6I5 10 68.719 59.618 ii 68.723 59.621 12 68.728 59-625 J 3 68-733 59.629 14 68.738 59-634 15 68.744 59-639 STATUTE NAUT. LAT. MILE. MILE. 45 69.044 59-899 46 69.056 59.910 47 69.068 59.920 48 69. 080 59-931 49 69.092 59-941 50 69.104 59-951 5i 69.116 59.962 52 69.128 59-972 53 69. 140 59.982 54 69.151 59-992 55 69.162 60.002 56 69.173 6O.OI2 57 69.184 60.022 58 69. 195 60.032 59 69.206 60.041 60 69.217 60.050 CURIOSITIES OF LATITUDE AND LONGITUDE. 73 STATUTE NAUT. LAT. MILE. MILE. 16 68.750 59-645 17 68-757 59-65I 18 68.764 59-657 19 68.771 20 68.779 59.669 21 68.787 59.676 22 68.795 59-683 23 68.804 59.691 24 68.813 59.699 25 68.822 59-707 26 68.831 27 68.840 59-723 28 68.850 59-731 29 68.860 59-740 3 68.870 59-749 31 68.881 59-758 32 68. 892 59-767 33 68.903 59-776 34 68.914 59.786 35 68.925 59-796 36 68.936 59.806 37 68.947 59.816 38 68.959 59.826 39 68.971 59-836 40 68.983 59.846 4 1 68.995 59.856 42 69. 007 59.866 43 69.019 59-877 44 69.031 59.888 STATUTE NAUT. LAT . MILE. MILE. 6l 69.228 60.059 62 69.238 60.068 63 69.248 60.077 64 69.258 60.086 65 69.268 60. 094 66 69.277 60. 102 67 69.286 60. no 68 69.294 60.117 69 69.302 60.124 70 69.310 60.131 7 1 69.318 60.137 72 69.326 60. 143 73 69-333 60. 149 74 69-339 60.155 75 69-345 60. 161 76 69-35I 60.166 77 69-357 60.171 78 69.362 60.175 79 69.367 60.179 80 69.371 60.183 81 69-375 60.186 82 69.378 60.189 83 69.381 60.192 84 69.384 60.194 85 69.387 60.196 86 69.389 60. 198 87 69.390 60. 199 88 69.391 60. 200 89 69.392 60.201 74 CURIOSITIES OF LATITUDE AND LONGITUDE. To convert nautical miles into statute miles, multiply nautical miles by 1.15266. To convert statute miles into nautical miles, divide statute miles by 1.15266. A nautical or sea mile is the length of a minute of longitude at the equator at the level of the sea. The circumference of the earth contains 131,459,- 328 feet *- 360 X 60 = length of a knot = 6086. + feet. The value of a degree of longitude at the equator is 60 geographical or 69^ English miles. To ascer- tain the distance between any two places on a globe or map on a globular projection, take the distance between the two places with a thread or the edge of a piece of paper, apply this to the equator, and get the exact number of degrees, then multiply by 60 or 69*^, as the case may be. ANGULAR MEASUREMENT. 60" = i'. 60' = i. 30 = i Sign. 90 = i Quadrant. 4 Quadrants, or 360 = i Circle. To CONVERT LONGITUDE INTO TIME, divide degrees, minutes and seconds by 15, or mul- CURIOSITIES OF LATITUDE AND LONGITUDE. 75 tiply by 4 and the result will be in minutes and fractions of a minute. For example: 86 - 24' - 30" 4 60) 349 m j and f| 5 49 38 To CONVERT TIME INTO LONGITUDE, multiply by 15, or divide the time reduced to minutes by 4. For example: 5 h - 49 38 s = 349 m and ff * 4 -87 -24' -30". 76 CURIOSITIES OF LATITUDE AND LONGITUDE. 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