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ON THE TERRESTRIAL GLOBE. BY JAMES PATERSON, PRINCIPAL OF THE SAIKT JOHN GRAMMAR- SCHOOt. *( Ere half of the school authors are read," says Milton, ** it <' will be seasonable for youth to learn the use of the Globes." "A Terrestrial Globe ought to be considered an indispen- ** sable article of apparatus in every school. ** SAINT JOHN, N. B: PRIRTID BT MENRT CHUBB, MAREET-SaVARE; AND 10LD ST Wf RSTirOLOSi D. m'HILLAK, AMO W. L, AVERY. t8384 r ! I ^■4*-V- -TT^-V^f^"'^'^"-," "W^^ '^ '"-' ' i •"i I PREFACE. The Author of the following; Manual has been directed in drawing it up by what appeared to him necessary for the Seminary over which he presides ; but he hopes, that it will not be unacceptable to other Teachers in this flourishing colony. Nothing is introduced foreign to a simple course of instruction on the Use of the Globes, and no- thing omitted that appeared to be absolutely neces- sary. The Explanations and Problems are made to follow each other in an easy and natural order, like the propositions in Euclid, every one forming a pre- paration for those that follow; so that even the youngest pupil may be easily initiated into a know- ledge of this elegant branch of youthful study. For two reasons, it has been thought proper to publish this Manual in two parts ; first, because in some schools the Terrestrial forms a subject of study to the exclusion of the Celestial Globe ; and next, because the greater number of young peo- ple take so little care of their books, that beforo their course of study is finished they require more than one copy of a book. Should a second edition be called for, any im- provement which may be suggested by others, or which the Author's own further experience may find necessary, will be introduced. f CONTENTS. «^^ Page. or llie Terrestrial Globe, 9 Explanation of Circleiy &c. 10 Problem I. To find the Latitude of a place, • - 19 II. To find those places which have the same lati* tudo as a given place, 20 — — III. To find the difference of the latitudes of two places, ib. IV. To rectify the Globe for the latitude of a place, 21 y. To find the longitude of a place, • - > 22 VI. To find the places that have the same longitude as a given place, 23 VII. To find the difference of longitude between two places, .---. --24 >— — VIII. To find a place when its longitude and latitude are given, - - - - - - - 25 IX. 'To find the distance between any two places on the Globe, - - - • - - ib. X. To find the angle of position of two places, • 28 — > XI. To find how many miles make a degree of lon> gitude on any parallel of latitude, - - - 27 XII. To find the Antceci of any place, - - 23 XIII. To find the Pcrioeci of any place, - -29 XIV. To find the Antipodes of any place, - '30 XV. To find the Sun'ii place in the Ecliptic, - 31 XVI. To find the day of the year, when thti Sun's place is given, • - - • - '^32 XVII. To adjust the Globe for the Sun's place and noon, at any place, on any given day, - - ib, XVIII. The place and day being giyen, to find the Sun's meridional i^Uitude, - - - 34 — — XIX. Given the sun's meridional idtilude on any day, to find the latitude of the placA, • - 34 «— XX. To find the day of the year when the Sun's meridian altitude at any place is known, - Z\ — — XXI. The place or latitude, and hour of the day being given, to find ihe Sun's aUitude> - - C6 jacs VI CONTENTS. I Pagi. Problem XXII. Given the Sun'ft Altitude, the day, and (he place or latitude, to find the hour, • - 37 — — XXIII. To find nt \vhai liour the sun rises or sets on a given day, in any given latitude, or at any proposed place, - 38 XXIV. To find the length of any day or night of the yeM at any places - • - - - 39 XXV. To find the length of the loDgest ddy atnny place within the temperate and torrid Zones, • 40 XXVI. To find (he length of theshortest day ai.any place in the temperate and torrid Zones, - 42 — — XXVII. The length of (he longest day being given, te find the latitude. of the place* • - -43 XXVIII, To find those places whose longest day corresponds with a given length, • - -44 — — XXIX, To find in what climate any place, not in the Frigid Zone, is situated, the latitude being given, ib. — — XXX. To find what other day of, the year will be of the same length with a given day, - - 46 XXXI. To find upon what point of the Compass the Sim will rise and set, at any place, upon a particular day, ib. — — XXXII. To find at what hours the Sun will be due East or West nt any place on any given day, - 47 XXXIII. To find the places that have the same hour of the day as a given place, - - - 49 XXXIV. The hour of the day at any place being given, to find what the hour is at any other place, -..--.-- - 60 XXXV. The hour being given at- any place, to find those places where it is any other givi^il, hour, 61 XXXVI. To find the Sun's declination for any gi- ven day, - 52 XXXVIl. The Sun's dtelimttion being given to find theday. of the: month, - ., -, - . ib. XXXVIII. To find I places to which the Sun is vertical on any given day, - - -63 ' XXXIX. A place in the Torrid -Zone being given, to find on what two days of:thQ.year the Sun will be vertiosLl, - - - - - - 54 CONTENl-S. vu Pagt. 50 5i 52 ib. .53 FruiMm XL. TKe dny tinti in>iir beiirg given at nnypHiM, to Hnd where the suii is vertical at tlrat time, <■ ib. .— — 'XLI. The day And hour being given at any place, to find where tiro sun is rising, setting, or on the meridian, . . . . . fiG XLII. To put the Globe in positions representing a parallel sphere, a right sph&re, ami an oblique sphere, 57 — — XLIH. To explain, higenernl, (he alteration of the lengllvortiiedays, and difference of the seasons, from a given latitude -67 —' — XLIV. To find on what day the sun begins to shino . constantly, and how long el any given plaoe in either of the Frigid Zones, . . . .60 — . XLV. To find tbe latitude of those places in the Frigid Zones where the Sun begins to shine constantly on any given day, . . .61 XLVI. To find in what parallel of latitude, in the Northern Frigid Zone, the sun does not ppt for any given number of days, not exceeding 180, . il). XLVII. A place and time being assigned, to find where it ia twilight, 62 — — XLVI II. On any proposed day, to 6nd when ntjorn- ing twilight begin?, and evening twilight ends, at any assigned place, ..... 64. XLIX. To find the duration of twilight at the JNorth Pole, and likewise how long night con* tinues there after the total cessation of tnilight, 69 -— L. To find in what latitude the lon^fst day is of any given length less than tweuiy-four huurs, . ib. — — LI. To find all those places to which a lunir eclipse is visible at any instant, . . . .66 — — LII. To find those places to which a solar eclipse will be visible, a particular day and hour being given, 68 — — LIIl. To find the right ascension of the sun for any day 69 — — LIV. To find the sun's oblique ascension for any given place and day 70> — — LV. To find the ascensional difference, and from it, the time tbe sun rincs before or after six, . 71 _1..--=3S VUl CONTENTS. Pagt. Problem LVi. The dny and place being given, to find the iun*fl nmplitude, 72 — — > LVII. The day of the year and the inn*s amplitude being given, to find the latitude, . .73 — — LTIII. The dny, hour, and place, being given, to find the 8un*8 Azimuth, . . .74 ^— — LIX. The place, the day, and the Sun't Azimuth being given, to find the hour of the day, . 75 LX. To find the Sun*sdepresaion below the horizon at any houp of a given night nt any place, . 76 -— — LXI. To find the equation of time, as far as it can be done by means of a Globe, . .77 Problems by the Analemma, 80 Problem LXII. To draw a meridian line, . .81 LXIII. To find the angular distances of the hour lines on a horizontal dial for any latitude, . 82 — — LXIV. To find the angular distances of ihe hour lines for an erect direct dial for a given place, . S3 •— -.— LXT. To find the hour •lines of a declining dial for any given place, 85 Miscellaneous Questions, . . i .87 Rules for the Construction of Maps, . .93 Table . 95 %v4' ■,'J lUAnrUAIi OIV THE USE OF THE GLOBES. PART I. OF THE TERRESTRIAL GLOBE. The terrestrial Glob,e represents the Earth in its form, its division into land and water, and into countries, kingdoms, oceans and seas. The first thing that strikes the youthful eje is its roundness, or spherical shape. That the earth is spherical, or nearly so, the pupil may be told, is demonstrated by the shadow it projects upon the disc* of the Moon, when tliat luminary is eclipsed, a phenomenon which is occasioned by the Earth intervening between it and the Sun, the great source of the light by which it is illuminated. Without * Tbq disc of a heavenly body is its face, which appeari flat oi) account of id immense distance. 10 MANUAL ON THE going so high for a proof, he may ascertain the correctness of the doctrine, by being led to consider that the part of a ship which ap- pears first when approaching the land, and the part which appears longest when going out to sea, is the top of the masts ; — the con- vexity of the earth concealing from view the hull, which, on account of its largeness, would, were the earth not spherical, be seen first and longest. To which might be added the testimony of navigators, who have sailed round the world. On a further inspection of the Globe, the pupil discovers a number of lines, circles and appendages, which it will be necessary for him to understand, before an attempt can be made to solve any problem. -rrr-T m: EXPLANATION OF CIRCLKS, 8tc. Tr The Circles* on the Globe are either great or small. Great Circles are such as divide the Globe into two equal parts, and whose centre is the centre of the Globe. Small Circles are such as divide the Globe into two unequal parts. All circles are divided into 360 equal parts, called degrees, but ,the de- m 1_ '^ A Circle is defined in geoinelry (o he a figure contained by oT.o line, every pnrt of which is equi-diatant from a point wllici^ id called the cenirc. / ''^ USE OF THE GLOBES. U > » f*. i r e m 3i~ le se ro lo e- by grees vary in magnitude with the circle. A degree of a great circle is divided into 60 minuites; and a minute into 60 seconds., I^e- grees are generally denoted by a small cipher over the figures, minutes by a small dash slo- ping from right to left, and seconds by two such dashes. For example, twenty-five de- grees, fifteen minutes and thirty-seven sec- onds, will be written thus, 25° 15' 37". . The rod or spindle, by the extremities of which the Globe is suspended, and on which it freely moves, represents the axis of the Earth, or polar diameter.* The Globe, re- volving on this from West to East, shews the Kliurnal rotation of the Earth, which causes the«phenomena of day and night, and the ap- parent daily rising of the Sun and Stars in the East and setting in the West. The ends of the axis are called the Poles, (from the Greek Poleo, to turn,) because on them the world is supposed to revolve. They are distinguished by the names Northern and Southern, or Arcticf and Antarctic. The great circle, equi-distant from the Poles, is called the Equator, (from the Latin j^quo, to equal,) either because it divides the Globe into two equal parts, called the Northern and * Diameter (Troin the Greek dta, through, and metron, m««- Burct) means thnt line which passes through the centre and ia terminated, both ways, by the circumference. # t Arctic (from the Greek Arctoi, n bear,) is applied to the Northern Pole, from Urea Major, the Greater Bear, a constel- Utton in the heavenn near the North Pole. Antarctic means opposite to the Arctic. » -a. - 12 MANUAL ON THE Southern Hemispheres,* or, more probably, because when the Sun in his annual course comes upon it, which occurs twice in the year, the day and night are equal in every part of the world. tyr The Circles that meet in and pass througli the Poles are called Meridians (from the La- tin Meridies, mid-day,) because the Sun, in his daily course, is on them at mid-day. There are ganerally twenty-fonr of these on the Globe, to represent the twenty-four hours of the day, 16° apart from each other. But every place has a meridian, and the Brazen Circle, in which the Globe is suspended, is employed to represent them all. This Bra- zen Meridian is graduated or divided into de- grees, measuring 90° from theEquatc^i- North- ward to the N. Pole, and 90° from the Equa- tor Sotithward to the S. Pole, on the upper semicircle, and 90° from the North Pole to the Equator, and 90° from the South Pole to the Equator, on the lower semicircle. The great Circle which intersects the Equa- tor obliquely at two opposite points, is called the Ecliptic, (from the Greek Ekieipsis, a wa- ning or eclipse,) because Eclipses of the Sun anci Moon take place only when these two bodies and the Eartli are all in the plane of that circle and in a direct line with respect to each other. It represents the Sun's orbit, or * flfinifpliere (frnin the Greek hemi, half, and sphaira^ n. fpliftre,) mean* Inlf of the glolje. . .; ;>.;»:? ,* -.!•>»<.'.. USE OF THE GLODES. ia ; n, .4 Ti \t: 8 n SB a / apparent path in the ^eavensi which he de- scribes in 365 days and nearly six hours. It is divided not only into 360 degrees, like other circles, but also into twelve equal parts, called Signs, each occupying 30®, which derive their names from the Constellations with which they correspond on the celestial Globe, and are as follow, * i. . ^ r / ' ^ J'' Aries, the Ram, , , ^^ Taurus, the Bull, 't Gemini, the. Twins, ~ , Cancer, the Crab, , Leo, the Lion, Viriro, the Vircin, ^ Libra, the Balance, Scorpio, the Scorpion, Sagittarius, the Archer, > ' Capricorn us, the Goat, Aquarius, the Water Bearer, Pisces, the Fishes, , H'"t'j ^ The first six are sometimes called the Northern Signs, because they embrace tlie Northern half of the Ecliptic, and the Id^t six the Southern Signs, because they embrace the Southern half of that circle. They are also divided according to the seasons of the year, thus, Aries, Taurus, Gemini, are called the Vernal Signs ; Cancer, Leo, Virgo, the Sum- mer Signs ; Libra, Scorpio, Sagittarius, the Autumnal Signs 1 and Capricornus, Aquarius, Pisces, the Winter Signs. Another division, which should not be omitted, is into Ascend- -'^^^ ^^ ]4 MANUAL ON THE ing and Descending Sighs. The Ascending Signs are Capricorn us, Aquarius, Pisces, Aries, Taurus, Gemini ; and the Descending Signs are Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius. ^ Four points in the Ecliptic require parti- cular notice, — the first degrees of Aries, Li- bra, Cancer and Capricorn us. The first de- grees of Aries and Libra are called the Equi- noctial points, — Aries, the Vernal Equinox, and Libra the Autumnal Equinox, (from the Latin -^quus, equal, and Nox, night,) — be- cause the Sun, when in these points, causes equal day and night,* The first degrees of Cancer and Capricorn us are called the Solsti- tial Points, — Cancer, the Summer Solstice^ and Capricornus the Winter Solstice, (from the Latin Sol, the Sun, and Sto, to stand,) the Sun appearing to stand still at these points, on account of some days together being of equal length at these periods. The two Meridional circles that pass through these £>ur points are called some- times Oolures, (from the Greek Kolos, cut, and Oura, a tail,) curtailed, because they are never seen above the horizon at once, and appear on that account to be cut or divided. Thev mark out the four seasons of the vear. - The upper flat surface of the wooden frame, in which the Globe is supported, is called the Horizon, (from the Greek Horidzo, to bound *H^iice also the Equttor i* ioin«tiinef called \k% EquinotttiuK 'i USE OF THE GLOBES. 15 or limit,) and represents the natural boundary of our vision, when the eye casts itself over and around the whole expanse that lies before it, or rather a circle parallel to that natural boundary dividing the Globe into two equal parts. As every part of the Globe has a me- ridian, so has every part a horizon, and these intersect one another at right angles. On the Horizon the pupil will observe se- veral concentric* circles, which are indispen- sably necessary in the solution of some pro- blems. Two of these circles exhibit the twelve Signs of the Ecliptic and the months with which they correspond. The next, which in some Globes is within, and in others without these, is a delineation of the Pointsf of the Mariner's Compass, in their proper position in regard to the Globe. The remaining cir- '■'*•'* Concentric menns having the same centre, which if, in this o»se, the centre of the globe. .j^t?sD;;;3 t These pointi are thirty*two in number, nnd are eicli deno> minated by means of the initials of the four firet points, N«rth, East, South, and West, viz:— North Eiist South West N. by E. E. by S. S. by W. W. by N. N. N. E. E. S. E. S. S. W. W. N. W. N. E. by N. S. E. by E. S. W. by S. N. W. by W. t, N. E S. E. S. W. N. W. N. E. by E. S. E. by E. 8. W. by W. N. W. by N. E. N . E. S. S. E. W, S. W. N. N. W. .: E. byN. S. by E. W. by S. M. by W. - - ' The four principal points, North, East, South and West, are called the Cardinal PoinlH, (from the Latin cardo, a hinge) AS if all the other points hung upon them as upon binges^ So we ipetk of Cardinal firlues. 16 MANUAL ON THE cle is divided into degrees, which are num- bered both ways, from the East and W^st, until they end at 90° in the North and South Points. ■ --♦:• J.:. j'^i p v., ■;::;: .-i^, _-,'•. The two dotted circles, which are drawn parallel to the Equator and through the Sol- stitial Points, are called the Tropics, (from a Greek word, Trepo, to turn,) because the Sun, when in his progress through the as- cending signs he comes to the Summer Sol- stice, turns into the descending signs, and again when in his progress he comes to the Winter- Solstice, he tt^rns into the ascending signs. The Northern Tropic is called the Tropic of Cancer, because then the Sun is in the first degree of Cancer, and the Southern is called the Tropic of Capricorn, because then the Sun is in the first degree of Capri- corn.* These circles arc just 23° 28' from the Equator. At the same distance from the Poles that these circles are from the Equator, the pupil will discover two other dotted circles. These are called the Polar Circles, the Northern the Arctic and the Southern the Antartic. Being 23° 28' from the Poles, they are consequently 66° 32' from the Equator. I The Polar Circles and the Tropics divide the surface of the Globe into &\e broad spa- ces, which receive the name of Zones, (from a Greek word Zoncy signifying a broad belt or girdle.) These are distinguished by names derived from the different degrees of heat and USE OF THE GLOBES. If 'A cold to which they are subjected by their si- tuation. That between the two Tropics is called the Torrid Zone. Those between the Tropics and the Polar Circles are called the Temperate Zones. And those between the Polar Circles and the Poles, the Frigid Zones. ^ Attached to the North Pole, and on some Globes also to the South, is a brass moveable : , circle, divided into twice twelve, denoting the hours of the day and night. It is called the Horary or Hour Circle. - On some Globes it is not moveable, but is furnished with a ~ moveable index or pointer. The Table of Equation of Time, which ap- pears delineated on the surface of the Globe, together with its use, will be explained under one of the Problems. There is an appendage of the Globe, which is not attached to it, consisting of a flexible slip of brass, the length of one fourth of a great circle, and divided into 90% called the Quadrant of Altitude, because invented for the purpose of ascertaining the altitude or height of the Sun and other heavenly bodies. It serves other useful purposes also, which tlie pupil will find in the course of the pro- blems. '# Note. — In solving problems it is necessary to adjust the Globe so as to have the gradua- ted side of the Brassen Meridian on the right hand. ¥ -".n .%■ Cv ■X-J0''i ril i;} *rii. r >-\fi>m f»o ■l./js 'r'^tl^:, ::f^ ■V V . ;; . 7 n; • ... ■ * • ■ . ..-...■■■■ CV' ah him " ■ . -'•\---r^ U>.« irfi Ofe^ii. fj tJ-/" . J J •■> • ' -: y.,,:,J|. |^'^r.!fff^^^^"- ' _ PROBliCmS^ ON THE TERRESTEIAL GLOBE. V^,'- iili PROBLEM L ^. To ^wii M^ Latitude of a place, Definitipn. — The Latitude of a place (from the Latin, latitude^ breadth), is its dis- tance from the Equator measured on the bra- zen meridian. When North, it is called North Latitude ; when South, South Lati- tude. Rule.— Revolve the Globe till the pftice comes under the brazen meridian, the degree then above it shows the Latitude. Examples, — What is the Latitude of Saint John, N. B.?— ^W5. 45° 15' N. ■ What is the Latitude of the Cape of Good Hope?— .4«*. Nearly 35° S. * Required the Latitude of the following places : — London, Paris, Bagdad, Canton, Saint Helena, Quebec, Rio Janeiro, Cape Horn, Mexico, Fredericton, Halifax, the Sandwich Islands, the extremes of Mada- 20 MANUAL on THE PROBLEM II. Tojind those places which have the same Latitude as a given place, ,. Rule. — When the place given is brought to the brazen meridian, and the Latitude of it ascertained, make tlie globe perform one revolution, and observe all the places that come under the same point of the meridian ; these have the same Latitude. Examples, — What places have the same Latitude as Petersburgh ? — Ans. Stockholm, Cape Farewell, Polym. . , . . What places have the same Latitude as Cape St. Roque ? — Ans. Loango, l^acassar, Southern extremity of new Ireland, Jind Bor- ja, on the Amazon. ^^-^'^^ ■ ' ^^^^ '^ Required the places vt^hose latitude is the same as that of St. John, N, B., Philadel- phia, Barbados, Archangel, Vienna, the Isle ofMan, Buenos Ayres, Ascension Island, the Maelstrom, Mount .^tna. PROBLEM III. To Jind the difference of the Latitudes of two places. Rule. — As the difference of Latitude is the Arc* of the Meridian intercepted between the points of latitude, if the places are both in the Northern, or both in the Southern Hemisphere, subtract the lesj latitude from * Am Arc {(torn the Latin Areus, a bow), U a part of n cur?a line; as ofu circle, &c. ::.M. use OF THE GLOBES. 21 ?s qf the greater, but if the one is North und the other South, add them together. Examples. — What is the difference of La- litude between Madrid and Petersburg ? — Ans. 60°— 40^=20° * What is the difference of Latitude between St. John, N. B., and St. Salvador? — Ans. 4.5° 15'-|-13°=58° 15'^ Required the difference of Latitude be- tween Halifax and New- York, Montreal and Boston, Edinburgh and Lisbon, Pekin and Calcutta, lev Cape and Cape Horn, St. Helena and Gallipagos, Dublin and Sierra Leone, Tunis and New Zealand, Botany Bay and Constantinople, St. John and London, Frederickton and Boston. u v , PROBLEM IV. • To rectify ihe Globe for the Latitude qf a place. vr>^'\: • By rectifying is meant, adjusting the Globe so that the place, v/hen brought to the brazen meridian, will be in the zenith,f or as it were at the top. ' r. . , ... RuLii. — If tlte place is in the Northern Hemisphere, raise the North Pole as many \x\ of ft * A flTnall horizontnl line — iitused to denote eiihiraclion; a h^risontal line crueoed by a porpendictilar, -<> to denote addi- tion; And two horizontal lines = to denote equality. vt Zenith (» corrnpiion of nn Arnbic tvord, eignifyinK the v^iical point), it the higlieat point on tlie Globe, or, when re- f^trcd to the henvcns, the point nxoctly over otir headf. The point directly opponite is rnl4ed the Nadir, (a'co a coiruplioin ol tn Arilii". ward.) ^t ••■».■ V Iv S f.sr"- 22 MANUAL OM ttlfi I' I 't degrees as the Latitude is — if it ii in the Southern Hemisphere, raise the South Pole. }^ote» — The pupil will see from this Pro- blem a reason for the graduation of the under semicircle of the Meridian beginning from the Poles. Examples, — Rectify the Globe for London. As the latitude of London is 51° 30^ vou raise the North Pole until 51° 30' on the lower limb of the meridian coincide with the hori- zon. Rectify the Globe for St. John, Toronto, Savannah, Cape Saint Roque, Otaheite, the Cape of Good Hope, Van Diemen's Land, Prince William's Sound, Cape Farewell, Bourbon Island, Trinidad, Straits of Magel- lan. I iU $\i« PROBLKM V. r" ^ To find the Longitude of a 'place, Def. — Longitude (from the Latin, Longi-- tndOf length) is the distance of a place from the first meridian, or meridian of Greenwich,* measured on the Equator. When East from * The first Meridian is that from which all the othem are reckoned, and is quite arbitrary. Different Meridians have beeii chosen fot \V.^ First nt different period)), and by different Geographers. Hippt-^zhiis who died 125 years B. C., fixed the firsi meridian si Fzt-r^ one) of the Canary Isles. Ptole- my chose tlie most "^Vc^.^itiiy ) ^e, son^r the Peak of Teneriffe, and others Cape Vrrti. hi iuodern times Geographers have generally chosen ih^^t rrieri^^itns of the > respective capitals, as, (he French, that of Pari^, the Spanieh, that of Madrid, and the English that of London, or the Observatory atGreenvrich. "^ USE OF THB OLOBES. 23 rom rom tefB are )s have iffcreoi piolo- •neriff*?! rt hav« ikid, •"* the first meridian, it is called East Longitude, nnd when West, it is called West ...)ngitiuic. The terms Latitude and Lon«]fitude vere adopted by the ancients in the infancy of geo- graphical knowledge. They applied the term longitude or length to the extent East and West, because t'leyknew more in that direc- tion than :.. he extent North and South, which irj contradistinction they called Lati- tude ur biCti 1th. Pv/ , — Bring the given place to the meri- dian, and deserve what degree of the Equa- tor is intersected by the meridian, that is the Longitude. Example, — What is the Longitude of Vi- enna ? — Ans, 16° E. What is the Longitude of Port Royal, Jamaica ?-'Afis. 76° 45i' W. Required the Longitude of the following places : — Saint John, Charleston, Trinidad, Cape Finisterre, Calcutta, Bombay, Bergen, Rome, Tripoli, Alexandria. . , PROBLEM VI. Tojind the jplaces that have the same longi-^ tude-as a gix)en place. iR ..«^. — Bring the given place to the meri- dian, and all the places that are under the upper side of the meridian from the North to the South^Pole, have the same Longitude. Examples. — What places have the same longitude as St. John, N. B. ? — Ans, Mitidle of Porto Rico, Ciudad Real, La Plata. \.;^ 24 MAW UAL ON THE w\ ■■■■' 'fi I" tl m \ t ■■ . i\ , ^ ■'/If * ■-■if «. What places have the same longitude as Buenos Ayres ? — Arts, The Caribbee Islands, the S. W. part of the Island of Newfound* land, and Cape Breton. Required the places whose Longitude is the same as that of Genoa, Madras, Lisbon, the Society Islands, Bombay, Amboyna, Pe- tersburg. PROBLEM VII. To Jind the difference of longitude between iuo places. Mule, — As the difference of Longitude is an Arc of the Equator intercepted between the points of Longitude, subtract the less from the greater if they are both East or both West, but if the one is East and the other West, add them. Examples, — What is the difference of lon- gitude between St. John and New- York ? — ^ Ans, 74°— 66°=8*=» Wliat is the difference of longitude between Rome and Pekin ? Ans. HQV-^°— ^f^ What is the difference of longitude between New- York and Constantinople? Ans. 74°^ 29° 30'=103° 30' Required the difference of longitude be- tween Cork and Calcutta, Vei* Cruz and Cape Comorin, Boston and Borneo, Mount Hecla and Mount ^Etna, Philadelphia and Siam. f/4 USE OF THE GLOBES. 25 PROBLEM VIII. (I Li, and :o To find a place when its Longitude and La- titude are given. ' ^^ r^;/i'^ vmnr.. RuxB. — Bring the point of the Equator which marks the Longitude to the meridian, and under the point on the meridian which marks the Latitude, the place will be found. Examples, — What place has 60 degrees of North Latitude, and 31 degrees of East Lon- gitude ? — Ans. Petersburg. .,.,- What place has 18° of North Latitude and T6° 45i' W. Longitude ?— .4ws. Port Royal. Required the places whose Longitudes and Latitudes are as follow : 4° 23' E. long. 51° 13' N. lat. 151° 21' E. long. 34° 0' S. lat. 58° 3P W. long. 34° 35' S. lat. 88° 30' E. long. 22° 35' N. lat. 18° 38' E. long. 54° 21' N. lat. 0° 0' long. 51° 29' N. lat. 9° O'' W. long. 37° 0' N. lat. 6° 0' W. long. 15° 0' S, lat. 155° 0' W. long. 19° 0' N. lat. PROBLEM IX. To find the distance between any two places on the Globe. Rule. — If both places are on the same mendian, their difference of Latitude multi- plied by 60 will give the distance in geogra- phical miles, by 69^ in English miles. But B f» /. :j 26 M^IIUAL 45' or 2645 geo- graphical miles, or 9971 English miles. Required the distance between Lisbon and Mexico, between New-York and Halifax^ between Toronto and Madrid, between Dub- lin and Calcutta, between Cape Sable and Cape of Good Hope, between Cape of Good Hope and Canton. : 1 PROBLEM X. To find the angle of position of two places. Observe, the Angle of Position is the angle made by a great circle passing through the two places with the meridian of one of them, and may be denominated the geographical bearing the one place has to the other. , f EuLB.— Rectify the Globe for the latitude of one of the places by Problem IV — bring 'h >• V$B OF 7HB GLOBES. 27 laces. the place to the Zenith) fix the Quadrant of Altitude over it and extend it over the other place, the end of the quadrant will shew on the Mariner's Compass on the horizon the angle of position or geographical bearing. Examples, — What angle of position does a great circle passing through London and Jer- usalem make with the meridian of London ? or what is the bearing of Jerusalem from Lon- don in a geographical sense ? Ans. 68 deg. south-easterly or 22 deg. from the east to- wards the south : E. S. E. point of the Com- pass. .. What is the Angle of Position made by the following places with the meridian of Saint John, N. B. ? Mexico, Toronto, Washing- ton, Sierra Leone, Halifax, London, Paris. PROBLEM XI. r To Jtnd ho*m many miles malce a degree of Longitude on any parallel of Latitude. Observe, that the circles parallel to the Equatpr, are called parallels of latitude, be- cause they shew the latitude of places by their intersection with the meridian, and that every place, not on the Equator, has such a paral- lel, though there are only eight of them from the Equator to the Pole, set down on the Globe, at the distance ot ten degrees from each other. Observe also, that the definiti- ons formerly given of small and great circles require particular attention. 28 MANUAL ON THE Rule. — With a pair of Compasses take off the distance between two meridians on the given parallel, and apply it to the Equator to see how many degrees of a great circle it makes, and then say, as the number of degrees between the same two meridians on the Equa- tor is to the number ascertained on the given parallel, so is 60, the number of miles in a degree of longitude on the Equator, to the re- quired answer. Examples, — In the parallel of London, lat. 51^, the space between the two meridiaa lines drawn at the distance of 15 degrees on the Equator, when taken with a pair of compas- ses and applied to the Equator, is found to contain 9;^ degrees. Then, as 15°:9i** : : 60:37 geographical, or 69J to nearly 43 Eng. miles. Required the number of geographical and English miles in the parallels of latitude in which the following places are situated — North Cape, Cape Farewell, St. John, N. B. New- York, Trinidad, Havanna, Tripoli, Mauritius, Icy Cape, the Marquesas Isles, Boston, London. PROBLEM ill. To Jind the Antcecians or Antceci of any place. Observe, the Antoeci of any people, (from the Greek Anti^ opposite, and oikos^ a house,) arc those inhabitants of the earth who live in the opposite } emisphere, having the same longitude and latitude, being as far south as the other are north. \A. I USE OF THE GLOBES. 29 any Tom ise,) re iu same Ith as I RVLE. — Bring the given place to the bra- zen meridian, and haying noticed its latitude, seek the same number of degrees in the oppo- site hemisphere, and that wul show the situa- tion of the Antceci required. Examples, — What are the Antoeci to the inhabitants of St. John, N. B. Ans» River Camarones, in South America. What are the Antoeci to the inhabitants of the Colony of the Cape in Africa ? Am, The part of the Mediterranean Sea, North of Barca. Required the Antoeci of Edinburgh, Rome, Constantinople, Sardinia, Smyrna, Moscow, Morocco, Charleston, New Orleans. What inhabitants have no Antoeci ? PROBLEM XIII. To find the Periceci or Perioecians of a place, ' • Note. — The Periceci (from the Greek peri^ about, and oikosy a house,) are those who live in the same parallel of latitude, but in opposite points of Longitude. Rules. — \st. Bring the given place to the meridian, bring XII on the hour circle, also lo the meridian, and turn the Globe half a revolution ; the Periceci will tnen be found under the same degree of latitude on the me- ridian ; or 2d, — Subtract the Longitude of the given place from 180% and the remainder will give the longitude of the Perioeci in the opposite so MANUAL OK THE PI rf ■^* u hemisphere, which bring to the meridian, then under the latitude will be found the place. EicampIes.-^Whvit are the Periceci of Saint John, N. B.? Ans, — A part of Chinese Tar- tary 5^° North of Pekin. What are the Pert- oBci of London ? Ans. — A spot P South of the Islands of the Northern Archipelago. Required the Periceci of Halifax, Cape Bretouj Berlin, Naples, Cairo, New Zea- land, Van Diemen's Land, North Cape. What spot on the Globe has no Periceci ? PROBLEM XIV. 1^0 ^nd the Antipodes of any proposed place. Note. — The Antipodes, (from the Greek, Anti, opposite, and podesj feet,) are the inha- bitants of two places on the earth, diametri- cally opposed to each other, and who there- fore walk feet to feet. Rules. — 1st. Find the Antaeci of the given place, and the Periceci of these will be the Antipodes ; or 2d, Bring the given place to the meridian and observe its latitude ; turn the globe half a revolution, then under the same degree of latitude in the opposite hemisphere, the Anti- podal place will be found ; or 3d, Bring the proposed place to the hori- zon ; then the opposite point of the horizon will give the Antipodes ; or i>tL Subtract the longitude of the git^fi USS QF THB QlOmES. ai place from 180° and It will give the longitude of the Antipodes — East, if the given place is West — and West, if the given place is East — vi^hich turn to the meridian, and under the latitude of the place, but in the opposite he- misphere, the Antipodes will be ^nd. Examples. — What place is Antipodal to London ? Ans» A spot a little South of New Zealand. , What are the Antipodes to the inhabitants of St. John, N. B. ? Arts, A portion of the Indian Ocean 10° South of the South Cape of New Holland. Required the Antipodes of the following places — The Friendly Isles, Cape Comorin, Jerusalem, Santa Fe de Bogota,. Quito, De- los, Cape Guardafui, Cape Horn, Icy Gape. . •; PROBLEM XV. ., T To Jind the Sun^t place in the Ecliptic, Rule. — Seek the day of the Month on the wooden horizon, and against it in the adjoin- ing circle are the sign and degree in which the Sun is for that day, which, referred to the Ecliptic, will giye the Sun's place required. Examples, — What is the situation of the Sun at the Autumnal Equinox ? Ans, P of Libra. What is the Sun's place on the 19th June. Ans, it 28° Required the Sun's place on the first day of each month. 'W- 32 MANUAL OK THE - PROBLEM XVI. Tojlnd the day of the year ^ ixihen the SurCs place is given. Rule. — Look for the sign and degree of the Sun's place on the wooden horizon, and in the calendar contiguous to it will be found the day of the year. On what day of the year is the Sun in the 10th of Taurus? Ans. 30th April. Required the days in which the Sun enters respectively the twelve signs of the Ecliptic, or first degrees of '^$ n> /j >5*> ^> H. • ^ ' PROBLEM XVII. To adjust the Globe for ^he Sun^s place arid Noon* at any place o,i any given day. Rule. — Rectify the globe first for the La- titude of the place, then, finding the Sun's place in the Ecliptic for the given day, bring it to the brazen meridian and set the Index to XII, or, if the Horary Circle is moveable, move it till XII comes under the meridian. Examples,-^ ^.di]\xst the globe for noon at Saint John on the 22d February. First rec- tify the globe for the latitude of Saint John, * Noon. — From the Latin nona hora^ meal-time ; liter- ally the ninth hour, or three o'clock; the Romans reckoning the hours from 6 A. u . ; and because the term was applied by succeeding nations to their dinner time> which was usually about the middle of the day» noon came te signify 12 o'clock.^ ¥SE OF THS GLOBES. 38 at rec- ohn. which is 45^ 15', then bring the 4th degree of Pisces, which is the Sun's place for the 22d of February, to the meridian, and, keep- ing the globe in this position, bring XII on the hour circle to coincide also with ihe me- ridian. Adjust the globe for Noon at Halifax, on June 30,— at Cadiz, 12th May,— at Cuba, 7th October, — at Paris, December 25, — at Mo- rocco, January 1, — at Surinam, February 20, — at Fredericton, March 18, — at London, October 25, — at Quiloa, April 17, — at Oc- hotsk, July 19, — at Cape Voltas, Dec. 20. PROBLEM XVIII. The place and day being given^ to find iht Sun's Meridional Altitude. Note \st, — By Altitude (from the Latin altitudo, height,) is meant an arc of a great circle intercepted between the body, whose altitude is required, and the horizon. The meridional altitude is the height of the sun at mid-day. 2d. At places in the North Temperate, and North Frigid Zones, the Sun's meridional altitude is always a Southern Arc of the me- ridian ; and at places in the South Temper- ate and South Frigid Zones, it is always a Northern Arc. But at places in the Torrid Zone, or within the Tropics, it is during, a part of the year a Northern Arc, and during another part, a Southern Arc. • RuL£. — Adjust the globe for the Sun's . daj^ tojmd the Latitude of the Place, Rule. — Bring the sun's place in the eclip- tic to the brazen meridian, and adjust the globe by moving the meridian, till the dis- tance between the sun's place and the horizon agree with the given altitude, — then observe the elevation of the pole ; that will shew the Latitude. That the Elevation of the Pole and the La- titude of a Place are equal, the young pupil will easily discover, when he considers, that, as the distance from the Equator to the Pols;, and the distance from the Zenith to the Ho** rizon, are, each a quadrant or 90°, it follows that whatever distance the Latitude xemQves USE OF THE GLOBES. iny the Equator from the Zenith, it raises the Pole tne same distance above the Horizon ; or in other words, it makes the elevation of the Pole equal to the Latitude. Examples, — The sun's meridional altitude on the 18th of May being 42° south, what is the Latitude? Ans. 67° north. The sun's meridional altitude on the 5th of August being 74° north, what is the Lati- tude? Ans. 2° north. Required the Latitudes corresponding with the following Meridional Altitudes of the Sun« on the annexed days : — Meridian Altitude, 38^ south, January IS ; 18% March 11 ; 30*' April 24 ; 64% May IT ; 35% June 4 ; 25% July 29 ; 48% August 6 ; 18% October 21 ; 50°, November 19 ; 45% December 10. Note. — The Sun's Altitude may be easily taken by any quadrant having sights ^p4 a plumb line : for holding it in sueh a pi^||on 5.f that its rays may pass through both sights, tho plumb line will then intersect that degree on the limb of the quadrant which is equal to the height of the sun. "'^ ■ PROBLEM XX. ' Tojind the Day of the Year^ when the sun*s meridional altitude at am/ place is known. Rule. — Rectify the Globe for the latitude of the place, count the degrees of altitude on the meridian upwards from the horizon — ^then i?evolving the Globe, observe what degree of the Ecliptic comes in contact with the degree 36 MANUAL ON THE of Altitude, and that will shew the Sun's place, which, referred to the calendar on the wooden horizon, will give the required day. Note. — Two different answers may be ob- tained to questions on this Problem, accord- ing as the ascending or descending signs are employed. Examples, — On what days of the year is the Sun's Meridional altitude at London, 59*^? Ans. May 24, and July 18. On what days is the meridional altitude at St. John 68° ? Ans. June 7, and July 5. Required the days in which the Sun's me- ridional altitude at Fredericton is 35°, 27°, and 49°— at London, 43°, 24°, and 29°— at St. Jago, 84°, 73°, 40°— at Quito, 84°, 65°, 49°— at Spitzbergen, 22°, 36°. PROBLEM XXI. The place, or latitude, and any hour of the day being given, to find the Sun*s altitude. Rule. — Adjust the Globe for noon, (by Problem XVIL) and if the hour is in the forenoon, turn the Globe Eastward, if in the afternoon, turn it Westward, till the given hour on the horary coincide with the Brazen Meridian ; then fix the Quadrant of Altitude over the Zenith or latitude, and extend it to die horizon over the sun's place in the Eclip- tic — the Arc of the Quadrant intercepted be- tween the Sun's place and the horizon will give the required altitude. USE OF THE GLOBUS. m • rd- are the eat me- 2Tf°, >— at 65% of the le. h (by in the in the given 3razen Ititude id it to Eclip- ted be- on wil^ Note. — Turning llie Globe Eastward or Westward is to give the Sun*s true position in the heavens at the given latitude— for ris- ing in the East, he is eastward of the meridian till Noon, after which he is Westward. Examples. — What is the altitude of the Sun at St. John, at the Vernal and Autum- nal Equinoxes, at 6 o'clock, a. m.* and 6 r. M. Ans, 0°. Required the Sun's altitude at London, at 8 A. M., July 1 6, and May 2 ; and at 4 p. m. December 1, and July 24; at Fredericton, at 6 A. M. May 1, and September 10 ; at Buenos Ay res, at 10 a. m. March 9 ; at Glasgow, at 7 A. M. August 22 ; at Stockholm, at 9 a. m. February 20 ; at Paris, at 10 a. m. September 4, and at 4 p. m. August 20 ; at Tristan D* Acunha, at 7J a. m. August 7, and 2 p. m. De- cember 25 ; at Anticosti Island, at 9 a. m. September 10, and 1 p. m. January 1. PROBLEM XXII. Given the Sun's altitude^ the ddy^ and the place or latitude^ to Jind the hour. Rule. — First adjust the Globe for Noon, (by Problem XVII.) and fix the Quadrant of Altitude over the Zenith, then move the Qua- * A. M. and P. M., so frequently used in ooromon ioter- course with regard to the hours of the day, are the initials or first letters of Latin words : the formar Ante Meridiem, signifying before mid-day, and the latter Pott Miridtem, after raid'day. u tf^f 3g MASUAI, ON THE „ai be the )J?«J «5S^ on this Problem Note.— To tn® 4"^, . j according as two answers "-^X,^^^, °S k ^he meridian the Eastern or Weston ^ ^^,, t?raty:on?:intforenoon,andag.n on the 19th of M^' ^f^ ],, or 3 P. M. , is abont 43F? , „^"/' ^^int John, February What i« *%^,Sutude is 20° ? 81. when the Sun s altuua ^^ • Bequired *« hour at St^tie ^^^^ ^^ 1, the sun's atot"'ll,^l;Lde 25° ; at Prince bUryU, the.«n^„S,tn'saltitude34°; William's Sound, J""^*;' ^er 16, the sun's at the Marquesas, D^cembe^^^ ' altitude ?f 5 J the Pe^ew ^io„, April 21, san^ S;uS°;alp2is.J«21,s^^^ '"^'®°^ PROBLEM XXIII. the proposed day, tnen Di b V8E OF THE GLOBES. 39 e y le ir %n \m as ian [nCj rain don tude uary uary 'rince sun's sun's s alti- or sets at any [oon on s place .^ to the Eastern edge of the horizon, the hour on the horary under the meridian will give the time of rising ; bring it to the Western edge, it will give the time of setting. Examples.^ — At what hour does the Sun rise at London, January 1? Ans, A quarter past eight. At the same place, June 2 J ? Ans, Twenty minutes before four, nearly. At St. John, March 1 ? Ans. About half past six. At what hour does the Sun set at St. John, 24th August? Ans. About three quarters past six. ' Required the hours of the Sun's rising and setting on the first day of every month in the year at St. John ? Required the hours of the sun's rising and setting at London on the days in which h« enters the twelve signs of the Ecliptic. PROBLEM XXIV. . ^ ' To jmxd the length of any day or night <^ the year at any place. Rules. — \st. Find the time of the Sun'g rising and setting (by Problem 23,) and count the hours between them for the length of the day, which subtracted from twenty-four will give the length of the night ; or 2d, — Double the hour of sun-setting for the length of the day, and double the hour of sun rising for the length of the night ; or Zd. — After rectifying the Globe for the la- titude, take the sun's place in the Ecliptic to the Eastern verge of the horizon, and adjust /^m ^ MAMUAI. ON THE f VTT then turn the sun's place the horary for XII- theni ^.^^ ^^^^^ to the western verge, the ^ ^ ^^^^^^ the length of the ^^3^ >[ [X, add the hour hours ; but if more th^n twe^ » ^^ ^^^^ ,hewn by the horaxy ^o ^J^' ^,^ ^ y, f of the day. In UKe m» ,^ ■^^^ t^ the night is required, W J"^ j^ ^^^.y for Ihe V^estern ^g^f^/Se Westwar'd till XII. and 'evolve the Wooe^^^^^ the sun's pl-fu'^TZO then be found by the length -^/J^i.^gtC twelve hours, but the horary, if " f f ^Vl the hour on the ho- if more than tw^lje. fwth of „; ^j. rary to twelve ^^^^^^ ^ ,„g,h of the day ^^'^r'^'Trs— and'winter solsti- at London, at the summ ^^ ^^^^ „ .he '.™ PJ';^ lit U" '»°8' »' "" solstice, titteen ^"" T^ ,f u ^^g long, winter, eight and a »^?™^' ''i, at Quc- Required the kngJyfJ-^^^^ Jj March %ec ; of Feby !»' *;\, g^ at Savannah ; of PROBLEM XXV. UIE OP THE GLOBiiS. 41 e ir ;h to or ill ye, by out ho- day »lstl- tlie tbe John ainer the lb Quc- larch of n •altar. at any Zones. the la- as it i» North or South, bring the first degree of Cancer or Capricorn to the Meridian, and ad- just the horary for XII,* then turn it to the Eastern edge of the horizon, and the horary will shew the time of sunrise, and take it to the western verge, the horary will shew the time of sunset ; the intervening hours will give the length of the longest day. Or, 2d. Having rectified the Globe for the la- titude, bring the first degree of Cancer or Capricorn, as the case may require, to the Eastern verge of the horizon, and adjust the horary for XII. and then revolve the Globe till the same degree come in contact with the Western edge ; the hour shewn by the hora- ry added to twelve, will give the length of the longest day. Note. — To find the length of the shortest night, subtract the length of the longest day from twenty-four, and the difference will give the answer. Examples, — What Is the length of the long- est day at St. John ? As St. John is in the Northern hemisphere, employ the first degree of Cancer, and the longest d-dy is found to be fifteen and a half hours. What is the length of the longest day at Port Jackson ? As Port Jackson is in the ■ "■^; * Teacberi will remember that when the hour circle is far- nished with a mavcable index or pointer, tbe expression *' set the index to twelve," is to be employed, io place of the one here nsed, wherever it occurs. T I) r 42 MANUAL ON THE Southern hemisphere, employlhe first degree of Capricorn, and the longest day will be found to be fourteen and a half hours. Required the length of the longest day at the foUowiflg places — Bristol, Terra del Fue- go, Lisbon, Truxillo, Medina, Rio Janeiro, Seringapatam, Nankin, New Caledonia, Jed- do, Cape Denbigh, Bay of Camarones. PROBLEM XXVI. To find the length of the shortest day at any place in the Temperate and Torrid Zones, Rule. — ^Rectify the Globe for the latitude of the place, and if it is in the Northern hemis- phere, bring the first degree of Capricorn, if in the Southern, the first degree of Cancer to the Eastern verge of the horizon, and adjust the horary for XII. ; then revolve the Globe till the first degree of Capricorn, or the first degree of Cancel, as the case may require, come to the Western verge, and the horary will give the length of the shortest day. Examples, — What is the length of the short- est day at Fredericton ? Ans, As Frederic- ton is in the Northern hemisphere, employ the first degree of Capricorn, and the length of the shortest day will be found to be about eight hours and twenty minutes. What is the length of the shortest day at Cape Saint Mary, the southern extremity of Madagascar ? Ans, As Cape St. Mary is in the Southern hemisphere, employ the first USE OF THE GLOBES. 46 igree II be [ay at Fue- neiro, , Jed- atany^ nes. latitude 1 hemis- icorn, it ancer to d adjust e Globe he first require, horary av. he sbort- rederic- employ le length be about St day at jemity 01 Vlary is i^^ the first degree of Cancer, and the shortest daj will be found to be ten and a half hours. Required the length of the shortest day at Philadelphia, Lima, Abo, Mozambique, Cape Comorin, Isle St. Juan, Straits of Perouse, the Friendly Isles, Owhyhee, Cape Clear. PROBLEM XXVII. T/ie length of the longest day being given, to find the latitude of the place, I Rule. — Bring the firtt degree of Cancer \ or the first degree of Capricorn, according as the latitude sought is North or South, to the brazen meridian — adjust the horary to XII, and revolve the Globe Westward till the ho- rary shews half the given number of hours ; then, keeping the Globe fiinedii move the me- ridian up or down, till the first degree of Cancer, or the first degree of Capricorn, as the case may require, coincides with the Western verge of the horizon; then observe what degree of the meridian is cut by the ho- rizon under the elevated Pole, that gives the latitude sought. Examples, — What is the latitude of a place, where the longest day is sixteen and a half hours? Ans, 61^°. Required the latitude of places, where the longest days are as follows : — 12 hours ; 32J hours ; H hours; 14J hours; 16 hours; 17^ hours ; 18 hours ; 19^ hours ; 20 hours ; 2l| hours ; 23 hours ; 23 J hours. u MANUAL Oir THE PROBLEM XXVIII. To find iliose places ithose longest days cor- respond with a given length. RuxE. — Find the Latitude corresponding with the given length (by Problem XXVII.) and revolve the Globe ; all the places that come under the degree of latitude on the me- ridian have their longest day of the same length. Examples. — What places have their longest day sixteen and a half hours long ? Ans. London, Brussels, Dresden, Leipsick, War- saw, Nootka Sound, Cape Saint James, and Belle Isle. Required those places where the day is twenty hours long ? where it is fifteen hours long? where twenty-two and a half hours long ? and where twenty-four hours long ? PROBLEM XXIX. To find in what climate any place^ ?iot in the/rigid Zones, is situated, the latitude being given. Note. — Climate, in its more common use, denotes the character of the weather peculiar to every country, as respects heat and cold, humidity and dryness, fertility, and the altera- tions of the seasons. But in this Problem we use it in its ancient geographical sense, (which is more agreeable to its derivation from the Greek Klima, a region.) Climate, in this sense USE OF TfiE GLOBES. 45 cor- I V iding VII.) J that leme- sanie ongest Ans. .War- es, and day is n hours f hours ong? f , 710^ in ide being tnon use, peculiar md cold, he altera- oblem we ;e, (which from the this sense ai of the term, is a part of the surface of the earth, bounded by two lesser circles parallel to the Equator ; and of such a breadth that the long- est day in the parallel nearest the Pole ex- ceeds the longest day in that next the Equa- tor by some certain space, as half an hour. Between the Equator and each Polar Circle are twenty-four half hour climates ; and be- tween each Polar Circle and its respective Pole, are six month climates, making sixty climates in all ; thirty on each side of the Equator. Rule. — Find the length of the longest day (by Problem XXV.) from which subtract twelve ; the remainder reduced to half hours will give the climate. Examples, — In what climate is Saint John, whose latitude is 45° 15'. Ans, The longest day at Sainc John is fifteen and a half hours ; from which twelve being subtracted, the re- mainder is three and a half hours or seven half hours, making Saint John to be in the seventh climate. Required the climate in which L9ndon, Leipsic, Warsaw, Cork, Ghent, Cologne, Breslau, and Belle-Isle are, the latitude be- ifig about 61i°. Required the climate in which Siam, Ma- dras, Pondicherry, Tobago, St. Vincent, and Barbados are situated, the latitude being about 16°? Required the climate of Jamaica, latitude about 23° J of the Canaries, latitude about 30°; 'il n I- 46 MANUAL ON THE of Ispahan, latitude about 36° ; of Samar- cand, latitude about 4F ; Cape Breton, lati- tude about 48°. PROBLEM XXX. 7b ^nd what other day of the year mil he of the same length ixiiih any given day. Rule. — Bring the Sun's place in the Eclip- tic for the giren day to the meridian, and ob- serve what degree of the meridian it inter- sects ; revolve the Globe till another degree of the Ecliptic intersect the meridian in the same point ; the day of the year that corre- sponds with that degree, found upon the ho- rizon, is the day required. Examples, — What day is of the same length as March 1 ? Ans, October 11. Required the day which is of the same length as January 10, February 28, March ?30, April 15, May 24, June 12, July 4, Au- gust 21, September 1, October 30, Novem- ber 25, December 16. PROBLEM XXXL To find upon what point of the Compass the Sun will rise and set, at any place, upon a particular day. Rule. — Rectify the Globe for the latitude of the place, and bring the Sun's place in the Ecliptic to the Eastern edge of the horizon, the point of the horizon intersected by it is the point required for the sun's rising ; bring :\' USE OF THE GLOBES. 47 mar- lati- ]3ill he Eclip- idob- inter- legree in the" corre- he ho- length same March 4, Au- >govem- Jompass e^ upon latitude ;e in the lorizon, Iby it is ; bring it to the Western edge, the point of the ho- rizon there intersected by it, is the point re- quired for the sun's setting. Examples, — On what points of the Com- pass will the sun rise and set at St. John on March 20 ? Ans. Due East and West. On March 1 ? Ans. It rises East by South, and it sets West by South. On April 20 ? Ans, It rises East North East 5° East, and sets West North West 5° West. Required the points of the Compass on which the Sun rises and sets at London on June 21 and December 22 ; at New-York, January 1 and June 1 ; at Aberdeen, Februa- ry 5 and July 8 ; at Berlin, March 9 and Au- gust 15 ; at Cape Horn, April 20 and No- vember 6 ; at Cape Ambro, the Northern extremity of Madagascar, May 16 and De- cember 5. PROBLEM XXXII. To Jind at 'what hours the sun ivJll be due East or West at any place on any given day. Rule. — Adjust the Globe for Noon, (by Problem 17,) fix the Quadrant of Altitude in the Zenith, and extend it to the Eastern point of the horizon ; then turn the Globe till the sun's place touch the graduated edge of the quadrant, the hour which then coincides with the meridian is the time when the Sun is due East; bring the quadrant to the Western point of the horizon, and turn the Globe till 48 MANUAL ON THE } the sun's place touch its graduated edge, the hour which then coincides with the meridian, is the time when the sun is due West. Note. — To places North of the Equator the sun is at no time of the day either due East or due West, from the Autumnal to the Vernal Equinox: — and to places South of the Equator the sun is never due East or West from the Vernal to the Autumnal Equinox. The questions on this Problem must therefore be regulated by this circum- stance. Examples. — At what hour is the sun due East at St. John on the 10th of May ? Arts, Rectify the Globe for noon on the given day, extend the quadrant of altitude from the Zen- ith to the East point of the horizon, and move the Globe till the 20th degree of Taurus, the sun's place for the 10th of May, come in contact with the graduated edge of the quad- rant; the hour then coinciding with the meri- dian is a quarter past seven, a. m., the hour required. At what hour is the sun due West at St. John on the 21st August? Ans, A quarter past five, p. M. At what time is the Sun due East at Edin- burgh, April 15; at Stockholm, May 30; at Portsmouth, (England,) June 12; at Rome, July 24; at St. Augustin, (Florida,) August 18 ; at Algiers, September 5 ; at Cook's Straits, October 20 ; at Falkland Isles, Nor USE OF TWS, GLOBES. 49 , the dian, aator L' due othe th of ist or imnal Dblem rcum- m due Ans. n day, p Zen- [move IS, the une in quad- meri- hour at St. uarter Edin- 30; at Rome, August Cook's S, NOr vember 14; at Guayaquil, December 25 ; at Paraiba, January 16 ; at Algoa Bay, Februa- ry 29; ? PROBLEM XXXIII. To find the places that have the same hours of the day as a given place. Those places that have the same longitude have the same hours, and therefore the Rule for Problem V. is to be adopted here. — To find the places that have contrary hours to a given place. Bring the given place to the meridian, and turn the Globe half a revolu- tion, and places then under the meridian will be the places required. Examples. — What places have the same hour of the day as Madras ? Ans, Pondi- cherry, Tranquebar and Candy in the island of Ceylon. What places have opposite hours of the day to St. John? Ans, The conjunction of the River Vitim with the Lena, the small islands in the middle of the China Sea, the Western part of Borneo, the middle of Java, and the Western lands of Nevr Holland. What places have the same hours as As- tracan, Charleston, Formosa, Bougainville Straits, Cayenne, Lake Michigan, Belgrade, Cyprus ? What places have contrary hours to Lon- don, Tunis, Constantinople, Panama, BernCa Cairo, Batavia ? 50 MANUAL ON TPIS PROBLEM XXXIV. ^ The hour of the day at anyplace being giv' euy tojindwhat the hour is at any other "place. Rule. — Bring the given place to the meri- dian, and adjust the horary so that the given l.our will also coincide with the mericlian ; then revolve the globe till the place for which the hour is required be brought to the meri- dian, the hour on the horary which then coin- cides with the meridian, will be the hour re- quired. Note. — The answer will be earlier in the day than the given time, if you have to re- volve the globe eastward ; but it will be later, if you have to revolve it westward. Examples. — When it is noon at Saint John, what is the hour at London? Ans> About half past four o'clock p. m. When it is three o'clock p. M. at London, what is the hour at New York? Ans, Ten o'clock A. M. Required the hour at Constantinople when it is noon at London ;— the hour at Vera Cruz when it is noon at Madras; — the hour at Rome, Port Royal, Bombay, Quebec, and New Britain, respectively, when it is noon at Saint John ; — the hour at Saint John, Mexi- co, Saint Helena, New Zealand, Halifax, California, Saint Jago, and Comoro Isles, when it is 6ix o'clock a. m. at London. Note. — Time may be converted into lon- gitude by multiplying the number of hours by USI OF THE GLOBES. 51 len era lour land In at lexi- ]fax, ^les, llon^ rsby fifteen, bccftiise the Sun passes over fifteen degrees of the Equator every hour; and, vice versa^ longitude may be converted into time by dividing the number of degrees by fifteen. Thus, if it is noon at St. John when it is half past four o'clock p. m. at London ; by multi- plying 15 by 4^, we get 67° 30', which is near- ly the longitude of Saint John. And again, if the longitude of New-York is about 75^ W. by dividing 75 by 15, we get five hours, the difference of time between New York and London. PROBLEM XXXV. The hoicr bei?ig given at any place^ to find tJiose places "uoliere it is anij other given hour. Rule. — Bring the given place to the brass Meridian and adjust tne horary for the given hour at that place ; ther iurn the globe till the other given hour coincide with the meridian : all the places which are then under that semi- circle of the Meridian are the places sought. Examples, — When it is 5 p. m. at London, where is it Noon ? Ans, New York, Cape Mayze, Saint Martha, and all other placets under the Meridian at the same time, or which have the same longitude. "When it is Noon at Saint John, where is it 6, 7, 8, 9, 10, and 11 o'clock a. m, and 1, 2, 3, 4, 5, 6, and 7 o^ clock p. m. ? ; - W^hen it is 4 a. m. at London, where is it 9 p. M. ? — 7 p. M. at Hai^over, v/here is it 11 52 MANUAL jON THK A. M. ? — half past 1 P. M. at the Pelew Is- lands, where is it half past 7 p. m. ? — 4 p. m. at Savannah, where is it 8 A. m. ? — 3 p. m. at Montreal, where is it 10 a, m. ? — when it is midnight at Boston, where is it midday ? PROBLEM XXXVI. . Tojind the SurCs Declination for any given day, ^ Definition. — Declination (from the La- tin Declino, to bend from the straight course,) is the variation the Sun is continually making with regard to his distance from the Equator, and is measured on the Meridian. Rule. — Bring the Sun's place for the given day to the Meridian, — the degree marked over it is the Declination. Examples, — What is the Sun's Declination at the Solstices, June 21, and December 22? Ans, 23^°, which is the greatest declination North or South. Required the Sun's Declination on January 10, February 15, March 20, April 25, May 5, June 16, July i, August 21, September 19, October 7, November 20, and December 1. PROBLEM XXXVII. The Sun^s Declination being given^ toJlnd the Day of the Month, Rule. — Turn the globe till some point of the Ecliptic intersect the degree of Declina- tion on the brass meridian ; that point refer- USE OF THE GLOBES. 58 try [ay 19, II. md of ina- Eer- red to the circle of Months on the wooden horizon will give the day required. Note. — As the sun is twice in every degree of declination, except the most Northerly and the most Southerly, two answers may be given to questions under this Problem. Bxamples. — On what days is the Sun's De- clination 20° N.? Ans.'-Miiy 19 and July 23. Required the days on which the Sun's De- clination is 0°; 10°* N.; 20° S.; 18° N.; 22° S.; 3° N.; 12° S.; 21° N.; \T S.; 7° N.; 23^° S. PROBLEM XXXVIII. To find those places to which the Sun is vertical on any given day. Observe, ist. To be vertical (from Vertex^ the top,) is to be in the Zenith, or directly over head. 2d. As the Sun never recedes from the Equator farther than 23^°, which distance is marked out by the Tropic of Cancer on the North, and by the Tropic of Capricorn on the South, the places given in answers to questions under this Problem, must be within the Torrid Zone. Rule. — Find the Sun's Declination for the given day, by Problem XXXVI. ; then, re- volving the globe, observe the places that come under that degree of the meridian ; these will have the Sun vertical on the given day. Examples. — To what places is the Sun ver- tical on the 10th of Mav? Ans. Jamaica, Midland parts of Africa, Pegu, &c. 54 MANUAL 0:i THE To what places is the Sun vertical at the SummerSolstice, or Juiie21? Ans. Canton, Calcutta, Mecca, and Havannah nearly. What places have the Sun in their Zenith on January IT, February 10, March 20, April 14, May 20, July 11, September 12, November 18, and December 21. PROBLEM XXXIX. A place in the Torrid Zone being given, to find on what two days of the year the Sun will be vertical. Rule. — Find the latitude of the place, and, revolving the Globe, observe what two points of the Ecliptic pass under the degree of lati- tude on the meridian, these shew the places of the Sun, which, compared with the calendar on the horizon, will give the days required. Examples* — On what days of the year is the sun vertical to Goyaz, Sergippo del Rey, the Comoro Isles, and Rotte Island ? A)is» — October 22, and February 17. On what days of the year is the Sun verti- cal at St. Lucia, Kingston in Jamaica, Can- dia in Ceylon, Trinidad, St. Jago in Cuba, Cape Verd, Tobago, Congo, Straits of Ba- belmandeb, Cambodia. PROBLEM XL. The day and hour being given at any place, to find where the Su7i is vertical at that time. Rule. — Ascertain the sun's declination by Problem 36 ; then bring the given place to USE OF THE GLOMES. 55 :ti- in- ice, by le to the brazen meridian, and adjust the hour cir- cle for the assigned hour. Next revolve the Globe ifU XII, at noon, on the horary coin- cide with the meridian ;* the place which is then under the degree of declination is that required. Examples. — Where is the sun vertical at twenty-three minutes after twelve at noon, at London, November 6. A?2S, The sun's place on November 6, is the fourteenth degree of Virga, which, brought to the meridian, shews the declination to be 15° 45' S. ; next bring London to the meridian, and adjust the ho- rary so that twenty-three minutes after twelve will coincid, the same time with the meri- dian. Thtii i'evolve the Globe till XII. at noon coincides with the meridian, and the place under tbe degree of declination will be found to be St. Helena, the place required. Where is the Sun vertical on the. 1st of March, when it is 9 o'clock, .a. m. at Saint John ? On the 25th October, at 5 hours, T minutes, p. m. at London? On the 1st of March at 3 p. m. at Boston ? On the 12th of May at mid-day at Washington ? On the 26th of March at noon at Botany Bay ? On the 8th of October, at three-quarters past 4 A. M. at Alderney ? At the summer solstice, at 7 p. M. at Madeira ? ♦Teachers will remember that when the globe is furnis^iod with a moveable index, the expression *' till the index points to XII, &c." is to be employed, in place of iho one here used, wherever it occurs. I« i 56 MANUAI OK THE PROBLEM XLL The day and hour being given at any place ^ to Jind *where the sun is rising, setting, or on the meridian, and whc' parts of the Globe are illuminated, and Xfohai m darkness, : Rule. — First find the place to which the Sun is vertical at the assigned hour, by Pro^ blem 39 ; next bring that place to the meri- dian, and rectify the Globe for its latitude ; then to all those places in the western semi- circle of the horizon, the sun it rising, to those in the eastern semicircle he is setting, to those under the meridian it is noon, to all ihe places above the horizon the Sun is pre- sent, and those under the horizon are depri- ved of his light. Examples, — To T.'hat places is the sun ri- sing, setting, and on the meridian, when it is 10 a m. at Saint John, N. B. on the 1st of March ? Ans, At the proposed time the sun is found to be vertical at Paraiba in South America. Rectify the Globe for the latitude of Paraiba ; then keeping the Globe fixed with Paraiba under the meridian, it is found that the en- lightened part of the Globe consists of all South America, nearly all North America, all Africa, the island of Madagascar, all Europe, excepting the north-west part of Russia, and Arabia and Turkey in Asia ; the sun is rising to Slave River, Port Saint Francis, and the places on the coast north of California ; he is \:!iJ&iy:, USK OF THE GLOBES. 67 9 L- O 5» ill •e- ri- ri- is of Ind setting to Bourbon Isle, the Almirante Isles, the Gulf of Persia, Bagdad, and Astracan. He is on the meridian of Bera Fyrth in Greenland, Cape Saint Roque, Paraiba and Olinda in South America, and the Island of Georgia in the South Atlantic Ocean. To what places is the sun rising, setting, and on the meridian, on June 5, at seven p. m. at London ? On August 21, at nine a. m. at Glasgow? On September 21, atone p. m. at New- York ? On the 26th April, at three quarters past six a. m. at London ? PROBLEM XLII. To put the Globe in positions representing a parallel sphere^ a right sphere^ and an oblique sphere. Rule.— ^To represent a parallel sphere, ele- vate the pole to the Zenith, or make the Equa- tor coincide with the horizon. To represent a right sphere, make the poles coincide with the horizon, or cause the Equator to move at right angles to the horizon. When the poles are neither in the horizon nor the Zenith, the sphere is in an oblique position, PROBLEM XLIII. To explain^ in general^ the alteration of the length of the dai/s, and difference of the sea- sonsy fro7n a given latitude. Rule. — Put several marks upon the Eclip- tic ; rectify the Globe for the given latitude, D ! f ' Kii 58 MANUAL ON THE turn it about, and it will 'be seen for a nortli- ern latitude that the nearer the marks are to the Tropic of Cancer, the corresponding di- urnal arcs will increase ; but as you approach the Tropic of Capricorn, the diurnal arcs of the marks will decn .•>'■ ; also the former arcs will be greater than a semicircle, and the lat- ter less, and the marks in the Equator will describe a semicircle above the horizon. Therefore, when the sun is in the Equator, the days and nights are equal ; as he advan- ces towards the tropic of Cancer, the days in- crease and the nights decrease; when he comes to the Tropic, the days are the longest and the nights the shortest. As the sun approach- es the P^quator, the length of the days dimi- nishes and that of the nights increases ; and when he comes to the Equator, the days and nights will again be equal. Then, as he ad- vances towards the Tropic of Capricorn, the days diminish and the nights increase, till he reaches that Tropic, when the days will be the shortest and the nights the longest ; and then, as he approaches the Equator, the days will increase and the nights decrease ; and when at the Equator, it will again be equal day and night. Whatever be the latitude of the place, when the sun is in the Equator, the days and nights are equal. At the Poles, the Sun is half a year above the Horizon and half a year below it. At the Equator, the days and nights are equal during USE OF THB GLOBES. 59 o 1- :h of cs at- n\\ ;or, an- , in- mes and acb- funi- and and ad- , the .11 be etbe ben, will ben and Iwben lifrbtS ibove .ttbe luting the whole year ; the sun being twelve hours above the horizon, and twelve below. By rectifying the globe for the latitude of the Arctic Circle, or 66^°, the longest day will be found to be twenty-four hours, and the longest night of the same length ; and it will be readily seen, that all places enjoy equal- ly the Sun in respect to time, and are equally deprived of it ; the length of the days at one season of the year being exactly equal to that of the nights at the opposite. Examples. — Illustrate the above facts by ta- king the Latitude of London. Rectify the globe for the latitude of London, and put marks upon the Ecliptic, say en the begin- ning of each sign. The' oy bringing each mark successively, beginning with the first point of Aries, to the eastern and western ho- rizon, and observing the time of its rising and setting, you will see, as follows, the increase and decrease of the days and nights : — He rises When the sun enters T 6h 0' When the sun enters y 5 "When the sun enters n 4 8 When the sun enters £5 3 47 When the sun enters SI 4 11 When the sun enters '"K 5 3 When the sun enters ^60 When the sun enters f^ 1 3 When the sun enters f 7 51 When the sun enters >)o 8 12 When the sun enters Z!Z 7 50 When the sun enters ^70 Length of He sets day. 6h 0' 12h 0' 7 14 7 52 15 14 S 13 16 26 7 49 15 38 6 57 13 54 6 12 4 57 9 54 4 9 8 13 3 48 7 36 4 10 8 20 i 10 Length o£ night. 12h 10 8 16 7 34 8 22 10 6 12 14 6 15 42 16 24 15 40 14 r e^ MANUAL ON THE ( ': The Pupil may be exercised in finding from the globe^ in the same manner as above, tlie increase and decrease of the days and nights for every 15° of the Sun's progress in the Ecliptic in the latitude of Saint John ; the increase and decrease of the days and nights for every 20° of the Sun's progress in the Ecliptic, in the latitude of New York ; the same for the first day of every month in the latitude of Archangel. PROBLEM XLIV. To find on "dohat day the Sun begins to shine constafitli/, and how long, at any given place in either of the Frigid Zones, Rule. — Observe the distance of the assign- ed place from the Pole, and reckon an equal number of degrees from the Equator towards the same Pole ; revolve the globe, and mark the two points of the Foliptic, which pass un- der that degree of the meridian ; and then find on the Horizon on what days of the year the Sun is in those points of the Ecliptic; the day nearest the Vernal Equinox is the one on which the Sun begins to shine constantly in the North 'jrn Frigid Zone, and the space of li' '.e between the two days is the duration of sunshine. Examples, — On what day does the Sun be- gin to shine constantly, and what is the time of its duration at the North Pole? A71S, — The Vernal Equinox ; duration six months. V8E OF THE GLOBES. 61 /- s e, id in he LltS the the the hine cein ign- jqual rards ark s un- then year ; the one tantly jspace :ation in be- time Ins. — • ahs. When does the sun begin to shine without intermission, and what is the period of its du- ration at the following places : — Sphzbergen, North Cape, James's Sound, Icy Cape, Beh- ring's Straights. PROBLEM XLV. To find the latitude of those places in the Frigid Zones where the Sim begins to shine constantly on any given day. Rule. — Find the Sun's declination for the given day and subtract it from 90° the re- mainder will give the latitude required. Note. — The same latitude in the opposite Hemisphere will show those places to which the Sun is beginning to disappear. Examples, — In what latitude does the Sun begin to shine without intermission on the 20th of March? ^ns.— Lat. 90°, or the North Pole. ^ Required the latitude of those places where the Sun begins to shine constantly at the Au- tumnal Equinox, April 15, May 20, June 18, August 24, October 29, November 1, and December 21. PROBLEM XLVI. To find in what parallel of Latitude in the Northern Frigid Zone the Sun does not set for, any given number of days not exceeding 180. Rule. — Count as many degrees on the Ecliptic, beginning at the first degree of Can- 62 MANUAL ON THE cer, if in the Northern hemisphere, at the first degree of Capricorn, if in the Southern hemi- sphere, as amount to half the number of as- signed days ; bring the point, where the count- ing terminates, to the meridian ; observe how many degrees are intercepted between it and the corresponding Pole; and then, reckon tlie same number of degrees on the meridian from the Equator towards the same Pole, and that will shew the required parallel of latitude. Examples, — In what parallel of latitude does the sun not set for 20 days in the North Frigid Zone. Ansxver, — Counting ten from the first degree of Cancer, and bringing the tenth degree to the meridian, the arc intercep- ted between that and the Pole is 67°, — this number counted from the Equator towards the Pole gives 67° on the meridian for the parallel of latitude required. Required the parallels of latitude in which the Sun does not set for 30, 40, 50, 60, 70, 80, 90, 100, 130, 150, 170 and 180 days. PROBLEM XLVII. A j}lace and time being assigned^ to find >mhere it is twilight, Eplanation. — Twilight, or crepusculum, is the time from the first dawn of the morn- ing to the rising of the sun ; and, again, be- tween the setting of the sun and the last re- mains of day. Without this twilight, the sun's light would not appear till its rising and i lich 80, USE OF THE GLOBES. 6S "would instantly disappear at its setting. The duration of twilight is different in different cli- mates ; and in the same place it varies at dif- ferent periods of the year. It is longest in a parallel sphere, and shortest in a right sphere ; and in an oblique sphere, the nearer the sphere approaches to a parallel, the longer is the twi- light, because it commences and terminates when the Sun is about 18° below the hori- zon ; for then the stars of the sixth magnitude, the smallest that appear to the naked eye, dis- appear in the morning and appear in the eve- nmg. Hence to solve Probleuis regarding the twilight, the Quadrant of Altitude is usu- ally furnished with what is called a crepuscu- lum graduation of 18 degrees. Rule. — Rectify the globe for the place to which the sun is vertical on the given day (by Problems 40 and 4), fix the quadrant over the zenith, move it round the globe betwixt the Zenith and the Horizon, and observe what places the crepusculum part of it passes over in its course ; these have twilight at the assign- ed time. Examples, — Where is it twilight on the 4th of June, when it is half past eleven, a. m. at Saint John ? Ans,-^Kt Otaheite, and other Society Islands it is morning twifight. At the Cape of Good Hope, the Channel of Mozam- bique, the Eastern part of Africa, the Eastern past ot Arabia, a great part of Tartary, and the South of Siberia, it is evenuig twilight 64 MANUAL ON THB Where is it twilight when it is noon at Lon- don, January 3 ? Nine A. M. at St. John, February 18? Nine A. M. at New-York, March 5 ? Three P. M. at London, April 17? PROBLEM XLVIII. On any proposed day^ tojind when morning ivcilight begins and evening twilight ends, at any assigned place. Rule. — Adjust the Globe for noon; fk^i the quadrant over the zenith, and extend it to the eastern verge of the horizon ; then turn the Globe till the sun's place comes in con- tact with the 18th degree of the crepusculuni graduation on the quadrant, and the hour then coinciding with the meridian will be the hour &t which the twilight begins at the pro- posed place on the given day. The same operation performed on the wes- tern side of the horizon will shew when twi- light ends. When does twilight appear at Saint John, March 5 ? Ans, About three-quarters past Four, A. M, When does twilight appear at London^ January 15? at Paris, February 20? at Phi- ladelphia, March 2? at Constantinople, April 25 ? When does twilight end at Edinburgh, May 6 ? at CuImi, June 1 ? at Tobago, July 50 ? at Cape Horn, August 15? USE OF TfiE GLOBlSS. 65 )ast PROBLEM XLIX. To find the duration of twilight at the 'North Pole, and likewise how long night continues there after the total cessation of twilight. Rule. — Adjust the globe to represent apar- nllel sphere (by Problem 42), turn the globe till some part of the Ecliptic, counted irbra the first degree of Libra, falls directly under 18° of the meridian in south declination, whick, will be in 26° of Scorpio, the sun*s place on the 12th November, the day when twilight ends ; then turn the Globe till some other point of the Ecliptic meets the same degree of south declination, which will be 10° of Aquarius, the sun's place for January 29, till which time the sun's light is totally absent ; from this time twilight begins again, and con- tinues till the sun enters Aries, when a day of six months commences at the North Pole. The pupil may exercise himself in finding in like manner tlie duration of twilight at the South Pole, and how long night continue ^ there after twilight totally ends. PROBLEM L. To find in what Latitude the longest day is of any given length less than twenty-four hours. Rule. — Bring the solstitial point to the me- ridian, and adjust the horary for XII., then turn the Globe westward half the given num- ber of hours ; keep the globe steady, and move 66 MANUAL ON THE the meridian up or down, till the solstitial point comes to the horizon ; the elevation of the Pole will then be the latitude sought. . Examples, — In what latitude is the longest day fifteen and a half hOv^rs ? Ans, 45J°. Required the latitudes where the longest day is 12, 13, 14, 15, 15J, 17, 18J, 19, 20, 21*^, 23, and 23 J hours. " PROBLEM LI. Tojind all those places to isohich a Lunar'*' Eclipse^ is visible at any instant. * Lunar from Luna the Moon. § An Eclipse (from the Greek, ekleipe, to fail) is u privation of light of one of the luminaries by the interposition of some opaque body, either be- tween it find the observer, or between it and the Sun. Eclipses of the Sun and Moon happen when the moon is near her nodes, or the points in which her orbit intersects the Ecliptic. Those of theSun happen only at new moon, or when the moon is in conjunction with the Sun, that is, when she is be- tween the Earth and the Sun: and those of the Moon happen at the time of full Moon, or when the Moon is in opposition to the Sun. Eclipses, with respect to their circumstances are divided into total, partial, annular and cen- tral. An Eclipse is iotalf when the body eclipsed is wholly out of view, a phenomenon that very seldom occurs with regard to the Sun. An Eclipse impar- tial when only part of a luminary is eclipsed. An Eclipse is called Central, when the centres of the luminaries exactly coincide, and are direct- ly in a line with the eye of the observer. USE OP THE GLOBES. 67 un s ia be- tbe )ar" tres I'ect- RuLES. — \st. Find the place to which the sun is vertical at the given time, bring that place to the meridian, and rectify the globe for its latitude ; then, as the moon must be directly opposite to the sun whenever she is eclipsed, the eclipse will be visible in all those places which are then under the horizon : or 2d. Bring the antipodes of the place, to which the Sun is vertical at the assigned time, to the brass meridian, and rectify the globe for their lathude; the parts of the earth then above the horizon will have the eclipse visible. Jlnnular (from the Latin Annulus, a ring), ia a term applied to an eclipse of the sun, in which a rinfj of light appears around the dark body of the moon. There can be no annular eclipso of the mooQ, on account of its being a much smaller body than the earth, whose fehadovv causes its eclipses. If the Moon's orbit were coincident with the plane of the Ecliptic, the Moon's shadow would fall upon the earvh, and occasion a central eclipse of the Sun at every conjui:{:tion, or new Moon ; whilst the Earth's shadow would fall on the Moon and occasion a totftl eclip&e of that body at Gv^ry opposition or full moon. For as the moon would then ahvr.ys move in the eclij)tic, the centres of the Sun, Earth and Moon, would all be in the same straight line at both of these times. But the Moon's orbit is inclined to the Ecliptic, and forms with it an angle of about 5 deff. 10m. ; and there- fore the Moon is never in the Ecliptic except when ghe is in her nodes ; hence, there may be a con- fiiderable number of conjunctions and oppositions of the Sun aad Moou, without any Eclipse taking place. 68 MANUAL ON THE Examples, — Suppose a lunar eclipse to take place at St. John, at 9 P. M. on April 9, to what places would it be visible ? Ans, The sun is vertical on the 9th April at 9 P. M. to the most easterly of the Carolinas, lat. 8° N. The globe, rectified for the latitude of their Antipodes, gives all Africa, all Europe, ex- cepting the north-east part of Russia, all South America, and all North America, ex- cepting the north-west part of it, as the places to which the eclipse is visible. Suppose Lunar eclipses to happen at the following times and places, to what parts of the earth will they be visible ? At London, May 27, at 7 o'clock, P. M. ; at Saint John, January 10 J P. M. ; at London, February 18, at 7, P. M.; at St. John, May .3, at 10, A.M.? PROBLEM LII. To find those places to 'which a Solar*" Eclipse will be visible^ a particular day and hour being given. Note. — This Problem cannot well be sol- ved by a globe merely, as a Solar eclipse, on account of the vast distance and size of the sun compared with the moon, does not hap- pen to the whole hemisphere of the earth next tlie sun, nor does it happen at the same time to those places where it is visible. But as it *' From the Latia SqI, the Sud. A. VSE OF THE GLOBES. 69 *.* Sol- on the lap- lext llime las it is generally given in Books on the use of the Globes, we here insert the common Rule. — Find the place to which the Sun is vertical at the given time ; keep that spot iinder the brass meridian, and rectify the Globe for its latitude; then, if the Eclipse be large, it will be visible to almost all those parts which are then in the upper hemis- phere. Examples, — Suppose the Sun were eclipsed at Saint John on the 21st of June, at half- past one p. m. to what other places would the Eclipse be visible ? — Ans. To all North and South America, almost all Europe, and the North-west part of Africa. Suppose Solar Eclipses to take place at Saint John, on the tbllowing days and hours, to what parts of the earth would they be visible ? April IT, half-past seven, a. m. — May 21, half-past nine, a. m. — June 10, half-past ten, a. m. — August 8, half-past 12, p. m. — Sep- tember 6, two p. m. PROBLExM LIII. To find the Right Ascension of the Sun for any day. Definition. — Right Ascension is that de- gree of the Equator which rises with the Sun in a Right Sphere, and which comes to the Meridian with the Sun in any position of the Sphere. It is reckoned from the first Point 70 MANUAL ON THE of Aries, or the Vernal Equinox, all round the Equator. Rule. — Bring the Sun's place in the E- cliptic for the given clay to the Brazen Meri- dian, and that degree of the Ecjuator which is cut by the Meridian is the Tlight Ascen- sion, f : NaTE. — The reason of thus referring it to the Meridian is, that it is always at right angles to the Equator, whereas the Horizon is so, only in a right sphere. Examples. — What is the Right Ascension of the Sun on the 20th of March, and 21st of Sept. — Ans, deg. and 180 deg. Required the Right Ascension on the fol- lowing days — Jan. 15; Feb. 20; March 12; April 10. May 16; June 19 ; July 22 ; Aug. 24. Sept. .30; Oct. 7; Nov. 15; Dec. 25. PROBLEM LIV. To ^find the Sun's Oblique Ascension for any given, place and, day, ♦ Definition.^ — The Oblique Ascension is that point or degree of the Equator which rises &i t: :e same time with the Sun in an ob- lique Sphere. Oblique Descension is that point of the Equator which sets with the Sun. Rule. — -Rectify the Globe for the latitude of the place, find the Sun*s situation in the Ecliptic for the given day, and bring it to the Eastern verge of the Horizon ; the degree of sJ USE OF THE GLOBES. 71 1 IS jicU ob- Ihat iun. lude the the le of the Equator then coinciding with the Hori- zon is the Oblique Ascension required. Examples. — What is the Sun's Oblique Ascension at Saint John on the 10th of March ? Ans, 355°. Required the Sun's Oblique Ascension at St. John, on the 20th of March and 21st of September ? at London, Jan. 15, and June 20 ? at New-York, Feb. 10, and July 15 ? at Turk's Island, March 5, and Aug. 20? at Kong, April 19, and Sept. 25 ? at Cor- dova, May 27, and Oct. 9 ? PROBLEM LV. To Jind the Ascensional Difference^ arid^ from it, the Time the Sun rises before or after Six, Definition. — The Ascensional Differ- ence is the difference between the Right and Oblique Ascension. Rule. — Find the Right and Oblique As- censions for the given place and day, (by the two preceding Problems) and take their differ- ence. This may be reduced to time by divi- ding by 15, the number of degrees corres- ponding with an hour. Note. — In Northern Latitudes, v/hen the Sun is in any of the northern signs, it rises before, and when in any of the southern signs, it rises after six o'clock. Examples* — Required the Sun's Right As- cension, Oblique Ascension, Ascensional u MAN U A3. eW THE Difference) and the time of his rising at St John on the 1st of June,-^Ans, Right As* cension, 69J deg. ; Oblique Ascension, 45 deg. ; Ascensional Difference, 24^ deg. ; which divided by 15, gives one hour and thirty-eight minutes for the Ume the Sun rises before six. Required the Sun's Right Ascension, Ob- lique Ascension, Ascensional Difference, and time of llishig at London, on the 1st of May ? at Edinburglu on the 12th of July? at Lisbon on the 8ti.' Ai^gust ? at New Or- leans, on the 1 0th Sept ? at Boston on the 17th Oct. ? at MageliaLis kStraits on the 9th 'Nov. ? at Mecca, oa the 16th of Dec. ? at the Straits of Sunda, on the 5th of Jan. ? at JessG; on the 25tli of February ? PROBLEM LVI. The day and Place being given tojind the Sun^s Ampliiiide, Definition. — The Amplitude of the Sun (from the latin Amplitudo, extent) is an arc of the Horizon, measuring the extent of the distance of his rising or setting from the East oi' West Points, and is accordingly distinguished into ortive or risings and occa-' $ive* or setting. Rule. — Adjust the Globe for the latitude * Ortive from the Latin Ortus, Sun-risings and Occaskve from X\iq Latin Occasus, Sun^set. t a th t7S& OF THE GLOBES. 7al the Sua arc )f the the bngly xocca" titude and bf the given place, and bring the Sun's place in the Ecliptic for the given day to the East- ern edge of the Horizon ; the number of de- grees then intercepted between the Sun's pk»c ■ and the East Point is the Rising Am- plita^iC, vi^hich will be north or south accord- ing as the Sun is in north or south declina- tion. Revolve the Globe till the Sun's place cc 'ncides with the Western verge of the Ho- rizon, and the Setting Amplitude will be? found in like manner. Examples, — What is the Sun's Amplitude at Saint John on the 12th of March ? Ans, The rising Amplitude is 6 deg. from the east, southerly, and ihe Setting Amplitude is 5 deg. from the west, southerly. Required the Sun's Amplitude at Lon- don, March 12; at Vienna, Jan* 6; at New York, Feb. 10 ; at Philadelphia, April IT ; at Fox Islands, May 21; at Surinam, June 25 ; at Morocco, July 29. PROBLEM LVir. The day of ihe Year and the Sun's Ampli- tude being given^ tojind the Latitude* EuLE. — Bring the Sun's Place in the E- cliptic for the given day to the eastern or western verge of the Horizon, according as the Ortive or Occasive Amplitude is given, and move the Brai^ Meridian up or down, till the Sun's place coincides with the given amplitude on the Horizon ; the elevation of the Pole will give the Latitude required. E H MANUAL ON THE ti i : I Examples. — If the Sun's Amplitude ijj S5 cleg, from the east towards the north on the 2 1st of June — what is the latitude of the place ? Ans, 45^ degrees. Required the Latitude where the Sun's Amplitude is 30 deg. from the east, north- erly on the 6th of June ; where it is 20 deg. from the east, southerly, on the 25th Oct. ; where it is 15 deft, from the west, northerly, on the 21st of April; where it is 40 deg, from the west, southerly, on the 4th of Ja- nuary. PROBLEM LVIH. The daij, hour, and place being given, to Jind the Sun's Azimuth, Definition. — -Azimuth (an Arabic term) is an arc of the Horizon intercepted between the Meridian of the place and an imaginary gieac circle, "* passing through the Zenith and the Sun at right angles to the Horizon. In the forenoon it is east of the Meridian, and in the afternoon, west. The imaginary great circle is represented in the solutions of this Problem by the Quadrant of Altitude fixed to the Zenith. Rule. — Adjust the Globe for noon on the given d^Y, (by Problem IT,) fix the Quad- rant of Altitude in the Zenith, move the Globe till it is adjusted for the given hour, • Such circles are generally called Vortical or Azioiuth circleii I yeen nary inith zon. Uan, nary s of tude the fuad- the lOur, :al 01- USE OF THE GLOBES. Ti then pass the quadrant over the Sun's place, and the point of its intersection with the Horizon will give the required Azimuth. Ej:amples, — What is the Sun's Azimuth at Saint John on the 22d of May, at 9 a. m.? Arts, About 71 deg. South Azimuth, that is, 71 deg. from the south-easterly ; or 19 deg. from the east, southerly, or 109 deg. Azi- muth from the north. Required the Sun's Azimuth at the fol- lowing places on the subjoined days and hours : — London, Jan. I, 10, a. m. — Cork, Feb. 15, 11 a. m.— Madrid, March 7, 2, p. m. — Boston, April 1, 8, p. m. — Nicara- gua, May 21, 4 p. m. — Tripoli, June 18, 6 a. m. — Samarcand, July 5, 7 a. m. — Aracan, Aug. 21, 9 a. m; PROBLEM LIX. The place, the day, and the SurCs Azinuth being given, to find Hie hour of the day, . Rule. — Adjust the Globe for noon, (by Problem XVII.) fix the Quadrant in the Ze- nith, and move its graduated edge to the given azimuth ; then revolve the Globe till the Sun's place coincides with the edge of the Quadrant, and the hour required will then be that on the hour circle, which coin- cides with the meridian. Examples, — Whai is the hour at London, July 22, the Sun's Azimuth being QQ deg. fiom the south, easterly ? — A7is^ 9 a, m» 76 MANUAL ON THE Required the hour at the following places^ on the annexed days, the Azimuth of the Sun being as subjoined. St. John, May 22, Sun's A-imtth 71 deg. from the south, easterly ; Edinburgh, Feb. 24, Sun's Azimuth 40 deg. from the south, easterly ; Guadaloupe, April 20, Sun's Azi- muth, 10 deg. from the east, northerly ; Mexico, Nov, 1, Sun's Azimuth 25 deg. from the west, southerly ; Calais, May 30, Sun's Azimuth 60 deg. ^-om the north, easterly; Fredericton, Aug. 15, Sun's Azimuth, 56 deg. from the south, easterly ; Halifax, Sept, 5, Sun's Azimuth 17 deg. from the south, easterly. PROBLEM LX. Tojind the Su7i*s Depression below the Ffo^ rizon at any hour of a given flight at anyplace. Rule. — Rectify the globe for Noon at the given place (by Problem 17), turn it westward, till it is adjusted for the given hour; then, keeping it fixed, find the Altitude of the De- gree of the Ecliptic exactly opposite to the Sun's place for the given day ; that altitude will be equal to the Depression required. E:tamples. — What is the Sun's depression at St. John on the 15th March, at 10 o'clock, p. ni. ? Ans. — The Sun on the 15th March is in the 25th of Pisces, the degree exactly op- posite which is the 25th of Virgo. The globe having been adjusted according to the Rule, the altitude of the 25th of Virgo is found to i ision lock, Ich is op- rlobe llule, id to USE OF TIIE aLOBCS ^7 be iS°, which is the Depression of the 26th of Pisces required. Note. — The Azimuth of the Sun when un- der the horizon may at the same time be found, by finding the azimuth of the degree of the Ecliptic of which the altitude is taken and re- ferring it to the opposite point of the horizon. Thus the azimuth of the 25th of Virgo is found to be S. E. by S. 5° E. which referred to the opposite point of the Compass is found to be N. W. by N. 5° W. the azimuth of the 25tli of Pisces at the specified time. • . Required the Sun's depression below the horizon at London, November 1, at 10, p. m. — at Petersburg, February 20, at 7, p. m. — at Lima, June 26, at 11, p. m. — at Mexico, November 8, at 1, a. m. — at New York, Ja- nuary T, at T, p. m. — at Cape Horn, July 20, at 10, p. m. — at Quito, Feb. 15, at midnight. PROBLEM LXI. To find the Equation of Time, as far as it can be done by means of a Globe. Explanation. — Were the Sun not to vary his Declination, but to move daily either co- incident or parallel with the Equator, a de- gree of the Ecliptic would be described in neither more nor less time than a degree of the Equator, and solar time would always be coincident with the time of a well regulated clock. But this is not the case. The Sun is continually varying his declination^ and ,1 I 78 MANUAL ON THE causing the well known obliquity of his path ; the consequence of which is, that the time in which he describes a degree of the Ecliptic is seldom exactly coincident with a degree of the Equator. This may be easily illustrated by placing patches on the Ecliptic and Equator at every tenth or fifteenth de- gree, and turning the globe slowly on its axis. By doing this, it will be seen that the patches pass under the brazen meridian at different times. Hence arises the Equation of Time*, which is greatest about February 6, May 5, August 8, and November 8, and is nothing about March 21, June 21, Septem- ber 23, and December 21. Rule. — Bring the Sun's place in the Eclip- tic to the brass meridian, count the number of degrees from the first point of Aries to the brass meridian on the Equator and on the Ecliptic; the Difference, reduced to time, reckoning four minutes to a degree, is the E- q nation of Time. If the number of degrees * One part of it, only, nowever; for the unequal moiion of the Sun in the Ecliptic, is another circumstarice which enters into the Equation of Time, hut which cannot, in any manner, be illustrated by an artificial Globe. 'I'hia part of the Equa^ tion 18 greatest about March 30(h and October 3J, and least or ■•thing on July 1st and December Slst, when the Sun is in his Apsides, or those points of his orbit which are nearest and most distant. As the Sun moves from the Apogee, or point inost distant from the Earth, where he is on the Ist of July, to the Perigee, or point nearest the Earth, where he is on th« 31st of December, the time shewn by the Sua, or apparent time, precedes that shewn by a well regulated clock, or mean time; but whilst it moves from the Perigee tu the Apogee, the ittcan lime precedes tbo apparent time. t USB OF THE GLOBES. 79 on the Ecliptic exceed those on the Eqiintor, the Sun is faster than the clock, but if the number of degrees on the Equator exceed those on the EcHptic, the Sun is slower than the clock. Examples, — What is the Equation of Time on the 2Tth of June ? Am, — The degrees on the Equator exceed those on the Ecliptic by One, hence the Sun is four minutes slower than the clock. Required the Equation of Time on the first day of every month, and on the days on wliicli the Sun enters the different Signs. Note. — The Equation of Time vs set down on the horizon of some globes, so that it can easily be obtained by reference. — On other globes an Analemma* is inserted on a vacant part of the torrid zone, constructed sornewliat in the form of the fioiure 8, extendinjjj from tropic to tropic, so as to embrace every de- gree of declination. The months and days of the year are inserted in it, in such a manner as to come under the degrees of declination on the meridian, that correspond with them. On some globes, through the point of this figure, where the opposite parts cross each other, a small line is drawn parallel to the Equator and divided as a scale, for the purpose of giv- I * An Analemma (from the Greek analamhanOy to lake backwardg,) is properly a planispliere, or projection of tho i{»bere on the plune of the meridian. But here ii is nothing, else but a Boale of DcchnatiuQ combined wiib a gcale of tho Equaition of Time. K { If/ r *o MANUAL ON THE ing the Equation of Time; extending to 20 minutes on one side, showing the slowness of the clock, and to 20 minutes on the other, showing the fastness of the clock, when com- pared with the solar time. To find the Equation of Time by the Ana- lemma ; bring the day of the month on the Analemma to the graduated edge of the brass meridian, and observe what point of the scale of time simultaneously coincides with it; that gives the Equation desired. Several other Problems may be solved with the greatest ease by the Analemma ; as — 1st. To find the Stints Declinatio7i. Bring the day of the month on the analemma to the brass meridian, and observe what degree it intersects. 2d. To Jind those tixo days in the year in which the Sun's Declination is the same. Let the analemma pass under the meridian, and the two days on the analemma which pass un- der the given degree of declination are those required. 3d. To Jind the Sufi^s place in the Eclipti . Revolve the globe till some point of the Eclip- tic pass under the degree of declination on the meridian, which has been previously ascer- tained by bringing the day of the month on the analemma to the meridian ; that will be the Sun's place required. If the day is on the decreasing scale, then the descending side of the Ecliptic must be taken^ but if on tne in- USE OF Tilf: GLOBUS. 81 the :er- on be on [side in- :1? creasing scale, the ascending eide must be ta- ken. 4tli. To^find xeJiere the Sun is vertical. Pass the analemma to the meridian to find the de- clination, and, revolving the globe, observe all the places that come under that degree of the meridian. - ; - . 5th. To ^ fid those two days of the year to which the Sun will he vertical to any place within the torrid zone. Find the latitude of the place and bring the analemma under it, 6th. To find what other day of the year will he equal to a given day. Find the given day on the analemma, and adjoining it will be found the required day. PROBLEM LXII. To draw a Meridian Line. Note. — A Meridian, or North and South Line, is of the greatest importance in all ca- ses relating to Astronomy, Geograpliy, and Diallinor, because on the exact determinrtion of it, all the other parts have their chief de- pendence. The following Rule is perhaps one of the most simple for young pupils : — Rule. — On a fiat board describe several con- centric circles or arcs of circles, and on the centre fix a style or pin, about half a foot long, perpendicular to the plane of the board, hav- ing a little hole drilled in its top, which should be made flat. Place the board in a true ho- H 82 MANUAL OK THE I ','U 1 1 ■i f sfli ffl I rizontal position, and about llie 21st of June between the hours of nine and eleven in the forenoon, and one and three in the afternoon, observe the points, wherein the lucid spot, projected by the hole, touches the several arcs. Divide the spaces between them in the several arcs into two equal parts, and draw a line through the points of bisection ; that line will be the meridian line required. PROBLEM LXni. To find the Angular distances of the hour lines on a horizontal dial for any latitude. Definition. — Dial (from dies^ a day), is an instrument serving to measure time by means of the shadow of the sun, on which account it was also called by the ancients, Sciathera- cuniy the shadow-hunter, (from the Greek sMa, a shadow, therao^ to hunt). A horizon- tal dial is one drawn on a plane parallel to the horizon, having its gnomon or style eleva- ted according to the latitude of the place, cr pointing to the pole. Rule. — Rectify the globe for the given la- titude ; bring any one of the twenty-four meri- dian lines to the brass meridian, and at the same time adjust the hour circle for XII. keeping the Globe in this position, mark off the dis'ances in decrees from the brass meri- dian, at which the different meridians inter- sect the horizon, these will give the angular distances of the hour lines required. J * to cr off eri- ter- ilar •■ USE OF THE GLOBES. g3 ! ''■if Example, — Find the angular distances for a horizontal dial at St. John, New-Brunswick? Ans, Having prepared the globe according to the Rule, the angular distances of 1 p. m. and 11 A. M. are found to be 10^° ; of 2 p. m. and 10 A. M. 21|° ; of 3 p. m. and 9 a. m. 35° ; of 4- p. M. and 8 a. m. 50 J° ; of 5 p. M. and 7 a. m. 69° ; of 6, both morning and even- ing, 90°.; of 7 p. M. and 5 a. m. 110° ; of 8 p. M. and 4 a. m. 128^.° As the gnomon does not cast a shadow strong enough on the dial to tell the hour before 4 a. m. or after 8 p. M. it is not necessary to proceed further in drawing the hour-lines. Find the hour-angles for horizontal dials at London and New- York ? PROBLEM LXIV. To find the Angular distances of the hour lines for an Erect Direct Dial for a given place. Definition. — An Erect Dial is one that stands perpendicular to liie horizon, and v/heii it faces one of the Cardinal points, it is called Direct, otherwise, Declining. Note. — As a tangent to a circle is parallel to a diameter drawn at the distance of 90 de- grees, so the plane of a horizontal dial must be parallel to tiie plane of an Erect dial for a place whose difference of latitude is 90 de^r, Rulb:. — Rectify the globe for a latitude GO vlegrees from .lie given latituae, and deter- mviie (by Problem LXIIL) the hour angles 8i MANUAL ON THE for a horizontal dial at that latitude ; the dia- gram will furnish an erect dial for the given place. The gnomon of this dial must make an angle with its plane equal to the latitude of the place where it is a horizontal dial. Ea^amplcs, — Find the hour angles for an Erect Direct South Dial at London ? Am. Having rectified the globe for 38^^ south, which is 90 degrees south of the lati- tude of London, and prepared the Globe as in the preceding Problem, it is found that the hour angles of a horizontal dial for that la- titude are as follows : for 1 and 11, 9^° — for 2 and 10, 19i°— for 3 and 9, 314"^— for 4 and 8, 47°--for 5 and 7, 66|°— for 6, both morning and evening, 90° — ^for 7 and 5, 112i°— for8and4, 132J^ This Dial will constitute an Erect Direct South Dial at London. Find the Hour angles of an erect direct South Dial in the Latitude of Saint John, in the latitude of Paris, and in the latitude of Jamaica. Note. — When the Dial is in its true po- sition, the morninir hours will be on the West side of the gnomon, and the afternoon hours on the East side. The line on which the gnomon stands is called the substile line. PROBLEM LXV. To find the Hour-lines of a Declining Di- al for any given place. Definition — A Declining Dial is an erect USE OF THE GLOBES. 85 rect po- test mrs the Di- jrect ■i0 one that does not face any of the Cardinal Points, but stands inclined to some one of them at a greater or less angle. Rule. — Bring the given place to the Me- ridian and rectify the Globe for its latitude. Note its longitude — find that place which \t in the Horizon at a distance from the Meri- dian equal to the declination of the required Dial, bring it to the Meridian, and note its latitude and longitude. Rectify the Globe tlien for that latitude, and bring Aries to the Meridian — then turn the Globe, till that de- gree of longitude, which is equal to the differ- ence of the longitude of the given place, and the longitude of the place found on the Ho- rizon come under the Meridian, and fix the Globe. Then the Meridians, passing through every fifteen degrees of the Equator, cut the Horizon in the respective distances of all the hours from the Substile, or the line on which the gnomon is erected. Example, — Find the angles which the hour lines make with the Substile of a verti- cal Dial, in the latitude of St. John, that de- clinos from the Souths towards the East, fifty degrees. Solution. — F ctify the Globe for the lati- tude of St. John, bring Saint John to the Meridian and mark its longitude, 66^ ; ob- serve that place on the Globe which is bO^ from the South towards the East, bring it to the Meridian and observe its latitude and longitude, the former of which is 26^° South 86 MANUAL ON THE and the latter 9® West. The difFerence of which and that of Saint John is 57°, Next rectify the Globe for '26|° South, aiid bring Aries to the Meridian : turn the Globe till 57° East longitude comes under the brass Meridian and fix the Globe. The Equinoctial colure will then cut the Horizon at 33° from the Substile line, which will be the hour line »>r XII ; the Meridian nearer the brass Meridian or substile makes an angle of 21° T^'itli *he substile, and is the hour line of XI ; the next makes an angle of 12° and is the hour line of X ; the next makes an angle of 5°, e hour line of IX ; the next makes an angle of 1}° to the West of the Substile line anH is the hour line of VIII ; the next is 9° the hour line of VII : the next 17° the hour line of VI ; the next 28^° the hour line of V ; the next 44°^ the hour line of IV. Going Eastward to the next Meridian beyond the Equinoctial colure, we find it cuts the horizon at 52° from the bra- zen Meridian, which gives the hour line of I ; the next is 78i'^ the hour line of II. Note. — If an Erect Dial Decline towards the East from the South, the Substile line will fall among the morning hours, as in the above example ; but if it decline Westward, the Substile will fall among the afternoon hours. 0- #: MISCELLANEOUS QUESTIONS rOR THE EXERCISE OF THE LEARNER. i •% What is the latitude, and what the longi- tude of that place where Bonaparte died ? What is the difference of the latitude of that great city which is unrivalled in its pur- suit after every improvement and the amelio- ration of mankind, and the latitude of that Other great city, which is as much distinguish- e3Smg from Saint John to London, at the rate of eight and a half miles an hour? What place is that which lies in the paral- lel of St. John as far East from London as St. John is West? How far would a ship travel in c'v "umna- vigating the Globe, if it should set out from London, touch at Bermuda, Trinidad, Bue- nos Ayes, Terra del Fuego, Chiloe, Truxil- lo, the Gallipagoes, the Marquesas, New Ca- ledonia, Van Diemen's Land, Kerguelen's Land, Cape of Good Hope, St. Helena, Sier- ra Leone, the Madeiras, and thence to Lon- don? In what latitude and longitude is that point from which a circle described would pass through St. John, London, and Paris ? What place has neither latitude nor longi- tude ? and what place has no latitude, and yet the greatest degree of longitude ? What are the Antipodes of the Perioeci of St. John ? What are the Perioeci of the Antoeci of London ? What is the distance in geographical miles of the Antoeci, and thence to the Perioeci, and thence to the Antipodes of Saint John ? "W^hat are those places of the earth where the shadow of the people go completely round them in the twenty-four hours ? What people have no shadow ? M ;^ USE OP THE GLOBES. 89 t ♦ ^ What people have their shadow pointing always Northward ? who have their shadow pointing always Southwarr^ ? and who have their shadow pointing Nortl^ward one half of the year anr South vyard the other half? • What is the distance of the Southern ex- tremity of the Andes from the Northern ex- ti'emity of the Iiocky Mountains ? What is ^hc difference of the longitudes of the highest ; aountains in America and Asia ? If a Steam Ves'sel should cross from Lon- don to New- York in 12 days, at whai rate per day would she sail ? What is the difference of the Sun's lowest Meridian Altitude, and his highest Meridian Altitude at Saint John ? — and what is the dif- ference of his rising amplitudes at those times ? At what hour are the Sun's Azimuth and Altitude equal, on the 1st April, at St. John? To what place must a person travel South from Saint John, to make his distance from Saint John equal to the distance of St. John from London ? On what day of the year is the Sun's Al- titude 35° due East at Saint John ? If London were made the centre of a cir- cle whose radius would reach from London to the North Pole, through what places would the circle pass ? If two ships sail from the same point on the F ]\- 90 MANUAL ON THE I globe, in opposite directions, the one East and the other West; supposing th^m to sail equal- ly, at the rate of ten miles per jur, on a great circle ; how many days would each of them count after having returned to the port whence they set out ? - On what point of the Compass does the Sun set at Fredericton, when he rises at 7, A. M ? What is the Equation of time, as far as it depends upon the obliquity of the Ecliptic, on the 1st of May ? At what hour will the Sun's Altitude be equal to his amplitude on the 10th of May at Saint John ? Would a ship, in setcing out from a Port, describe what is called the angle of position by keeping her head alvrays towards one point of the Compass ? And if not, what constitutes the difference between Geogra- phical bearing and Nautical bearing ? l)escribe a Horizontal Dial for the lati- tude of Cape Horn ? At what hour does the Sun first make his appearance at Saint John on the 1st of June, and what o'clock is it then in London ? How many miles are the Inhabitants of St. John carried per hour by the Earth's ro- tation on its axis ? How much longer is the 1st of May at St. John than at New- York ? When the clock is ten minutes slower tbon 4. USE OF THE GLOBES. 91 the Sun, what is the sun's place in the Echp- tic, and the day of th-^ year? Describe the phenomena that attend a Pa- rallel Sph( re? Describe the phenomena that attend a Right Sphere ? What day of the year at London is ^^qual to the longest day at St. John ? When the Sun's depression bclo Ji n. - rizon at St. John is 25° on the 15th oi ^.ii y» what is the hour of the night? When the sun's altitude is equal to his am- plitude on the 1st of June at St. John, what is his Azimuth ? If a steamer, sailing from Liverpool to New York, proceeds at the rate of 11^ miles per hour, in what time will she reach her desti- tination? How often will a coach wheel, whose cir- cumference measures ten feet, go round, in describing the parallel of latitude on which St. John is situated ? If two steamers should start the same in- stant of time, the one from Boston, bound to Cork, sailing at the rate of ten miles per hour, and the other from Cork bound to Boston, sailing at the rate of twelve miles per hour, in what latitude and longitude might they be expected to meet ? How many geographical miles from the first meridian is that place whose longitude is 69° W. and latitude 5T° N. ? ^, IMAGE EVALUATION TEST TARGET (MT-3) ^O ^ **% 1.0 I.I 1.25 ■so III ^ us. 12.0 injii U 11.6 ^ 71 r'^ > 'V' Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 c^ 92 MANUAL. Find the longitude of that place in 50° of latitude, which measures on its parallel of la* titude 5000 miles West from the meridian of Greenwich. What is the meridian altitude of the sun at St. John, when the day is eighteen hours long at the Arctic circle ? Required the hour angles of a vertical dial facing the South for New- York ? When the sun's right ascension is 56°, what is his oblique ascension at St. John, and what is the lenjjth of the dav ? For what latitude is a horizontal dial con- structed, the angular distance of whose XH. and I, is 14°. f.. £AS¥ R€LBI$ ^m- FOR THE CONSTRUCTION OF MAPS. MJ 1st. Draw marginal lines to contain the numbers expressing the latitude and longi- tude. 2d Draw a line up and down through the middle of the Map, to represent a meridian, and divide it into as many parts as there are to be degrees of latitude. 3d. Take a line equal to one of these de- grees, and subdivide it into any number of small spaces to measure minutes. 4th. Find from the subjoined table, the length of a degree of longitude on the paral- lel of latitude which is to pass through the top of the map ; and to the right and left of the meridian, drawn through the middle of the map, divide the line along the top into de- grees of the length found in the table. 5th. Find the length of a degree of longi- tude on the parallel which is to pass through 94 EASY RULES. the bottom of the Map ; and on each side of the Central Meridian, divide the line along the bottom of the Map, into degrees of the length found in the table. 6th. Draw meridians from the degrees marked along the bottom to those marked along the top. 7th. Produce the Central Meridian and any two of the others at an equal distance on each side of it, till they meet in a point ; from which as a centre, describe lines from one side of the Map to the other, passing through the degi'ees marked on the Central Meridian. 8th. Number the degrees along the sidesi, and the top, and bottom, antl subdivide them into such parts as the scale of the map will admit. 0^- 9th. From an accurate Map, or a table of latitudes and longitudes, lay down the capes, # towns, an ther prominent places in their ' proper situanons, and then trace the bounda- | ries, rivers, mountains, &c. c > •If- i«» f ■''*'■ :yj y^^ 95 TABLE Showing the length of a Degree of Longitude on any parallel of Latitude, from the Equator to the Pole. Veneo of 1 D«g. of Long.' Degree of Deg. of Lon^. Dcgice of Deg. of Lone Litilude. ticog. Miles. Latitude. Ge«e. Milei. Latitude. Geog. Miles. 1 69.99 31 51.43 61 29.09 2 59 96 32 50 83 62 28.17 3 59.92 33 60.32 68 27.24 4 59.85 34 49.74 64 26.30 5 59.77 35 49.15 65 25.36 6 59.67 36 48.54 66 24.40 7 59.55 37 47.92 €7 23.44 8 59.42 38 47 28 68 22.48 9 69.26 39 46 63 69 21.50 10 69 09 40 45.96 70 20.52 11 58.90 41 45.23 71 19.53 12 58.69 42 44.59 72 18.54 13 58.46 43 43.88 73 17.54 % 14 58 22 44 43.16 74 ]6.54 ^^ 15 57 96 45 42.34 75 15.53 16 57.67 46 41.68 76 14.52 17 57 38 47 40.92 77 13.50 18 57.06 48 40.15 78 12 47 19 56.73 49 39 36 79 11.45 20 56.38 50 38.57 80 iO.42 21 56 01 61 37.76 81 9.39 22 55 63 52 3694 82 8 35 23 55.23 53 36.11 83 7.31 24 54.81 54 35 27 84 6 27 25 54.38 65 34.41 ■ 85 5.23 26 63.93 56 3355 86 4.19 27 53.46 57 S2.6S 87 3.14 "^28 52 98 58 31.80 88 2.09 29 52.48 59 30.90 89 1.05 30 51.96 60 30 00 90 0.00 K 1^ Part 11 on the Celestial Globe will apptar in a short time. . ; , ^ 'uK ; ti •* m .*#'*' ^'S'^. aat!: E » fc-. «*i»* t - -«« fc'.' '"itfiiliiiiiirrt ppfar in