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Les diagrammes sulvants illustrent la mAthode. by errata led to ent jne pelure, apon A 1 2 3 32X 1 2 3 4 5 6 m m *» I* •• ' -Hi.- ■••■• ' I I \ \i y ■',■ 1 ! 1 H HAND BOOK OF THE IlSdllPI^O^V^EID NEWTONIAl OR, COMBINED ASTRONOMICAL AND TERRESTRIAL GLOBE. BY M. TURNBULL. WILLING & WILLIAMSON, PUBLISHERS AND BOOKSELLERS, TOROITTO- 188L Entered according to Act of Parliament of Canada in the year one thousand eiffht hundred and eighty-one, in the Office of the Minister of AgricultLTc, and Patented in the United States of America, by M. TURNBULL. » INDEX. \ghi Introduction : paor The figure and size of the Glo))e "» The study of the different mechanical appendages around the Globe, and what they each represent •> Solution of Pkoblkms : 1. To find the latitude of any given place 8 2. To find all those places whose latitude is the saine as that pi any given place 9 3. To find the longitude of any given place 9 4. The latitude and longitude of a place being given, to find the place 10 5. To find the two days in the year when the sun will be vertical over any place within the Tropics 10 6. To find the length of any particular day at a given place, and the times of sunrise and sunset.. 10 7. To find the length of the longest day, and of the shortest night, at any given place 11 8. To find the day when the sun begins to shine constantly — how long it continues to do so — how many days it rises and ■eta — and how many days it never rises — at any given place in the two Frigid Zones ; 12 9. To find the sun's meridian altitude on any particular day at any given place 13 10. To find the sun's place in tlie ecliptic on any given day 14 11. The sun's place in the ecliptic being given, to find the day of the month 14 12. To find when twilight begins and ends at any particular place Oil any given day 15 13. To find the longitudo between two given places 15 14. Given the day and hour at any place, to find where the sun is then vertical HI 15. To find the sun's north or south declination for any day in theyear 16 16. To find how many miles, either geographical or statute, make a degree of longitude on any parallel of latitude 17 IV. INDEX PAor,. 17. Find the rtite per hour at which t!io inliabitants of any given place arc carried from west to east by the rotation of the earth on its axis . . 17 18. Given a nlace within the Tropics, to find all the places which have the same distance from it within the circle of solar illumination 18 19. The hour of the day at any place being given, to find what hour it is at any other place 18 20. To find the place which has the same longitude as any given place 19 21. To find all the places over which the sun will pass vertically on any given day 11> 22. To find by the Globe tlie three cases, viz. : the Antceci, Perieing about 26 miles longer than the polar diameter ; whence it results that the equa- tor is, on an average, about thirteen inilvs further from the earth's centre than are the poles. Before detailin;^ the various problems which the new globe is intended to solve, it will be desirable to give a clear descrip- tion of all the mechanical appliances used. These are six in number, as follows : 1. The first is what may be called the great datum circle of the solar system. This is the large conspicuous circle in the model which rests upon the tripod stand. This repre.sents tlie plane of the ecliptic, or the apparent annual path in the heavens described by the sun and the earth when viewetl the one from the other. This circle of 360 degrees is divided into twelve constellations of thirty degrees each. On the circle is also marked the calendar of 365 days, so that each day of the year is coincident with the point in the circle of the constella- tion, or zodiac, where the sun's centre is situate on that particu- lar day. Thus, the sun enters the constellation Aries in March and Taurus in -Vpril ; and on examining the ecliptic circle of the model, we find the days of the month of March placed co- incidently with Aries, those of April with Taurus, and so on throughout the entire circle. Another point to l)e noticed is that the ecliptic is divided into a northern and a southern por- tion, the former being the portion north of the equator, from Aries to Libra, and the latter being tlie portion south of the equator, from Libra to Aries. The ecliptic may also be divided geographically into an ascending and a descending portion ; the first f i*om the winter solstice, when the sun is at its greatest southern declination on the 21st December, to the 21st June, when it reaches its maximum northern declination ; and the descending portion, from the 21st June to uic 21st December. AND nn U8E. It will he neen, then, that this appliance of the model exhibits the causes of the seasons. 2. The next mechanical appliance which may Imj noticed is the brass semicircle which extends from one pole to the other, representing the solar meridian. As the graduated edg(? of this semicircle always follows the sun's centre, and is regulated in position by the inclination of the axis of the globe, it is always in the true plane of the solar meridian. Thus, on moving the sun's place on the 2l8t December to its place on the 2l8t June, and onwards to the 21st December again, the meridian is in- clined to the riff/U hand from December to June, and to the left hand from June to December ; the student being thus enabled to draw geometrically all the circles of latitude and the meridians in their true positions within the illuminated portion of the earth. It will be noticed, too, that as a consequence of the inclination of the axis of the globe, the graduated edge ~of this semicircle, in its motion over the sun's centre, rises above and sinks below the ecliptic plane, thereby reading oft' in degrees the declination from the equator, and illustrating the sun's northerly motion from December to June, and its south- erly motion from June to December. 3. The third mechanical appliance is a double ring perma- nently fixed round the globe, on which the times of sunrise and sunset are marked. These rings divide the earth at all hours into two hemispheres of sunlight and total darkness respectively, the edge next the sun being the "circle of illumination" The space between and including the breadth of the two rings represents the zone of twilight, and is eighteen degrees, or about 1,250 miles, in breadth on the earth's surface. 4. The fourth point to be noted with regard to the mounting of this globe, is that the axis of the earth is made to incline at an angle of 23° 28' 10" to the ecliptic, thus exhibiting the true 6 STUDY OP THE GLOBE inclination, and at the same time the parallelism of the axis to itself throughout the year. 5. The fifth appliance is a semicircle of brass revolving round the sun's centre. It extends half way round the earth, 90° on each side of the sun, and is divided into degrees to measure the angular distance of any place from the zenith sun, thus furnishing a means of approximately measuring the rela- tive intensity of the sun's heat at any place in sunlight, as de- duced from the law that heat diminishes with the sqtiare of the angular distance from the zenith sun. 6. The sixth point to be noted is the introduction of an improved graduated hour circle, placed round the south polar axis. It is divided into 360 degrees, and also into hours of civil time. This circle, being carried round the globe by the solar meridian, will always be with the sun, and thus indicates the longitude east or west, and the hour of the day at any place on the earth's surface. The mechanical appliances having thus been described, a number of the more important problems which they are adapted to serve, and their solutions, will now be given. m PROBLEM I. TO FIND THE LATITUDE OF ANY GIVEN PLACE. Rule. — Rotate the globe on its axis until the place is under the graduated solar meridian : the degree over the place is the required latitude. Solve with the globe the latitude of the following places : Q. Edinburgh? A. 56° north. Q. San Francisco 1 A. 38' 15' north. i n of the axis iss revolving nd the earth, to degrees to le zenith sun, ring the rela- nlight, as de- ^quare of the uction of an south polar ito hours of ?lobe by the us indicates at any place described, a are adapted DE. ce is under •lace is the places : AND ITS USE. d I PRQi .EM II. TO FIND ALL THOSE PLACES WHOSE LATITUDE IS THE SAME AS THAT OF ANY GIVEN PLACE. Rule. — Rotate the globe, and all places passing under the degree of a given place have the same latitude. Solve with the globe the following places : Q. What places have the sanu^ approximate latitude as Edinburgh 1 , A. Copenhagen, Riga, and Omsk. Q. What places have the same approximate latitude as Quebec ? A. St. John's, Jassy (HuDgary), and Odessa. PROBLEM III. TO FIND THE LONGITUDE OF ANY GIVEN PLACE. Rule. — Bring the prime meridian (that is, the meridian from which the longitude is calculated) to the solar meridian's place ; then fix the vernier on the earth's axis to the prime meridian; rotate the globe till the given place comes beneath the gradu- ated meridian ; then, if the prime meridian has moved east, the arc passed over by the vernier will show the degrees of west longitude, and if it has moved west, the arc will show the degrees of east longitude. Solve with the globe the longitude of the following places : Q. What is the longitude of Washington 1 A. 5h. 8 min. west of London. Q. What is the longitude of Dublin ? A. 25 min, west of London. 10 STUDY OP THE GLOBE PROBLEM IV. THE LATITUDE AND LONGITUDE OF A PLACE BEING GIVEN, TO FIND THE PLACE. Rule. — Work out as directed in the three previous Problems. Solve with the globe the following: Q. What island is situate 157° east longitude, 30° north latitude? A. Lot's Wife. Q. What city is 35° north latitude, and 16' east longitude'? A. Algiers. PROBLEM V. TO FIND THE TWO DAYS IN THE YEAR WHEN THE SUN WILL BE VERTICAL OVER ANY PLACE WITHIN THE TROPICS. Rule. — Bring the sun's centre directly over the place given, and the day opposite to the sun's centre will be the day required. Solve: When will the sun be vertical to the following places : Q. Mexico? A. May 11 and July 30. Q. Tahiti? A. January 28 and November 6. PROBLEM yi. TO FIND THE LENGTH OF ANY PARTICULAR DAY AT A GIVEN PLACE, AND THE TIMES OF SUNRISE AND SUNSET. Rule. — Bring the given place to the solar meridian ; screw the axial pointer to the same plane ; rotate the globe till the place reaches the edge of the twilight zone in the forenoon, and AND ITS USE. 11 longitude, 30' north . 16' east longitude*? note the degree on the hour circle ; then rotate the globe till the place reaches the edge of the twilight zone in the afternoon, and again note the degree on the hour circle. The two arcs indicate the time of sunrise and sunset respectively, and, added together, give the length of the solar day. Solve Avith the globe the following: Q. What time does the sun rise and set at Toronto, Dec. 25th, and how long is the day? A. Sun rises at 7h. 40m, a.m., and sets at 4h. 44m. p.m. Length of day, 9h. 4m. Q. When does the sun rise and set at Chicago, on Janu- ary 1st, and how long is the day ? A. Sun rises at 7h. 20m. a.m., and sets at 4h. 32m. p.m. Length of day, 9h. 12m. tical to the following PROBLEM VII. jTO FIND THE LENGTH OF THE LONGEST DAY AND OF THE SHORTEST NIGHT, AT ANY GIVEN PLACE. Rule. — For the Northern Hemisphere, bring the sun to the first of Cancer, and for the Southern Hemisphere, to the first I of Capricorn; then work out as directed in Problem VI. Solve with the globe the following: Find the length of the longest day and shortest night, at the following places : * Q. Edinburgh? A. Day, ]7h. 49m.; night, 6h. 11m. Q. Boston. U.S. ? A. Day, 13h. 24m.; night, lOh. 36m. Day here is meant to be the time between sunrise and sunset. 13 STUDV OP THE OMbe PROBLEM VIII. TO "IND THE I,AV ,VHEN THE ,„„ '7 -V« .T CO.T«„:;:: ~ '" ""- -— T.V, "^ra ,T n,SES ANB SETS !v' ''°-™''^". HOW «,«,' «--. - A»v 0,VE. p'oETT^lr ^ "*™ " "-- ""-t the sun, of the 'H^Z^ *<'7''' - "ght beW, jh, , '^y in the calendar Thentl "'' °' ■"«'«. nation,.' andlh! y'f -ili be found. Set 'V",.""""^""^ *» "in" n^ calendar where the given 2 "' *" ^^ *« the day in 2 zone nevf fk P™'' *gain comes f« *v .^ ""' PeriL f ™"' ""'' the interval ^ " "''«" °^ the Penod of eotant arctic sunshine " ''"^^ ^'" "« the Solve w,th the globe the following. V- When does fhe mm k • ^" rsiand of Disco in the Ar:t c Se*" J^ ^ ^"-^ - the J7/''"">^™t;andonhowida*'" , ""^ '* "■'^PP^'"-; ^- The sun shines constantlv ! ^ ^' does it rise and set J;^28th; itisabsent ,54ty ^:* ^;-> from May I2th to ■n the year. "''^^ ^nd ,t rises and sets 99 times V- I>r. Kane in iri^a Jn the Arctin n' , ' ^P"""* *^at year af T? , risp .. j^ '''^^^' ^^ latitude 78° w , ^^^^s^laer Bay, "«« and set, and how W T. /. ' ^^^^ ^^d the s«n ^^•^;;.; ^Xf^'aXT 'T ^''■^' '««• '"August _ «h. llOaxial rotations- and it , "^ ^'^'h to f-ebruarv -''* hours, fro™ February' ,Tth J ""'' '"^ »" « ev2 again from August 03 Jf i '° ^pril ]9th=64 dav, - ^ ----__!!!l;f^^J^^»l'er 27th==54 daysV ' *"'' year-the reader being ii; l< AND ITS USE. 13 PROBLEM IX. TO FIND THE SUN's MERIDIAN ALTITUDE ON ANY PARTICULAR DAY AT ANY GIVEN PLACE. Rule. — Find the arc in degrees on the solar meridian, be- expected, with the globe before him, to place the sun in the ecliptic to +he days mentioned in the doctor's notes : Reksselaer Bay, October 11th. — The long staring day, which has clung to us for months past, to the exclusion of the stars, has begun to intermit its brightness ; even Aldebaran, the red eye of the "bull," flared out into familiar recollection as early as ten o'clock, and the heavens, though still somewhat reddened by the gaudy tints of midnight, gave us Capella and Arcturus, and even that lesser light of home memories, the Pole Star. November 7th. — The darkness is coming on with insidious steadiness, and its advances can only be perceived by comparing one day with its fellow of some time back. We still read the thermometer at noon- day without a light, and the black masses of the hills are plain for about five hours, with their glaring patches of snow, but all the rest is dark- ness. The stars of the sixth magnitude shine out at noonday. Our darkness has ninety days to run before we shall get back again even to the contested twilight of to-day ; altogether, our winter will be sunless for about one hundred and ten days. November 19th. — Wishing to get on the south-west cape of our bay before the darkness set in thoroughly, I started in time to reach it with my Newfoundlanders at noonday, the thermometer indicating 23° below zero. December 15th. — We have lost the last vestige of our midday twi- light ; we cannot see print, and hardly paper ; the fingers cannot be counted a foot from the eye ; noonday and midnight are alike ; ami except a faint glimmer in the sky that seems to define the hill outlines to the south on the meridian, we have nothing to tell us that this arctic world of ours has a sun. January 21st. — First traces of returning light, the southern horizon having for a short time a distinct orange tinge. February 31st. — We have had for some days the sun silvering tl>e ice between the headlands of the bay ; and to-day, towards noon, I started out to be the first of my party to welcome him back. I saw him once more, and upon a projecting crag, nestled in the sunshine, it was like bathing in perfumed waters. 14 STUDY OF THE GLOBE tween the given place and the sun's centre on the given day ; then subtract the value of the arc from 90°, and the remainder will give the southern altitude if the place be north of the sun's centre, and the northern altitude if the place be south of the sun's centre. Solve with the globe the following: Q. What is the altitude of sun at Ascension, April 1 8 f A. 77° 30' north. Q. What is the altitude of sun at Boston, May 23? A. 64° south. PROBLEM X. TO FI.VD THE SUN's PLACE IN THE ErLIPVlC ON ANY GIVEN DAY. Rule. — Find the given day in the calendar circle, and directly opposite to it, on the outer graduated circle, will be found the sign and degree of the sun's place. Solve with the globe the following : What is the sun's place in the ecliptic for the following days : Q. Where is it on December 22nd'? A. V Capricorn. Q. Where is it on May 12th? i4. 22° Taurus. PROBLEM XI. THE SUN S PLACE IN THE ECLIPTIC BEING GIVEN, TO FIND THE DAY OP THE MONTH. Ride. — Find the sign and degree in the ecliptic, and directly opposite, on the inner circle of days, Avill be found the day of the month. Solve with the globe the following: Q. On what day is the sun in the 1 4° Aries 1 V '-^sail on the given day; and the remainder north of the sun's ce be south of the on, April 18 'f May 23? AND ITS USE. 16 ANY GIVEN DAY. fcle, and directly ill be found the t* the following A. April 4th. Q. When is the sun in the 8° Virgo 1 A. August 5th. PROBiEM XII. TO FIND WHEN TWILIGHT BEGIi S AND ENDS AT ANY PARTICULAR PLACE ON ANY GIVEN DAY, Hule. — Bring the sun's place over the given day in the calendar, and the particular place to the solar meridian; tix the hour pointer to noon; then bring the place given to the two edges of the twilight zone, and the pointer will show when twilight began and ended in the morning. Do the same for the evening portion of the zone, and the pointer will show when the evening twilight began and ended. Solve with the globe the following: Q. When did the twilight begin and end at Toronto, June 28th'? A. Twilight dawned at 2h. 16m. a.m., and ended at -th. 24m. a.m. Q. When did twilight begin and end at Venice, March 5th 1 A. It began at 4h. 28m. a.m., and ended at 6h. 8m. a.m. TO FIND THE ', and directly nd the day of , PROBLEM XIII. TO FIND THE LONGITUDE BETWEEN ANY TWO GIVEN PLACES. Utile. — Bring one of the places to the solar meridian, and set the axial pointer at noon; then rotate the globe till the other place is beneath the meridian, and the degrees of arc passed over by the pointer will show the difference of longi- tude.* * To convert degrees of longitude into hours of time, divide by 15; to convert them into minutes of time, multiply by 4. I \J 16 STUDY OF TH£ OLOBE! Solve with the globe the following : Q. Find the ditference of longitude between London (Eng.) and Toronto? ' A. Toronto, Sh. 17ni. west. Q. N(^w York and Toronto 1 A. Toronto, 20m. west. PROBLEM XIV. GIVEN THE DAY AND HOUR AT ANY PLACE, TO FIND WHERE THE SUN IS THEN VERTICAL. Jiule. — Set the sun's place to the given day in the calendar, and also the given place to the solar meridian ; tix the pointer to noon ; then rotate the globe till the pointer on the hour circk is at the given time, and the place on the globe which is exactly beneath the sun's centre will have the sun vertical at the time. Solve with the globe the following : Q. Where is the sun vertical when it is 22 minutes to 8 a.m. at Toronto, on April 22nd 1 A. Over the mouth of the River C4ambia. Q. Where is the sun vertical when it is 2h. 20ni. p.m. at Montreal, Canada, on July 1st? A. Cape St. Lucas, Old California. PROBLEM XV. TO FIND THE SUN's NORTH OR SOUTH DECLINATION FOR ANY DAY IN THE YEAR. Jiule. — Bring the sun's centre to the required day in the calendar, and the degree on the graduated solar meridian, ex^ actly beneath the sun's centre, is the declination sought. Solve with the globe the following : 'en London (Eng.) AND IT8 U8K. r Q. What is the sun's declination on the following days in the year : Nov. 14th? A. 18° 30' south. Q, March 20th ? A. On equator, or no declination. *'IND WIIKKK THE in tJie calendar, ; e found. Next, the periceci l»eing situate on the same latitude hut on opposite meridians, set the hour pointer to the given meridian, and rotate the globe 180" in longituile ; then the place on the globe below the same degree first assumed will be the periceci required. Again, as the anti PODES lie opposite upon the globe, with feet towards feet, on opposite meridians and parallels, the antipodes will be found under the same degree of the opposite solar meridian where at tirst the antieci stood. Solve with tlie globe the three above-mentioned cases ; Q. What place upon the globe is the antieci of Quebec 1 A. Gulf of Penas, Patagonia. Q. What place on the globe is the antceci of Tobolsk, Russia ? A. Kerguelen Land. Q. What place on the globe is the periceci of Toronto 1 A. Mouth of Onguan River, Mongolia. Q. What place is the perkeci of London, England ? A. Tanga Island, Kamtschatka. Q. What place upon the globe is opposite to, or is the antipode of, Sydney, N.S.W. ? A. South of the Azores Islands. Q. What place is the antipode of Cook's Straits, New Zealand t A. Toledo, Spain. AND ITS U8R. 21 [••■ TIJE ANTOSCI, »'I.ACK. »». and uot« its reos from the ANTCECI of the |'^'»»K situate on sft th«' Jiour K'ol'e 180" ill '♦' sanu' degree in, as the anti "wards feet, on wiii be found meridian where ^ cases ; of Quebec ? I of Tobolsk, Toronto ? land? o, or is the PROBLKM XXIII. TO FIND AT ANY PLACK TIIK SI'n'h KLKVATION OR DISTANCK IN DKiJKKKS FKOM TIIK HOLAK TKRMINATOR, OR POINT WIIKRK IT R08K AND WlhL HKT, ON AKV DAY AND AT ANV OIVKN HOrK'l Ruff-, Hriii^ th«« .sun's t-nntiv to the solar meridian for the given day, and H.\ tiie hour pointer to th«' above plant' ; rotate the j^Iobe on its axis till the pointer is at thr rtMjuirrd hour » then rais«' tin* brass semicircle which revolves round t!ie sun's centre, and the dt^gree above the given place will show the solar altitude at the lime. Solve with the globe the following : Q. What is the altitude of the sun at Montreal on May 15, at 8h. 12m. a.m. I A. '2r. Q. What is the solar altitude at Detroit on Nov. 20, at 3h. 10m. p.m. 'i A. 15" 30'. PROBLEM XXIV. THE TIME OF A LUNAR ECLIPSE BEING GIVEN, TO FIND ALL THE PLACES ON TIIK OLOHE WHERE IT WILL BE VISIBLE. Jiule. — Find by Problem XIV. where the sun will be vertical at the given time ; bring the place to the solar meridian ; then, as the sun will be visible to all parts of the earth above its horizon, the moon being at the time of an eclipse exactly oppo- site the sun, will be visible to the other, or dark hemisphere, at any point of which the different phases of the eclipse in local time can be pointed out. traits, New Of the foregoing Problems, Nos. V., VI., VII., VIII., IX., X., XL, XIL, XIV., XV., XVIIL, XIX., XXL, XXII. and XXIV., cannot \ie solved correctly by any other terrestial globe now in use except the present Combined Astronomical and Terrestrial Globe. 22 STUDY OF THE GLOBE i^HEiNOMENA OF rWJLlGHT -hereb., when the ^^ ^T'' f "" """''^ "^'-Phe-. '»um,nation occurs as iLas T '"'" '«'"^°>'- This ^"-l- the edge of twih^fle J"" " '"^ ''^'^ '' "^^-s "-n that angular distance, ZLh " 1'""^"''^ ^'■■•*- perspective from the outs de f "'""^' ^^-^d "' 'he line joining the eaT t thr ' T" "' "^''* »«'- '» *e following appearance at fm' *'' r'^'' ™»''' P--"* *esu„; then a band or ^ofe 1 "f ~."''""P''^^^ '^-d^ g^ees, or about 1,250 miles wMe t". /'^';'' '"' '""'«'''. '8 de- of a hemisphere in total dark„es, ^^^' ""' '"^^^ P»«™ «eept the Frigid Zones passinlT' T"^ P°'^'°'' of the earth, » each twenty-four hou^ hII""' A'^ '""'«^' P^ase twice duration of twilight, accordt a ^ f """""""•'" '"^ ^o ar horizon perpendiculari; '„ " wt "^^ T'" '"'"^ the ;hen the place passes perpend"',! ^T'^' ^* '^ *vi„us that d-tance of ,8 degrees belowtt .ontm T" """ *« ""«"'- ■t passes very obliquely, " '"'"='' ^"""er than where As illustrative of fh^ f twilight at the two eil:::Z' ::r '^' ^^^ -^^^ions of ^ere deUiJed : ^ '' ^^^ ^* *^« two solstices inay be 1. ^^^nal equinox : March 20th an4tLi?rt:X'Sar^^^^^^^^^ ~ric with *an, when it comes to the ed'^e !! ,' "'""^ "* "«'' »«- « edge, passes from '.elow it at the AND ITS USE. 23 same instant of time — an occurrence which takes place at no other time, except the two equinoxes. Hence at the two equinoxes every place on the earth has its shortest twilight, because every parallel of latitude moves through the zone at nearly right aij^les, which, of course, is the shortest path. It is also to be observed that, as a consequence of terrestrial curvature, the twilight lengthens as we proceed from the equator to the poles. At the equator, every degree of longitude being equal to four minutes of civil time, and the twilight zone being 18 degrees in breadth, it follows that the length of twilight will always be 18 x 4, or 72 minutes. At the parallel, 72° N, lat., every place north is below the zone of twilight after sunset, and consequently mid- night darkness there entirely ceases, and there are 12 hours of sunlight and 12 hours of twilight. Thus, in both hemispheres, the twilight varies from 72 minutes at the equator to 12 hours at all latitudes north or south of 72 degrees — that is, within 18 degrees of the two poles. 2. Summer solstice : June 21st. Bring the sun to the first of Cancer, when it will be seen that it has 23° 30' north declination. Notwithstanding this obliquity, however, the twilight at the equator is practically the same as at the equinoxes, or about 72 minutes. At the parallel of Toronto, or about 44° N. lat., it will be found that the twi- light is a little over two hours and twenty minutes ; so that real midnight then only lasts for three hours and 40 minutes. At the edge of the twilight zone, next to the dark hemisphere, it will be seen that we have reached the parallel of 48° 30', N. lat., and from this parallel up to that of 66° 30', N. lat., or 18 degrees further north, twilight lasts throughout, from sunset to sunrise, and there is no real midnight. North of the latitude 6^° 30' N., the sun does not set during the 24 hours, so that there is neither night nor twilight. At the summer solstice the twilight phenomena of the Southern Hemisphere are the opposite to those 24 STUDY OP THE GLOBE i just described, and similar to those of the Northern Hemisphere at the winter solstice. 3. Autumnal equinox : Sept. 22nd. Bring the sun to its place in the ecliptic on this day. The conditions as regards twilight are now identically the same as at the vernal equinox, except that the terrestrial axis, when viewed from the sun, now inclines to the left hand instead of to the right. 4. Winter solstice : Dec 21st. Bring the sun to the first degree of Capricorn. It will be seen that the twilight zone is now concentric with the equinoctial colure, and that the other conditions are similar to those of the summer solstice, but reversed as regards the Northern and Southern Hemispheres. From the parallel 48° 30' N. lat. to the pole, it is constant night ; between 84° 30' N. lat., and 66° 30' N. lat., there is a zone of alternate night and twilight ; and at all latitudes between 66° 30' N. and the equator, there are alter- nations of day, twilight and night. I'l !i AND ITS USE. 25 TWILIGHT PROBLEMS. PROBLEM I. TO FIND WHEN CONTINUOUS TWILIGHT TAKES PLACE AFTER SUN- SET, AND HOW LONG IT CONTINUES, AT THE FOLLOWING PLACES IN ENGLAND, SCOTLAND AND IRELAND. Mule. — Work as directed by the Rule given in Problem XII. Solve with the globe the following : Q. London? A. Begins May 21st, and ends July 22nd. Q. Bristol? A. Begins May 22nd, and ends July 19th. Q. Land's End 1 A. Begins June 4th, and ends July 10th. Q. Edinburgh? A. Begins May 25th, and ends August 4th. Q. Dublin? A. Begins May 16th, and ends July 26th. Q. Liverpool? A. Begins May 14th, and ends July 27th. PROBLEM II. Q. What places in British America have continuous twilight during the open summer months ? * A. Every place within the parallels of latitude of 50' and 66° 30' have continuous twilight after sunset, which includes a region in the Dominion of Canada, from the Lake of the Woods in the south, to the southern shores of the Great Bear Lake, besides the Copper Indian territory, in the north. Hence the * By summer here is meant the time the sun takes to pass from the vernal to the autumnal equinox^^l84 days. 2fi STUDY OF THE (iLOBK I: twilights are continuous over the whole of Hudson Bay and all the surrounding territories, from about the end of May to nearly the 10th of July; and during that period every lake north of the [ arallel of latitude of the mouth of the St. Law- rence has no midnight, which includes all the fishing lakes in the Dominion. PROBLEM III. TO FIND, FOR A GIVEN DAY, WHEN THE MORNING AND EVENING TWILIGHTS BEGIN AND END, AND HOW LONG THEY ARE, AT A GIVEN PLACE. Rule. — Bring the place to the solar meridian of the day, and follow the directions given for twilight. Solve with the globe the following: Q. When is the beginning and end of twilight at Boston, July 12th? A. Twilight begins at 2h. 28ni. a.m., and ends at 4h. 45m. a.m.; duration, Ih. 56m. Q. Quebec, July 7th 1 A. Begins at Ih. 28m. a.m.; ends at 6h. 8m. a.m. Q. Montreal, January 1st? A. Begins at 3h. 56m. a.m.; ends at 6h. 40m. a.m. Q. London (Ont.), May 5th ? A. Begins at 2h. 52m. a.m.; ends at 4h. 52m. a.m. Q. Canton, September 12th? A. Begins at 4h, 32m. a.m.; ends at 5h. 44m. a.m. Q. Berlin, December 4th ? A. Begins at 3h. 40m. a.m.; ends at 5h. 36m. a.m. Q. Venice, April 9th ? A. Begins at 3h. 52m. a.m.; ends at 5h. 24m. a.m. 2^ In drawing to a close this part of the subject, the reader now may readily observe with what ease and accuracy the fore- AND ITS USE. 27 going new problems can be solved l>y the astronomical system of mounting; hence it is almost unnecessary to allude to its importance in the practical study of the earth's surface, whether it is viewed either as land or water, since you cannot reason or point out intelligently any particular place on the globe without its use. In fact, in a great measure the terrestrial globe, without all the astronomical appendages, is something like a man's body without the head, the intellectual part ])eing wanting. In line, in reviewing and tracing the causes of the distribution of lighl- and heat upon the earth, and all the variations in the length of days and nights in a year, with the observed variable periods of light and darkness within the polar circles, the following con- clusions may be safely come to as to whence they arise: 1st. To the orbital revolution of the earth round the sun in the ecliptic, and to the fact of the centres of the two bodies remaining always in the same plane. 2nd. To the inclination of the terrestrial axis to the earth's path in the solar system. 3rd. To the parallelism of the earth's axis to itself, com- bined with the rotation of the globe every twenty-four hours upon its imaginary axis. In the study of this branch of knowledge with the astrono- mical mouncing, it may now be added that all the geographical definitions should be firmly riveted in the memory, and in particular the mechanical details which the mounting is meant to represent; and these should be taken from the real mechan- ism, as exhibited in the appliance itself. Also, it should be observed that the full structure of terms used by geographers is of a mixed character, a portion being purely astronomical, or relating to the "Doctrine of the Sphere;" and the other portion strictly confined to describe the condition of the surface of the Earth. Hence the use and necessity of uniting the study of the two branches of knowledge in class instruction. I i 28 STUDY OP THE GLOBE DEFINITIONS. 1st. The great imaginary axis of the earth is a straight line or diameter, around which the whole mass turns once in twenty-four hours. 2nd. The poles of the earth are the two places on the sur- face at the very extremity of its axis, north and south. 3rd. The North Pole determines the direction in which the axis points to in the heavens, and the South Pole determines the opposite extremity. In the present age no star happens to be exactly over the two points. 4. Meridians on the globe's surface are hour circles, and when read on the equinoctial they are right ascensions ; but when read on the ecliptic, they give the longitude. 5. The angles of right ascensions are at the poles of the earth, and the angles of longitude are at the poles of the ecliptical axis. 6. The EQUATOR is a great circle, equidistant from the two poles. It divides the globe into two hemispheres, named after the poles, Northern and Southern. 7. The parallels of latitude are circles parallel to and diminishing in diameter on the globe, from the equator to the two poles. 8. The latitude of a place in degrees or arc is the distance of the place from the equator, north or south. Hence all places north have north latitude, and places south have south latitude. 9. The LONGITUDE of a place on the globe is its distance east or WEST from a given assumed meridian, called the first or PRIME meridian. Greenwich, England, is always used on globes in the British Empire, but the Americans often use the prime meridian of Washington. ice IRST on Ithe AND ITS USE. 29 10. The DECLINATION of the sun is its distance in degrees of arc from the equator (often called the equinoctial). When it is north of this line it is named north declination, and when it is south it is south declination. 11. The ecliptic (or datum circle of the solar system) is the sun's apparent place among the stars, or the earth's exact path or orbit. In the manufacture of these new globes the greatest care is taken to insure excellence of workmanship and accuracy of adjustment ; and the inventor is contident that any one who is desirous of procuring improved school or library apparatus will find that, in point of simplicity of construction, and for giving clear and precise exhibitions of terrestrial phenomena, his new astronomically mounted globe is far superior to any other now in use. 30 StUDY OF THE GLOBE SELECT TESTIMONIALS. Mr. M. Turnbuli. read a most interesting paper on Terrestrial Globe Mounting, illustrating his remarks upon one of his own patent instruments, which seemed to possess many features to recommend it, being a decided advance on the oltl unscientific mounting. — Proceedings 0/ Canaiiian Insiitttte, Toronto, March 11, 187^. M. TuRNBULL, Esq. Toronto, Oct. 28th, 1879. Dear Sir,— I have no hesitation in stating that your " New Improved Terrestrial Globe " is the best I have ever seen. Yours truly, J. CARLYLE, M.A., Mathematical Master, Normal School, Toronto. November ist, 1880. Mr. Turnbull, of Toronto, has arranged a form of Terrestrial Globe which is useful for showing the changes of the seasons, for finding the duration of twilight, and for solving various problems. "THE OBSERVATORY," London, England. Testimonial received by Charles Bloomfield, Esq., Harrowgate, Yorkshire, who forwarded the New Mounted Globe for inspection to the Royal Geographical Society, London, England : I Saville Row, Burlington Gardens, June 17th, 1880. Dear Sir, — I shall be obliged if you will kindly let me know the approximate price of the Globe which you sent here for inspection, as it is necessary to publish it, and any notice I publish must have some price named. I like the Globe very much, and, if not too expensive, I should like to purchase one for my own private use in giving instructions in Astronomy, for which purpose it seems to be admirably adapted. I have, however, as yet been unable to give attention to more than the principle on which it is constructed. Yours truly, JOHN COLES, M.A., Curator and Lecturer on Practical Astronomy ^ ^^ Royal Geographical Society," London, England, AM> ITS USK. 31 Toronto, Dec. 17th, I880. I have carefully investigated the principles on which Mr. M. Turnbull, oif this city, has constructed his Newtonian, or Combined Astronomical and Terrestrial Globe. These principles are at once natural, scientific and easy of comprehension. By this Globe, the study of geography, which was before a task for the young, will now become a pleasure. The ap- paratus presents a complete and visible explanation of the physical phe- nomena which characterise the earth as a member of the solar system. From the time when globes first came into use for illustrating the science of Geography, down to the present day, no such invention as Mr. Turnbull's has been given to the world. His Globe will mark the beginning of a new era in the art of geographical and astronomical instruction. It is the work of a man who has been gifted with the rare faculty of translat- ing great scientific knowledge into the shape of an apparatus which is a masterpiece of practical and beautiful mechanism. S. J. WATSON, Librarian^ Ontario Parliament. We confidently recommend the Turnbull Globe to the notice of teachers and students, and of all others interested in the study of astronomical geography. It should find a place in every well furnished library and school-room. — The Canada Educational Monthly, Dec, j88o. Any improvement in the mechanical appliances for the use of the teacher must be a matter of deep interest to all who watch the progress of education, and therefore the invention of a new kind of astronomical globe, which bids fair to drive the old-fashioned terrestrial globe out of schools, is a matter of no small importance. It is impossible to draw a sharp line between geography and astronomy, because all the imaginary circles on the earth's biirface are really astronomical and not terrestrial, and for this reason the inventor of the globe has preferred the title "astronomi- cal" to the epithet "terrestrial."— 77/^ Globe, Oct. 16, 1880. Mr. Turnbull's invention is a most ingenious yet simple mounting for terrestrial globes, and seems to be well adapted and calculated to exhibit to pupils the real causes of all those changes of light and heat which take place in different portions of the earth's surface. — Toronto Evening Tele- gram, Oct. 16, 1880.