54 



INTRODUCTION. 



latitude as a given place, suppose J^eio York. — Turn the 

 globe round, and all the places that pass under the same 

 uoint of the meridian as the given place does, have the 

 same latitude willi it. 



IV. To find all the places that have the same longitude 

 or hour icith a given place, as Keio York. — Bring the giv- 

 en place, New Yoi-ii, to the meridian, and all places then 

 under the meridi;in have the same longitude. 



V. To find thr difference in the time of the day at any two 

 given places, and their difference of longitude. — Bring one 

 of tlie places to the meridian, and set the hour-index to 

 twelve at noon, then turn tlie globe till the otlier place 

 come to the meridian, and the index will point out tlie dif- 

 ference of time. By allowing 15 degrees to every hour, 

 or one degree to four minutes of time, the difference of 

 longitude will be known. The ditference of longitude 

 may also be found without tlie time, in the following man- 

 ner : — Bring each of the places to the meridian, and 

 mark the respective longitudes. Subtract the one num- 

 ber from the other, and we obtain the difference of longi- 

 tude sought. 



VI. The time being hnown at any given place, as A''eiD 

 York, to find iclial hour it is in any other part of the world. 

 —Bring the given place, to the meridian, and set the index 

 to the given hour ; then turn the globe till the other place 

 come to the meridian, and the hour at which the index 

 points will be the time sought. 



VII. To find the distance of two places on the Globe. — 

 If the two places be either both on the equator or both on 

 the same meridian, the number of degrees is the distance 

 between them, reduced into miles, at tlie rale of GOJ to the 

 degree, will give tlie distance nearly. If the places be in 

 any other situation, lay the quadrant of altitude over them, 

 and the degrees intercepted upon it by the two places, and 

 turned into miles, as above, will give their distance. 



VIII. To find the antaeci, periceci, and antipodes * of any 

 given place, suppose jXew York. — Bring New York to the 

 meridian, and find by the meridian the point upon the 

 globe, of which the latitude is as much south as that of 

 New York is north. The place thus arrived at will be the 

 situation of the antceci, where the hour of the day or night 

 is always the same as at New York, and where the seasons 

 and lengths of the days and nights are also the same, but 

 at opposite times of the year. New York being still under 

 the meridian, set the hour-index to ^^i at noon, or pointing 

 towards New \''ork,then turn the globe half round, till the 

 index points to the opposite hour, or 13 at night. The 



* Ascii, Amphiscii, Hclero.<;cii, and Periscii. The inhabi- 

 tants of the dilferent regions of the earth are somi-tlmes dis- 

 tinguished by tlie ancient geographers, according to the direc- 

 tion of their shadows. When the siin at mid-day is vertical 

 to any place, the inhabitants of that place were said to be 

 ascii, that is, without shadow. All the inhabitants between 

 the tropics must be ascii twice a year. 



The inhabitants of the torrid zone, having the sun some- 

 times to the north, and sometimes to the south, will project 

 shadows directed by turns towards either pole, and they were 

 therefore said to be amphiscii, that is, having both kinds of 

 shadows. 



Those who inhabit the temperate zones were called Itetero- 

 scii, because their shadows fall in opposite directions. 



Within the polar circles the inhabitants must, for a while, 

 project shadows in all directions, and they are therefore said 

 to be periscii. 



Periceci and Antceci, and Antipodes. The seasons which 

 the inhabitanrs of opposite ])laces on the earth enjoy at the 

 same time, as well as the hours of the day at these places, be- 

 ing contrasted, give rise to certain distinctions with which it 

 is also necessary to be acquainted. 



Those who live under opposite meridians, at equal distan- 

 ces from the equator, and upon the same side of it, are term- 

 ed pei ioeci. They have the same seasons, but reckon at the 

 same instant opposite hours : it being midnight with the one 

 when mid-day with the other. 



Those who live under the same meridian on opposite sides 

 of the equator, and at equal distances from it, are called an- 

 tceci. They have the seasons at opposite times, but reckon at 

 the same instant the same hours. 



The people who live at equal distances from the equator, 

 and under opposite meridians, are termed antichthones, or an- 

 tipodes. They have both the .seasons and the hours of the 

 day at opposite limes. 



place that comes under the same point of the meridian 

 where New York was, is where the periceci dwell, or peo- 

 ple that have the same seasons, and at the same time, as 

 New York, and the same length of the days and nights, 

 but have an opposite hour, it being midnight with the one 

 when noon with the other. Lastly, While the place of the 

 periceci is at the meridian, count by the meridian the same 

 degree of latitude south, and that will give the place of the 

 antipodes of New York, Tliey have all their hours and 

 seasons opposite to those of New Yoik, being noon with 

 the one when midnight with the other, and winter with 

 the one when summer with the other. 



IX. To find the sun's place in tlie ecliptic and also on tlie 

 Globe at any given time. — Find in the calendar, on the 

 wooden horizon, the given month, and day of the month, 

 and immediately opposite will be found the sign and de- 

 gree which the sun is in on that day. Then in the eclip- 

 tic drawn upon the globe, find the same sign and degree, 

 and that will be the place of the sun required, 



X. The time being given at any place, to find the place 

 on the earth to ichich the sun is then vertical. — Find the 

 sun's place on the globe by the last problem ; and turn the 

 globe about til! that place come to the meridian ; mark 

 tlie degree of the meridian over it, which will show the 

 latitude of the required place. Then turn the globe till the 

 given place come to the meridian, and set the index of 

 the hour-circle to the given moment of time. Lastly, Turn 

 the globe till the index points to twelve at noon, and the 

 place of the earth corresponding to that upon the globe, 

 which stands under the meridian at the point marked as 

 before, is that which has the sun at the given time in the 

 zejiith. 



XI. To find all those places on the earth to which the sun 

 is vertical on a given day. — Find the sun's place in the 

 ecliptic on llie globe, as in the last problem, and bring that 

 place to the meridian. Turn the globe round, and note all 

 the places which pass under the same point. These will 

 be the places sought. This problem enables us to deter- 

 mine what people are ascii on any given day. It is evi- 

 dent, that in a similar manner we may also find to what 

 places on the earth the moon or an}' other planet is vertical 

 at a given time : the place of the planet on the globe at 

 that time being found by its declination and right ascension. 



XII. Ji j/lace being given in the torrid zone, to find on 

 what two days of the year the sun is vertical at that place. — 

 Bring the given place to the meridian, and note the degree 

 it passes under. Turn the globe round, and note the two 

 points of the ecliptic which pass under the same degree of 

 the meridian. Then, find by the wooden horizon on what 

 d.ays the sun is in these two points of the ecliptic, and on 

 these days he will be veitical to the given place. 



XIII. To find, how long the sun shines without setting in 

 am/ given place in the frigid zone. — Subtract the de- 

 grees of latitude of the given place from 90, which gives 

 the complement of the latitude, and count this comple- 

 ment upon the meridian from the equator towards the 

 pole, marking that point of the meridian ; then turn the 

 globe round, and observe what two degrees of the ecliptic 

 pass exactly under the point marked on the meridian. It 

 is evident, tliat the sun will shine upon the given place 

 without setting while it is in tlicse, and all the points of 

 the ecliptic that are nearer to the given place. Find, 

 thereforei upon the wooden horizon tlie months, and days 

 of tlie months in which the sun is in the two points in 

 question, and the intermediate time will be that during 

 which the sun constantly shines at the given place. 



XIV. To find, how long the sun never shines upon any 

 given place in the frigid zones. — Count the complement of 

 latitude towards the south, or farthest pole, and then pro- 

 ceed exactly as in the last problem, 



XV. To rectify the globe to the latitude of any place. — 

 Move the brass meridian in its groove, till the elevation of 

 the pole above the horizon be equal to the latitude, 



XVI. To rectify the globe to the horizon of any place- 

 Rectify the globe to the latitude of the place by the last 

 problem ; and then turn the globe on its axis till the given 

 place come to the meridian. The place will then be ex- 

 actly on the vertex of the globe, 90 degrees distant every 

 way U'om the wooden horizon ; and that horizon, there 

 foie, .vill represent llie horizon of the given place. 



