80 



THE POPULAE EDUCATOR 



SPRING. 



MARCH 20. 



AUTUMN. 



earth, or there are twelve hours of light and twelve hours of 

 darkness to every spot on the earth's surface for this day. 

 Hence this day is called the equinox of autumn, or the autumnal 

 equinox. Lastly, at mid-winter, or Dec. 21st, the half of the 

 globe is illuminated from the circumference of a small circle of 

 the globe at the distance of 23 28' from the south pole, s, to 

 the circumference of a small circle at the distance of 23 28' 

 from the north pole, N, and the day is twenty-four hours long 

 at all places of the earth contained in the space between the 

 email circle and the south pole ; that is, there are twenty-four 

 hours of light and no darkness at all to every spot within 

 this space 

 on this day ; 

 but the night 

 is twenty-four 

 hours long at 

 all places of the 

 earth contained 

 in the space 

 between the 

 email circle and 

 the north pole ; 

 that is, there 

 are twenty- 

 four hours 

 of darkness 

 and no light 

 at all to every 

 spot within 

 this space on 

 this day. 



In looking 

 at the dia- 

 gram, you see 

 at the equinox 

 of spring, or 

 March 20th, 

 the whole of 



the illuminated half of the globe, because from the represen- 

 tation of its position it is turned in front both to the sun at F, 

 and to you the spectator ; at the summer solstice, or June 21st, 

 you see only half of the illuminated half of the globe, because 

 it is turned in front to the sun at F, but only sideways to you 

 the spectator, you being outside of the orbit ; at the autumnal 

 equinox, or Sept. 23rd, you see none of the illuminated half 

 of the globe, because it is turned in front to the sun at F, but 

 at the back to you, the spectator, you being 

 outside the orbit and as it were behind the 

 globe; and at the winter solstice, or Dec. 

 21st, you again see half of the illuminated 

 half of the globe, because it is turned in 

 front to the sun at F, but only sideways to 

 you, the spectator, for the same reason as 

 before. But were you placed in the middle 

 of the orbit at the point F, you would, 

 by turning round and round to the different 

 points of it we have been describing, see the 

 whole of the illuminated half of the globe at 

 each point ; and were you placed outside of 

 the orbit in the directions of the major and 

 minor axes, and made to look at the globe in 

 these directions only, you would see none of 

 the illuminated half of the globe, but only 

 the dark side in each position. 



We must now explain the nature of some 

 of the more important circles on the sphere 

 or globe of the earth. If in Fig. 5, which we suppose to be a re- 

 presentation of the globe of the earth, p p denotes the axis that 

 is, the diameter of the sphere, passing through the centre, c, on 

 which th sphere or globe revolves like a wheel on an axle then 

 it is evident that every point on its surface will, in the course of 

 its revolution or whirling on its axis, describe a circle. Thus the 

 points, M, E, and T on the surface, will describe Mie circles M s, 

 E Q, and T N respectively ; and it is evident that the point E, 

 equally distant from the two points P P, the extremities or poles 

 of the axis, will describe the largest circle of all in the course of 

 the revolution ; and that if the sphere were cut by a plane or flat 

 surface, like an orange by a knife, through the circle E Q, it 



SEPTEMBER 23. 



FIG. 4. DIAGSAM SHOWING THE CHANGES OF THE SEASONS. 



would pass through c, the centre of the sphere. Every circle, 

 whose plane thus passes through the centre of the sphere, is 

 called a great circle of the sphere. It is further evident that 

 every point, such as M, on the surface of the sphere, will describe 

 a circle smaller than the circle E Q in proportion to its distance 

 from the point E on either side, or to its vicinity to either of the 

 points P P ; and that if the sphere were cut by a plane or fla.t 

 surface, like an orange by a knife, through such a circle as M s, 

 it would not pass though c, the centre of the sphere. Every 

 circle whose plane does not pass through the centre of the 

 sphere, is called a small circle of the sphere. Accordingly, the 



circles M s and 

 T N are called 

 small circles of 

 the sphere ; and 

 if the points 

 M and T be 

 equally distant 

 from the point 

 E, these circles 

 will be equal in 

 size, and their 

 planes will 

 cut the axis 

 in two points 

 equally dis. 

 tant from the 

 centre, c. The 

 plane of a great 

 circle, such 

 as E Q, cuts 

 the globe or 

 sphere into two 

 equal hemi- 

 spheres; but 

 the plane of 

 a small circle 

 cuts it into two 



unequal parts, or segments (cuttings) of a sphere* For some pur- 

 poses, the circumference of a circle, large or small, is divided 

 into 360 equal parts, in order to enable us to measure distances 

 along the circumf erence ; each of these equal parts being 

 called a degree; for other purposes, the circle is divided into 

 two equal parts called semicircles, and these are also divided 

 into degrees, each containing 180 degrees, and both 360 

 degrees as before ; and for other purposes still, the circle is 

 divided into four equal parts called quad- 

 rants, each containing- 90 degrees, and the 

 whole containing 360 degrees as before. 

 Each degree is divided into 60 equal 

 parts called minutes, and these minutes 

 (minute parts) are employed to express 

 any part or fraction of a degree which may 

 be found over and above a certain number 

 of degrees in any distance. Again, each 

 minute is divided into 60 equal parts called 

 seconds, and these seconds (second minute 

 parts) are employed to express any part 

 or fraction of a minute which may be found 

 over and above a certain number of degrees 

 and minutes in any distance ; and so on, 

 to thirds, fourths, etc. This division of the 

 degree is called the sexagesimal (by sixtieths) 

 division of the degree ; the division of 

 the quadrant of a circle into 90 degrees ia 

 called the nonagesimal (by ninetieths) division 

 of the quadrant. The French, in some of their scientific works, 

 adopt a different division of the circle and its parts. They 

 divide the circle into 400 equal parts, calling them degrees ; and 

 of course, the quadrant into 100 degrees ; also the degree into 

 100 parts called minutes; and so on: this is called the cente- 

 simal (by hundredths) division of the quadrant. Any number of 

 degrees is marked by a small circle placed on iihe right of the 

 number in a small character, and above the line ; thus 27 

 denotes 27 degrees. Any number of minutes is marked by one 

 dash from right to left, on the right of the number ; of seconds, 

 by two dashes, and so on ; thus 10' denotes 10 minutes, 10" 

 denotes 10 seconds, etc. 



