LESSONS IN GKOOKAI'HY. 



103 



definition, tho circle p M T p N s. But aa every spot on the 

 aurfaco of the globe has t'fi own meridian, if we wish to have a 

 proper notion of the distance of the meridian of any place from 

 that of the place where we dwell, we must fix upon the meridian 

 of some one place aa a standard to which we shall refer tho dis- 

 tance of every other meridian. Accordingly, the meridian of 

 Greenwich has been fixed upon by common consent in this country 

 aa the standard or FIRST MERIDIAN, to which we are to refer 



all others in point of 

 distance. 



The second great 

 circle of importance on 

 the terrestrial globe 

 is the equator. This is a 

 great circle which passes 

 through all the points 

 |Q on the earth's surface 

 situated at an equal dis- 

 tance from the two poles, 

 p P, of the earth's axis ; 

 it is called the equator, 

 because when the sun's 

 rays are vertical to this 

 line there is no shadow 

 to the gnomon or style 

 at noon, and there is an 

 equalisation of light all 

 over the globe (on the days when this takes place), this position 

 of the sun being the equaliser (equator). The equator is also 

 made the starting place for the measurement of the distances 

 of places on the surface of the earth as to their position in 

 the northern or southern hemisphere ; for the equator divides 

 the globe into two equal parts, called the northern and southern 

 hemispheres or half-globes : that hemisphere in which wo live 

 is called the northern hemisphere, because our Saxon ancestors 

 called the point opposite to the sun at noon the north; and that 

 hemisphere in which the point opposite to the sun in tho con- 

 trary direction is seen, is called the soutliern hemisphere, because 

 they called the point where the sun is seen at noon the south. 



The distance of any place on the earth's surface in the 

 northern or southern hemisphere from the equator is usually 

 measured in degrees of the quadrant of the meridian of that 

 place. Thus, the meridian of tho place or point M on the sur- 

 face of the globe (Fig. 6) being tho circle P M p s ; tho distance 

 of >i from the equator, E Q, is measured by the number of degrees 

 of tho quadrant, E p, contained in the arc E M, tho extent of 

 opening of the angle E c M. Now the quadrant E p is divided 

 into 90 from E to P, that is, from the equator to tho north polo 

 at P, and the degrees are reckoned from E, which is marked 

 (no degrees), to p, which is marked 90 (ninety degrees). Hence, if 

 M be any point on the earth's surface to which the rays of the sun 

 are vertical on the 21st of June as shown in tho diagram of the 

 seasons (Fig. 4, page 80) at K at mid-summer then tho distance 

 of the point M from tho equator is 23 28' N. ; that is, 23 

 degrees 28 minutes north. The reason for thia is plain ; for, if 

 from the right angle or 90 formed between the plane of the 

 earth's orbit and the perpendicular to that plane (see Fig. 4, 

 page 80), and also from the right angle or 90 formed between 

 the plane of the earlh's equator and tho perpendicular to that 

 piano in the axis of the earth, we take away the common angle 

 NOR, the inclination of the earth's axis to the plane of the 

 earth's orbit, which is 66 32', we shall have 23 28' in either 

 case ; and this is the distance between the polar circle and the 

 pole, or the inclination of the plane of tho earth's equator to 

 the plane of the earth's orbit, and consequently the distance M E 

 (Fig. 6). The distance of any point on the earth's surface, mea- 

 sured in degrees, from the equator ia called its latitude (from 

 the Latin latitude, breadth), because the extreme distance of the 

 earth from north to south was by early geographers reckoned 

 less than its extreme distance from east to west ; the term longi~ j 

 tude (from the Latin longitudo, length) being applied to distances 

 reckoned east or west from the first meridian. The latitude of j 

 the point M on the earth's surface is thus reckoned 23 28' N. 

 In like manner the latitude of the point T on the earth's surface, 

 or any point to which the rays of the sun are vertical on the 21st 

 of December, is reckoned 23 28' S. ; that is, 23 degrees 28 minutes 

 south. 



The two circles of the greatest importance in Geography and 



Navigation are the meridian and the equator. We proceed now 

 to show their two. 



To do this clearly let 01 suppose that a golden treasure wa* hid 

 in a field, and that two of it* bonndariec oooafoted of on* fenc* 

 lying north and south, or such that at noon iU ahadow mbtJMtH 

 with itself that is, lay in the same direction ; and another fact 

 lying cant and weat, or such that it :. 

 sected or crossed the former fence at right V 

 angles, as in Fig. 7. In thin figure, the 

 straight line AT represents the north and 

 south fence, and the straight line A X the eatt 

 and west fence j that is, if yon go from A to 

 T you go north, and if you go from T to A yon 

 go south ; but if yon go from A to x you go 

 east, and if you go from x to A you go west. 

 The directions of the fences being thus 



Fl. 7. 



understood, suppose that you were told the exact distance of 

 tho place where the golden treasure lay from the fence A x, ay 

 20 yards ; this would no' be enough to enable you to find it, 

 because there are ever so many points in the field, all at 20 

 yards distance from tho fence A x. Now suppose yon were abx> 

 told tho exact distance of tho place where the golden tnmnui 

 lay from the fence A Y, say 25 yards ; thia alone would not be 

 enough to enable you to find it, because there are ever BO 

 many points in the field, all at 25 yards distance from the 

 fence A Y. Among these latter points, however, there can be 

 only one which is at the exact distance of 20 yards from the 

 fence A x ; so that if you were told both distances at once, yon 

 could evidently, by some means or other, determine the place 

 where the golden treasure lay hid. It is necessary, therefore, 

 and sufficient, to inform you of the exact distances of the place 

 in the field from both fences, in order to enable you to find it. 



With the information now supposed to be given, the next 

 question is, how should you proceed to determine the exact 

 place of the golden treasure. A little reflection would suggest 

 the following method. In Fig. 8, measure off 

 from the point A, along the fence A x, the 

 given distance of 25 yards, at which the 

 place is said to be situated from tho fence 

 A Y ; let this distance be A M. Then, from 

 tho point M, draw a straight line, M p, paral- 

 lel to tho fence A Y ; or, which is easier in thia 

 case, draw M p a perpendicular to the fence 

 A x from tho point M ; for M p and A Y being 

 both at right angles to A x, are parallel to 

 each other. Lastly, measure off from the point X, along the 

 straight line M p, tho given distance of 20 yards, at which the 

 place is said to be situated from the fence A x ; and the point 

 p will be the place in tho field where the golden treasure ia to 

 be found. 



That this mode of determining the place of the golden 

 treasure is correct may bo proved thus : in Fig. 9 let P be the 

 place in question ; from p draw p N perpen- 

 dicular to A Y, and P M perpendicular to A X ; Y 

 then, according to the data (things given), 

 p M is a distance of 20 yards, and p N is a 

 distance of 25 yards. But by the nature of 

 the construction, tho figure A M p N is a rect- 

 angular (right-angled) parallelogram, and its 

 opposite sides are therefore equal; whence 

 AMIS equal to N p, and A N equal to K p. It 

 follows, therefore, that the point P is found 



M 



Fig. 8. 



Fig. 9. 



by the method shown in the preceding paragraph. In mathe- 

 matical language, the distances p N and p M of the point p froa 

 the fences A Y and A x, are called tho rectangular co-ordinates 

 of that point ; but the distances A x and x p, which are equal 

 to the former, are more usually denominated the rectangular 

 co-ordinates of the P ; and by these co-ordinates we can always 

 determine the position of any point, when their exact lengths 

 are given. The straight lines A X and A Y, from which the 

 given distances are measured, are called rectangular ares, and 

 the point A, where those axea intersect each other, ia called 

 the origin of the rectangular axes. With the origin and the 

 direction of the rectangular axes (in our figures, the fenoea at 

 right angles), and the lengths of tho rectangular co-ordinates, 

 all given), in reference to any point on a given surface, we can 

 always find the true position or place of that point when 

 required. 



