176 



THE POPULAB EDUCATOR. 



Wo shall find this table of the utmost importance in con- 

 structing maps and charts on Mercator's projection : indeed, 

 it would be impossible to work with accuracy without it. 



On referring to the table, in the present case, we find that 

 the distance of the loth parallel of latitude north or south of 

 the equator is 910 minutes (neglecting the decimals, which are 

 unimportant in small maps), or 10 minutes more than the space 

 Assumed for 15, in which, of course, there is 15 X CO, or 900 

 minutes. In other words the distance between the equator and 

 the 15th parallel of north or south latitude is more than the 

 space assumed for 15 at the equator by its 90th part. To 

 measure these fractional parts a diagonal scale must be con- 

 structed on the principle shown in Fig. 16 (Vol. II., p. 356), a 

 square being constructed on the space assumed for 15, and the 

 aides being divided into six parts, each representing 150 minutes, 

 and the top and bottom into ten parts ; diagonal lines being 

 drawn from side to side, as shown in the figure to which reference 

 has been made, and perpendiculars from top to bottom the 



the parallels of latitude. It is generally considered sufficient to 

 carry the map of the world on Mercator's Projection as far as 

 the 80th parallel of north latitude and the 60th parallel of 

 south latitude, as all the land on the earth's surface of which wo 

 have any certain knowledge is included within these limits. 



The meridians of longitude must now be drawn on either side 

 of, and parallel to, the straight line D E, through the points num- 

 bered 15, 30, 45, 60, etc., and carried as far as the lines H L, 

 K M, which form the limits of the map at the top and bottom. 

 The central line, D c E, is the meridian of Greenwich. The pro- 

 i jection must be completed by drawing the border, and marking 

 ' or numbering the meridians and parallels at the sides and top 

 and bottom of the map. If it be desired to divide the spaces 

 between each ruled parallel in the inner part of tho border into 

 degrees, the distance of each degree must be separately set off 

 from the equator, in terms of minutes of the equator, by aid 

 of the table and diagonal scale. 



It should be said that in Mercator's Projection the relative 



Fig. 19. DIAGRAM OF MERCATOR'S PROJECTION. 



perpendiculars will divide the diagonals into fifteens, from 

 which the fractional parts maybe taken with tolerable accuracy. 

 The proportionate length of a line of 91 minutes being thus de- 

 termined, it must be marked off on either side of F and G, along 

 the lines F H, F K, G L, G M. In the diagram this is shown by 

 the points numbered 15, above and below F and G. Straight 

 lines drawn through these opposite pairs of points, above and 

 below the equator, will determine the 15th parallel of latitude 

 north and south of the equator. 



In the same way the parallel of 30 north and south latitude 

 will be found to be 1,888 minutes in distance from the equator, 

 which is equal to twice the space assumed for 15 X 88 minutes. 

 It will therefore be necessary to take the length of 88 parts from 

 the diagonal scale and add it to twice the space assumed as 15 

 at the equator, and again set off the whole of the distance thus 

 obtained on the lines F H, F K, G L, G M, from the points F and G. 



This distance is shown by the points marked 30 above and 

 below F and G. The parallels of 30 north and south of the 

 equator must be drawn through the opposite pairs of these points, 

 as in the case of the parallels of 15. A similar course must be 

 adopted for the remaining parallels, and the tropics of Cancer 

 and Capricorn, which are not shown in the diagram. The 

 parallels may be carried as far north and south of the equator 

 as may be considered desirable, and the limits of the map fixed 

 by drawing straight lines, H L, KM, parallel to the equator or 



proportions of the land and water between every successive pair 

 of parallels, and even of the meridians and parallels themselves, 

 are carefully preserved ; but the necessity that exists of increas- 

 ing the size of the meridians and parallels towards the north 

 and south of the map, renders a far greater space to be given 

 to the land and water in these regions than they actually 

 occupy, and unless this is fully understood a false notion is apt 

 to be conceived of the relative proportions of different parts of 

 the world at the equator, and in high northern and southern 

 latitudes, in length, breadth, and superficial area. For this 

 reason it is impossible to effect measurements on a map of this 

 kind by a scale of miles, as no scale can be constructed that 

 would suit every part of the map. 



Mercator's Projection is especially used for drawing charts for 

 the use of sailors, because on a map of this kind a ship's course 

 may be laid down in a straight line, since a straight line drawn 

 in any part of it, and in any direction, would intersect all the 

 meridians at the same angle, and this would also be the case 

 with the parallels. This part of the subject, however, belongs 

 properly to navigation, and we need not enter on it here further 

 than to point out the advantage which this kind of construction 

 offers to the mariner who, in an ordinary map, or on a plani- 

 sphere or projection of a hemisphere on a flat surface, would 

 have to mark his course by a curved line, which would be at- 

 tended with considerable difficulty. 



