LESSONS IN GEOGBAH1Y. 





that the space thus auumud in not taken too long in proportion 



i .OHO lino of the map, and set off from K along the straight 



lino E B eight of these spaces, and number the point*, begin. 



l<), 45, 50, 55, 60, 05, 70, 75, ax in the figure, 



point marked 75 draw the straight line u a 



i >. Tho line o u will be the limit of the map to* 



\\MI-.I.S the t"i', tiiul the points numbered upwards in uuooession 



from will be thu points through which will pass the parallel* 



rronpondiug with the numbers. To find tin- 

 from which to draw the parallels of latitude, measure four 

 upwards from the point marked 75, along A B, and num- 

 ber them 80, 85, 90, and F. The point F, just five degree* 

 than tho polo marked 90, is the centre from which the 

 of latitude are to be described. This point corre- 

 upends to the point M in l'i-_-. 1 I. in \\hieh the sphere is sup- 

 to be entered by a cone passing through it in parallels 

 : 05, the spaces from 45 to M, along tho line L M, in Fiu r . 

 ! tho spacer from 45 or r to F, along the line A B, in Fi_r. 

 17, corresponding in number, as the reader may ascertain on 

 comparing them. The actual distance of tho point F beyond 

 tho pole is 4 30' 30', when determined by calculations involving 

 a knowledge of trigonometry ; but for maps on a small scale 

 it is near enough to consider it as being equal to five degrees, 

 and therefore to tho space assumed to represent five degrees in 

 th*e construction of tho projection. The point F being thus 

 determined, tho parallels of latitude may be described through 

 tho points marked on the central meridian with a finely pointed 

 pencil, or, as there is no absolute occasion to describe these arcs 

 until tho limits of tho map on either side are determined, it will 

 be sufficient to draw a single arc o p Q through the point 

 marked 45 or p. This arc should be drawn for some distance 

 beyond tho ultimate limits of the map on either side. 



We now proceed ta draw the meridians, and to determine their 

 position. The learner will have to refer to the table at tho end 

 of this lesson, which shows the number of geographical miles 

 contained in a degree of longitude under each parallel of lati- 

 tude, supposing tho earth to be a perfect sphere in form. 



It will bo remembered that the cone on which our map of 

 Europe is projected was supposed to pass through the sphere in 

 the parallels of 45 and 65, and that the measurements on the 

 cone along these lines aro exactly equal to measurements along 

 the same lines on the sphere, or, in other words, that tho degrees 

 of longitude on these parallels, both on the cone and tho sphere, 

 are exactly equal. On looking at the table, we find that a 

 degree of longitude under the parallel of 45 is equal to 42*43 

 geographical miles on the sphere, while a degree of longitude 

 under tho parallel of 65 is equal to 25'36 geographical miles. 

 What wo want to do, then, 's to find a line bearing tho same 

 proportion to the line which we assumed at first to represent 5 

 degrees, as 42*43 geographical miles bears to 60 geographical 

 miles, to enable us to set off points along the arc o p Q on 

 either side of tho central meridian, through which the other 

 meridians may be drawn from the point F. It would do equally 

 well to find a line bearing the same proportion to the lino 

 assumed to represent 5 degrees as 25*36 bears to 60, and to set 

 off spaces equal to this line on either side of the central meridian 

 along the arc representing tho parallel of 65 ; but it is always 

 safer, and ensures a higher degree of accuracy, to deal with the 

 larger arcs and spaces instead of the smaller. 



To enable us to find lines bearing the required proportions to 

 the lino originally assumed to represent 5 degrees, wo must take 

 a straight line exactly equal to it, as in Fig. 15, and on it con- 

 struct a square. The sides of this square must be divided into 

 six equal parts, and numbered upwards at the points of section 

 from to 60, while the top and bottom must be divided into ton 

 equal part*, the points of section between the extremities being 

 numbered from 1 to 9. Lines must then be drawn diagonally 

 across the square, from on tho left hand to 10 on the right 

 hand, etc., and perpendicular lines parallel to the sides through 

 the points of section numbered 1, 2, 3, etc. This diagonal scale, 

 constructed on tho same principle as the scale shown in Lessons 

 in Geometry, Vol. I., p. 113, enables us to measure with accuracy 

 any part not less than one-sixtieth of tho "line assumed to repre- 

 sent 5 degrees. The lino required has to bear the same proper- 

 tion to this line as 42*43 bears to 60, and will be represented by 

 the dotted line in Fig. 15, drawn midway between the lines 

 n ^resenting 42 and 43, and a little nearer to the. former than 

 to the latter. In Fig. 16 a larger diagonal scale is given, from 



which the reader may construct * projection for a map of 

 Kurupe, taking the dotted line A B to represent the Ait*mi* 

 to be net off along the aro representing the parallel of 45; bo* 

 it will be bettor for hiia to construct ftcaioa for himself, much 

 .n size than the Urgent which we have given to Fig. 10. 



Distance* equal to the lino a fc that repreeenU 42-43 on the 

 mall acale in Fig. 15, most now bo net off on cither aide of the 

 central meridian, represented by the straight line A B, aloof the 

 arc o P y, and straight line* most be drawn from r with fine 

 drawing-pen through the point* thus obtained. The dotted lines 

 between r and the top of the map need not be drawn bj the 

 learner. The remaining area mart then bo drawn with acompaw 

 pen, and tho limit* of tho map to the eait and weei determined 

 by drawing the straight lines x L, x M at right angle* to the 

 base lino c D, tho former a little to the left of the meridian 

 5 west longitude, and tho latter a little to the right of the 

 meridian 45 cast longitude. Tho border linen should then be 

 drawn as shown in the engraving. The double lines at the side* 

 and top and bottom of tl o inner space, which contains the map, 

 should be divided into single degrees and ruled, as in the figure, 

 to present a distinction of colour, and thus afford a readj means 

 of counting and measuring degree lines not marked and num- 

 bered on tho map. The meridians should be numbered in the 

 border at the top and bottom, and the parallels of latitude at 

 the sides. The Arctic Circle must be inserted in the form of a 

 dotted line at the distance of 1 30' above the parallel of 65. 

 A blank space should bo left in tho upper left-hand corner, or 

 the lower right-hand corner, for the title and scale of geographi- 

 cal and British miles. To construct these scales, it must be 

 remembered that 60 geographical miles are equal to 69*07 

 British miles, or that tho line which was at first assumed as 

 being equal to 5 degrees, represents 60 x 5, or 300 geographical 

 miles, and 69*07 x 5, or 345 British miles, very nearly. 



In order to fix tho position of places with accuracy, the student 

 is advised to divide the field of his map by pencil lines into 

 spaces of a degree each way, as shown in the lower part of 

 Fig. 17. This, however, can only be done when the map is 

 on a sufficiently large scale. Learners are cautioned to use 

 Indian ink instead of common ink in drawing maps, as the ordi- 

 nary ink will run and spoil the map where a final wash of colour 

 is given to the sea, and the boundary lines are distinguished by 

 contrasting tints. 



TABLE SHOWING THE NUMBER OF GEOGRAPHICAL MILES IK 

 A DEGREE OF LONGITUDE UNDER EACH PARALLEL OF 

 LATITUDE, THE EARTH BEING SUPPOSED TO BE A PERFECT 

 SPHERE. 



As the learner will he TO to refer to this table when engaged 

 in the construction of a conical projection of any portion of the 

 sphere, whether large or small, he should carefully study it, and 

 endeavour to commit to memory the number of geographical 

 miles under every fifth parallel of latitude, counting from the 

 equator, that is to say, the 5th, 10th, 15th. 20th, etc. 



