Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/219

Rh w MATHE 1m'rIc_.xL.] GEOGRAPHY 205 Figure 19 is a perspective representation of more than a The co-ordinates originating at the centre, take the central hemisphere, the radius [-3 being 108°, and the distance /L of meridian for the axis of 3/and a line perpendicular to it for the point of vision, 1'40. the axis of ac. Let the latitude of the point G, which is to The co-ordinates my of any point in this perspective may occupy the centre of the map, be 7; if 4;, u) be the latitude be expressed in terms of the latitude and longitude of the and longitude of any point P (the longitude being reckoned corresponding point on the sphere in the following manner. from the meridian of G), u the distance PG, and u. the ("' £5 «E ' ./ ;. / ’ <5» z  — _ / /' ’ A ‘-X 74 25/ . T ‘  i “ 13% l ‘ ‘W // (i E :. ,1 I J23 . 4 T ‘H 17.9.. _./¢C< 1 ‘ - Z x ‘-3., . 9 l’ w ¢ 5 U R 0 ‘ ". 1 off’? I a fv‘ i Q /My TIC <2 _‘,.- I‘ i m A J ‘ A r R I C W111 S R l 5 9 I / xi‘ ‘ £ R 0 U l H A Tl[_ A N 1 If
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_ v ‘ l‘  “ 1 ‘l 4‘  “  x_'_»: ‘ gag. H I, g ﬁx ‘i .J__,_»// I_ “  L ‘L-——+'«—--7?‘ ' ' ‘ » / . " 1 ;-= ’ ~X_ V i‘ I ‘ -_,,-_7*// / .§   "/ / i I T‘?.T'‘ / ,/‘ FIG. 19.—Twi1ight Projection. azimuth of P at G, then the spherical triangle whose sides are 90° — y, 90° — 4;, and it gives these relations-— sin n sin p.=cos 95 sin w, sin 20 cos ;u.=cos 7 sin 95 - sin 7 cos 95 cos w, cos it =sin -y sin 95+ cos 7 cos 95 cos w. New .7c=psiu p., 3/=p cos }I., that is,
 * 2: cos 9: sin to

' h+sin -y sin 95+cos 7 cos 9) cos w ’ cos 'y sin 9: — sin 7 cos 95 cos w h+sin -y sin 95+cos 7 cos 95 cos w ’ K 1’ I‘. by which an and 3/ can be computed for any point of the sphere. If from these equations we eliminate to, we get the equation to the parallel whose latitude is gb ; it is an ellipse whose centre is in the central meridian, and its greater axis perpendicular to the same. The radius of curvature of this ellipse at its intersection with the centre meridian is L‘ cos 95 h sin 'y+sin 95 ' The elimination of 4; between ac and 3/ gives the equation of the meridian whose longitude is m, which also is an ellipse whose centre and axes may be determined. for a map of Africa, which is included between latitudes 40° north and 40° south, and 40° of longitude east and west of a central meridian. Values of :c and 3/. (P V w:O° w_10° w:20° w:30° (422400 0., :13: 0'00 9'69 19'43 29'25 39'17 3/: 0'00 0'00 0'00 0'00 0'00 we :3: 0'00 9'60 19'24 28 '95 3876 2 : 9'69 9'75 9'92 10'21 10'63 20., :13: 0'00 9'32 18'67 28'07 37'53 y: 1943 19'54 19'S7 20:43 21'25 300 :3: 0'00 8'84 17'70 26'56 3544 2 :29'25 ‘29'40 29'87 30'67 31'83 40° 3:: 0'00 8'15 16"28 24'39 3244 ’ I 3/:39'17 I 39'36 39'94 40'93 4'2'34 C’om°cal Development. The conical development is adapted to the COIISWICUO11 The following table contains the computed co-ordinates of maps of tracts of country of no great extent in latitude