Page:Encyclopædia Britannica, Ninth Edition, v. 10.djvu/224

Rh 210 I Radius for S Radius for 1 LM' I Parallel. I'M" l'a1‘allel. 0° no | 1 -0000 45° 57-30 -7071 5 054-59 -9902 50 43-03 -0423 10 3-34 -94 -9548 - 55 40-12 -5736 15 213-33 '9659 | 60 33-03 -5000 20 157-42 -9397 05 26-7-2 -42-26 25 122-57 -9063 70 20-85 -3420 30 99-24 -8060 75 15-35 '25SS 35 81'83 -s191 so 10-10 -1736 40 6828 -7660 85 5-01 -0372 With regard to the distortion involved in this system of development, consider a small square described on the sur- face of the sphere, its sides being parallel to and perpendicu- lar to the meridian. Let u and ‘.20; deﬁne its position, and let i be the length of its side. If we differentiate the equa- tion tanqb = to cos u, n being constant, sec“’qb clqb = cos mlm. But the representation of 2dm is 2tanudqb, which is equal to sinu cos‘-’qbd.‘2m; hence that side of the square which is parallel to the equator is represe_nted by icosgqb. And similarly the meridional side is represented by 2' cos9¢(1 + w‘-'+ w‘-' sin‘-'21). Therefore the square is represented by a rectangle whose sides are in the proportion of 1 : 1 +w'-’+w'-’ sin‘~’u, and its area is increased in the proportion of 1 +w'-‘+w'-’ sin‘-’u. : (1 +w‘-’ cos‘-‘u)2. Fig. 30 is a representation on this system of the con- tinents of Europe and Africa, for which it is well suited. For Asia this system would not do, as in the northern latitudes, say along the par- allel of 70°, the representation is much cramped. With regard to the distor- tion iu the map of Africa as thus constructed, consider a small square in latitude 40° and in 40° longitude east or west of the central meridian, the square being so placed as to be transformed into a rect- angle. The sides, originally unity, become 0'95 and 1'13, and the area 108, the diagon- als intersecting at 90° i 9° 56’. In the perspective projection a square of unit side occu- pying the same position, when transformed to a rect- angle, has its sides 1'02 and 1'15, its area 1'17, and its diagonals intersect at 90° i 7° 6'. The latter projection is therefore the best in point of “ similarity,” but the former represents areas best. This applies, however, only to a par- ticular part of the map ; along the equator towards 30° or 40° longitude, the polyconic is certainly inferior, while along the meridian it is better than the perspective—ex- cept, of course, near the centre. Upon the whole, the more even distribution of distortion_gives the advantage to the perspective system. The system of lines ordinarily used for the map of Africa is objectionable, and has scarcely the excuse of facility of construction, since the perspective co- ordinates given above are so easily computed. Fig. 30. Ordnance ;S'm've_y Jlaps. The method of development used in the Ordnance Survey maps of England on the scale of one inch to a mile, as also in the county maps of England, Scotland, and Ireland, on the 6-inch scale is this. A central meridian having been selected, let a perpendicular are be draw11 from any trigono- GEOGRAPHY [.x'r11EM.u‘1c.L. metrical station p to the meridian, meeting it in q. S being a point of reference selected in the central meridian, make Sr[=3/, pq=.r. Then in the development, a straight line drawn to represent the central meridian is the axis of 3/, and a line at right angles to this is the axis of .2‘. The point whose coordinates are .1‘: pg, 3/: Sq is the representation of )1. Supposing the earth spherical, if qb, to be the latitude and longitude of p, then, to being small, that is, only a few degrees, d.r:= — m tan¢>d¢>+('0s ¢(1 — ._1,.2-9 tan‘-’g!>Ww, u7y:(1 +§Jc'3 — tan‘-'q‘>) + .1‘ sinr/> rlw, from which the distortion can be computed. It principally consists in the exaggeration of the scale in a north-and—south direction at the extreme longi- tudes, where o=sec Contours. In maps of a large scale, it is usual to show the relief of the ground by contour lines, which are the intersections with the actual surface of a system of equi- distant horizontal planes. Con-/ tours indicate not only the height of the ground but its slope. Fig. 31 shows a piece of contoured country, including two summits and a “col” between them. The dotted lines, which, l1ow- ever, are not shown in maps, are lines of greatest slope, cutting contours at_right angles. At each summit, supposing the contours there to be ellipses (Dupin’s in- dicatrices), there is an inﬁnity of steepest lines having a common Fig. 31. tangent there. At the col, where the indicatrix is an hyper- bola, there are two steepest lines intersecting at right angles, of which one IS the “ water-shed” joining the sum- mits. R. C.) III. PHYSICAL GEOGRAPHY. This term in its ordinary aceeptation 111ca11s a description of the physical features of the earth. It includes an account of the phenomena of the atmosphere; of the composition, distribution, and movements of the sea ; of the forms of the land, with its water circulation, earthquakes, and volcanoes ; of the distribution of plant and animal life. Its object, however, is not to present a mere bald enumeration of facts, but to group the facts together in such a way as to bring before the mind a lu1ni11ous picture of the whole structure a11d working of the earth as a habitable planet. I’hysic:1l geography is not so much a science or branch of science as a collection of the data ascertained, and probable conclusions arrived at, by different sciences, in so far as these bear upon its own subject. Accordingly, it culls from all departments of inquiry whatever helpsto give additional distinctness -.md vividness to that broad conception of the daily economy of the globe which it is its aim to form and develop. So vast a subject, if treated in its entirety, would demand a very large allotment of space for its adequate discus- sion. Some of its branches have, during the last few years, received so much development that in the present edition of this work it has been considered more expedient to make them the subject of special articles; and here, therefore, to avoid the repetition which a general article on physical geography would involve, there will be given, instead of a formal essay, a mere outline or synopsis of the branches of knowledge embraced in the subject, with references to the other parts of the work where detailed