Map projections . bove; it is KLMNO in the figure. KL andMN pass through the centres of their faces. The meridianswhich cut KL and MN are perpendicular to the equator, andmay be constructed as in the normal case already considered ;they may then be continued across the adjacent faces, to passthrough N and 5. The places where the meridians cut LMand NO may be found from the formula: distance from centre of LM or NO = R tan AZ, sec . And these points may be joined to the poles by the rules givenabove. Thus all the meridians are constructed. N *^S% A /L D! c NM s V Fig. 8. The parallels on the fa
Map projections . bove; it is KLMNO in the figure. KL andMN pass through the centres of their faces. The meridianswhich cut KL and MN are perpendicular to the equator, andmay be constructed as in the normal case already considered ;they may then be continued across the adjacent faces, to passthrough N and 5. The places where the meridians cut LMand NO may be found from the formula: distance from centre of LM or NO = R tan AZ, sec . And these points may be joined to the poles by the rules givenabove. Thus all the meridians are constructed. N *^S% A /L D! c NM s V Fig. 8. The parallels on the faces KL and MN may be constructedas in the normal case, or traced from it. The parallels on the other faces are somewhat more trouble-some. From C draw a perpendicular CH to any meridian, and let0 = tan-1 CH/R. Then the latitude of H is tan1 (cos 6. DH\R). Call this <jj0. The distance of any parallel of latitude from H is thenR tan ((f) — 0) sec 6, as before. ZENITHAL PROJECTIONS 45. 46 ZENITHAL PROJECTIONS Thus the points where the parallels cut any meridian can becalculated. If great accuracy is not desired, they can be constructed bytaking a tracing of the projection on a normal face, or on KL,which is similar; and placing it with centre on C and meridiansparallel to HD. Read off the latitude of H. Take out thedifferences of latitude between H and the desired parallels ;and set them off by estimation from the tracing. The process is tedious to describe. With a little familiarityit becomes quite easy in practice. If desired, the meridian through C may be made construction then proceeds in a way similar to the above,but is more tedious. Measurement of the distance on a great circle. The method is obvious from what immediately precedes. The portion on each face must be measured separately. From the centre C of any facedraw CH perpendicular to the greatcircle, and let 0 = tan-1 CH/R, as be-fore. Then UV= UH+HV = tan-1 (cos 0. C/H/R)± tan-1 (cos 0. VH\R
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Keywords: ., bookcentury1900, bookdecade1910, bookpublisherlondo, bookyear1912
