The publisher of this book utilises modern printing technologies as well as photocopying processes for reprinting and preserving rare works of literature that are out-of-print or on the verge of becoming lost. This book is one such reprint.

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER V. THE PROJECTION. 84. In charts used for surveying purposes it is of prime importance that angles between lines on the earth's surface should be shpwn in their true size, and were this the only requisite, the Mercator's chart would be the most convenient for use and in construction. This chart, however, presents so many objectionable features that it cannot be employed in plotting; work, the distortion of distances and the oval form of the geodeeic line being insuperable objections. Considering the earth as a sphere or spheroid, it is readily seen that no chart can be constructed which will rigidly fulfil all the desired requirements. The one which seems to approach nearest to perfection is the one used in our Coast Survey, known as the ordinary polyconic projection. The principle of its construction is as follows: 85. Let PA be a portion of any meridian on the earth's sur face, P being the pole and A being at the equator. Conceive a series of cones tangent to the surface, whose vertices are in the produced axis (OP) of the earth. Imagine these cones, cut along elements, tangent to meridians A on either side from PA. Now conceive a plane tangent to the earth at A, and capable of being tilted toward /"without motion along AP, becoming tangent successively at each point of the arc AP. Now if, as the plane is tilted to contain the successive elements of the cones tangent to AP, the portion of the cone included be- tween the slit elements be developed on it, the portions of the bases will appear on the plane as arcs of circles whose radii are the respective slant heights of the cones, which, considering the earth as a spheroid, will be represented by the formula a , . a ,.T-cot L. The plane will then contain a polyconic (1 e s1n Z) ' - projection of...