PRO 



PRO 



of the surface of a sphere on a plane, 

 according to the laws of perspective. In 

 projecting a spherical surface on a plane, 

 some parts must be unduly contracted 

 or enlarged in proportion to others. The 

 projections chiefly used in maps are the 

 orthographic, the stereographic, and 

 Mercator's. 



1. In the Orthographic projection, every 

 point of the hemisphere is referred to its 

 diametral plane or base, by a perpendi- 

 cular let fall on it ; so that the represen- 

 tation of the hemisphere thus mapped on 

 its base, is such as it would appear to an 

 eye placed at an infinite distance from 

 it. In this projection, only the central 

 portions are represented of their true 

 forms, while all the exterior is more and 

 more distorted and crowded together as 

 we approach the edges of the map. 

 Owing to this cause, the orthographic 

 projection, though very good for small 

 portions of the globe, is of little service 

 for large portions. 



2. The Stereographic projection is in 

 great measure free from this defect. 

 The eye is supposed to be placed at the 

 surface of the sphere, and to view the 

 concave of the opposite hemisphere 

 through the plane of that circle, in the 

 pole of which the eye is placed. Hence, 

 the position on this plane of any point 

 of the spherical surface will be indicated 

 by a line drawn from that point through 

 the plane to the eye. This is a true 

 perspective representation : all circles 

 on the sphere are represented by circles 

 in the projection ; every very small tri- 

 angle on the sphere is represented by a 

 similar triangle in the projection. This 

 and the preceding mode of projection 

 may be considered natural, inasmuch as 

 they are really perspective representa- 

 tions of the surface on a plane. 



3. Mercator's projection is entirely 

 artificial, representing the sphere as it 

 cannot be seen from any one point, but 

 as it might be seen by an eye carried 

 successively over every part of it. In it, 

 the degrees of latitude, and those of 

 longitude, bear always to each other their 

 due proportion ; the equator is conceived 

 to be extended out into a straight line, 

 and the meridians are straight lines at 

 right angles to it. Like the stereo- 

 graphic projection, it gives a true repre- 

 sentation, as to form, of every particular 

 small part, but varies greatly in point of 

 scale in its different regions ; the polar 

 portions in particular being extrava- 

 gantly enlarged, and the whole map, 



273 



even of a single hemisphere, not being 

 comprisable within any finite limits. 



4. In the Gnomonic or Central projec- 

 tion, the eye is supposed to be placed in 

 the centre of the sphere, and tlie various 

 objects to be delineated are transferred 

 from the sphere to a plane, which is a 

 tangent to its surface. The entire hemi- 

 sphere can never be represented by this 

 projection, since the circumference which 

 terminates it is on a level with the eye, 

 and is therefore parallel to the plane of 

 projection. In this case, the parallels of 

 latitude will be concentric circles, and 

 the meridians straight lines radiating 

 from the centre. This method is chiefly 

 employed in dialling, and derives its 

 name from the connexion between the 

 methods of describing it and those for 

 the construction of a gnomon or dial. 



5. Projection by Development. By this 

 expression is understood the unfolding 

 or spreading out of the spherical surface 

 on a plane. As a preparatory step, how- 

 ever, the sphere must be converted into 

 a cone or a cylinder, inasmuch as por- 

 tions of these forms most resemble 

 portions of a sphere, and the forms 

 themselves are susceptible of the re- 

 quired development. 



PROLEGS. The wart-like tubercles 

 which represent legs on the hinder seg- 

 ment of caterpillars. 



PROLI'FEROUS {proles, offspring, 

 fero, to bear). A term applied in botany 

 to a flower which produces another flower 

 from its centre, as in certain roses. 



PROMERO'PIDiE. The Hoopoes; a 

 family of the Insessores, or Perching 

 birds, one species of which, the upupa 

 epops, occasionally visits Europe. See 

 Tenuirostres. 



PROOF AND INFERENCE. In 

 addition to what has been adduced under 

 the article. Inference and Proof, the 

 learned author of the " Elements of 

 Logic" observes, that proving may be 

 defined "the assigning of a reason or 

 argument for the support of a given pro- 

 position;" and Inferring, '*the deduc- 

 tion of a conclusion from given premises." 

 In the one case our conclusion is given, 

 and we have to seek for arguments ; in 

 the other, our premises are given, and we 

 have to seek for a conclusion. He adds, 

 that "proving" may be compared to the 

 act of putting away any article into the 

 proper receptacle of goods of that de- 

 scription ; " inferring," to that of bringing 

 out the article when needed. 



PROPA'GO; PROPA'GULUM. The 

 N5 



