GEOGRAPHY. 



GEOMETRY. 



370 



affect the health of the inhabitants in a sensible degree. As to moisture 

 or rain, not only the annual quantity that falls should be noticed, but 

 also its distribution at the different seasons. The character and the 

 duration of the seasons must also be observed, and the prevalent 

 winds ; and especially the effect of the seasons on the progress of vege- 

 tation. It is necessary to know all these facts before a just notion can 

 be formed of the fitness of any given tract of country for providing a 

 population with food. And this capability of a country for the pro- 

 duction of food, or, in other words, its capabilities for agricultural 

 purposes, is one of the most useful branches of geographical inquiry. 

 The nature of the soil, and its fitness for different productions adapted 

 to the climate of the tract, are therefore matters of primary importance 

 in a geographical description. It is here proper to enumerate those 

 objects of agriculture which are raised for food and as materials for 

 clothing, and the proportion between the labour which they require 

 and the value of the produce ; and, in the next place, such productions 

 as could be raised with ease and advantage, but which are not culti- 

 vated to any extent. Those objects which form articles of export, and 

 enter into the market of the world, also claim a notice ; and also such 

 indigenous plants an are either of some use in the domestic economy 

 of the inhabitants, or furnish a commodity for 'foreign trade. It is not 

 the business of the geographer to enumerate all the particulars which 

 constitute the botany or zoology of a district, for that would enlarge 

 his science beyond all bounds and encroach upon the limits of others : 

 the principle that must guide him in determining how much and what 

 he must include in his geographical description of the botany and 

 zoology of a country, will always be indicated by the question, Does 

 the thing or object inquired after materially influence the capability of 

 the country as a place fitted for the residence of man ? Besides the 

 useful domestic animals, it is only necessary to mention such wild ones 

 as are useful to the inhabitants, either by providing them with food 

 and clothing, or by supplying an article of commerce : and these ani- 

 mals only need be mentioned when they are found in great numbers. 

 As for the mineral wealth of a country, the notice of that will be 

 limited to those substances which are worked for the use of the 

 inhabitants or for exportation. 



In this way we conceive the geographer ought to describe in detail 

 each natural division of a country ; and when he has described two 

 such tracts which are contiguous to one another, he must point out 

 the boundary-lines by which nature has separated them, and the ob- 

 stacles which she has placed to their mutual intercourse. If he finds 

 that such boundary-lines are formed by mountain ranges, he has to 

 notice their mean elevation, and likewise that of the mountain-passes 

 by which the dividing range is crossed. He must also add what 

 natural productions of the range contribute to the sustenance or 

 comfort of the inhabitants of the adjacent tracts. When the 

 range has numerous offsets and extensive valleys, and consequently 

 occupies a considerable part of the country, he must treat it as a 

 separate natural division, and describe it in detail like any other 

 natural division. 



When the geographer has described every natural division of a 

 country in this way, and incorporated in his description the best 

 attainable information on all the above-mentioned points, we think 

 that he has done his duty, and may consider his labour as terminated. 

 But our geographical treatises still contain other matter, which is not 

 comprehended within the above enumeration of objects belonging to 

 the science of geography. This extraneous matter is taken either from 

 statistics, or from what is popularly called natural philosophy or from 

 history ; and it ought to be considered how far it is expedient to admit 

 such matters into geographical treatises. 



The knowledge of a country would properly be considered as incom- 

 plete without a general notion of the most important commercial and 

 manufacturing towns within it. Such towns must therefore be 

 mentioned, and at the same time it should be stated how far 

 they facilitate the internal and external intercourse of a country. 

 The political divisions of the country may be added or omitted ; 

 when added, they should be mentioned briefly, and in a very general 

 way. Good maps supply any deficiency in geographical works in this 

 respect. 



We do not venture to exclude entirely from geographical works all 

 mention of natural phenomena peculiar to a country. Some of these, 

 as volcanoes and earthquakes, though they do not exercise a permanent 

 influence on the welfare of the inhabitants, are frequently destructive 

 of property or life, or of both. For that reason they ought to be 

 noticed. Such phenomena as warm or mineral springs seem also to 

 claim a notice, especially if distinguished by peculiar characters, as the 

 Geysers in Iceland. 



Its more difficult to determine how far it is proper to describe the 

 remains of antiquity in geographical works. When the ruins of a 

 great city still exhibit remarkable traces of its ancient grandeur, they 

 certainly cannot be altogether excluded. But the true solution of 

 these and other difficulties of the kind that may be suggested as to the 

 matter admissible into a geographical treatise, seems to be this : 

 these subjects are specialties, and if they belong to geography at all, do 

 not belong to it an necessary component parts of it, but stand to it in 

 *uch a relation as to admit of being introduced or omitted according to 

 the taste and judgment of the writer, who in this, as in all branches of 

 knowledge whose boundaries are incapable of precise determination, 

 ARTS AND 8C1. DIV. VOL. IV. 



will show his good sense and his clear comprehension of his subject as 

 much by what he omits as by what he takes in. 



The political institutions of a country belong to its history, and not 

 to its geography, and ought certainly to be excluded from geographical 

 treatises, though they form a necessary part of most statistical and of 

 all historical works. In the Admiralty ' Manual of Scientific Inquiry,' 

 third edition (London, 1859), will be found the views which are 

 suggested by the recent rapid progress of geographical science, on 

 the principal points to which, in respect of geographical investigations, 

 the attention of travellers should be mainly directed, embodied in an 

 article by Mr. W. J. Hamilton, F.R.S., some time President of the 

 Royal Geographical Society of London. 



The local subjects of Descriptive Geography constitute in their 

 alphabetical arrangement the GEOGRAPHICAL DIVISION of the ENGLISH 

 CYCLOPEDIA. The subjects of Physical Geography, considered as 

 objects of science, such as DESERTS, FORESTS, MOUNTAINS, RIVERS, 

 &c. will be found in their proper alphabetical places in the present 

 division ; and those belonging to the Geographical Distribution of 

 organised beings have been given under their appropriate heads in 

 the NATURAL HISTORY DIVISION. [ASTRONOMY ; CHART ; CLIMATE ; 

 GEODESY.] 



GEOMETER, a person who is skilled in geometry ; but the term 

 had its meaning settled at the time when geometry was by very much 

 the most important branch of mathematics : and now it generally means 

 mathematician. For instance, the French (who make considerable use 

 of the term) call Laplace nn gomtre, though his writings are exclu- 

 sively algebraical. The term must then be understood to signify 

 simply mathematician. 



GEOMETRICAL. Of this term, as opposed to algebraical or arith- 

 metical, nothing need be said ; bxit the peculiar conventions of geometry 

 oppose it most frequently to the term mechanical. Every construction 

 which can be made by the ruler and compasses, that is, which demands 

 no points except such as can be found by the intersections of straight 

 lines and circles, is geometrical : every construction which requires any 

 other curve, or which tacitly requires such a motion of a straight line 

 or circle as would generate any other curve, is mechanical. The reason 

 is that it pleased the Greeks to use these terms as distinctive of the 

 things which can and cannot be done by the straight line and circle 

 only : a real and important distinction with an unfortunate name. 

 For though names, when clearly understood, are of little consequence, 

 yet this convention of geometry has caused many to waste their time 

 and misapply their talents. A man, for instance, not well versed in 

 mathematics, hearing that a geometrical quadrature of the circle has 

 long been sought, and never been found, sets his invention to work, 

 easily discovers a (mechanical) method of proceeding, and imagines 

 that everything is geometrical which employs lines, solids, &c. in 

 space. 



The conic sections were not considered by the Greeks as geometrical 

 instruments. Several writers speak as though the contrary had been 

 the case ; but it is certain that the solution by Menechmus of the 

 problem of two mean proportionals, which employs the parabola, was 

 not considered by Eutocius (who records it) as more geometrical than 

 the others which he gives. 



GEOMETRICAL PROGRESSION, PROPORTION, &c. [PRO- 

 GRESSION, PROPORTION, &c.] 



GEOMETRY (ytiM>furpla,geom^tria, or land- measurement), the science 

 which investigates the relations existing between parts of space, whether 

 linear, superficial, or solid. But at the same time, the most common 

 meaning of the word implies that the investigation is to take place 

 under restrictions as to the instruments which may be employed. Of 

 this we shall see more when we come to the geometry of the Greeks ; 

 in the meanwhile, geometry may be generally denned as the science 

 of space. The closeness of the connection between geometry, and 

 Euclid its founder, has made the two names almost identical. Although 

 therefore, a part of the present article has been given in the Bioo. DIV. 

 under the name of EUCLID, it is repeated here with some additions. 

 As geometry is in all probability the most ancient subject to which 

 actual demonstration was applied, we may thus account for the per- 

 manent association which has always existed between the idea of this 

 science and that of rigorous deduction. To reason geometrically is a 

 synonyme for to reason strictly : but abandoning this particular 

 view of geometry, we shall devote the present article principally 

 to such an imperfect sketch of the early progress of the science as 

 its meagre history, combined with the narrowness of our limits, will 

 allow. 



There is a stock history of the rise of geometry, supported by the 

 names of Strabo, Diodorus, and Proclus, namely, that the Egyptians, 

 having their landmarks yearly destroyed by the rising of the Nile, 

 were obliged to invent an art of land-surveying in order to preserve 

 the memory of the bounds of property ; out of which art geometry 

 arose. This story, combined with another attributing the science 

 directly to the gods, forms the first light which we have on the subject, 

 and both in one are worthily sung by the poet who figures at the head 

 of an obsolete English course of mathematics : 



" To teach weak mortals property to scan, 

 Down came geometry and formed a plan." 



There is no proof whatever that the Egyptians were more of geometer* 



11 B 



