May 8, 1891.] 



SCIENCE. 



261 



swans, geese and ducks, and sea-fowl may be mentioned. In the 

 southern rivers salmon is plentiful. 



The southern part of the peninsula is inhabited by Kamtchadales, 

 numbering some 4,000 souls. They have submitted to Russian in- 

 fluence, and are Christians in name, but still cling to the rites of 

 Shamanism. Their mud huts have given place to houses, round 

 which gardens are laid out. They keep cattle and a few horses 

 and fowls, but neither sheep nor pigs. In the north about 3,000 

 Koriaks live, who are still in a primitive state, and subsist on the 

 produce of the chase and fishing. Their most important domestic 

 animals are dogs, which draw their sleighs. 



THE MEAN COAST-DISTANCES OF CONTINENTS. 



The proximity of countries to the sea has a most important 

 bearing on their climate, commercial development, etc., and 

 therefore the problem of ascertaining the relative advantages in 

 this respect of different parts of the world has long attracted the 

 attention of geographers. In Petermann's Mitlheilungen, Bd 36, 

 Nos. 3 and 4, Dr. Carl E. M. Rohrbach explains a new method of 

 solving the problem, in which the mean distances of the conti- 

 nental lands from the coast play an important part. As quoted 

 in the Scottish Geographical Magazine, he shows, as a prelimi- 

 nary investigation, that the mean distance of a circle from the 

 circumference is one-third the radius, and that this distance is the 

 same for a square, or other rectilinear figure, circumscribing the 

 circle. It is found by integrating the product of an elementary 

 area into its distance from the perimeter and dividing by the 

 whole area. The process is, therefore, similar to that of finding 

 the centre of gravity of the area, and, accordingly, the value may 

 be very simply found by dividing the circle or square into indefi- 

 nitely small triangles by radii drawn from the centre, the centres 

 of gravity of which are, of course, at one-third of the radius from 

 the perimeter. From this result Dr. Rohrbach deduces the mean 

 distance for a rectangle, and shows how to find it for a calotte, or 

 the spherical area contained by a small circle of a sphere. Even 

 for a large calotte it diflfers very little from that of a circle of 

 equal area. These investigations prove that of all figures con- 

 taining the same area the circle and its circumscribed figures are 

 those in which the distances from the perimeter are greatest, and 

 this proposition is exhibited in a convenient form by means of 

 curves, in which the abscissae are proportional to the areas, and 

 the ordinates to the distances from tlie perimeter. In the diagram 

 thus constructed the curve (a parabola, of course) for the circle 

 lies outside all the others, and as the area deviates more and more 

 from the circular form, its curve approximates more closely to a 

 straight line. Owing to this property the circle gives a convenient 

 standard for mean distance from the coast, as will be seen presently. 



In dealing with continental areas Dr. Rohrbach draws contour- 

 lines on a map parallel to the coast-line at certain chosen intervals, 

 and measures the areas contained with a planimeter. If great accu- 

 racy be desired, the lines must be traced on a map in which there 

 is no distortion, and then transferred for measurement to an equal- 

 area map, but in a first essay, to demonstrate the applicability of 

 the method and the value of its results. Dr. Rohrbach considered 

 Bonne's projection sufficiently accurate for tracing the lines as 

 well as for measurement. A map of the world and another of 

 Europe are appended to the article, on which the contoui'-lines 

 are drawn, and the coast-distance of the areas between them de- 

 noted by different colors. The relative conditions of the conti- 

 nents are also shown, both by rectangles of which the bases are 

 proportional to the areas, and the altitudes to the mean coast- 

 distances, and also by curves — chorigraphic, as Dr. Rohrbach 

 calls them — where the ordinates represent the coast-distances 

 corresponding to the areas indicated by the abscis?se. Tables are 

 given showing the areas lying beyond different distances from the 

 coast in the various continents, both in square kilometres and in 

 percentages. The following shows the mean coast-distances: 

 Europe, 208 miles; Asia, 482 milt's; Eurasia, 433 miles; Africa, 

 417 miles ; Australia, 314 miles ; North America, 292 miles ; South 

 America, 343 miles; the five continents, 381 miles. 



As a measure of the accessibility of continents from the coast. 

 Dr. Rohrbach proposes the quotient obtained by dividing the 



mean distance in a circle, or in a calotte, of equal area by the ac- 

 tual mean distance, and gives the numbers in the latter case, but 

 the result is scarcely satisfactory. As he himself points out, 

 Eurasia appears to greater advantage than Euiope, because the 

 mean distance in the calotte is calculated as though sea instead of 

 land lay to the east, and thus the quotient is increased. It is 

 also startling to find North America represented by a higher figure 

 than Europe, and the five continents by a number more than twice 

 as great. It is easy to see that these discrepancies arise because the 

 numbers represent only the advantage each continent derives 

 from its actual shape compared with its accessibility if formed 

 into a calotte, and do not indicate the relative accessibility of the 

 continents. A more correct idea is obtained by taking the mean 

 coast-distance (1,416 miles) in a calotte of area equal to that of the 

 five continents, or the actual mean distance (381 miles), as unity. 

 In the latter case the numbers are as follows : Europe, 1.83; Asia, 

 0.79; Eurasia, 0.88; Africa, 0.91; Australia, 1.78; North America, 

 1.30; South America, 1.11; the five continents, 1.00. 



Dr. Rohrbach claims that his method is superior to those before 

 employed, because the mean coast-distance is a quantity admit- 

 ting of simple definition, and not deduced by any artificial means 

 from the geometrical forms. Its value also is easily reckoned, and 

 can be worked out to any desired degree of accuracy, maps of 

 various scales being employed according to the extent and con- 

 figuration of the countries under examination. In almost all other 

 methods the length of the coast-line has been used, the estimation 

 of which leaves much room for speculation, causing great uncer- 

 tainty in the results. In the present method this quantity is not 

 needed, and yet the meanderings of the coast-line exercise their 

 due influence on the curvature of the contour-lines, as may be 

 clearly seen on the map of Europe already alluded to. And not 

 only is the method applicable to purely morphological investiga- 

 tions, but charts may also be constructed, showing the relative 

 conditions of the various parts of a country with regard to means 

 of communication. Thus, an ice-bound coast may be treated as 

 an inland boundary, and, w'here a chain of mountains intervenes, 

 the contour-lines may be drawn so that their normals run to the 

 sea past the extremities of the chain, or converge to the passes. 

 Navigable rivers, railways, etc., may also be taken into account, 

 and also the elevation, etc., charts being constructed to show the 

 work required to transport a unit weight of goods, say a hundred- 

 weight, from the coast. Each contour-line in such charts will 

 pass through all places to which the labor of transport is the same, 

 and will therefore resemble an isobar or isotherm. 



BOOK-REVIEWS. 



Orammatica elementar do Kimbundu. Kimbundu Grammar. 



For Heli Chatelain. Genebra, 1889. 

 La Lengua Cunza. For Francisco de San-Roman. Santiago 



de Chile, 1890. 

 Kreolische Studien. Ueber das Malaisportugiesische von Batavia 



und Tugu. Von Hugo Schuchahdt. Vienna, 1891. 

 Etudes de Graynmaire Comparee. De la Categoric des Modes. 



Far Raoul de la Geasserie. Louvain, 1891. 

 This batch of recent linguistic works, in widely diverse fields, 

 is but a faint indication of the activity in this branch of scientific 

 research. 



Mr. Chatelain has been connected with the American mission 

 in south-west Africa, and his grammar of the Kimbundu, a 

 member of the wide-spread Bantu group, has particular interest, 

 not only for its practical value in missionary work, but because 

 the Smithsonian Institution is about to publish the author's 

 collections of folk tales and legends in the original tongue, 

 together with translations and notes. 



The Cunza language is spoken by a native tribe on the south- 

 west coast of South America, at the northern border of the Desert 

 of Atacama. It is supposed by the eminent linquist von Tschudi 

 to be the ancient Calchaqui. Although San Roman does not 

 furnish a full grammatical view of the tongue, we are glad to 

 have even his incomplete notes, as heretofore there has been ab- 

 solutely nothing on its grammatic structure. 



