10 



SCIENCE. 



[Vol. L, No. 1. 



canoes, and mode of navigation, by which they have 

 frequently visited the Society Islands, a distance of 

 2,4U0 miles. They knew much of astronomy, and 

 possessed an accurate calendar, dividing their year 

 into twelve months of thirty days, with allowance for 

 the bissextile. Their year begins at the time when 

 the Pleiades rise at sunset. They count to millions, 

 with names for all their numbers. The priests know 

 every plant on the islands, and are especially familiar 

 with their toxic properties. Interesting remarks 

 were made on their language, their mythology, and 

 their religion. Legends and royal pedigrees are 

 handed down with great exactness by a special class 

 who make this their only business. The language 

 of their classic lore is archaic, and unintelligible to 

 the common people. The genealogy of kings is 

 traced back a hundred generations. Descent is here 

 in the male line, but descent of property among the 

 other classes is in the female line. This is ren- 

 dered necessary from the fact, that with the excep- 

 tion of the queen, who is tabu and therefore chaste, 

 chastity in women is regarded as a disgrace, in that 

 it denotes a want of attractions. Monogamy prevails, 

 but divorce is easy and sexual morality excessively 

 lax. The dead are buried in caves in the mountains, 

 in a sitting posture. Until recently human sacrifices 

 were of frequent occurrence. Criminals are executed 

 secretly with a club. Walled enclosures constituted 

 their " cities of refuge." Their temples in the form 

 of parallelograms were also described. 



Captain Dntton closed his remarks by rapidly glan- 

 cing at the influence of the missionaries, and the 

 modern innovations and modifications in Hawaiian 

 society. 



VARIATIONS IN THE VERTICAL DUE 

 TO ELASTICITY OF THE EARTH'S 



SURFACE. 



In the Philosophical magazine for "December, 1882, 

 Mr. G. H. Darwin discusses this subject. He con- 

 siders first the disturbance due to variations of baro- 

 metric pressure; second, those due to the rise and 

 fall of the tides. Mr. Darwin has previously investi- 

 gated "the state of stress iiroduced in the earth by 

 the weight of a series of parallel mountains" of such 

 shape that the equation to the outline of the section 

 made by a plane traversing all the mountains and 



X being supposed vertical, and that of 2 horizontal 

 and perpendicular to the mountain chains. 



Taking the origin in "the mean horizontal surface, 

 which equally divides the mountains and valleys," 

 and midway one of the mountains, and letting " a, y, 

 be the displacements at the point x, z, vertically down- 

 wards and horizontally," lie finds, when x = 0, 

 gwh , z ^ da gwh . z 



a = -j: — 6 cos 7-, y = 0, i;-- = —^ — sm r- 

 2v b' ' ' dz 2v> b 



In these equations, w is " the density of the rocks of 

 which the mountains are composed; g, gravity; u, 

 modulus of rigidity." 



If we suppose the region to have been originally a 

 plane, such as would be formed by toppling liver the 

 upper half of each mountain into the neighboi-ing 



valley, the quantity - above is the present real in- 

 clination of what was originally the horizontal sur- 

 face stratum. 



The apparent inclination, however, as measured by 

 means of the plumb-line, is something different from 

 the above, owing to the change in the direction of the 

 latter due to the chnnged distribution of the attracting 



masses about it. One of the most interesting [jortions 

 of Mr. Darwin's present paper is the proof of a very 

 simple ratio, for any such case as that now imder con- 

 sideration, between the deflection of the plumb-line 



da 

 and the slope y- of the stratum x = 0. 



This relation, which was pointed out to Mr. Dar- 

 win by Sir William Thomson, though tlie proof here 

 given is due to the former alone, is as follows : — 



If <i be the earth's mean density, r the earth's 

 radius, and b, g, as above, the deflection bears to 



B 1 

 slope the same ratio as - to ;; r S. " This ratio is In- 



(I 3 

 dependent of the wave-length 2 ff 6 of the undulating 

 surface, of the position of the origin, and of the 

 azimuth in the plane of the line normal to the ridges 

 and valleys. Therefore the proposition is true of any 

 combination whatever of harmonic undulations; and 

 as any inequality may be built up of harmonic undu- 

 lations, it is generally true of inequalities of any shape 

 whatever." With rigidity as great as that of steel, 

 the slope is 1| times as great as the deflection. 



" In the problem of the movmtains, w h is the mass 

 of a column of rock of one square centimetre in sec- 

 tion, and of length equal to the height of the crests 

 of the mountains above the mean horizontal plane. 

 In the barometric problem, w h must be taken as the 

 mass of a column of mercury, of a square centimetre 

 in section, and equal in height to a half of the maxi- 

 mum range of the barometer." 



This maximum range is assumed to be 5 centi- 

 metres. The rigidity of the earth is supposed to be 

 3 X 10^ million grammes per square centimetre, — 

 greater than that of the most rigid glass. The dis- 

 tance from the region of high to that of low barometer 

 is taken as 1,500 miles. 



With these data, it is found "that the ground is 9 

 centimetres higher under the barometric depression 

 than under the elevation." 



The maximum slope of the surface, which is found 

 midway between the regions of higli and low barome- 

 ter, is 0".0117; and for the maximum axipareut deflec- 

 tion of the plumb-line, "this is augmented to0".0146 

 when we include the true deflection due to the attrac- 

 tion of the air." ' 



In the problem of the tides, Mr. Darwin imagines, 

 as before, "an infinite horizontal plane which bounds, 

 in one direction, an infinite, incompressible, elastic 

 solid." Upon this he lays off straight strips of equal 

 and uniform width, representing alternately areas of 

 land and of water. At full tide, the surface will be 

 such that for it x will be a discontinuous periodic 

 function of z. This function having been developed 

 according to Fourier's theorem, the results of the 

 previous investigations become applicable. 



It is thus found that "midway in the ocean and on 

 the land there are nodal lines, which always remain 

 in the undisturbed surface," whether the tide be high 

 or low on either coast; " that the land-regions remain 

 very nearly flat, rotating about the nodal line, but 

 with slight curvature near the coasts." 



I Mr. Darwin remarks that this last result is independent of 

 tVie wave-lengtli of the barometric inequality, and so it appears 

 from the formula. It would seem, however, that the above cor- 

 rection for the attraction of the air is only applicable when the 

 wave-length is very considerable compared with the height of 

 the etTective atmosphere. 



This apparent deflection is so great, that, with the deflections 

 caused by the tides, Mr. Darwin concludes it will probably for- 

 ever mask the lunar disturbance of the plumb-line, tlie amplitude 

 of this latter disturbance being by calculation only 0". 0216. This 

 conclusion will probably put an end to the laborious and refined 

 experiments which he and his brother have been conducting for 

 two or three years in order to detect and measure the lunar 

 action. 



