August i, 1907] 



NA TURE 



minute measuremenl has given us some certain know- 

 ledge as to the distances of the stars within a certain 

 limited portion of spare, and in the cryptograms of their 

 spectra has been deciphered the amazing truth that the 

 stars of both streams arc alike in design, alike in chemical 

 constitution, and alike in process of development. 



But whence have come the two vast streams of matter 

 out of which have been evolved these stars that now 

 move through space in such majestic procession? 



The hundreds of millions of stars that comprise these 

 streams, are they the sole ponderable occupants of space? 

 However vast may be the system to which they belong, 

 that system itself is but a speck in illimitable space; may 

 it not be but one of millions of such systems that pervade 

 the infinite? 



We do not know. 



"Canst thou by searching find out God? canst thou 

 find out the .'Mmighty unto perfection?" 



SECTION A. 



MATHEMATICS AND PHYSICS. 



Opening Address by Prof. A. E. H. Love, M.A., D.Sc, 

 F.R.S., President of the Section. 



I PROPOSE to use the opportunity afforded by this 

 .Address to explain a dynamical theory of the shape of 

 the earth, or, in other w^ords, of the origin of continents 

 and oceans. 



The theory which has for more than a century been 

 associated with the phrase " the figure of the earth " is 

 the theory of the shape of the surface of the ocean. 

 Apart from waves and currents, this surface is determined 

 by the condition that there is no up and down upon it. 

 This condition does not mean that the surface is every- 

 w'here at the same distance from the centre of the earth, 

 or even that it is everywhere convex, but that a body 

 moving upon it neither rises against, nor falls in the direc- 

 tion of, gravity (modified by the rotation). .^ surface which 

 has this character is called an equipotential surface, and 

 the surface of the ocean coincides with part of an equi- 

 potential surface under gravity modified by the rotation. 

 This particular equipotential surface runs underground 

 beneath the continents. It is named the " geoid." The 

 height of a place above sea-level means its height nb( ve 

 the geoid. If we knew the distribution of density of the 

 matter within the earth it would be a mathematical problem 

 to determine the form of the geoid. As we do not know 

 this distribution we have recourse to an indirect means of 

 investigation, and the chief instrument of research is the 

 pendulum. The time of vibration of a pendulum varies 

 with the place where it is swung, and from the observed 

 times we deduce the values of gravity at the various places, 

 and it was shown many years ago by Stokes that the shape 

 of the geoid can be inferred from the variation of gravity 

 over the surface. 



The question to which I wish to invite your attention 

 is a different one. If the ocean could be dried up, the 

 earth would still have a shape. What shape would it be? 

 Why should the earth have that shape rather than some 

 other? In order to describe the shape we may imagine 

 that we try to make a model of it. If we could begin 

 with a model of the geoid we should have to attach addi- 

 tional material over the parts representing land and to 

 remove some material over the parts representing sea. 

 Our model would have to be as big as a battleship if the 

 elevations and depressions were to be as much as 3 or 

 4 inches. In thinking out the construction of such a model 

 we could not fail to be impressed by certain general features 

 of the distribution of continent and ocean, and we may 

 examine a map to discover such features. Fig. i is a 

 rough map of the world drawn in such a way that to every 

 degree of latitude or of longitude there corresponds the 

 same distance on the map. Certain very prominent features 

 have often been remarked : the tapering of America and 

 .\frica towards the south, the disproportion between the 

 land are.ns of the northern and southern hemispheres, the 

 excess of the oceanic area above the continental area, 

 which occupies but little more than one-quarter of the 

 surface: the wide extent of the Pacific Ocean, which with 

 the adjoining parts of the Southern Orcxn covers nearly 



NO. 1970, vni,. 76] 



two-fifths of the surface, .\nolher prominent feature is 

 the antipodal position of continent and ocean. South 

 America south of an irregular line which runs from a 

 point near Lake Titicaca to Buenos Ayres is antipodal to- 

 a portion of Asia which lies in an irregular triangle with 

 corners near Bangkok, Kiaochau, and Lake Baikal ; but 

 no other considerable parts of the continental system have 

 continental antipodes. The Antarctic continent is antipodal 

 to the Arctic Ocean, Australia is antipodal to the central 

 Atlantic, and so on. Another notable feature is the skew 

 position of South America to the east of North .-Xmerica ; 

 South America lies to the east of the meridian 85° west 

 of Greenwich ; most of North America lies to the west 

 of it. But although we may observe prominent general 

 features of the distribution, we should find it far from 

 casv to attribute to the form of our imaginary model any- 



Trmnrnnrmr^WniH^r 



thing that could be called a regular geometrical figure. 

 When we begin to think about the removal of material 

 from the parts of the model which are to represent oceans 

 and seas, we require a map which gives inforination about 

 the depth of the sea in difl'erent places, .\round all the 

 coasts there is a margin of not very deep water. If some 

 part of the sea could be dried up, so that more land 

 v.-as exposed around all the coasts, the area of the surface 

 of the sea would be diminished ; and it is known that the 

 depth of water that would have to be removed in order 

 to make the area of the sea just half the total area is 

 about 1400 fathoms. The contour-line at this depth would 

 divide the surface into two regions of approximately equal 

 area — the continental region and the oceanic region. 

 Fig. 2 represents the contour-line at 1400 fathoms, 



the 



line of separation of the continental and oceanic regions. 

 The continental region is shaded. In drawing this map 

 I have omitted a number of small islands, and I have 

 also omitted a few enclosed patches of deep water. Two 

 of these are in the Mediterranean, one in the Arctic 

 Ocean and others are in the Gulf of Mexico and the 

 Caribbean Sea. The Red Sea, the Mediterranean, and the 

 Arctic Ocean belong to the continental region, and so do 

 the Gulf of Mexico and the Caribbean Sea. At this depth 

 Asia and North .'\merira are joined across Behring's Strait, 

 and Europe is joined to North America across the British 

 Isles, Iceland, and Greenland ; Australia is joined to 

 Asia' through Borneo and New Guinea, and the Austral- 

 asian continental region nearly reaches the Antarctic 

 region by wav of New Zealand. At this depth 

 also South .America does not taper to the south, but 



