TRANSACTIONS OF THE SECIIONS. 
Section A.—_MATHEMATICAL AND PHYSICAL SCIENCF. 
PRESIDENT OF THE SECTION—Professor A. E. H. Love, M.A., D.Sc., F.R.S 
THURSDAY, AUGUST 1. 
The President delivered the following Address :— 
I propose to use the opportunity aflorded by this Address to explain a dynamical 
theory of the shape of the earth, or, in other words, 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 condi- 
tion that there is no up and down upon it.- This condition does not mean that the 
surface is everywhere 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 direction of, gravity (modified by the rotation). A 
surface which has this character is called an equipotential surface, and the 
surface of the ocean coincides with part of an equipotential 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 above 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 
a 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 P 
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 additional 
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 three or four 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, 1 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 
