THE PRESIDENTIAL ADDRESS. 5 
material and even the esthetic possessions of the world. And in that 
assurance, we may rejoice that science has never been so widely and so 
enthusiastically cultivated as at the present time, with so complete 
sincerity, or (we may claim) with more brilliant success, or even with less 
of international jealousy. 
Passing from these reflections which are, I hope, not altogether in- 
opportune, it is expected that the President for the time being should deal 
with some subject in which he has himself been interested. For a mathe- 
matician this obligation is a specially difficult one, if he is not to overstrain 
the patience of his audience. I propose to speak briefly, and mainly from 
the mathematical and physical standpoint, about some branches of Geo- 
physics, and in particular those relating to the constitution of the earth. 
It is a subject which in the past has often engaged the attention of the 
Association ; I need only recall the names of Kelvin and George Darwin, 
and the controversies with which they are associated. Historically, it is of 
special interest to the mathematician and the physicist, for it was in his 
researches on the figure of the earth that Laplace initiated the theory 
of its potential, with its characteristic equation, and so prepared the way for 
Poisson, Green, Cauchy, and a host of followers, who developed the theory 
of electricity and ultimately that of light. To go further back, it was in this 
connection that Newton found an important verification of his law of 
gravity. Quite recently, the whole subject has been reviewed in a valuable 
treatise by Dr. Jeffreys, who arrives at conclusions which are at all events 
definite, and maintained with great ability. 
I do not propose to deal with the fascinating speculations as to the past 
history of the earth and its reputed child, the moon, which will be more or 
less familiar. I must confine myself to a rapid survey of the information 
as to its present constitution which can be gathered from observations 
made in our own time, and capable of repetition at will. This, though less 
exciting, is at all events a region in which imagination is more subject to 
control. 
The accurate investigation of the figure of the earth is intimately 
connected with the variation of gravity over its surface. In view of the 
local irregularities, some convention was necessary as to what is meant by 
the shape of the earth as a whole. The usual definition is that it is a level 
surface as regards the resultant of true gravity and centrifugal force : often 
that particular level surface of which the sea forms a part. I need not 
dwell on the immense amount of theoretical and practical labour which-has 
been devoted in various countries to the determination of the geometrical 
