34 PRESIDENTIAL ADDRESS SEt TION A. 



determine very accurately at as many vertices as possible pre- 

 cisely how a plumbline would hang with reference to the sides 

 of the triangles that meet at the vertex. One may imagine the 

 whole network as a system of triangles whose sides are made of 

 long, straight wires with plumblines hanging from as many of 

 the vertices as possible. Now the problem of the geodesist is to 

 find what shape of flattened spheroid will pass as nearly as pos- 

 sible at right angles to these various plumblines, and will start 

 from the mean sea-level at some chosen point of the coast. This 

 shape gives the figure of the earth as calculated from that par- 

 ticular survey. 



When the average figure lias been calculated that will most 

 nearly cut the plumblines perpendicularly, it is invariably found 

 that practically all the plumblines show minute deviations from 

 perpendicularity. These deviations, usually called residual deflec- 

 tions, are. of course, related to local irregularities of surface or 

 of density. They throw a clear light on the density of the crust 

 underlying the surface to depths far beyond those we can reach 

 by boring, and we shall return to their consideration towards 

 the close of this address. 



It is well to remember how enormous the dimensions of the 

 earth are, when compared with the thickness of the surface rocks 

 with which we are directly acquainted. On a model of the earth 

 of a diameter of six feet, the ten miles' vertical interval which 

 separates the highest mountain-top from the greatest ocean depths 

 would be represented by a thickness of only i/ii of an inch, and 

 the elevation of a sea-coast through a mile, with its consequent 

 profound change of climate and its exposure of the surface to 

 agencies of new character and intensity would be represented by 

 a movement of the model surface through merely the thickness 

 of thick paper. These comparisons will help us to realize how 

 gentle a tilting of the earth's crust would cause surface changes 

 of the greatest biological and geological importance. 



The density of the earth, as determined by recent accurate 

 comparisons of its gravitational attraction with the gravitationr^l 

 attraction exerted by a small body of known shape and mass, 

 is very nearly five and a half times as great as that of water. The 

 mean density of the chief rocks of the crust being only about 

 two and three-quarter times that of water, it is obvious that the 

 parts towards the centre must have a density so far exceeding 

 the average as to make up for the deficient density of the crust. 

 It may therefore be regarded as very probable that the central 

 parts contain predominant quantities of iron and other heavy 

 metals, though it is to be noted that the pressures that obtain in 

 the interior are so enormous that they must compress all ma- 

 terials considerably and cause their densities to rise proportion- 

 ately. As we do not know how the different layers increase in 

 density, we cannot calculate these pressures exactly, but it is 

 easy to give rough approximations. At a depth of 40 miles, 

 i.e., only one hundredth part of the earth's radius, the pressure 

 must be about 250,000 lbs., or (say) no tons to the square 



