2 W. Boivie — Relation of Isostasy to 



portion of the earth, are heterogeneous and onr spheroid 

 of revolution which depended on the assumption of normal 

 densities, will depart somewhat from this mathematical 

 surface. The mountain masses and the deficiency of mass 

 in the ocean volumes will cause the actual water surface 

 to be higher or lower than the mean surface which we 

 shall call the spheroid of revolution. 



It would be well to conceive of sea-level canals cut into 

 the existing areas of the earth. The surface of the oceans 

 and of the waters in these canals will form a figure of 

 equilibrium which we call the geoid. The deviation to 

 this imaginary surface over land areas from the mean 

 spheroid of revolution will be a maximum of possibly 100 

 meters. This maximum occurs under the great mountain 

 masses. 



The fundamental problem of the geodesists is to deter- 

 mine the shape and size of the mean sea-level surface of 

 the earth and the deviations from this mean surface of 

 the geoid or water-level surface. The only way in which to 

 determine the shape and size of the earth is by means of 

 astronomic observations which are connected by triangu- 

 lation or direct measurements. The shape, but not the 

 size, can also be obtained from gra\dty measurements. 



Deflection of the vertical. 



Some years ago, when attempts were made to determine 

 the figure of the earth, it Avas found that the direction of 

 the plumb line at the astronomic stations was materially 

 affected by the masses above sea-level and the deficiencies 

 of mass in the ocean areas. Corrections were applied to 

 the deflections of the vertical for the positive and nega- 

 tive attractions of these masses, but then it was found that 

 the directions of the corrected plumb lines had anomalies 

 of opposite sign to those which obtained before what 

 might be called the topographic corrections had been 

 applied. 



It is easily seen that if we should have a spheroid of 

 revolution without any local disturbing influences, three 

 or four latitude stations, somewhat widely separated 

 along a meridian, with triangulation connecting them, 

 would furnish us data from which to compute the elements 

 of the ellipse, which would be the meridional section of 

 the spheroid. Owing to the irregularity of the actual 

 surface of the earth, the problem is not so simple, and 



