WHAT IS TERRA FIRMA? WILLIS. 397 



sea level are excesses of mass which exert a similar extra attraction. A 

 similar correction must therefore be applied to all observations which 

 are calculated under that hypothesis. This was the reasoning of 

 Bouguer, a French mathematician, who calculated the gravity obser- 

 vations made from 1736 to 1739 in Peru. The method is therefore 

 known as Bouguer's method, and the mathematical formula as 

 Bouguer's formula. 



Had the lighthouse in this illustration not been an extra mass, 

 added to the rock mass of its foundations, the correction for excess 

 of mass should not have been made. But under the hypothesis of 

 complete isostatic balance there is no excess of mass, since that hy- 

 pothesis rests upon the assumption that all parts of the earth's crust 

 which are, we will say, a mile square have the same mass, the heights 

 of the columns above some common level within the earth being 

 inversely proportioned to the density of the materials. The common 

 level of the bases of the columns may be 100 miles below sea level, 

 or it might be the center of the earth. All columns of the same cross 

 section rising from it to sea level or to the heights of the Hima- 

 layas have the same mass by hypothesis. Hence there should be no 

 correction for excess. The assumption of complete isostatic equi- 

 librium is the basis of Hayford's work, which we shall see is the 

 most recent and most exhaustive investigation of the subject. We 

 shall therefore refer to the method of reduction based on it as Hay- 

 ford's method. 



Some thinkers on this subject hold that isostatic equilibrium can 

 not be complete for every hill and valley of the surface, nor even 

 for every mountain. They admit, however, the assumption that ex- 

 tensive masses, such as that of a whole mountain range or plateau, 

 and defects of mass, such as that of the basin of the Black Sea, may 

 be compensated or in equilibrium. The reasoning in this case pro- 

 ceeds on the basis that the mass of any large feature would be bal- 

 anced at the altitude of a "mean plain," which is a hypothetical 

 plain, that would be produced by leveling off the hills till the mass 

 removed from them just filled the valleys. The total mass remains 

 unchanged, since nothing has been added and nothing subtracted. 

 The position of the mean plain depends upon the irregularities of 

 the surface and is independent of the altitude of the station at which 

 the observation for gravity is made. The mean plain may therefore 

 lie above or below the station. If it lies above, there is a mass be- 

 tween the two which exerts an upward attraction and reduces the 

 observed value of gravity by an amount which must be added to 

 it; whereas if the mean plain lies below the station there is an 

 excess of mass whose attraction is included in the original value 

 observed and for which a deduction must be made. This method 

 was first suggested by a French mathematician named Faye, and is 



