A.— MATHEMATICAL AND PHYSICAL SCIENCES 27 



Richtkraft ' according to Eotvos — is the product g{ci — c^), where 

 Ci and C2 are the greatest and least curvatures of the local ' level ' or 

 equipotential gravitational surface ; its direction is horizontal and in the 

 vertical plane of least downward curvature. The suspension in the 

 instrument responds to this curvature difference in so far as the mass- 

 distribution in the beam partakes of the nature of a Coulomb beam — i.e. 

 in its simplest form two equal heavy masses at the ends of a light hori- 

 zontal rod. Such a beam would have no tendency to turn horizontally if 

 the level surface were truly spherical ; but otherwise it would, if free to 

 do so, set itself along the direction of least downward curvature. 



The other departure from gravitational uniformity which the balance 

 measures is the gravity gradient, or the rate of change of the vertical 

 gravitational intensity with horizontal distance in the direction in which 

 the change is greatest. It is a vector, and both its magnitude and direc- 

 tion can be obtained from the instrumental observations. The response 

 in this case is due to the unsymmetrical vertical distribution of the 

 masses in the beam, the effective mass on one side of the suspending 

 wire being lower than that on the other. This causes the beam to tend 

 to set with the lower mass pointing in the direction of the gravity gradient, 

 and there is torsion in the suspension if the beam occupies any other 

 azimuth. 



It will be seen, I think, without further elaboration, that in any given 

 location of the instrument there are, in effect, two differential ' fields ' 

 acting simultaneously upon it. Its reaction to them provides the means 

 of measuring the particular gravitational distortions which they represent. 

 This part of the work is pure physical measurement of a straightforward 

 character, and attaining, as I have indicated, a surprising degree of 

 precision. It is in the interpretation of the results that the real difiiculties 

 arise. The problem is to ascertain to what extent the gravitational 

 irregularities measured are due to density differences in the buried struc- 

 ture, and to assign to the latter a position and shape consistent with the 

 observations. In country where the surface is otherwise than virtually 

 horizontal it is necessary to survey its irregularities, and make calculated 

 allowances for their contribution to the total measured gravitational 

 distortion. This topographical effect may indeed sometimes be so large 

 in comparison with that of hidden structure as to render gravitational 

 surveying ineffective. The earth's rotational effect, of course, has always 

 to be eliminated, but this presents no difficulty. What remains after these 

 corrections constitutes the data for geophysical interpretation ; and this 

 is the stage where the geologist's ' selection rules ' have to be applied. 

 As in all geophysical methods, interpretation is necessarily indirect. 

 Underground structures, agreeable to the geologist's experience, have to 

 be taken as hypotheses, and tested by calculation and comparison with 

 the data provided by surface observations. 



The most important example of successful application of gravity sur- 

 veying is in the detection of salt domes, and in the determination of their 

 depth and extent. The first survey of this kind, in 1918, provides a 

 striking illustration of the way in which geological knowledge has generally 

 to be used in combination with the physical measurements, in order tp 



