538 ' JOSEPH BAKRELL 



as measured against the demands of the hypotheses made in that 

 solution. In Fig. 12A is reproduced a portion of Hayford's chart. 

 A general inspection of the map of the residuals of Solution H 

 shows that many of the large deflections of opposite sign lie compar- 

 atively close together. On a line connecting two stations, Fx is the 

 component of the deflection which lies in that line, Fy is the com- 

 ponent at right angles to that line. In most cases not enough 

 stations are located on an approximately straight line to permit 

 well-defined curves to be drawn for Fx and Fy. But it has been 

 shown that for spheres and other concentrated masses the curve 

 for Fx rises steeply from zero to maximum value and sinks away 

 more gently beyond. Even for flat disks the outer part of the 

 deflection curve will be flatter than for the inner part. Random 

 locations on the curve are therefore more likely to give the maximum 

 measurement at some point beyond the real maximum rather than 

 at some point between the epicenter and the real maximum. Using 

 these stations giving maxima for Fx as if they were at the points of 

 real maxima will therefore give on the average too great a distance 

 from the center to the point of real maximum Fx and consequently 

 too great a depth to the centers of attraction. Interpreting the 

 disturbing masses as spheres is also an assumption likely to give 

 too great a depth, as is indicated later. Minor centers of out- 

 standing mass will affect the positions of the points of maxi- 

 mum value, but in a sufiicient number of examples this effect will 

 largely cancel out. The tabulation of the distances measured from 

 Hayford's map between ten pairs of notable Fx maxima is given 

 in Table XXVII. 



It is seen that the distance between these maxima is more 

 largely dependent upon the length of the sides of the geodetic 

 triangles than upon the depth to center of mass, since in less than 

 half of these illustrations did a station fall between the two maxima. 

 The distance between the real maxima is then probably somewhat 

 greater than 86 km., the average of the six distances without 

 intervening stations, but is probably somewhat under the general 

 mean of no km. This mean distance of no km. between ten 

 notable maxima of Fx corresponds to a mean depth of spheres of 

 79 km. Considering the various assumptions made, it is seen that 



