THE GRAVITY OBSERVATIONS OF 1 895 COMPARED 293 



general, and this over compensation resulted in a positive difference, ob- 

 served minus theoretical force of gravity. Under either a regional or a 

 local idea of compensation, the over compensation of the region surround- 

 ing a station will result in a positive gravity anomally. There has been 

 some misconception as to this free air reduction. It is based on the 

 theory of isostasy and takes account of both the attraction of the topog- 

 raphy and of its compensation; but it does this only in a general way, 

 and when it is applied to summit and valley stations there is no theory 

 to justify it. It has been stated that it assumes that "each piece of topog- 

 raphy is compensated for at zero depth" and also "a very plastic crust." 

 A conception of compensation as located vertically beneath a station and 

 affecting gravity only at that station and not in the surrounding regions 

 is evidently an impossible hypothesis and one that is not called for by the 

 free air reduction formula. 



3. Average elevation reduction. 8 The large residuals resulting from 

 the Bouguer reduction showed the incorrectness of the hypothesis of un- 

 compensated topography above sealevel. The disappearance of these large 

 residuals at stations in level regions or near the average elevation with 

 the free air reduction was proof of a general condition of isostasy, but 

 the residuals remained still large for stations on high peaks or in deep 

 valleys, proving the inadequacy of the free air reduction. As the latter 

 residuals had a marked relation to the height of the station above or 

 below the average elevation, in discussing the 1894 results a reduction 

 term was introduced by me corresponding to the attraction of the topog- 

 raphy above or of the deficiency of topography below the average plain 

 for stations whose elevations were respectively greater or less than the 

 average elevation, this average being taken within an arbitrarily assumed 

 radius of 100 miles of the station. This procedure was equivalent to 

 subtracting the attraction of the topography, as in the Bouguer reduction, 

 and then adding as a compensation term the effect of a plate of average 

 surface density, whose thickness is the average elevation of the surround- 

 ing region, as illustrated in the diagram. 9 The result of this was to 



8 In 1895 this was called the Faye reduction, on account of a suggestion in his papers, 

 but it had not previously been applied. A similar reduction was independently used by 

 Gilbert, termed by him a reduction to mean plain, and using the average elevation within 

 30 miles of the station. 



9 The average elevation correction to reduce to sealevel was this : 



i1g = + r_^L _ 2 3 H3 S + T + 2011,35 



r /4A r 4 A 



_ 2firH_ 2ghS8 (form 1805). 



r r 4 A 



where g is gravity at sealevel, H is elevation of station above sealevel, H a is average 

 elevation above sealevel, h is FI^-H, r is radius of the earth. § is density of matter lying 



