294 G. R. PUTNAM CONDITION OF THE EARTH'' S CRUST 



eliminate the effects of over and under compensation developed by the 

 free air method in mountainous regions. This method of applying the 

 compensation as the negative attraction of a horizontal plate corresponded 

 to the method then in use of computing the attraction of the topography. 

 The results did not afford any proof of regional as against local compen- 

 sation of topographic features, as was then thought from a comparison 

 with the free air reduction results, for the reason that, as shown above, 

 the latter do not correspond to a theory of complete local compensation. 



As will be pointed out later, recent complete reductions by the Hayford 

 method show almost no differences in results between local compensation 

 and regional compensation to some limit less than 104 miles, so that the 

 results, using an average elevation compensation, taking the average 

 within 100 miles of the station, as was done in 1895, should be practically 

 the same as with a complete local compensation. 



This average elevation reduction was computed by me and published 

 for 59 stations, about twenty-five years ago, and the resulting anomalies 

 as computed and published at that time for the three methods above de- 

 scribed are given in the following Table I, with also the anomalies for 

 Hayford's method (1912). The results are given for 42 stations, these 

 being all for which a direct comparison can be made from the originally 

 published results. 10 



above sealevel. A is mean density of the earth, and T is a topographic correction due to 

 departure of the surface from a plain (explained in Appendix No. 1. 1894, pp. 22. 23 1 . 

 In the second member of the first equation above, the first term is the correction for 

 elevation, the second term for attraction of matter above sealevel. and the last term for 

 compensation. The first three terms constitute the Bouguer reduction and the first and 

 third the free air reduction. The treatment of ocean areas is explained in the same ref- 

 erence, page 26. The compensation term above represents the attraction, on a point on 

 its surface or without it. of an indefinitely extended horizontal plate, and it therefore 

 does not require any assumption as to the depth of compensation or its density or dis- 

 tribution, so long as it lies in homogeneous horizontal layers and its total amount is 

 equivalent to the weight of a plate of the average surface density and having a thick- 

 ness equal to the average elevation. 



10 Coast and Geodetic Survey Report, 1894, App. No. 1. pp. 26, 28, 29-; Report. 1897, 

 App. No. 6. p. 309 : Am. Journal of Science, vol. i, March. 1896. pp. 188. 191 ; Coast and 

 Geodetic Survey Special Publication No. 10, pp. 76, 81, and No. 12, p. 24. 



