14 OLDHAM: THE STRUCTURE OF THE HIMALAYAS, ETC. 



(2) A compensation similarly distributed between the depths 



of 27 and 37 miles. 



(3) A compensation produced by a defect of density 



decreasing uniformly from double the average value 

 to zero ; for this the depth which gave the best results 

 was found to be 1754 km. 



(4) A compensation such as that suggested by Prof. Cham- 



barlin, at first increasing and then decreasing at a 

 variable rate ; for this the depth which gave the best 

 result was found to be 287*4 km. 



Taking ten stations as typical of the different regions of the 

 United States, and comparing the residuals with those resulting 

 from the solution G, the mean differences were found to be *26, 

 •22, - 19, *09 seconds of arc, for the four hypotheses respectively, 

 and the maximum differences were 1*13, 1-04, -80, -38 respectively. 

 As the mean of the residuals resulting from the solution G was 

 3*04" and the maximum 1235", it is evident that there are five 

 different hypotheses of compensation, which vary widely in the 

 assumed distribution of the compensation, but agree in giving it 

 a mean depth of from 30 to 35 miles, and in giving almost identical 

 results. This jshows that the supposed depth, to which compensa- 

 tion extends, has no real meaning, and that, although the effect 

 of compensation, as it actually exists in the United States, is on 

 the average very much the same as would result from a uniform 

 defect of density extending to 1 13 7 or 122 km , according to whether 

 the earlier or later solution of the problem is accepted, any other 

 distribution of density might be equally in accord with observa- 

 tions provided that the position of the centre of effect was not 

 materially different. In this way we are introduced to the concept 

 of the locus of the centre of compensation. 



In any given mass, forming part of a visible protuberance on 

 the earth's surface, or of the underlying portion through which 

 the compensation is distributed, there will be a point, so situated 

 that, if the whole of the mass were concentrated at that point, 

 the effect at the station of observation would be the same as that 

 actually produced by the sum of the effects of all the separate 

 particles of which the mass is composed. This point may be called 

 the centre of effect, and in the case of the defect of density by which 

 compensation is brought about the expression centre of compensa- 



L 1C2 ] 



