/:'. IK Preston— Measurement of the Peruvian Arc. 11 



When the necessary reductions were made ir was found that 

 gravity at the sea level, was diminished by 1/1331 part at 



Quito, and by 1 845 part on the summit of Pichincha. Since 

 the distance from the earth's center had been increased in the 

 first Instance by its 1 223Y part and in the second by its 1/1348 



part the results indicated a law, not very different from that of 

 the inverse Bquarc o\' the distance. But gravity had not 



changed enough, in either case, to satisfy the law. The con- 

 clusion therefore was, that some influence, not exactly under- 

 od, increased the force of gravity in both cases. Naturally, 

 attention was drawn to the high table land lying between the 

 stations and the sea. It was estimated that the effect of this 

 would he one-half of that of a shell of matter of the same den- 

 sity and thickness encircling the whole earth. Granting this, 

 the diminution of gravity in passing from the sea to the 

 summit would be 



2/t 



/ 36\ 



where h is the height of the station above the sea, r is the 

 radius of the earth and d and J are the respective mean densi- 

 ties of the table land and earth. 



Now this diminution was found by the pendulum to be 

 1/1331, which, compared with the above expression, leads to 

 the conclusion that the matter composing the table-land has 

 only about one-fifth the density of the earth. The result was 

 something of a surprise at the time, and doubts began to arise 

 as to whether the interior of the earth could be, as some sup- 

 posed, a fluid mass surrounded by a thin shell. It could not 

 be denied that the density of the surface was less than that of 

 the interior, because it was shown that, in order that their 

 densities be at least equal, the length of the second's pendu- 

 lum must be in error by about one-thirtieth of an inch, which 

 even with the rough method employed was too great an error 

 to be admitted. 



If the land lying between the upper station and the sea be 

 regarded as a plain of infinite extent the same result ensues, 

 and the formula deduced from this point of view is of some- 

 what simpler derivation. Clarke arrives at the same result by 

 regarding the intervening matter as either a cone, cylinder, or 

 segment of a sphere, where the horizontal dimensions are great 

 compared with the vertical ones. In calculating some attrac- 

 tions in the Hawaiian Islands, the matter was treated rigor- 

 ously as a cone, and the resultant attraction at the foot of the 

 mountain, based on this value, agreed closely with that derived 

 independently by the latitude observations and triangulation. 



