14 E. D. Preston — Measurement of the Peruvian Arc. 



amount. The error in the base is now disregarded because, 

 although it is much larger than the results of the measures 

 would'indicate, its effect on the last side would still be small 

 in comparison with that resulting from the angle equations. 



The astronomical observations agree among themselves, but 

 it was not suspected at the time, that the mountains might 

 affect the plumb-line by at least thirty times as much as the 

 results were supposed to be in error. When the work was 

 done instruments and methods had not been brought to that 

 degree of perfection necessary to detect these small influences. 

 Since then many striking cases have been brought to light, 

 22" deviation having been noticed in India, 16" in Russia, and 

 29" in the Hawaiian Islands. In the example near Moscow 

 there are no mountains to account for the phenomena, and the 

 supposition is that the density of the underlying strata may be 

 sub]ect to great variations, or that large subterranean caverns 

 mav exist. Archdeacon Pratt has shown that small changes of 

 density, if extended over a considerable area, may produce very 

 perceptible deflections of the vertical. The Indian example is 

 produced by the Himalayas. The Hawaiian is the result of 

 the attraction of Haleakala, an extinct volcano ten thousand 

 feet high. 



When •we consider that between the extremities of the 

 Peruvian arc there is a continuous range of mountains, varying 

 in height from nine thousand feet on the plateau of Cochesqui, 

 to nineteen thousand at the summit of Chimborazo, and remem- 

 ber that the arc was terminated at a point where the eleva- 

 tion dropped suddenly several thousand feet, it is evident there 

 must have been enormous differences between the astronomical 

 and geodetic latitudes. 



Judging from analogy with other cases, similar, either in the 

 volume of the mountains or the density of the matter, it seems 

 not unlikely that the amplitude of the arc may be in error by 

 many seconds. Indeed if we take the data used in La Place's 

 first discussion, the Peruvian latitudes should be changed by 

 about 10" in order to give an elliptieity conforming reasonably 

 with our present value. And the required change shows that 

 the plumb-line was drawn toward the mountains. 



The errors in the measures of the two bases, in the triangu- 

 lation, in the altitudes, or in the azimuths, could not have ah 

 influence at all comparable to this, so that a simple redetermin- 

 ation of the latitudes would very much improve the result. 

 In fixing the figure of the earth an equatorial arc enters with 

 great weight, and we find that in a combination by least 

 squares of nine arcs used by La Place, an error of one minute 

 in the amplitude of the equatorial arc would reduce the ellip- 

 ticity to one-half its original value. This seems to be a great 



