12 K D. Preston — Measurement of the Peruvian Arc. 



The value of the radius of the earth employed in the Peru- 

 vian investigation was about 12,000 meters too large. Intro- 

 ducing the value now accepted we get a density for the Andes 

 somewhat greater. The change is in the right direction but it 

 is not enough. The rocks in Peru probably have a density of 

 about 2, or possibly less, and if the sea level is in error by 

 one hundred toises, the pendulum work would. give about this 

 density for the underlying mass. 



The method used in finding the absolute height of the base 

 line, to which all the elevations were referred, was by triangu- 

 lation. The results were roughly checked by the barometer. 

 From Niguas, a point between Quito and the mouth of the 

 Inca river, angles of elevation were taken to several mountain 

 peaks, of which Pichincha was one. Niguas was also visible 

 from a point near the sea level. The distances being approxi- 

 mately calculated, with some of the angles concluded, the 

 elevations could be determined with some degree of accuracy. 

 The last station was estimated from barometer readings to be 

 about thirty toises above the sea. But that not much confi- 

 dence could be placed in the instrument is plain from the fact, 

 afterward stated, that weighing all circumstances it was con- 

 cluded to fix the difference at forty or forty-two toises. The 

 result was checked by a very rough estimate of the inclination 

 of the river bed and the velocity of the current. Knowing 

 the relation between the velocity and inclination at a point 

 near the station, and determining the velocity farther down 

 the stream, the inclination was calculated. Then from the 

 measured horizontal distance and the inclination the vertical 

 height resulted. It is evident that not much reliance is to be 

 put in such a determination, but perhaps the error is consid- 

 erably inside some others entering into the deduced height of 

 Pichincha. 



The angles of elevation were measured with a quadrant 

 which might give results as much as 30" from the truth. 

 Then, as there were mountains back of the station, twelve 

 thousand feet high in one case, and fifteen thousand in the 

 other, the angles of elevation may have been in error in either 

 case by the greater part of a minute. And errors from attrac- 

 tion would be accumulative, since Niguas is on the mountain 

 flank. The distance from the .sea to Ilinissa, with which 

 Pichincha was connected, was found from the known differ- 

 ence of latitude and the azimuth. It seems therefore probable 

 that the total elevation may have been in error by as much as 

 fifty toises. This is not enough to bring the mean density of 

 the Andes into tolerable accord with that of the surface rock. 



It is difficult to accurately estimate the probable error of the 

 distance between the two extremities of the arc, because 



