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16 E. D. Preston — Measurement of the Peruvian Are. 



It is a singular fact that the first combination of the Lapland 

 and Peruvian arcs gave a value for the ellipticity quite as near 

 the truth as was deduced by La Place fifty years later, using 

 the accumulated data furnished by improved instruments and 

 methods. This is partly owing to the fact that the two arcs, 

 having the greatest influence from their position and length, 

 remained unaltered. 



La Place's combination gives a value in excess, and the sup- 

 position of the plumb-line being deflected toward the center 

 of the arc changes the value in the right direction. How 

 much attraction should be allowed for it it is difficult to say as 

 the configuration of the land is not known with sufficient 

 accuracy. The indications are, that even admitting the small 

 density of the mountains, the deflections are much larger than 

 would be necessary to bring this arc into accord with the 

 others, and give a value for the ellipticity called for by modern 

 observations in middle latitudes. If we accept the data in 

 La Place's first combination a deflection of eleven seconds at 

 each end of the arc would be required for this purpose. 



There seems to have been some compensation of errors, 

 which has given the Peruvian arc a value conforming closely 

 with our present spheroid. But its agreement in this respect 

 is no exciise for not remeasuring it. The measures of the base 

 line agree within a few inches, but no one who has examined 

 the case believes that this is anything but an accident. The 

 combination of this arc with some other recent ones in the 

 determination of the figure of the earth, gives corrections for 

 the equatorial latitudes even smaller than those required by 

 points whose positions were determined with greater precision, 

 and where the direction of the plumb-line is much less dis- 

 turbed by attraction. These small corrections would probably 

 not be confirmed by a new measure. 



Notwithstanding, this work was well done considering the 

 circumstances and the state of science at the time. Bouguer 

 and his associates were scientific men who thoroughly under- 

 stood the requirements of the case, and executed the work with 

 the utmost fidelity. The necessity for a greater or less degree 

 of accuracy, according to the kind of observations, and the 

 bearing of each partial result on the final one was the source of 

 constant study. Many principles of work here practiced for 

 the first time have been adhered to by all later observers. But 

 the advantage of repeating this work would come from the 

 great improvements in instruments, and the consequent bring- 

 ing to light of influences that were then unknown. Nothing 

 at the time was known of spherical excess in geodesy. The 

 theory of least squares was undiscovered, and the method of 

 equal zenith distances had never been applied to the determin- 



