A". D, Preston — Measurement of the Peruvian Arc 3 



Bouguer set out on May 6th, 1 785, and af ter a journey of 



more than a year, arrived at his destination. The party was 

 absent about nine years, but the triangulation and base mei 

 nrenients were executed between December, L736 and August, 

 L739. Astronomical observations to determine the amplitude 

 of the arc were made between July, 1741 and January, 1743, 

 and the party arrived at the mouth of the Magdalena river on 

 ember 30th of the same 1 year. The pendulum was swung 

 at Porto Hello on the outward trip, and at Petit Goave, Ilayti, 

 on the return voyage. The results are incorporated in the ac- 

 count of the equatorial work. Three gravity determinations 

 were made in Peru; at the sea-level, at Quito (9,374 feet eleva- 

 tion), and on the summit of Pichincha (15,564 feet). Mag- 

 netic observations were also carried on, and a general study ' 

 made of the natural history and physical features of the 

 country. 



We must not lose sight of the fact that the work was under- 

 taken to decide between the relative lengths of the earth's 

 axea Several methods of arriving at this result were therefore 

 sidered. It was once thought to supply sufficient data to 

 decide the whole question by the equatorial observations alone : 

 measuring for this purpose a degree of latitude and one of 

 longitude in tne same locality. But recognizing the fact that 

 with the means at hand, the former would be subject to an 

 error of 1/1 500th part while the latter would be uncertain by 

 about six times as much, the preference was given to the 

 degree of the meridian. Measures had already been made in 

 France, and from the nature of the involute curve, formed by 

 the intersection of the earth's radii for any given meridian, it 

 was admitted that combining the equatorial measures with 

 those of a middle latitude, the error to be expected in the ratio 

 of the two axes was only l/1440th part ; and that a combina- 

 tion with arctic measures would reduce the error to about two- 

 thirds as much (1/2030). The errors attributed to accidental 

 causes rest on the assumption that in each astronomical obser- 

 vation the observer is liable to be mistaken by three or four 

 seconds of arc ; and that in noting signals for longitude one 

 second of time would be the error expected. 



After the arc had been measured it became a matter of some 

 difficulty to combine it with the French and arctic work. 

 Every supposition made in regard to the meridian, supposing 

 that it could be represented by an elliptical curve, seemed to 

 do violence to the results of observation. 



A combination was first made, using the arctic and equatorial 

 arcs, the law being that of the square of the sines. This led 

 to a ratio of 214 to 215 for the axes. Then when the middle 

 arc was re- measured, and to the three meridian arcs a longitudi- 



