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



mulation of these throughout the entire work would produce an 

 error in the second base of about twenty-five toises but adds 

 that a certain compensation must be expected among so many 

 errors. 



After having finished the triangulation, astronomical obser- 

 vations were undertaken to determine the amplitude of. the 

 arc. They were made with a sector having a radius of twelve 

 feet and a graduated arc of about three degrees. Although 

 this is confessedly the weakest part of all the equatorial work, 

 the methods employed show a keen appreciation of many 

 sources of error. The limb was graduated by laying off an 

 aliquot part of the radius as a chord. This was chosen with 

 reference to the particular star to be observed, and the true 

 zenith distance was found by applying to this known arc, a 

 small micrometer correction. The modern work with the 

 zenith telescope is but a repetition of this same principle ; for 

 here the absolute zenith distance of the two stars is for the 

 moment disregarded, but the excess of one over the other is 

 measured, and applied to a function of their declinations, which 

 are quantities determined by other investigations. 



The precaution was taken in the Peruvian work to make 

 part of thje measures on the same star, and at the same time, at 

 both extremities of the arc. This would eliminate any effect 

 of uncertainty in the constants for precession, aberration and 

 nutation, which were not, at that time, very well determined. 

 But Zach has re-reduced the observations of 1742 and 1743,* 

 ana finds a difference of less than 1" between the results for 

 the simultaneous observations and that deduced from all the 

 work during these two years. The instrument was reversed 

 several times, thus giving values under different conditions, 

 and it is said that no discordant observations were rejected.f 

 The method of reversal is referred to as having been invented 

 by Picard, and it is probable that this principle, now so often 

 applied, and so essential in all instrumental work was here sys- 

 tematically used for the first time. Its effect in this case was 

 to eliminate the eccentricity of the zero point of the microm- 

 eter. 



The value of the micrometer was found from terrestrial 

 measures, using the known length of portions of the base, and 

 lines erected perpendicular thereto. The meridian was found 

 by observing, at the moment of culmination, the direction of 

 a beam of sunlight, admitted through a hole in the roof of the 

 observatory. The method was supposed to give the true direc- 

 tion with an error not larger than one minute of arc. 



*Ueber die Grradmessung am Aequator ; Monat. Corres. vol. xxvi, page 39. 

 f Figure de la Torre par Bouguer, Paris, 1749, p. 262. 



