/:'. I>. Preston — Measurement of thi Peruvian Arc 9 



The accuracy of the measurement of a star's zenith distance 

 appears to depend principally on the stability of the limh of 

 the instrument, and the ability of the observer to Bet the 



initial point of the arc in exact coincidence with the plumb-line. 

 There seems to be nothing said as to how this was accom- 

 plished, but it is easily seen that it must have been a work re- 

 quiring much care. The measures of the star's zenith distance 

 are given to the nearest second. Indeed the three results for 

 the arc's amplitude have a range of only three seconds. The 

 following were the results from the three stars : 



e Orion 3° 7' l" 



6 Aquilffi 59 



a Aquarius... _ _. .6 58 



These are the results considered by the observers to be the 

 best. They do not represent all the observations, hut were 

 selected on account of the favorable conditions obtaining at 

 the time they were made. The sector had also undergone 

 some improvement. But a mean value from all the results 

 obtained at both stations gives 58" which agrees more closely 

 than one would expect from the range of the individual values. 

 Zach estimates that the total error in the equatorial degree will 

 not exceed fifty toises, thirty-eight being for the astronomical 

 and twelve for the geodetic part of the work (Monat. Corres. 

 1807). This is based, however, on Bouguer's, and La Conda- 

 mine's estimates of the accuracy of the astronomical work 

 (page 25]). Since the radius of the sector was twelve feet, 

 one second on the limb would be about l/1400th of an inch. 

 To make a plumb-line, suspended freely, coincide with a mark 

 on a scale at its side, to within less than this quantity, must 

 have been a matter of difficulty. In this operation we have in 

 all •probability the source of the largest discrepancies. 



The flexure of the sector was also studied. Experiments 

 were made on an iron bar, from which it was concluded that 

 the flexure varied as the fourth power of the length. It was 

 found moreover that when the radius of the sector was placed 

 horizontally its flexure amounted to one-twelfth of an inch. 

 This was shown to be inappreciable when the inclination was 

 only a few degrees, and when the objective of the telescope 

 was attached to the center of the sector. 



Azimuth observations were made at both bases and at three 

 intermediate points. The agreement between the observed 

 directions and those determined by triangulation is always 

 within less than one minute; the discrepancy at the last base 

 being forty seconds. The sun was invariably used, and the 

 angle between it and a signal was measured with a quadrant. 

 The errors in orientation, estimated liberally, will not change 



