TRACING THE PARALLELS. COMPUTATIONS. 143 



While the results confirm the excellence of the zenith telescope for field operations, thej indi- 

 cate the necessity of a more extended and accurate catalofcue of stars 



IV. Geodetic Measurement. 



The azimuth lines were ascertained by ohservations on the elongation of Polaris and the 

 measurement on the face of the earth was made with several different instruments. Those in 

 California with a transit by Ertel & Son, Munich ; with a horizontal limb of fifteen inches 

 diameter, graduated to read to 10'^ The instruments used in tracing the parallel of latitude 

 were a ten-inch azimuth circle, by Gambey, of Paris ; two by Bruner ; and one by Draper, of 

 Phihadelphia. Some of the barometers used were by Bunten, of Paris ; but they were chiefly 

 made by James Green, of New York. They, together with the thermometers, were ccmparod 

 with the standard at the Smithsonian Institution, both before and after being used. 



In tracing the parallels of latitude 31° iT and 31° 20', and also in prolonging the azimuth 

 line across California^ and from the Rio Colorado to the 111th meridian of longitude, it 

 frequently happened that it was convenient to take the meridians determined by the transit 

 instrument, but most usually they were taken from the measurements of the elongation of 

 Polaris. 



Y. Tracing the Parallels, 



The parallels were determined by tracing a tangent to the prime vertical at any given point, 

 and measuring the ordinates to the parallel. The use of the tangent instead of the chord was 

 preferred, because the measurement of the ordinates, confided to a variety of assistants, pre- 

 sented always an increasing series, and was less liable to lead to confusion ; a precaution very 

 necessary in a country where water is scarce, and where parties operating have constantly to be 

 on the alert against attacks of Indians. A general sketch of the stations established in latitude 

 to trace these parallels is stated in the agreement with the Mexican commissioner, which will 

 be found under the head of Personal Account, in Chapter II, audit is therefore unnecessary to 



repeat it here. 



Great as were the embarrassments in other respects, the absence of trees gave us great facility 

 in tracing these lines, and enabled us easily to correct errors resulting from producing long 



lines. 



In the determinations of latitude along the same parallel, it will be seen we used the same 



instrument, and, as far as practicable, the same sets of stars; so we were quite certain of getting 

 correct differences of latitude between two stations. In no case was it attempted to produce the 

 same tangent in one direction more than thirty miles, and it was then always compared with 

 the tangent from the new latitude station. The parallel of latitude thus deduced by separate 

 and independent operations seldom differed more than a few feet ; and in no case was the dis- 

 crepancy suflSciently great to make it necessary to retrace our steps. The tangents, being few 

 in number, were generally laid off by myself, and prolonged by the principal assistant sur- 

 veyors, who were furnished with tables of ordinates and angles, which will be found in the 

 appendix, that enabled us at once, and by simple measurements, to establish points in the paral- 

 lels forming the boundary, 



YI, Computations. 



The computations were all made in the field originally, and subsequently revised in the 

 office. 



