April i, 1920] 



NATURE 



141 



Geodetic Survey in North America.^ 



THE United States Coast and Geodetic Survey 

 has long had in progress an arc of primary 

 triangulation along the 98th meridian of longitude. 

 This arc was completed to the north, up to the 

 Canadian boundary, in 1907. To the south there 

 is a similar arc along the same meridian through 

 Mexico, originally surveyed by the " Commission 

 G^odesique Mexicaine " between 1906 and 1910, 

 terminating to the north at the international 

 boundary on the Rio Grande and extending south- 

 ward to the Pacific Ocean. 



It was obviously desirable that these two arcs 

 should be connected, and it was accordingly 

 arranged to make the connection in 191 3, when 

 the last section of the work in the United States 

 was done. The internal condition of Mexico, how- 

 ever, did not permit any joint operations at that 

 time, and a postponement was necessary. Oppor- 

 tunity was taken of the improved condition of the 

 country in 191 5 to revive the question. The 

 arrangements proceeded without hitch and the 

 final observations were successfully made in May, 

 1916. The publication under review gives an 

 account of the southern end of this arc in Te-sas, 

 surveyed in 191 3, the junction with the Mexican 

 arc in 1916, and a general summary of the pro- 

 gress to date of the lines of first order triangulation 

 in the United States. 



Since 1901 the Coast and Geodetic Survey has 

 reduced all its work to a common datum and 

 computed all positions and azimuths upon Clarke's 

 1866 spheroid. These, both datum and spheroid, 

 have been accepted, on one hand by the Cana- 

 dian, and on the other by the Mexican, Geodetic 

 Surveys, so that they are now common to the 

 whole of North America. An inspection of the 

 index map of the triangulation lines in the 

 United States computed to these data shows, how- 

 ever, that there is still a considerable block of 

 triangulation in the Eastern States not yet re- 

 adjusted. When this readjustment is made and 

 when certain lines in the Central and Western 

 States, now in progress, have been completed, the 

 network over the whole area will be so close that 

 no point will be situated at a greater distance from 

 a main triangulation line than about 170 miles. 

 In fact, even this distance will be rarely attained, 

 and over almost the whole area the maximum 

 distance will be under 150 miles. 



Such a network of absolutely first-class work is 

 amply suflRcient to satisfy the most ' exacting 

 geodesist and is, of course, more than a suflficlent 

 basis for any possible map upon any practical 

 scale. We may, therefore, congratulate the 

 U.S. Coast and Geodetic Survev upon the now not 

 distant completion of one of the main sections of 

 its great task. 



' Department of Commerce, U.S. Coast and Geodetic Survey. fSeodesy. 

 Serial No. 97. Report on the Connection of the Arcs of Primary Triangu- 

 lation alon? the Ninety-eif hth Meridian in the United "States and in 

 Mexico, an-i on Triansiulation in Southern Texas. Ry William Rowie. 

 (Special Publication No. 51.) Pp. 93. (Washington : Government Printing 

 Office, 1919.) Price 10 cents. 



NO. 2631, VOL. 105] 



The execution of the small section of triangula- 

 tion under review was marked by no special tech- 

 nical advances ; but as exhibiting a high level of 

 technical eflftciency and as being of possible use 

 for future guidance in similar work that may be 

 planned in British territories, we may briefly advert 

 to one or two practical points. One question of 

 considerable importance is to decide whether it is 

 desirable to restrict observations to the night 

 or whether day observations should be included. 

 The U.S. Survey adopts the principle of allowing 

 only night observations, for the stated reason that 

 experience has shown that there is less deviation 

 in the geodetic azimuths of the lines when this 

 restriction is enforced than when the observing is 

 done by day or is a combination of day and night 

 work. In other words, the atmospheric conditions 

 are rnore stable at night and observations of 

 angles, therefore, more accurate. This is in ac- 

 cordance with general experience and practice. 

 It has, however, been argued, not without a 

 certain show of plausibility, that though undoubt- 

 edly the apparent errors are thus reduced, this may 

 be at the risk of introducing systematic errors, 

 due, let us say, to unsymmetrical atmospheric 

 refraction operating only "when observations are 

 made upon a falling temperature, which might 

 be eliminated if observations under different 

 atmospheric conditions were combined. Though 

 plausible, this argument is, we think, not tenable, 

 or, perhaps more correctly, not applicable to the 

 case of a triangulation. 



The ultimate test as to whether, in deriving the 

 most probable mean of any set of observations, 

 systematic errors are likely to be diminished by 

 the inclusion of observations of an inferior degree 

 of accuracy but differing in their conditions can 

 be decided only by experience. Now in this case 

 the " experience " is immediately available, being, 

 in fact, implicitly contained in the figure express- 

 ing the closing error of the triangle. Any method 

 of observation and any system of combining the 

 results of the observations into a mean value which 

 reduce this closing error ipso facto increase the 

 probable accuracy of the finally derived figures of 

 position and azimuth. Night observations, pre- 

 ferably, between, say, three hours after sunset and 

 one hour before sunrise, fulfil this condition and 

 are therefore rightly accepted as ideal. 



The U.S. Survey, operating over a huge area 

 with a necessarily limited budget, has perforce to 

 pay attention to the question of cost. Survey is, 

 in fact, on exactly the same basis as other en- 

 gineering operations. The problem is to get the 

 maximum output of work of a strictly defined 

 and practicable degree of precision at the mini- 

 mum cost, and not, as has sometimes been 

 assumed, to reach the highest attainable precision 

 regardless of cost. 



The standard for first order work in the United 

 States is an average triangular error of one second 

 of arc and a maximum error of under three 



