Mat 12, 1911] 



SCIENCE 



r49 



the area of a country to furnish control for the 

 detailed operations. The tertiary is used for the 

 immediate control of detailed topographic, boun- 

 dary and other surveys, while the secondary tri- 

 angulation is mainly for the purpose of connecting 

 the detached tertiary work with the primary 

 schemes. 



Owing to the difEerence which must exist at 

 every station between the geodetic position and 

 the corresponding astronomic position, it is neces- 

 sary to adopt a mean position called a geodetic 

 datum upon which to reckon geographic positions 

 over the entire country. It is the principal object 

 of the primary triangulation to carry standard 

 positions by a connected net to the remotest por- 

 tions of the area. 



An incidental purpose of triangulation, and es- 

 pecially of the primary, is to furnish means for 

 determining the shape and size of the earth. 



In the two recent investigations of the figure 

 of the earth by Mr. John F. Hayford, while he 

 was inspector of geodetic work and chief of the 

 computing division in the Coast and Geodetic Sur- 

 vey, he applied Pratt's hypothesis of isostasy and 

 he stated that the application of this theory nearly 

 doubled the accuracy of the results. 



Including about 2,000 miles by the Lake Survey, 

 there are now approximately 11,000 miles of pri- 

 mary triangulation in the United States. Eecently 

 about 400 miles have been added each year. The 

 latest addition is the Texas-California triangula- 

 tion, an arc of over 1,200 miles in length. It 

 extends from the 98th meridian triangulation in 

 central Texas to the Pacific coast arc in the 

 vicinity of San Diego. It carries standard posi- 

 tions into an area badly in need of control and 

 adds very valuable data for use in a future in- 

 vestigation of the figure of the earth. 



The probable errors of the observed directions 

 are not available, as the office computations have 

 not yet been made, but we may get a measure of 

 the accuracy of the work by the size of the errors 

 of closure of the triangles. The average closing 

 error is 0.9 second of are, and the maximum error 

 is very little more than 3 seconds. This makes the 

 accuracy equal to the average of the best half of 

 the work previously done in the United States. 

 , The observations for horizontal measures were 

 made entirely on heliotropes or on signal lamps. 

 No serious diflSculty was encountered in observing 

 over even the longest lines under average condi- 

 tions. The longest line was 127 miles in length. 

 Some of the heliotropes had reflectors 4 and 8 

 inches square but most of the reflectors were only 



2i inches in diameter. The signal lamps burned 

 acetylene gas. They were the commercial auto- 

 mobile headlights, modified for use on a stand 

 erected over the station. 



Some years ago it was believed that a great 

 many observations were necessary to get an accu- 

 racy represented by an average closing error of 

 one second and that the observations should be 

 made on a number of different days. In recent 

 years only sixteen positions are used, making 32 

 pointings on each object. All the horizontal ob- 

 servations at each of many stations have been 

 made in a single day without materially affecting 

 the accuracy. In fact, the average accuracy of the 

 work done under the present methods is greater 

 than the average accuracy of the work previously 

 done. 



It has been found that the sun effect on the 

 towers, in causing twist, is very slight with the 

 present type of tower, and that the effect, if any, 

 is practically eliminated from the results by the 

 system (always employed) of having a determina- 

 tion depend upon observations made while re- 

 volving the instrument clockwise and then in the 

 reverse direction immediately afterwards. 



The instrument had one horizontal wire and two 

 vertical ones which were 20" apart. It is not 

 necessary for the image to be absolutely stationary 

 for, with practise, one can place the cross wires 

 close to the mean position of the image, even 

 though the object may subtend an angle of more 

 than 20" and move 10" to each side of the mean 

 position. Observations made under this condition 

 seem to have about the average accuracy. 



Where the country is flat and the line close to 

 the intervening land the wind tends to cause a 

 distortion of the image. It sometimes appears to 

 flare to one side, the flaring being away from what 

 seems to be the nucleus or center of the image. 

 In nearly every case where an asymmetrical image 

 is observed the flaring seems to be with the wind. 

 Under such a condition it is difficult to make sat- 

 isfactory observations. If the flaring portion of 

 the image is given equal weight with the nucleus 

 a constant error is introduced, while if this flaring 

 part is given no consideration a constant error of 

 the opposite sign is made. Such an image is a 

 severe test of the skill of the observer. 



A remarkable case of lateral refraction was 

 encountered on the twenty-mile line joining sta- 

 tions Clayton and Kennard, in Texas. This line 

 passed very close to the west slope of a flat -topped 

 hill about two and a half miles from Clayton. 

 Observations made during several days at Clayton 



