XXVI REPORT UNITED STATES GEOLOGICAL SURVEY. 



the accurate length of a line 20, 30, or 40 miles in length, the mean dis- 

 tance between stations of the triangulation. 



For this purpose, points are selected on the right and left of the base 

 line, at such distances from it that the triangles formed by each of these 

 points, and the two ends of the base, will be "well conditioned"; that is, 

 that the angles of the triangles will be as nearly equal as possible. Then 

 all of the angles of each of these triangles are measured. 



Now, were these angles measured perfectly, the sum of the three of 

 any triangle would be 180*^ plus the spherical excess. The amount of 

 the discrepancy is an indication of the accuracy of the work. Now, in 

 each of these triangles there is given a side and the three angles, and 

 a simple trigonometrical calculation gives the lengths of the other sides; 

 these other sides, thus calculated, furnish bases for further triangles, each 

 larger than those used before, and thus the enlargement goes on until the 

 normal length of sides of triangles is reached. This completes the expan- 

 sion, and thence the triangulation goes on by the simple measurement of 

 angles, the sides of the triangles being kept as nearly as possible of the 

 same length and the angles as nearly equal as possible. 



A second base is usually measured as a check on the first. From it 

 an expansion is made, and the work connected with that from the first. 



To ascertain the direction or azimuth of these lines, it is necessary 

 to know only the direction of any one of them, although practically the 

 directions of several are measured, as checks on one another. The 

 measurement consists in measuring the angle between the line and some 

 slow-moving star, usually the pole star, whose distance from the north 

 pole is known at the time. Now, this system of triangulation is consist- 

 ent in itself, but its position on the earth's surface is unknown. To de- 

 termine this requires the aid of astronomy. One or more of the stations 

 in this triangulation must be fixed by astronomical means, and the char- 

 acter of the work is such as to warrant the employment of the best in- 

 struments and the most refined methods for the determination of the 

 latitude and longitude of this or these points. For the determination of 

 the latitude, we use the zenith telescope, and the method of zenith dis- 

 tances of stars. To describe this method would require more space and 

 technical language than could be used here. Suffice it to say, that this 

 method determines the latitude within a few tenths of a second, where 

 a second is about 100 feet. 



The longitude is determined by the comparison of the local time of 

 the station with that of some point whose position is known. This com- 

 parison is made by telegraph. The heats of the chronometer are trans- 

 mitted back and forth by telegraph, and recorded side by side on paper, 

 by an ingenious instrument known as the chronograph. 



The difference between the local times of the two stations is the differ- 

 ence in longitude. This local time is determined at each station by ob- 

 serving the transits of stars, whose positions are known, with a transit 

 instrument. These observations give the error ot the chronometer and 



