352 ANNUAL OF SCIENTIFIC DISCOVERY 



have one upwards of 10 miles in length. Having established the 

 length of this base, a series of triangles is adopted, of gradually increas- 

 ing sides, the lengths of which, or distances between the angular points, 

 are known from the base and measured angles. By measuring the an- 

 gles from the extremities of the base, the length of which is exactly 

 known, we obtain the direction and distance of a new point, and thus a 

 new base line. That line, in turn, establishes another at a still greater 

 distance ; and thus the surface of the earth is covered with a network 

 of triangles, each side of each triangle being calculable from the meas- 

 ure of the angles, and from the length of the originally determined 

 base. This would be easy, were the triangulation upon a plain sur- 

 face ; but the calculation is not so simple as it would at first appear. 

 The earth must be considered, in computing these large triangles, not 

 merely as a sphere, but as a spheroid. Next comes the astronomical 

 part of the survey. The direction of the lines with reference to the 

 meridian must be known. The latitude of the points must be ascer- 

 tained, and their longitude must be determined. Having these data, 

 we then know from computation the latitude and longitude of any 

 point, and the angle with the meridian of any line connected with the 

 triangulation. This is the second part of the work. 



" We have thus a great scheme, in which the progress may be very 

 rapid, because the steps may be very great. You may have as we 

 have in some cases in our New England triangles a side of 60, 

 90, or even 100 miles in extent ; and thus you may make vast strides 

 along the coast at once, by taking advantage of hills properly situated 

 in the interior of the country and overlooking the ocean shore. Hav- 

 ing determined these points with great nicety, with large instruments, 

 and a great deal of care, the work between them need not be done so 

 elaborately. New points are determined between the former, upon the 

 same great system of triangulations, called the secondary triangulations. 

 Upon this, with a still less exact mode of working, namely, with the 

 plane table, the topography is laid down so far as it may be necessary 

 to show the coast to the navigator, and for purposes of defence. AU 

 the points are checked by the secondary triangulations, which in their 

 turn are checked by the primary ; so that, having taken great pains in 

 the first part of the work, you cannot wander far out of the way in the 

 second part, or in the topography. Having thus determined the outline 

 of the coast, the hydrography gives you a picture of the sea, just such as 

 the topography gives you of the land above its surface, and this com- 

 pletes the survey. 



" Originally, I divided the survey into eight sections. Texas made a 

 ninth, and Oregon adds a tenth section. In the first section, from 

 Point Judith to the boundary, we have now finished the primary tri- 

 angulations, from the base on the Boston and Providence Railroad, 

 along the coast of Rhode Island, Massachusetts, and New Hampshire, 

 into Maine. The hills of New England seem as if they had been made 

 for triangulation. They are so situated that we can pass rapidly 

 along the coast with long strides ; and the only difficulty is to avoid 

 being tempted to make the lines too long. I have frequently, however, 

 in taking such long lines, taken also an intermediate shorter line, for the 



