ON ASTRONOMY. 



89 



and D A M, and also the elevation, if any, of D and E above A. The 

 instrument is then transported to D, and A D E and E D F are 

 measured, and also the elevations of F and E above D ; and thus in 

 succession the instrument is taken to each of the stations and all the 



horizontal and vertical angles are measured. The sides of all the 

 triangles, varying in length from 10 to 40 or 50 miles, may now be 

 very easily computed. Beginning with A D E, and taking them in 

 succession, we have in each case all the angles and one side given to 

 find the other sides. To test the accuracy of the work a second line, 

 as H B, at or near the extremity of the line is measured. This is 

 called the base of verification. If any considerable error is found to 

 exist between the measured and computed length of this line the 

 whole work must be gone over again. But before we can expect any 

 close agreement between the computed and measured length of the 

 base of verification the several stations, D E F and G, must be reduced 

 to the level surface, that is, to the surface of the water, if we should 

 suppose the ocean to flow freely over 

 the land. We must reduce each of 

 the stations to the continued ocean 

 surface. Thus, in fig. 3, A mny be 

 situated on the beach, E on the 

 summit of a mountain, A G the 

 curve or line of the ocean surface 

 continued. We must, in fact, re- 

 duce the point E to G and compute 

 the length of the curved line A G 

 from knowing the length of the 

 straight line A E and the elevation 

 of the point. My object here is not 

 to give any abstract or synopsis of 

 the method of making this reduc- 

 tion, but only to indicate what is required to be done. The process, 

 though somewhat laborious, presents no peculiar difficulty. 



It now remains to find the distance from A to B along the meridian 

 line reduced to the ocean surface. This we do by resolving in succes- 

 sion the triangles, fig. 2, A D M, M E M, N F 0, G P, and P H B, 



