﻿BETWEEN THE UNITED STATES AND MEXICO. 217 



II. Discussion of Lines of equal Magnetic Declination, Dip, and Horizontal 



Intensity. 



In this discussion, the observations made in preAious years in connection with the 

 Mexican boundary surveys, and published in the fifth vohime, new scries, of the Me- 

 moirs of the Academy, have been combined with those communicated in the present 

 paper. Observations made under the direction of Professor A. D. Bache, Superintend- 

 ent of the Coast Survey, at stations Dollar Point, East Base, and Jupiter, near Gal- 

 veston, Texas, and near San Diego, Monterey, and San Francisco, and affording im- 

 portant co-ordinates for the curvature of the lines, have also been introduced ; likewise, 

 an observation of the declination at the Great Salt Lake, by Captain Howard Stans- 

 bury, U. S. Topographical Engineers, published in his report of the survey of that 

 region. 



The method employed ui determining the lines of equal declination and dip was 

 partly graphical and partly analytical, being the same pursued by Professor Bache and 

 Mr. J. E. Hilgard in their discussion of the Coast-Survey magnetic observations. 

 (Coast-Survey Report for 1855, Appendix, p. 47.) The stations were projected on a 

 map, and their positions referred to a right line graphically assumed as axis of co- 

 ordinates, the origin being chosen about the mean position of the stations, and the 

 direction so as nearly to divide the positive and negative ordinates equally. 



The co-ordinates being read off on any convenient linear scale, conditional equations 

 are formed for each station or group of stations, and the whole scheme is solved by the 

 method of least squares. The conditional equations representing an interpolation by 

 second differences are of the form, 



V= T^o + ^' + ^v X-^^Y^z X Y-\-p X' -f- qy\ 



when V is the observed declination (or dip) ; 



Vq, the assumed declination at the origin ; v, the correction to be applied ; 

 X and Y, co-ordinates of position. 

 on, y, z, p, q, coefficients to be determined. 

 The solution of a considerable number of such equations involves a great deal of 

 labor, which the results amply repay, however. The process being well known, there 

 is no occasion to give the steps of the calcidations in this place. After determining 

 the coefficients, the co-ordinates of points in the lines sought were computed, the lines 

 projected on the map, and the latitudes and longitudes of points read off and tabulated. 

 In the absence of any data to determine the secular changes, the results are doubt- 



