Introduction.—Magnetic observations have been made by the Department of Terrestrial Magnetism of the Carnegie Institution of Washington, in some part of the area indicated in the title, every year since 1905. At the conclusion some time in 1925, of the work of an observer now in South America, the project undertaken in 1922, of reoccupying selected stations distributed with fair uniformity over the entire land area of the western hemisphere south of 33° north latitude, will have been completed, and a series of observations of recent date will be available for the study of secular variation. Before undertaking a mathematical discussion of this material, it is advisable to determine the general character of the lines of equal annual change of the three elements, declination, inclination and horizontal intensity, by a general review of the data, and the construction by simple graphical processes of preliminary charts showing the lines for some suitable epoch.