Page:Popular Science Monthly Volume 75.djvu/436

432 of 1907 is represented in Fig. 6 taken from the Astronomische Nachrichten, No. 4187. The large square represents a piece of ground fifty feet on a side. The small circles represent the position of the pole for each tenth of a year beginning with 1899.9 and ending with 1907.0. By starting at the beginning and following out the motion of the pole a roughly spiral path is found with a clearly marked period of about seven years, the position of the pole at the beginning of 1907 almost coinciding with the initial position, 1899.9.

The observations made at the International Latitude Observatories have determined the motion of the pole with a degree of refinement and continuity never before attained, and it is now found that the laws deduced by Chandler fifteen years ago are no longer sufficient to accurately represent the observed motion. Dr. Kimura has recently made a harmonic analysis of the variation of latitude and finds, in addition to the two principal motions of periods of fourteen months and one year found by Chandler, two smaller motions with periods of 0.75 and 0.6 of a year. Kimura also finds that the principal motion of fourteen months is in an ellipse and not in a circle as found by Chandler, the interpretation of which would be, that the equator is an ellipse and not a circle, if we assume the earth to be made up of homogeneous layers, or, in technical language, that the equatorial moments of inertia are unequal.

The change of latitude being so very small is, of course, of no consequence whatever to the navigator who has to determine his position at sea. It is, however, of great interest and importance from a scientific standpoint, and it is hoped that the work at the various stations may be carried on long enough to make a definitive determination of the laws of the polar motion possible, so that a mathematical formula may be constructed from which the position of the pole, or the latitude of any place, may be computed for any time past or future.

One way in which the variation of latitude might have political or commercial significance is in cases where a certain parallel is designated as the boundary line between two countries, states or counties. For instance, the forty-ninth parallel is, for a portion of the distance, the boundary line between the United States and the Dominion of Canada. If any question should be raised, however, a court of arbitration would probably decide that, inasmuch as the actual line shifts its position, the one already established, if not egregiously in error, should continue to be considered the boundary line. A case similar to this has recently been decided by the courts of California. The boundary line between Mendocino and Trinity counties is defined as being the fortieth parallel of latitude. When the counties were first established a surveyor was employed to locate this line, but some score or so of years afterward other surveyors found that the established line lay about two miles too far south. Thereupon Mendocino County brought suit against Trinity