432 THE POPULAR SCIENCE MONTHLY 



ginning 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 de- 

 duced by Chandler fifteen years ago are no longer sufficient to ac- 

 curately 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 Chand- 

 ler, 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 in- 

 ertia are unequal. 



The change of latitude being so very small is, of course, of no con- 

 sequence whatever to the navigator who has to determine his position 

 at sea. It is, however, of great interest and importance from a scien- 

 tific 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 



