THE VARIATION OF LATITUDE The deflections of the vertical in the meridian depend on both the astronomical latitude and the geodetic latitude. The latter, as has been noted, involves a certain convention, that is, the assumed geodetic datum, and moreover depends upon surveying operations to connect the initial point of the datum with the point whose geo detic latitude is sought. The astronomic latitude, though de pending on observation at the place in question, is not absolutely invariable. The variability is due to a displacement of the axis of rotation in the body of the Earth. There is in every body, however irregular in shape, an axis of figure, the axis about which the moment of inertia is a maximum. If for any reason the axis of figure and the axis of rotation do not coincide, the pole of the axis of rotation will describe in the body a closed curve about the pole of the axis figure. For a nearly spherical body like the Earth, the axis of rotation will retain in space a nearly invari able direction.
The laws of these phenomena were first stated for a rigid rotating body by Leonhard Euler (q.v.). With Euler's theorems in mind astronomers sought to detect by observation a possible variation in latitude, but succeeded only in reaching the conclu sion that if any such existed, it must be small. Finally S. C. Chandler undertook a careful study apart from any preconceived theory, basing it both on observations of his own and a study of old records, notably those of Greenwich Observatory. At about the same time, the reality of a change in latitude due to a motion of the pole was proved by simultaneous latitude observations in Berlin and Honolulu, places differing in longitude by nearly 180°. It was found that an increase in latitude in one occurred simul taneously with an approximately equal decrease at the other. This could not have been due to local conditions nor to defective star places, but it must have been due to a motion of the pole of rotation which in approaching one place receded from the other.
Chandler found that the motion of the pole of rotation about the pole of figure required about 14 months where Euler's theory had led astronomers to expect a ten-month period. The longer period was soon explained by Newcomb as due to the fact that Euler's theory was based on an ideal body absolutely unyielding and unchangeable in shape, a thing unknown in nature. The elastic yielding of the earth and the mobility of the ocean water lengthen the period from io months to r4.
There is also a motion of the pole of rotation in the body of the Earth due to the fact that the pole of figure itself is not invariable but undergoes a displacement due to seasonal variations in barometric pressure, snow-load, etc. The period of these seasonal changes is obviously one year.
The amplitudes of both the annual and the fourteen-month variations are of the order of magnitude of o".r. The quantities sought are small and difficult to measure, but it appears that both components of the polar motion are subject to unpredictable changes. Since the maximum deviation of the pole from its mean position is about o".3, which is small in comparison with the usual deflections of the vertical, the reduction of the observed astro nomical latitudes to some more or less conventional mean value is not a very vital matter in ordinary geodetic work. (It should be noted that the motion of the pole affects longitudes and azimuths also.) The interest of the subject is more on the astronomical and geophysical side. Many interesting problems into which we can not here enter are raised by this phenomenon and still awai` complete solution.
The International Geodetic Association (see § of this article) organized in 1899 an International Latitude Service with six special latitude observatories, all on the parallel of 39° o8', three of which have remained in continuous operation. The advantage of having them all in the same latitude is that the same stars may be used at all of them and uncertainties in the star places do not affect the conclusions. The observations may in fact be used to correct the star places.