Another, wholly different, method of deter mining the form, though not the size, of the earth is afforded by the force of gravity, as determined by the length of the seconds pen dulum. It is well known that gravity is less in the equatorial regions of the earth than at the polar regions, from two causes. One is the centrifugal force of the earth's rotation, and the other is the greater distance of the centre of the earth's surface at the equator. The result is that a clock pendulum, swinging exact seconds near the pole, would lose several seconds a day when taken to the equator; hence, a pendulum which would beat exact seconds must be made continually shorter as we approach the equator. The determination of its length in various- lat itudes thus becomes an important problem in geodesy. When it is known, the ellipticity or flattening of the earth may be determined from it.
What makes all the problems associated with this so complex are the small irregularities in the direction and force of gravitation wherever measures and determinations have been made. It is always found that when the latitudes of places are determined by the direction of the plumb-line, which is the only astronomical method, they seldom agree with the differences between the places as determined by geodetic measurements. The reason is, that the plumb
line is deflected by the attraction of mountains and denser portions of the interior of the earth which do not admit of exact computation. These irregularities are-greater in mountainous regions, in the Himalayas sometimes rising to 30 seconds. BOt.even to Vain Oattntries devia tions of two or three seconds are found. The errors arising from these deviations would not be important in themselves, the difficulty being that they operate like a small error in a foot rule when the latter has to be used for measur ing a very long stick of timber. In such a case an error even so small as one-eighth of an inch in the rule would amount to an error of a foot in measuring a pole 100 feet long. As the measurement of a whole continent, even of the earth itself, has to start from short base lines, the error may be multiplied many fold in the final result