Mat 15, 1914] 



SCIENCE 



699 



points, probably not exactly at the sea 

 shore, the mean figure of the earth — the 

 spheroid — would intersect the actual sea 

 surface, the geoid. Under the coastal 

 plains the geoid would be slightly above 

 the spheroid; while under great mountain 

 ranges the geoid would be far above the 

 spheroid, possibly as much as one hundred 

 meters. Over the oceans the geoid would 

 be under the spheroid surface by amounts 

 varying directly with the depths of the 

 water. 



There is only one way to determine ac- 

 curately the size of the earth, and that is 

 by measurement on the continents of the 

 lengths of arcs connecting points where the 

 astronomic latitude and longitude have 

 been determined. The measurements of 

 such arcs may be direct, or they may be by 

 means of triangulation. The earliest meas- 

 urements were by the former method, but 

 with the introduction of accurately gradu- 

 ated circles and the application of wires in 

 the eye-pieces of telescopes, the indirect 

 method came into general use. 



At frequent intervals, in triangula- 

 tion, the sides of some of the triangles in 

 the scheme are accurately measured, in 

 order to control the lengths. At the pres- 

 ent time, this is done almost exclusively 

 with nickel-steel (invar) tapes or wires. 

 The probable accidental error of a meas- 

 ured length is seldom greater than about 

 one part in one million. The constant 

 error in such a measurement may be as 

 great as one part in three hundred thou- 

 sand. This accuracy is, however, far 

 greater than that of the lengths of the tri- 

 angle sides, as computed through the chain 

 of triangles. The uncertainty of any one 

 line between bases is about one part in one 

 hundred thousand, on an average. A long 

 are, say one across a continent, can be 

 measured with greater accuracy than that, 

 for even the systematic and constant errors 



of the various sections of the arc would 

 probably act as accidental errors, and the 

 greater portion of their effect would be 

 eliminated. 



The observations for latitude, longitude 

 and azimuth, or direction, are made on the 

 stars; and in the most refined work a cor- 

 rection is made for the variation of the pole. 



One might think that the determination 

 of the figTire and size of the earth is a very 

 simple process, consisting merely of ob- 

 taining by astronomic observations the ac- 

 curate angular distances between each two 

 of several points on a meridian, and then 

 measuring accurately the linear distances 

 between them. Three such points being 

 sufficient to obtain the equation of the 

 curve formed by the intersection of the 

 meridional plane and the spheroid, the 

 shape and size of the earth would be known. 

 This would be true if the spheroid and the 

 geoid coincided throughout, but, as stated 

 above, they do not do so. The plumb line 

 to which all astronomic observations are 

 referred is, at each point, normal to the 

 geoid, which is a very irregular surface 

 and, therefore, very many astronomic sta- 

 tions must be established and used. The 

 greater part of each of the differences be- 

 tween the astronomic positions, as actually 

 observed, and the theoretical positions, 

 based on an adopted smooth mean surface, 

 must be treated as an accidental error. 

 These differences reach a maximum value of 

 about twenty-five seconds of arc (within 

 the area of the United States) which is 

 nearly one half mile. In the island of 

 Porto Eico, the relative deflection between 

 two astronomic stations, one at Ponce and 

 the other at San Juan, was 56 seconds of 

 are, about one mile. 



The shape, but not the size, of the earth 

 may be determined from the observed value 

 of gravity at stations widely distributed in 

 latitude. But here again a few stations are 



