698 



SCIENCE 



[N. S. Vol. XXXIX. No. 1011 



the question as to whether the earth has 

 the form of an oblate or prolate spheroid, 

 and to settle it the French Academy sent 

 expeditions to Peru in 1735 and to Lapland 

 the following year to measure arcs near 

 the equator and within the arctic circle. 

 The result of these measurements con- 

 firmed the theory of the oblate spheroid. 

 A revision of the computations of the Paris 

 arc also showed that the northern degrees 

 were the longer, thus confirming the re- 

 sults obtained from the work done in Peru 

 and Lapland. 



The first near approach to the size of the 

 earth resulted from triangulation done in 

 the last decades of the eighteenth century 

 to connect the observatories of Paris and 

 Greenwich and to determine the length of 

 the earth's meridian quadrant. For the 

 latter purpose an arc of the meridian of 

 nearly ten degrees was measured in France, 

 One ten-millionth of the resulting length 

 was adopted as the standard of length (the 

 meter) . Any other length could have been 

 selected as the standard, for the meter 

 bears no such exact relation to a quadrant 

 as later and more accurate data show. 



Geodesists were very active during the 

 nineteenth century and will be for some 

 time to come, in making geodetic measure- 

 ments to determine the mean figure of the 

 earth with greater and greater degrees of 

 accuracy. There comes a time, for any one 

 given area, when it is useless to add more 

 geodetic data for the purpose of obtaining 

 a more exact mean figure, for there are 

 constant ■ or systematic errors present in 

 the data, the effect of which is probably 

 much greater than that of the accidental 

 errors. 



But there is much to be gained by ex- 

 tending geodetic surveys to new areas and 

 especially to new continents. (By geodetic 

 survey is meant, here, triangulation and con- 

 nected astronomic stations.) All of the 



values of the earth 's figure now available are 

 the results of geodetic measurements in the 

 northern hemisphere and, with the excep- 

 tion of India, the measurements have been 

 confined to Europe and the LTnited States. 

 We may hope to get, before long, values for 

 the figure of the earth from geodetic oper- 

 ations in South America and Africa, most 

 of whose areas are below the equator, and 

 Australia, all of which is in the southern 

 hemisphere. It is believed that the mean 

 figures resulting from accurate and exten- 

 sive geodetic data in those continents will 

 agree closely with the figures gotten from 

 continents in the northern hemisphere. 

 The geodetic surveys of the several nations 

 on each continent should be connected and 

 the reductions made on one spheroid and 

 referred to a single initial position for each 

 continent. Should this be done we shall 

 be able eventually to compute a mean fig- 

 ure of the earth which will be of such great 

 precision that it will satisfy the most ex- 

 acting demands of science. The same 

 spheroid and datum have already been 

 adopted by Mexico, Canada and the United 

 States.- 



Coincident with the extension of geodetic 

 surveys there will be carried on the com- 

 putation of the geoid or the actual surface 

 of the earth. This surface is probably so 

 complex in shape that the work necessary 

 to define it will have to be continued long 

 after the satisfactory spheroid has been 

 determined. 



The geoid may be defined as that surface 

 which coincides with the surface of the sea 

 at rest. We can imagine an extension into 

 the continents of an intricate network of 

 sea-level canals. Then the surface of the 

 oceans and the water in the canals would 

 define the surface of the geoid. At some 



2 See news note in Bulletin of the American 

 Geographical Society, August, 1913, page 614, on 

 ' ' The Adoption of the North American Datum. ' ' 



