170 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
1866, and another in 1880; and Helmert in 1887. Clarke in 1866 also 
investigated the dimensions of the earth regarded as an ellipsoid hay- 
ing three unequal axes, using the same data as in determining the 
spheroid, and, as was to be expected, it satisfied the observations 
better than the spheroid. The compression of the Equator—which 
on this assumption is an ellipse of small eccentricity—was thus found 
to be 1/3,281, and the longitude of one extremity of its major axis 15° 
31’ KE. Another similar investigation made by Clarke in 1878 re- 
duced the compression of the Equator to 1/13,706 and made the longi- 
tude of an extremity of its major axis 8° 15’ W. The fact that the 
use of additional data diminished the eccentricity of the Equator is 
perhaps significant, showing that, disregarding local irregularities, the 
earth probably departs but little from the spheroidal form. 
Tt must not be inferred, however, that any spheroid or ellipsoid 
could ever be found that will exactly represent all observations. 
There will always be differences between the computed or geodetic 
positions of points and those found by astronomical observation 
greatly in excess of the errors of observation. ‘These differences arise 
from deviations in the direction of the plumb line, due to local irregu- 
larities of density of the matter composing the earth’s crust. 
An important improvement in the method of investigating the 
form of the earth was recently made by J. F. Hayford, of the United 
States Geodetic Survey, using the data of that survey alone. He 
made use of 507 astronomical observations of latitude, longitude, and 
azimuth, connected with their triangulations, and allowed for the 
attraction of the earth’s crust on the assumption that the condition 
termed ‘‘isostasy”’ exists at a depth of 114 kilometers. Three differ- 
ent assumptions of depth were made, but this gave the best results. 
His values were: 
a=6,378,283 meters, c= 1: 297.8 
The following is a tabular statement of some of the determinations 
of the elements of the terrestrial spheroid made during the nineteenth 
century and to date: 
| Length of Length of 
Years. By whom.% Cc. | meridian Years. By whom. c. meridian 
| quadrant. quadrant. 
155956 eIoe Delambre...} 1:334 10,000,000 || 1866.......-..- Clarke......- 1:295 10, 001, 887 
iets SSS eas 8 Walbeck....| 1:302.8 | 10,000,268 |) 1868.........- Fischer......} 1:288.5 10, 001, 714 
ISSOE ES see) aa Schmidt....| 1:297.5 | 10,000,075 || 1872.........- Listing...-..- 1:289 10, 000, 218 
USSU arcisistemeie U Nitin See 1:299.3 | 10,000,976 || 1878.......... Jordan.....- 1:286. 5 10, 000, 681 
SA teste merace Bessel....-.- 1:299.2 | 10,000,856 || 1880.......... Clarke..-....| 1:293.5 10,001, 869 
SSO bees oes ee Clarke......- 13298. 1 | 10; 001;,.515))|| 1887-25-22 Helmert..... 1:299.15 | 10,002,041 
NBGSHe e = F)-1-).\23 Pratt.o2..<--|, 13295: 3.,|., 10; 001,924 || 1906... ...-..-- Hayford..... Ie OOTSSpalsceoee ease < 
In addition to the method of determining the earth’s figure by 
geodetic measurements there are others that must be considered 
