1292 
determined by geodetic measures, which are practically all made in 
mean latitudes. 
The several definitions of the mean radius’) are identical to the 
first order of the compression ¢. I adopt as mean radius the radius 
at the geographical latitude whose sine is V/1/,, and which is given 
by the formula 
7, bl 4 ee eS EREN gee 
Hetmert has recently *) collected the following determinations of 
b, from which I derive the value of 7, by means of the corresponding 
value of «. 
1. From four European ares, all reduced with Besser’s €! = 299.15. 
h = 6378150 f= Garvie 
2. From ares in India and South-Africa, reduced with e—! = 298.3. 
b = 6378332 r, == 6371237 
3. From the geodetic measures in the United States, reduced with 
el A06 00: 
h = 6378388 r, = 6371268 
It will be seen that the agreement of the several values of 7, is 
much better than of 5. 
Combining these values of +, with the weights assigned by HELMERT 
to the corresponding values of 4, we find 
r=6871287 +49... U 
N 
The mean error has been derived from the residuals. If the values 
of h are combined in the same way we find from the residuals the 
mean error + 66. 
2. A similar reasoning applies to the acceleration of gravity. 
HELMERT *) finds 
g = 9.78080 {1 + 0.005302 sin? p — 0.000007 sin? 2g}. 
1) Hetmert, Höhere Geodäsie, 1, pages 64—68. 
2) Geoid und Erdellipsoid. Zeitschr. der Ges. für Erdkunde, 1913, page 17. 
5) Eneyelopädie der Math. Wiss.; Band VI. 1 B, Heft 2, page 95. The alternative 
formula given there, viz.: 
g = 9.78028 $1 + 0.005800 sin? g — 0.000002 sin? 2 gy} 
must be dismissed, since for theoretical reasons the coefficient of sin? 29 must be 
included between the limits —0 0000955 and —0.0000088. The theoretical expres- 
sion of the coefficient is + pe? — Jep — 432 By, where B, is necessarily positive, 
and smaller than = J. Taking « = 0.00338, « = 0.00345, J= 0.00165, we find 
the stated limits. The value of the coefficient in the formula of the text corresponds 
to DARWIN's value of B4 viz; 0.0000029, 
