682 
STATISTICS: G. A. LINHART 
Proc. N. a. S. 
If we write 
where c is the constant velocity of Hght, and in accordance with assump- 
tion V require that (16) be satisfied by expressions approximating the 
coefficients in (17), we obtain = — ^-^ , — = 1 + 2(p], where h is 
a constant. Hence, if we take c = i , r = sin X2, which is a set of solu- 
tions of (18), we obtain the form (3). Another choice gives at once one 
of the forms found by Levi-Civita.^ 
^ Berlin Sitzungsherichte , 1915 (831). 
^Ihid., 1916 (189). 
3 Rendiconti dei Lincei (Ser. 5), 27, 1918 (350). 
4 Ann. Physik, 54, 1917 (117). 
5 Ibid., 56, 1918 (401). 
® Eisenhart's Differential Geometry, (449). 
7 Ibid., (157). 
A SIMPLIFIED METHOD FOR THE STATISTICAL INTER- 
PRETATION OF EXPERIMENTAL DATA 
By Gkorge a. IvINHArt 
Division of Soil Chemistry and Bacteriology, University of California 
Communicated by W. J. V. Osterhout, June 1, 1920 
One of the fundamental postulates of the law of probability of errors 
is that positive and negative errors are equally frequent and that, there- 
fore, the arithmetical mean is the most probable mean. This is true 
when we are dealing with small independent errors, but in cases of inter- 
dependent values of natural frequencies (physical, biological, agricultural), 
it may or may not be true, depending upon the maximum deviation 
from the mean. Thus we can conceive of a molecule of oxygen gas with 
a momentary velocity of zero or of "infinity."^ Yet the average velocity 
as determined from density and pressure measurements is but a few hundred 
yards per second, a value not very far from zero, but infinitely different 
from "infinity." When the frequencies of such data are plotted on rec- 
tangular coordinate paper, we obtain what are called skew curves. Within 
the last twenty -five years a great deal has been written concerning skew 
curves and their types, and, judging from the number which have thus 
far appeared in print, they promise to be of infinite variety. To these 
various types of frequency curves have been fitted mathematical formulas 
and with their aid statistical constants have been obtained, many of which 
we have reason to believe are theoretically inapplicable and practically 
misleading. 
