678 
MATHEMATICS: L. P. EISENHART Proc. N. A. S. 
extraordinarily high values of solar radiation, but it has been not only a 
cold winter but a cloudy winter. Hence it may have been that the direct 
effect of the outburst of solar activity was to produce excessive cloudiness 
which by high reflection diminished the radiation available to warm the 
earth. 
In the preceding table I give the mean values of the solar radiation above 
mentioned. In each ijionth I have indicated the successive five day 
periods by the capital letters A, B, C, D, E, and F. The values given are 
the number of thousandths of a calorie by which the solar radiation of a 
given time interval exceeds 1.900. Thus, for the first period of June the 
mean value is 1.946. 
March Values. — On or about March 22, great sunspot activity was 
reported. On March 22 and 23 there were intense magnetic disturbances 
affecting all observations of terrestrial magnetism and the operation of 
telegraphs and cables. Remarkable auroral displays followed. In con- 
nection with these conditions it is interesting to note the very unusual 
progress of the solar constant of radiation during the month of March. 
This is given in the following table 
Date Mean, 11 to 17 18 19 20 21 22 23 24 
Value 1.968 1.954 1.940 1.931 1.941 1.927 1.866 1.905 
It is highly probable that the results just given will have a special 
significance in connection with the remarkable outbreak of solar activity 
to which attention has been drawn. 
THE PERMANENT GRAVITATIONAL FIELD IN THE EINSTEIN 
THEORY 
By Iv. p. Eisknhart 
Department of Mathematics, Princeton University 
Communicated by E. H. Moore, June 7, 1920 
1. In accordance with the theory of Einstein a permanent gravitational 
field is defined by a quadratic differential form 
1,. .4 
ds' = gikdXjdXk, {gik = gki), (1)- 
i,k 
where the g's, called the potentials of the field, are determined by the 
condition of satisfying ten partial differential equations of the second 
order, Gik = O. When the four coordinates Xi are functions of a single 
parameter, the locus of the point with these coordinates is a curve in 
four-space. If these functions are of such a character that the integral 
f^XgikdXidxk (2) 
