The nose whistler dispersion equation was numerically integrated using the following assumed functions for the electron density distribution:
(2) N = KR−3.
(3) N = KR−3 exp(3.03/R).
N is the electron number density, R is the distance from the earth's center, and K a constant of proportionality.
Several whistlers that were received at College on March 19, 1959, were analyzed to obtain electron densities. Each of these whistlers consists of a number of branches having successively lower nose frequencies. Measurements of the nose frequencies and the time of propagation of the nose frequency yield values of the constant K from which the electron density can be determined at any point.
It was found that the results for the first two functions disagree systematically with the curve of the assumed function. The third function, suggested by F. S. Johnson on the basis of theoretical considerations, fits the data well within the experimental errors. The resulting distributions cover the range between 4 and 6 earth's radii, giving densities varying from 20 to 5 electrons per cubic centimeter.