CHANGE IN DIRECTION OF EARTH’S MAGNETIC FIELD. 271 
Having found an approximate empirical equation with an 
assumed value of the period of the cycle and computed a 
table of differences between the observed and computed 
values, I differentiated the equation and obtained one of the 
form: 
dl — dA + sm - t. dB + cos - 1 . dC 
m m 
360 ( -q 360° . n . 360° , \ , 
— — r ( B cos - t — C sm -- t ) dm, 
m \ m m J 
in which m represents the assumed period, t the interval of 
time of observation from an assumed epoch, and A, B, and 
C the constants of the approximate empirical equation. 
A series of conditional equations were then formed by put¬ 
ting for dl the successive differences between the observed 
and the corresponding computed values from the approx¬ 
imate equation and the corrections dA, dB, dC, and dm to 
the constants of the empirical equation were then found by 
the method of least squares. 
The present work is devoted largely to the southern hemi¬ 
sphere, with reference to which I am not aware that any sim¬ 
ilar extensive investigations have been made, and its field is 
altogether outside of the United States and Europe, concern¬ 
ing which data have been made abundant by the observa¬ 
tories and by the labors of Mr. Charles A. Schott, Mr. Louis 
A. Bauer, and Mr. Henry Gannett. 
Having accomplished my object with reference to the sep¬ 
arate use of the investigations concerning the declination and 
the inclination in their practical bearing upon navigation, 
I have endeavored to support the general effort of the geo- 
magneticians of the day by putting the available data 
relating to the secular change of the earth’s magnetism 
in the form already employed by Bauer,* Schott,f and my- 
* Beitrage zur Kenntniss des Wesens der Sacular-Yariation des Erd- 
magnetismus, von Louis A. Bauer. Berlin, 1895. 
t Secular Variation of the Earth’s Magnetic Force in the United States 
and in some Adjacent Foreign Countries, by Charles A. Schott. Appen¬ 
dix No. 1, U. S. Coast and Geodetic Survey Report for 1895. 
