OF THE EARTH'S MAGNETISM. 529 
38. If we consider the total curve as derived from the three partial ones, we 
find the epochs of maxima and minima as follows :*— 
Makerstoun. ‘Hobarton. 
Principal minimum , : October 1 : : : September 16 
Maximum : ‘ ‘ A December 22 . : 5 January 9 
Minimum i : , 5 March 6:5 P , F April 4 
Maximum : A ; : June 30°5 , , ; June 17 
For the total curve, therefore, we have as before the epochs of maxima near the 
solstices, and of minima near the equinoxes. 
39. The monthly means for the period 1842-45, as given in the last columns of 
Tables VIII. to XIL., have been projected in Plate XXIV.; from these we may 
conclude for the horizontal intensity,— 
1st, Makerstoun and Hobarton. 
Maxima in June and January. 
Minima in September and April. 
2d, Munich. 
Maxima in June and December. 
Minima in September and March. 
It should be remembered that Dr Lamont’s instrument is not a bifilar, but a 
* The usual method to determine the epochs of maxima and minima is to obtain by approxima- 
tion the roots of the equation to the maximum or minimum. The following method has been 
adopted by me for the computation of the above epochs :— 
Let the general term of the equation (1) to the curve be 
p;= 4, sin (16+ ¢,), 
and let 
gi=4, cos (16 + ¢;). 
If, then, we obtain an approximate value of @ for the maximum (or minimum) from the projected 
results (observed or calculated), and substitute this value in the above equations, and if « be the 
correction of the approximate value of 6 to the true value, we shall have 
hq: 
La dp! ? 

or, for a very accurate determination, 
1 
“= FZ3. <2, 
2°q; . Sip; 
D5. Sig. 


In the same way we may obtain the correction @ of the approximate epoch for the mean value of y 
from the equation 
and for points of contrary flexure, which ought not to be neglected in some cases, we have the 
correction «’ to the approximate epochs substituted as before in the values of p,, q; 
2 
Aes 2 
3°; 
These values are easily calculated with the aid of a table of natural sines to three decimal places for 
every 15’ of the circumference, and of a table of multipliers like Crexur’s, 
