528 MR JOHN ALLAN BROUN ON THE HORIZONTAL FORCE 
32. An examination of these numbers and the corresponding curves will show 
in each case that there is an annual period of horizontal intensity, consisting of 
two maxima and two minima—the maxima near the solstices, the minima near 
the equinoxes; the principal maximum being sometimes at the December solstice, 
sometimes the June solstice. The most marked minimum in the pairs of years 
has been in September or October. 
33. When we examine the observations, especially the daily means, it will be 
obvious that the exact epochs, as well as the values of the maxima and minima 
for different years, depend greatly on the disturbances: if these are greater near 
the winter solstice than near the summer solstice, as they generally are, the winter 
maximum will become less marked than it ought to be, since the principal dis- 
turbances are negative at all places. 
34. I have calculated the constants for the annual curve at Makerstoun and 
Hobarton from the monthly means for the four years July 1844 to June 1848 
(the longest period of years at Hobarton without any break in the series of obser- 
vations), by the formula, 
y=a,+4, sin (+c¢,) +a, sin (2 6 +¢,)+a, sin (36+ ¢,), - , : ‘ Ci) 
The resulting equations are (= 0, July 16), 
Makerstoun, 
y= 5°20 + 1-66 sin (0 + 161° 47’) + 2:98 sin (204 129° 34’) + 0°80 sin(304+31°42) 2.) 
Hobarion, 
y= 4:90 + 1-64 sin (8+ 217° 38) + 2:54 sin (24 + 129° 11’) + 0°45 sin(304+172°46’) 3.) 
—the values of @ being in ten-thousandths of X at the respective places. 
35. If we consider the partial curves we find, 
Makerstoun, the maximum May 4; the minimum Nov. 3. 
Hobarton, ss Mar. 9; Be Sept. 8. 
It should be remembered that the Hobarton result is derived from hourly observa- 
tions, whereas at Makerstoun in 1846-7-8 there were only a few observations 
daily (see 16 ; foot-note). 
36. The annual period from the partial curve at Hobarton has its maximum 
near the March equinox and its minimum near the September equinox. This, 
however, is not satisfied at all times, since in some cases the spring minimum of 
the whole variation is as marked as that in autumn. 
37. For the double curve at ( the maxima are June 29, and December 26. 
Makerstoun and Hobarton, the minima are March 27, and September 25. 
This is the most important movement; the coefficient is about one-seventh less at 
Hobarton than at Makerstoun, but the epochs are the same at both places. This 
curve at both places has its maxima a few days after-the solstices, and its 
minima a few days after the equinoxes. 
For the single curve at 

y 

