MAGNETIC INEQUALITY AT HOBAETON. 
7 
The lunar-diurnal variation for these periods may therefore be respectively represented 
by the following formulae, in which the coefficients are expressed in seconds of arc, and 
a is reckoned in hours (multiplied by 15°) from the epoch of the moon’s superior culmi- 
nation. 
1841 — 1842 . , . A^= — 0-35 — 3-61 sin (a-f- 21’8)-}- 6-69 sin (2«+61-8). 
1843—1844 . . . A,= H-0-61+l-08sin(a+284-4)+10-7 sin (2«-f 43-6). 
1845—1846 . . . A,= + 0-26+5-14sin(«-l-339-2)-l-10-4 sin(2a-l-27-6). 
1847—1848 . . . A,= +0'32+2-7 sin(a+ 55-1)4- 7-7 sin (2a4- 65-0). 
Mean of the eight years A^= 4-0-254-0-98 sin («4-318-4)4- 8-75 sin (2«4-45'8). 
We may at once perceive, from the relative magnitude of the coefficient of principal 
significance (that of sin 2 ( 2 ), that the differences in the lunar -diurnal variation corre- 
sponding to different years show no conformity to the inequality manifested in those of 
the solar-diurnal variations. 
The curves severally corresponding to these formulae are shown in Plate I. fig. 2. for 
each of the four two-yearly periods. They exhibit such differences as are to be expected 
from periods of such limited dui’ation ; but the differences present no appearance what- 
soever of a systematic variation corresponding to the decennial inequality of the solar- 
diurnal variations. There are in each curve four extremes nearly equidistant from each 
other, two of which are easterly and two westerly extremes : if in each period we take 
the sum of the extremes, not indeed as an exact measure, but as furnishing an approxi- 
mate indication of the relative magnitudes of the respective variations, the periods 
arrange themselves in the following order : — 
1. 1843 — 1844. Sum of extremes 
2. 1845 — 1846. Sum of extremes 
3. 1847 — 1848. Sum of extremes 
4. 1841 — 1842. Sum of extremes 
y/ 
41-8 
41-6 
30-6 
28-1 
If we should prefer as a criterion of the magnitude of the variation, the sum of all the 
deflections at the different hours in the respective periods, we should have the succession 
as follows, taking the deflections as calculated by the formulae : — 
1. 1845 — 1846. Sum of deflections 
2. 1843 — 1844. Sum of deflections 
3. 1847 — 1848. Sum of deflections 
4. 1841 — 1842. Sum of deflections 
169-9 
165-5 
120-5 
113-4 
Or taking the deflections as actually observed at the different hours 
1. 1845 — 1846. Sum of deflections 
2. 1843 — 1844. Sum of deflections 
3. 1847 — 1848. Sum of deflections 
4. 1841 — 1842. Sum of deflections 
170-8 
168-3 
123-5 
117-6 
