Deke ae lcm lalaalda 
and Directive Force of the Magnetic Needle. 209 
In what precedes the law of variation of the angle included be- 
tween the ecliptic and meridian, from one hour 
to another, or from one season to another at a be 
given hour, has been assumed. I propose now 
toestablish it. Let ER (Fig. 8) represent the 
equator, ES the ecliptic, and DSR a merid- 
lan; put ESR=S, ES=L, SER=»=234°. ° R 
Then 
cot # sin LdL tang L 
tang S= at d (tangS)= te 7 = cot o. —— ai. 
: ; tang L 
Thus the hourly variation of tang S is proportional to — 
For L=19, 119, 22°, 33°, 45°, 55°,°65°, 75°, 85°, d(tang S)= 
‘O17, +197, -436, -765, 1-41, 2°50, 5:07, 14-4, 131. The corres- 
ponding values of S are, 663, 66° 53’, 68° 3’, 69° 58’, 72° 55’, 
76°, 79° 35’, 83° 35’, 87° 5U’.. The variations of the angles cor- 
responding to the above variations of the tangent are as the num- 
bers 1, 11, 22, 33, 44, 53, 60, 64, 64. If the hourly variations of 
the obliquity of the ecliptic current, as one or another part of the 
i 
§ 
} 
; 
t 
BolensB50: 950 g50 age age 33° ae we 1° Eq. 
ecliptic is on the meridian, be represented by the ordinates of a 
cutve, we have a curve of the form shown in fig 9; nearly straight 
toward the solstitial point and again nearly straight in the vicinity 
and least at the equinoctial points. A curve showing the hourly 
change of declination that would result from the actual change 
of position of the current, would then differ from the prece- 
ing in being slightly more curved toward the solstitial point. 
The law of variation would be the same if we take apy individual 
ecliptic current, instead of the primary current (so called ) just con- 
sidered, for this does not depend on the value of the constant, cot #; 
it would also be the same for any single current taken as the rep- 
resentative of the ecliptic currents more remote from the equator. 
{ appears to me that the two laws recently made out by M. 
Secchi are deducible from the theory of ecliptic currents, taking 
Szoonp Saris, Vol, XIX, No. 56—March, 1855. 27 
