Combined Motions of the Magnetic Needle. 
Ixxi 
motion, the magnetic dip, deduced from the observations of the bifilar magnetometer for the years 1842-6 and 
the balance magnetometer for the years 1843-6, has been employed to construct figure B ; the same declination 
being used as in figure A. For both figures the monthly mean values for the three magnetometers have been 
obtained from the curves (Plate VI.) passed freely through or among the projected points. 
149. From near the vernal till the autumnal equinox the annual motion forms the half of an ellipse whose 
major axis, passing at the vertex through June, makes an angle of about + 1 1° in figure A and of +16° in figure 
B with the projection of the magnetical meridian. At the autumnal equinox the north end of the needle again 
ascends till the winter solstice, after which it descends till the vernal equinox. In its descent, the north end of 
the needle having crossed its previously ascending path, it forms a loop which, when untwisted and continued 
downwards from the equinoxes, completes the ellipse ; the portion formed by the loop having almost exactly the 
same perimeter as that regularly formed when the sun is north of the equator ; the completed portion is indi- 
cated by dotted lines in figures A and B. It does not seem improbable that in southern latitudes the figure 
will be inverted, and that it will be a simple ellipse near the equator. 
1 50. Monthly Motions. — The motion corresponding to the moon's varying phase has not been projected, chiefly 
because of the irregularities still existing in the result of the four years' observations for the magnetic declina- 
tion, the epoch of minimum being ill -determined ; it is conceived that the figure is a simple ellipse with its 
major axis in the astronomical meridian, the northern exti-emity being at conjunction, the epoch of minimum 
dip, and the southern extremity at opposition, the epoch of maximum dip ; this, however, is doubtful. 
151. The motion for the moon''s position in declination has been obtained in the following manner : — Hav- 
ing first projected the means of magnetic declination for each three days of the moon's position in declination, as 
obtained from the Tables for the years 1843-6, the day after the farthest northerly position being the abscissa, 
a curve was passed freely among the points ; the values of the ordinates at the points of intersection by the 
curve were then taken as the interpolated values of magnetic declination for the corresponding abscissae : a 
similar operation was performed for the magnetic dip. In both cases very satisfactory curves, agreeing nearly 
with the true points, were obtained. These values are projected in figure C, Plate VI. From this figure the north 
end of the dipping-needle commences its ascent about two days after the moon is north of the equator, attains 
its highest point about two days after the moon is farthest north, and afterwards it descends till the moon is 
again near the equator ; thus forming a figure like a portion of an ellipse with its vertex about one day after 
the moon is farthest north, the major axis making an angle of about — 30° with the magnetic meridian. It 
will be remarked that so far this motion is quite similar to that for the sun's position in declination, with 
the .exception of the axis of the figure being on the opposite side of the magnetic meridian ; when we trace the 
figure farther the analogy still subsists ; — as the moon proceeds south of the equator the north end of the needle 
again ascends till the moon is farthest south, thereafter descending, and, in crossing its previously ascending path, 
a loop is formed lying partially out of the principal figure, as in the case of the annual motion. 
152. The correspondence of the two results gives a great weight to the accuracy of both ; this will be more 
evident when it is remembered, that the whole motion of the dipping-needle for the moon's varying declination is 
included by a small circle with a diameter of little more than one-tenth of a miyiute of space, and, that no obser- 
vation in the sixty thousand employed for this result has been rejected, however greatly affected by disturbance ; 
although the graphic interpolation to remove slight ii'regularities may be considered an equivalent operation. 
153. Diurnal Motions. — The monthly mean diurnal variations for the magnetic declination and magnetic dip 
in Tables 12 and 57, still present irregularities, especially from 10'' p.m. till 4^ a.m., the hourly positions for 
this time depending on only two years' observations. For this reason, the values from these Tables having 
been projected, curves were passed freely among the points, and the interpolated ordinates thus formed, were 
taken for the projections in Plate VII. : the interpolated quantities diflPer very little from the actual values, 
and this is especially the case for the summer months. 
154. The diurnal motions for the 4 winter months November to February, are of the same class, and they 
differ considerably from those for the other months (see Plate VII.) ; in each of these months the motion 
consists of a figure of two closed loops : the north end of the needle moves eastwards with little change 
of dip from about 1'' p.m. till or 10^ p.m., after which it turns westwards, and begins to ascend about 4'^ a.m., 
crossing near its position at 6** p.m., thus forming an eastern loop, which is small compared with the western 
loop, excepting in December. After 6*^ a.m., the north end of the needle having moved a little westwards, 
again descends, crossing a second time the afternoon track near 5*^ p.m., still moving westwards, it ascends 
about A.M. till it meets the position of I'' p.m., thus completing the western loop. The eastern loop 
is not formed in March, the north end of the needle not rising sufficiently high to cross the afternoon 
track. The change in the figure from February to March is very great ; in April and May the remains of the 
eastern loop are still visible, but in June and July its position is indicated by a simple inflection in the figure ; 
in August and September the germ of the eastern loop becomes mere distinct, and in October the loop is 
actually formed. The transition in form from autumn to winter is quite gradual, unlike that from winter to 
MAG. AND MET. OBS. 1845 AND 1846, 
