MAGNETIC VARIATION AT TORONTO. 
505 
In fig. 5 the darker line represents the defleetions in Table VI., constituting the 
lunar-diurnal variation derived from the mean of the six years ; and, for the purpose 
of showing the accordance of the results when the whole period of six years is divided 
into three portions, each consisting of two years, viz. July 1842 to June 1844, July 
1844 to June 1846, and July 1846 to June 1848, the curves for each of those periods 
have been computed by the subjoined formulae, obtained from the values in Table IV., 
and are represented by the fainter lines in fig. 5. The formulae are, — 
1842 to 1844 A^=+0"-41— 2"-09sin (a+291°)— 18"T sin (2a4-87°7), 
1844 to 1846 A^=+0"-30+3"-04sin (a + 78°7)+20"-6sin (2a + 270°T), 
1846 to 1848 A^=— 0"-58 — 5"-23sin(a+53°-5) + 18"-9sin (2a+276°T). 
The number of hourly observations employed in the investigation of which this 
paper contains the results, is, of the Declination 40543 ; of the Horizontal Force 
34303; and of the Vertical Force 31773; making in the whole 106,619 observations. 
General Conclusions . — The three magnetic elements concur in showing that the 
moon exercises a sensible magnetic influence at the surface of the earth, producing 
in every lunar day a Variation in each of the three elements, which is distinctly ap- 
preciable by the instruments employed in the Observatories established to carry out 
the system of observations recommended by the Ptoyal Society, when due care has 
been taken in conducting the observations, and suitable methods are adopted for 
elaborating the results. 
The Variation in each of the three elements constitutes a double progression in each 
lunar day: the declination has two easterly and two westerly maxima in the interval 
between two successive passages of the moon over the astronomical meridian ; and 
the inclination and the total force have each two maxima and two minima due to the 
moon’s action in the same interval ; the variation passing in every case four times 
through zero in the lunar day. The easterly maxima of the horizontal deflection 
of the north end of the magnet synchronise with the moon’s superior and inferior 
passages of the meridian; the westerly maxima with the lunar hours of 6 and 18. 
The maxima of the increased magnetic force due to tiie moon’s action occui‘ about 
the lunar hours of 3 and 16, and the minima about the hours of 9 and 20. The 
maxima of the inclination, i. e. of the dip of the north end of the magnet, occur about 
the lunar hours of 3 and 14, and the minima about 9 and 20. The extent of the 
Variation in the lunar day, or the range between the extremes that are widest apart, 
is in the Declination 38"’33, in the Inclination 4"'4, and in the total Force *000012 
parts of the whole terrestrial magnetic force at Toronto. These are the values derived 
from the whole period of observation, i. e. from six years of the Declination and from 
five years of the Inclination and total Force. When the whole period is subdivided 
into two half-periods, the hours of maxima and minima and the extent of the range 
accord with the results of the whole period in each of the three elements, with slight 
