506 
ON THE LUNAR-DIURNAL MAGNETIC VARIATION AT TORONTO. 
and wholly insignificant exceptions. The reality of the variations is thus attested 
no less by the accordance of the results when the whole period during which the 
phenomena were observed is subdivided into separate and independent portions, than 
by the systematic character which the Variation is seen to possess when the strictly 
independent results at the several lunar hours are brought together and exhibited 
continuously. 
As it happens that in the declination the variation lesulting from the moon’s action 
is greater, relatively to the instrumental means for measuring it, than either in the 
inclination or in the total force, it is reasonable to conclude that we have a better 
opportunity of judging of the particular nature and character of the noon’s mag- 
netic influence, by studying the effects produced on the declination than those pro- 
duced on either of the other elements. 
Referring to the Table (Table IV. p. 503) which exhibits the coefficients of all the 
twelve terms in the formula of sines and cosines by which the results of observation 
are strictly represented, we perceive that the coefficient of the cosine of twice the 
hour-angle is not only the one of greatest account, but is in fact the only one which 
we can with confidence regard as possessed of a substantial value. All the other 
coefficients are, without exception, not only extremely small in comparison with the 
one above noticed, but are so small, that they may well be supposed to represent such 
small deviations from a natural law as may well be ascribed to errors which cannot 
wholly be extinguished in averages derived from not more than six years of observa- 
tion. On the other hand, the coefficient in the second term has a value far beyond 
any explanation resting on the supposition of errors of observation. The probable 
error at any single hour is l"’37, whilst the range of the variation is not less than 38". 
Whilst, therefore, the general result of this investigation is to establish conclusively 
the existence of a lunar-magnetic influence sensible at the surface of the earth, the 
lunar-diurnal variation which is thus manifested appears to be consistent with the 
hypothesis that the moon’s magnetism may be, in great part at least if not wholly, 
derived by induction from the magnetism of the earth. 
It is further observable, that in the lunar-diurnal variation there is no appearance 
of the decennial period which constitutes so marked a feature in the solar-diurnal 
variations. 
