ON TERRESTRIAL GALVANIC CURRENTS. 
221 
© 
On constructing curves of each month, with the northerly and westerly tendencies for 
coordinates, it appeared desirable to eliminate some of the irregularities by a systematic 
process. The numbers in each ordinate, for any month, being arranged in order, and 
extended as necessary by repetition of the first terms of the series, the means of adjacent 
numbers were taken to form a second series ; the means of adjacent numbers of the 
second series to form a third series, and so on. This operation was repeated six times. 
It will be proper to examine the effect of this process upon periodical terms of different 
orders. 
The inequalities which we seek being essentially periodical with respect to one day, 
the expression for the inequality at the pt\\ hour may be expressed in the form 
+ <L cosine) 
+ b x sine 
cosine) , 
) i ro , { T ^2 cosine) _ - eo _ 0 0 
F Xl5 +{ + Mine P Xl5+ { + Mine ^ Xl5 + &C ' 
+ | + « cosine) ^ 
(+5, sine j 
Confining our attention to the cosine of the general term ; three successive terms in the 
series for hours, for the p — 1 hour, the p hour, and the jJ-j-1 hour, will be 
a n cosine {np X 15 °— n X 15°} 
a n cosine {np X 15°) 
a n cosine {np X 15° -\-n X 15°} ; 
then, taking the means of the adjacent terms, and again taking their means, we arrive 
by this double operation at the expression 
a n . (cosine {nxT 30'}) 2 X cosine {npx 15°}. 
And, repeating the operation six times, we obtain 
a n . (cosine {nxT 30'}) 6 X cosine {npx 15°}. 
The argument npx 15° remains unaltered; but the coefficient is diminished, not much 
for n— 1, but very much when n is large, as for instance, =8 ; which makes 
(cosine {nX 7° 30'}) 6 =- 6 1 4-. 
It appears therefore that the effect of this process is, practically to annihilate the 
advanced terms of the series, and to diminish the earlier terms in different degrees. 
And, when we have formed a smoothed series by the process described, and resolve it 
into terms depending on the arguments p X 15°, 2/jx 15°, 3/>xl5 0 , See., we must, in 
order to find the terms of the same kind in the original or unsmoothed series, multiply 
the terms found by the following factors : 
The first, by (secant 7° 30') 6 ; 
The second, by (secant 15°) s ; 
The third, by (secant 22° 30') fi ; 
and so on. And the effects of these ought, if possible, to be introduced into the curves 
which we may form, using the smoothed terms for ordinates ; an introduction, however, 
which will not in practice be easy. 
The two following Tables are formed by smoothing the numbers in Tables I. and II., 
by the process described above. 
MDCCCLXX. 2 G 
