between the magnetic declinations of 8 a.m. and 1 p.m. does not contain (apart from the irregular anomalies and the secular decrease) any very important fluctuations dependent on season; at least there is no certain indication of any such difference between the summer and winter months.
The mean declination itself, deduced from the observations of the three years, is 18° 37′ 56″·9 for the 1st of October, 1835; meaning, of course, thereby, only the mean value of the hours chosen for our observations, from which the mean value of all hours of the day may perhaps differ a little, though probably but little. But all our previous researches abundantly show that without very long and wearisome labour nothing can be fixed with certainty respecting this.
Hitherto we have spoken only of monthly mean numbers. The complete publication of the separate observations would for the present be regarded as superfluous, since, being confined to one place, they present no interest but that arising from the irregular fluctuations which they display. This end may however be attained in a better manner than by the mere view of the numbers, by a methodical combination, in which the amount of the fluctuations is reduced to a definite measure, and the general character of the periods, in respect to the magnitude of the fluctuations during them, may be accurately compared. For the sake of precision, I understand here by fluctuation of the magnetic declination, the difference from that of the preceding day at the same hour; and, (according to analogy with what are called mean errors of observation,) I understand by mean fluctuation, during any given interval of time, the square root of the mean of the squares of the several fluctuations. It must here be remarked, that when several equal intervals, or intervals considered as equal, are united in one, the arithmetical mean of the partial mean fluctuations must not be taken as the general mean, but we must revert to the squares, and take the square root of their arithmetical mean. The results of the three years' observations, calculated in this manner, and expressed in seconds, are contained in the following table:
