Page:Scientific Memoirs, Vol. 2 (1841).djvu/57

the final result is to rest on five partial results, we note the actual position of the needle for the six times:

$T-{\frac {5}{2}}$, $T-{\frac {3}{2}}t$, $T-{\frac {1}{2}}t$, $T+{\frac {1}{2}}t$, $T+{\frac {3}{2}}t$, $T+{\frac {5}{2}}t$.

If the divisions of the scale noted are called $a$, $b$, $c$, $d$, $e$, $f$, then ${\frac {1}{2}}(a+b)$ will be the result for the time $T-2t$; in the same manner ${\frac {1}{2}}(b+c)$, ${\frac {1}{2}}(c+d)$, ${\frac {1}{2}}(d+e)$, ${\frac {1}{2}}(e+f)$ for the times $T-t$, $T$, $T+t$, $T+2t$; and the mean of these partial results, or the fifth part of their sum, is to be taken as the corrected final result for the time $T$.

The detail of the observations in Göttingen, on the 17th of August, 1836, for 15^h 30^m may serve as an example. The observer was Dr. Wappäus. 20^s was taken as the value of $t$.

15h 29m	10	865·2	866·35
	30	867·5		866·85
	50	866·3	867·10		867·16
30	10	868·0		867·65
	30	867·3	867·90
	50	868·5

The first column contains the times of observation; the second the divisions of the scale noted; the third the means between each two successive notations; which are, consequently the partial results corresponding to 15^h 29′ 20″, 15^h 29′ 40″, 15^h 30′ 0″, 15^h 30′ 20″, 15^h 30′ 40″, and the final result to 15^h 30′ 0″. In this example the continual variation of the declination in the course of the observations is evident, and is also confirmed by the preceding and following results: which were

15h	25′ 0″	………	862·82
15	35 0	………	872·32

For the short time which this method of observation requires, it more frequently happens that the declination is nearly stationary throughout: when it is so, the greater or less deviation of the partial results from the mean serves as a sort of measure of the greater or less confidence due to the observations; whether depending on the degree of skill and attention on the part of the observer, or the goodness of the apparatus, or on more or less favourable external circumstances.

The method described is that which is followed by most of the participators in the term-observations. It presupposes the knowledge of the time of vibration of the needle, which, as is well known, is dependent on the magnetism of the needle, and on the intensity of the horizontal portion of the terrestrial magnetic force; so that, strictly considered, it is not quite