630 GAUSS’S OBSERVATIONS OF THE 
needle deviating considerably from its axis of rotation. Each 
of the sixteen numbers may of course be itself the mean of a 
greater or less number of readings, obtained by raising and 
lowering the needle repeatedly in each combination. 
The method which I followed differed from the above, inas- 
much as I observed each day with two needies without inverting 
the poles as usual during the observations: the inversion of the 
poles took place between two successive observations, and alter- 
nately always with one neeedle only. It is obvious that in this 
manner the observations of four days comprise all the combina- 
tions of the different changes of poles with both needles. 
Needles 1 and 3 were observed in this way, July 6 to 9, and 
needles 2 and 4, July 17 to 20. A continuation of similarly 
combined alternations during eight days of observation, with 
needles 1 and 2 from May 20 to June 5,and with needle 3 and 
4 from June 5 to June 8, gave therefore each combination with 
the direct and inverted poles twice. The observations on each 
day were arranged so that the results of the two needles should 
be as nearly as possible simultaneous. With this view the four 
combinations above mentioned were first observed throughout 
with one needle, which was raised four times in each; the second 
needle was then observed in the same four combinations, raising 
it eight times in each; and, lastly, the first needle was again 
observed in the same combinations, but repeated in the reverse 
order, and the needle raised four times in each. 
In this arrangement the observations of a single day taken 
alone do not give any determination of inclination; but when 
the observations of the following day are combined with them, 
it is clear that the needle, which has not had its magnetism in- 
terfered with, will show how much the inclination differed on 
the two days, and the one-sided observations with the other 
needle can be thus reduced to one epoch, and so be completed. 
With a view to a more rigorous treatment, comprehending the 
totality of the observations for all the twenty-four days, it will 
be necessary first to investigate more closely the mutual re- 
lations of the partial results. 
4h 
This development, which is important in more respects than 
one, may be most conveniently connected with an example taken 
from an observation made in the usual manner, of which I have 
made some on several days. 
ea a 
