MAGNETIC INCLINATION AT GOTTINGEN. 659 
observations with each of the four needles (and we have no rea- 
son to depart from this supposition), the mean uncertainty of a 
value of (f+ g) or }(/’ +g’), as found from the observations 
and subjected to our calculations, is, as far as we can form a 
judgement from our numbers, 
9 
ks =] 24389 _ gons, 
if we speak only of accidental or irregular errors of observation. 
The mean of two such numbers, founded on observations inde- 
pendent of each other, is therefore charged with a mean uncer- 
tainty nk yg easier > 
> 
and this may also be regarded as the mean error of an inclination 
determined in the usual manner (i. e. with one needle in both 
positions of the poles), in as far as the small correction required 
for i(f+9+,/' + g') may either be regarded as quite insensi- 
ble, or may be based on an independent determination of wu or y 
(compare Art. 21.). Of course this valuation of the error applies 
only to the instrument under consideration, and to observations 
of which the fundamental circumstances are similar to these. 
With a less number of positions than eight in each combination, 
the degree of confidence due to the result would be less, al- 
though I would not choose to affirm the mean error of the final 
result to be in an exact inverse proportion to the square root 
of the number of readings after successive raising and lowering 
by means of the Y’s. 
On the other hand, I must not omit to notice that during the 
whole of the above observations the agate planes could not be 
adjusted as perfectly as I wished, and afterwards accomplished 
by means of the instrument alluded to in Art. 5. Any possible 
increase of the error of observation from an imperfect adjustment 
of the planes (wherein a constant amount of influence is the less 
supposable, because frequent alterations were made in the planes) 
is already included in the above number, and I have there- 
fore reason to expect that future observations with the same in- 
strument would rather show still smaller errors. It results from 
a separate investigation, of which I omit the details, that the 
mean uncertainty of the forty-eight inclinations in the preceding 
article does not differ much from the mean uncertainty of } (f+ ), 
and that nearly twice the weight, and consequently a mean error 
