MAGNETIC INCLINATION AT GOTTINGEN. 635 
justment had been rectified with the greatest care by the aid of 
the apparatus mentioned in Art. 5, we obtain eight different 
determinations of a, namely, 
al 34il 
28 
29 
50 
Sil 
50 
34 
16 
The sum of the squares of the differences from the mean value 
of 2' 56" expressed in seconds, is=57214; if then we regard these 
differences as wholly accidental, we obtain the mean error of the 
57214 
7 
woowrrh RYE we WD 
result of a pair of coordinate positions = ve =90!'"4. We 
see that with this instrument the anomalies of position are much 
more considerable than the mere errors of reading. 
12. 
It is however otherwise when the supposed exact adjustment 
of the supports has not taken place. If we assume the surfaces 
of the agates to be indeed in one plane, but this plane not to 
be normal to the vertical axis, then it will be inclined to the 
horizon in opposite ways in the two positions of the instru- 
ment: it is however only the inclination of the planes in the 
direction of their surfaces, or parallel with the plane of the circle, 
which comes into the consideration, for a small inclination in 
the cross direction, or in that of the axle of the needle, has no 
sensible influence on the position of repose of the needle. Now 
let L denote that inclination of the needle (understood as above) 
which would take place with a perfectly horizontal support ; let 
8 be the corresponding directive force, i.e. the coefficient by 
which the sine of a deflection from the position of rest must be 
multiplied, to express the rotative moment of the force tending 
to bring the needle back to this position ; lastly, let L + 6 be 
the actual inclination in the first position with the inclined plane. 
It may then be easily shown that 
dsinB = ppsiny, 
where p denotes the weight of the needle, p the semi-diameter 
of the axles, and y the inclination of the planes to the horizontal 
