634 GAUSS’S OBSERVATIONS OF THE 
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The mean of the readings of the two ends of the needle gives 
us the angle between the straight line joining those points, or 
a line parallel thereto, and the zero diameter of the vertical 
circle. I subjoin these 16 means in pairs :-— 
End B a North Pole. 
Azimuth Marked face of Azimuth Marked face of 
circle. needle to the front. circle. needle to the back. 
°o ra fe} 4 “sh ° ‘ ‘ 4d 
90 5| 67 28 270 5 | 1i2 36 23 
180 5] 89 52 45 05] 90 12 
270 5| 112 17 48 | 90 5| 67 45 15 
0 5| 89 58 10 || 180 5| 90 11 30 
End A a North Pole. 
90 5 68 2 42 || 270 5| 112 6 20 
180 5 90 13 34 0 5 89 54 6 
270 5| 112 24 57 90 5 67 36 7 
0 5 90 15 8 180 5 89 51 24 
Those positions are here placed next to each other, in which 
the vertical circle faced in opposite directions, while the position 
of the axle of the needle relatively to the different quarters of 
the heavens was the same. The relation of two such numbers 
J and /' is a very simple one, when the supports are so adjusted | 
that a plane normal to the vertical axis of rotation is tangential 
to them. Assuming this, the axle of the needle is in both posi- 
tions in a horizontal plane, and the position of rest of the needle _ 
is evidently the same; that is to say, if we understand by L the — 
angle formed by the straight line drawn from the upper to the 
lower point of the needle with that horizontal radius of the 
circle which is cach time on the right side of the marked face 
of the needle, then L will have equal values in both positions. — 
But this angle in the first position will be 
=l—a, 
and in the second 
= 180° — (i! — a); 
a denoting the error of the zero point (i.e. the reading at that — 
radius which is at right angles to the vertical axis). Thus on the 
above-mentioned supposition we have 
=i(+/) —90° 
=1(0+ 180° — 7”). 
From the observations of the 23rd September, when this ad- 
Ss 
