626 GAUSS’S OBSERVATIONS OF THE 
seeing whether in the two positions the sharp extremities of the 
two ends of the needle project an equal quantity in front of the 
margin of the circle. In countries where the inclination of the 
magnetic needle is of moderate amount, the two positions may 
be obtained by a half revolution of the instrument, so that the 
plane of the circle shall on both occasions be near the magnetic 
meridian. 
For examining the second condition a similar method may be 
employed, only with the difference that it is two opposite nearly 
vertical positions which are required, one of which is given at 
once by bringing the plane of the circle nearly at right angles 
to the magnetic meridian, and the other must be obtained either 
by loading the needle suitably, or by reversing the poles. But 
it is easy to see that this method is only equivalent to that with 
the level before described, when the seventh condition is ful- 
filled; therefore, by combining the two methods a kind of test 
of the last-named condition is obtained ; a very imperfect one it 
is true, because the equal projection of the points of the needle 
in front of the limb of the circle can only be judged of by esti- 
mation. 
These combined positions of the needle serve also for exami- 
ning the two remaining conditions: the sivth condition is ful- 
filled, if each end of the needle in the first nearly horizontal posi- 
tion is at the same distance from the inner periphery of the circle, 
as in the second position. The same thing applies to the third 
condition in the two nearly vertical positions. It is evident that 
it would be sufficient for this examination, to compare with each 
other the distances of the two ends of the needle from the inner 
periphery of the circle in one nearly horizontal and one nearly 
vertical position, if the two halves of the needle were of exactly 
equal length ; but in our instrument, where the intervals are so 
very small, this is not sufficient ; even avery small inequality in 
the two halves of the needle would be sensible. 
5. 
The difficulty of satisfying in this manner all the conditions 
at the same time, is evident from the circumstance that the two 
screws on which each agate plane rests are only eight millime- 
tres apart, so that, as the width of a turn of the screw amounts 
to 0°283, a half revolution of a screw turns the agate one 
degree. 
