636 GAUSS’S OBSERVATIONS OF THE 
line ; the latter quantity being positive when the agate support on 
the right side of the marked face of the needle is the lowest. 
But it is now evident that in the second position — y must be 
put instead of y, whereby 6 passes into — 6; hence in this 
second position the inclination of the needle will be L — 6. We 
have thus 
l—a=L+ 8 
180° — (/ -~a)=L—6; 
and consequently, as in the preceding article, 
L(+ 180° =?) = L; 
on the other hand, in lieu of the other equation in that article, 
we have now 
2(¢4+ 7) —90°= a4 86. 
But if the surfaces of the agates are not in one plane, these 
two formule will still be sufficiently exact, if we only take for y 
the mean of the inclinations of the two sides, assuming the 
centre of gravity of the needle to be nearly equidistant from the 
two points of the axles which rest upon the agates. Strictly 
speaking, there is still a small modification, arising from the cir- | 
cumstance, that in the case supposed, the straight line joining — 
the two points of contact of the axles and the supporting planes 
has not quite equal azimuths in the two positions; but the 
influence of this circumstance on the direction of the needle 
may be regarded as quite insensible even where it is greatest, 
namely, in observations made in the plane perpendicular to the 
magnetic meridian. 
13; 
It may not be uninteresting to show, when the adjustment of 
the planes is not perfect, how far their inclination affects the — 
position of the needle ; I therefore subjoin what is still wanting 
for this purpose for the needle employed on the 23rd of Septem- — 
ber. With a view to determine the moment of inertia of the — 
needle, I had previously observed its horizontal vibrations, both F 
with and without the super-imposition of a ring, the moment of — 
inertia of which could be calculated with sufficient exactness — 
from its weight and dimensions. On the 21st of September the 
time of vibration was 
Without the rmg. . . 5:°88431 
With thering . . . 7°32835 
Weight of the ring . . 19°2385 grammes. 
