624 GAUSS’S OBSERVATIONS OF THE 
180°; an uninterrupted reading from 0 to 360° would be more 
natural and convenient, and the readings are so expressed here. 
A space of one millimetre on the level corresponds to an inclina- 
tion of 9 seconds. 
2. 
The instrument has four needles, which I distinguish as 1, 2, 
3, 4, of which 3 and 4 have revolving axles, an arrangement to 
be spoken of in the sequel. A microscopic examination and 
measurement showed no sensible difference in the thickness of 
the eight terminations of the axles, which was found to be 
= 0'590 millimetre. Needles 1 and 2 weighed each 16°5 
grammes, and the other two each 20°5 grammes. 
Small differences were found in the lengths of the several 
needles. They measured respectively 
Needle] . . . . 240°931 millimetres. 
OPI verbs bs > 240°866 
OMe Savin via: 62205938 
4 ; 240°954 
The shortest of the needles is therefore only 0°303, and the 
longest only 0°215 less than the diameter of the circle. This 
circumstance is favourable to exact reading, but at the same 
time it renders a very small excentricity capable of disturbing 
the free movement of the needle, making it difficult to adjust in 
a perfectly satisfactory manner those parts of the instrument on 
which the excentricity depends, the adjustment having also to 
satisfy four other conditions, making in all siz conditions. 
3. 
These six conditions are the following :— 
The two agate planes, on the upper surfaces of which the 
cylindrical terminations of the axle rest during observation, are 
to be adjusted by the supporting screws in such manner that — 
1. Their upper surfaces may be in the same plane. 
2. That this plane may be perpendicular to the plane of the 
vertical circle. 
3. That it may be below the centre of the vertical circle, a 
distance equal to half the thickness of the cylindrical termina- — 
tions of the axle. 
4, That the line of intersection of the two planes above- 
mentioned may form a right angle with the vertical axis. 
Further, the Y’s by means of which the needle is raised off © 
