628 GAUSS’S OBSERVATIONS OF THE 
tions of the vertical circle nearly perpendicular to the magnetic 
meridian : the differences found were always quite unimportant, 
showing that the auxiliary needle is sufficiently sensitive, and 
that it produces no constant deviation. A small deviation of the 
vertical plane in which the observations are made from the 
magnetic meridian, which, be it remembered, is not altogether 
invariable during the observations, has, on the dipping or inclina- 
tion needle, only an influence of the second order, which may 
be regarded as insensible. 
rod 
f: 
The coincidence of the centre of gravity of a needle with the 
axis of rotation can be effected only approximately even by the 
most skilful artists: there almost always remains a deviation, the 
influence of which, on the position of the needle, is sought to be 
determined or eliminated, by combining observations made under 
circumstances varied in several respects. Among these artifi- 
cially varied circumstances, a principal one is the reversal of the 
poles of the needle. Other circumstances being equal, the in- 
fluence of the above-mentioned deviation is the stronger the 
weaker the magnetism of the needle ; and, as we are not justi- 
fied in assuming this magnetism to be of equal strength before 
and after the reversal of the poles, an exact reduction of the ob- 
servations becomes dependent on our knowledge of the relative 
amount of force. This is obtained by observing the time of 
vibration of the needle; but I have, for several reasons, em- 
ployed, by preference, horizontal vibrations, and have used in 
this observation a particular apparatus made by M. Meyerstein. 
The needle oscillates in a wooden case with glazed lids, and is 
supported by a light stirrup suspended to a silk thread 270 mil- 
limetres in length, and protected from the air by a glass tube: 
scales at either extremity of the needle comprise each forty 
degrees, and are divided to half degrees: five minutes can be 
estimated with certainty. ‘The time of vibration of the needle 
is always determined before and after the reversal of the poles 
by 150 vibrations divided into three sets, which, after a proper 
reduction to infinitely small arcs, always give extremely accord- 
ant results. The commencing are was usually about thirty-six 
degrees ; and it is deserving of notice, that, contrary to our ex- 
perience with heavier bars (Resultate, vol. ii. p. 70), the rate of 
decrease of the arc is almost the same on all days and with all 
needles, so that the time within which the arc was reduced to a 
