(148 ) 
it will suffice to consider only the nutation of the ideal 
unyielding Earth, although IT shall draw attention in 
passing to the modifications to be introduced in order to 
allow for the elastic yielding of the planet. 
When P, the place of observation, lies near the circle 
described by F, the instantaneous axis, the oscillations of 
the astronomical about the geographical meridian will 
be large; and when it is inside the circle the astrono- 
mical meridian will describe a complete cireuit relatively 
to the geographical meridian, but with variable angular 
velocity. 
The linear dimensions of the circle or curve described 
by the instantaneous axis are actually excessively small 
compared with the Earth’s radius, and it is not likely 
that observations will be taken within a very short 
distance of the pole, yet when we are endeavouring to 
secure the highest possible accuracy in astronomical 
observations the oscillation of the astronomical meridian 
ought to be examined. 
It 1s clear that in discussing this subject the preces- 
sion and forced nutations, due to the attractions of the 
Sun and Moon, may be omitted and that we need only 
consider the free Eulerian nutation. We have then to 
determine the position at any time of a system of rectan- 
gular axes fixed in the Earth relatively to a system of rec- 
tangular axes fixed in space. The axes fixed in the Earth 
will be C the geographical north pole and a pair of 
mutuallv perpendicular axes A, B in the geographical 
equator. Since ex hypothesi the system moves free from 
the action of external force, we may take the axis of resul- 
tant moment of momentum as axis of Z fixed in space, 
