226 A. Hall— Variations of Latitude. 
mate solution of these equations, but it is sufficient for all 
the purposes of observations. , B, C, are the noe 
of inertia about the principal axes, and g denotes the latitude, 
the general expression for the latitude is 
P=P,t+p. cos} aS (fn) 9 tt& t, 
substitute the values of the moments of inertia, the expressiO® 
takes the following form in which the unit of time is a year: 
P=P, +p. cos (431°°0 . t+). 
i ‘ 10D 
Hence the instantaneous axis of rotation makes a revolutio 
around the principal axis in 805 days. : ai 
We have now to see what the observations have show 
regard to this periodical variation of latitude. The first caret 
: : : n 
Ertel vertical circle. These observations extend over thirtee 
p=0":079 + 0-017. 
ries 
A similar discussion was made by Nyrén of the three 
of observations made by Peters, Gylden and himself with © 
‘same instrument, and the results are, 
p=0"101 +4 0"-014, Peters, 1842. 
p=0 °125+4 0 020, Gylden, 1866. 
p=9 -0584 0 ‘015, Nyrén, 1872. 
