194 
[582 
582. 
NOTE ON THE THEORY OF PRECESSION AND NUTATION. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxxv. (1874—1875), 
pp. 340—343.] 
We have in the dynamical theory of Precession and Nutation (see Bessel’s Funda- 
menta (1818), p. 126), 
C d { t +(B - A) qr= IS (x'y- xy') dm' (1 - i). 
A Tt+< c - B "> v p = LS - y*') dm ' (I* - p) • 
J> Tt +{A ~ 0 ' n = / '‘ S< h ' x _ ,lm ' (^« - p) • 
where L is the mass of the Sun or Moon, x, y, z the coordinates of its centre referred 
to the centre of the Earth as origin, 
r = fx 2 + y 2 + z 2 , 
the distance of its centre, and 
A = f(x — x') 2 + (y - y’) 2 + (z- z') 2 , 
the distance of its centre from an element dm', coordinates (x', y', z') of the Earth’s 
mass, the sum or integral S being extended to the whole mass of the Earth—I have 
written dm, r for Bessel’s dm, r 1 —, we have 
. A 2 = r 2 — 2 (xx + yy' + zz') + x' 2 + y' 2 + z 2 ; 
and thence 
N? - = % ( Ͼ> + yy' + zz ') - f iV + y 2 + z ") O' 2 + y' 2 + z>2 ) - 5 (oox' + yy + zz') 2 } + etc.