Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., sadlerian professor of pure mathematics in the University of Cambridge (Vol. 3)

where 12 is regarded as a function of r, v, y, or (as this may be expressed) where 
fl=il(r, v, y). 
If we neglect the disturbing forces, the planet moves in an ellipse; and taking 
a to represent the semi-axis major, the mean motion will be n. The mean anomaly, 
which I call g, will be a function of the form nt + c; but as c only enters through g, 
it will be convenient to use the mean anomaly g (considered as implicitly involving 
an arbitrary constant c) in the place of an element, and I write 
а, the semi-axis major, 
e, the eccentricity, 
g, the mean anomaly, 
б, the longitude of node, 
(f), the inclination, 
<D, the distance of pericentre from node. 
f, the true anomaly, 
z, the distance of planet from node, 
x, the reduced distance from node. 
We have then r and f given functions of t and the elements, viz. we may write 
r = a elqr (e, g), 
f= elta (e, g), 
(read elqr. elliptic quotient radius, and elta. elliptic anomaly). These values 
satisfy r = Moreover z, x, y, are the hypothenuse, base, and perpendicular 
of a right-angled spherical triangle, the base angle whereof is cf>; the equations which 
connect these quantities are therefore
	        
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