140 REPORT— 1899, 
We can now define 7 ; let 
n cos r=K cos '+ 3x, cos {(c—c,) v—T,} 
n sin w= sin '— 3x, sin {(¢c—c,) v—T,}. 
Thus 7 contains only elementary terms, and 
(e)=n cos {(1—c)v—7}. 
n is called the diastemmatic function, and (l—c)v—7z is called the dia- 
stemmatic argument. 
If in the expressions for the coordinates we strike out all the co- 
ordinated terms, leaving only those which are elementary, these modified 
expressions for the coordinates will define a new orbit, which will be so 
near to the true orbit that the difference between them will be only cf the 
same order of magnitude as the disturbing forces. This new orbit may be 
called the absolute orbit. The radius vector in the absolute orbit (r) is 
thus defined by 
a(1—n?) 
a =~ 
*) 1+(e) ° 
The variable z can be divided into two parts just as p was; thus 
2=(z)+Z, 
where (z) contains all the elementary terms ; (x) is of the form 
loa) 
(z)=7 sin {(1+7r)v—O} + >i. sin {(1+7,)v—9,} 
n=1 
where 7 (called the anastemmatic modulus) and © (called the longitude 
of the absolute node) are two more of the six constants of integration of 
the problem, and r, ¢,, 7,, ©, are constants depending on them. If this 
be written in the form 
(z)=J sin {((1+7)v—0}. 
J is called the anastemmatic function, and (1+7)v—Q is called the 
anastemmatic argument. 
Gyldén (who, however, is not in this particular followed by his pupil 
Harzer) further introduces a quantity ¢ called the reduced time, which is 
defined by the equation 
df at (1—n?)}, 
dv M? {1+( i 2 
and a quantity c 
W therefore satisfies the differential equation 
nie 148 
a =o Hy pee ies 
the integration of this will clearly introduce another arbitrary constant, 
