817 
In each of the two series of sums we can start with an arbi- 
trary constant. 
When the computations were carried out it appeared that always 
the values of dn summed up over a complete Saros gave a very 
small total, while the perturbation in longitude showed a very marked 
periodicity, with the Saros as period. 
Accordingly I have divided the total perturbation into two parts: 
‘the periodic Saros and the remaining non-periodie part. I call An, 
and A), the increase of the mean motion and the longitude during 
the pth Saros, if the initial constants for both series of sums are 
taken zero. The purely periodic part of the perturbation during that 
Saros is then derived by taking for the initial constant of the first 
series of sums — i.e. the initial value of the perturbation in n — 
1 1 
a value », determined from the condition i n, + AA =—0 (375 
is the length of the Saros in our units of time } The perturbation in 
longitude at the end of the pt. Saros is then: 
5 
Pp 4 | 
hy = Aly + St + 37 
k=) 
p 
pn, + XZ (pk) Ang 
k=l 
where An, and A}, are the initial constants of the two series 
of sums, i.e. the values of n and 2 at the beginning of the first 
Saros. Putting now 
1 
Ad; — A zin (A À)e : lied An, = Av is (Av)s, 
I 1 
Pe An, = —A,A+ mr Ar Hv, 
we have: 
1 
A, = A), + pr, + zr, v saa 5 nae At fae: a ke (A,»)x, (11) 
k=1 
which formula still contains two Se contants A), and »,. If 
ii 
for AA and A,» we choose the mean values of Ad; and 37 Ani, 
the terms under the signs = are small and of varying sign. The 
term containing p” is of the nature of a secular acceleration. If we 
denote the time expressed in centuries by 7, then p is equivalent 
to 5.55 1, or 3p? to 15.4 7’. 
The individual values of dn will be given in the second part of 
this paper. Table | contains the values of An, A2, A,y and A À for 
each Saros. 
