approximation. So we shall have to find in the equations (2) which 
terms give rise to the failure of the application of the method of 
consecutive approximations. These terms we shall have to include in 
the abridged equations, serving to determine the first approximation. 
We shall consecutively discuss the cases: 
5 = 3 (2«, = n 2 + Q ), 5 = 4 (Sn, = n, + c ,) t 5 = 2 («, = + *,). 
S = 3. 1 ) Strict relation. 
$ 4. We suppose q — 0; therefore 
n 2 = 2 « t . 
In the equations of motion appear for the first time among the 
terms of order h' terms which, according to what was said in $ 3, 
must be included in the abridged equations. They are: in the first 
equation 2 d 2 xy, in the second d t x\ These are the most important 
among the terms referred to. Omitting the remaining terms of higher 
order we therefore have to consider: 
a: +n * a -\-2d t xy = 0,\ 
V + y + d t ar 8 = 0 . 1 
We may also write this system as follows: 
•• , , , dR i 
y + 0; 
1 which: 
To this 
R — d t y. 
apply the method of the variation of the canonical 
constants. This means, asMs known, that the equations, arising 
when the terms ^ and ~ are omitted, first are solved; in which 
solution 4 arbitrary constants appear; we then investigate what 
funchons of the time must oe the quantities just now regarded as 
constants, so that the expressions for ^ and y, taken in this way, repre¬ 
sent the solution of the complete equations containing ^ and - The 
...an d * 
which — and — are lacking, are solved according to 
') In a following paper we shall discuss the 
