jj cme 8) Ve 
i 607, 607, 
tente! pent tate Be geese 
es 60 1, ae 607, 
Gees NEK) 
oe 720 ZO) 
In the remainder which belongs to this expression for 7,, the term 
of the 5 order : 
4 LZ, (t,{—1,° tt —t, Tr), (t,—T,) 
will vanish if 7, = 0.5806 ae ees the em can never vanish 
at the same time for 7, and for 7, 
jb fficient of ihe developnaty nn 
[, occurs as coefficient of 7, in the development of ——————— 
2 triangle P, VTA 
in ascending powers of T—=k(t‚—t), while K, indicates the coefficient 
ae . ees TAI , 
of t° in the development of ———_——\. where the variable rt 
triangle P,ZP,’ 
means Á (t—1t,). 
If the first of these developments were performed in powers of 
k (t—t,) = — t, there would exist between each pair of corresponding 
coefficients a relation implying that its sum with regard to +, would 
be of one order higher than the coefficients themselves. Therefore, 
neglecting terms of higher order than the 5'", we may assume that 
the coefficients A, and £, are identical in absolute value, yet differ 
in sign. 
Of a similar relation I have made use on p. 755, where in the 
remainders of the 4" order I assumed the coefficients identical. In 
the new expressions for 7, and m, we can now, by putting 1,=—A,, 
derive the following value for the remainder of the 5" order of n,--n,: 
4K, 1,1,T, (t,—7,) (2t,? + 7,7,). 
Therefore when the intervals of time are equal, the error in 
n, +n, is of the 6% order. 
If according to the indicated method we include the terms of the 
4th order, we find for the 3'¢ relation nst = 
triangle P, ZP, ny 
mee ite As i22 + Banes + Car2228 
ny (Aes eB ee Asen 
and with it as Sue of the 5 order 
> aa) 
NT 
+ 4 K, = aa (Gan aE t,t = Tet + CeCe -++ Te) 
From one of the ae from Gauss’ Theoria Motus (Libr. II, 
Sect. 1 ce. 156—158) 1 have computed the 3 relations according to 
the formulae 1, II and III. The rigorously correct values of those 
