( 234 ) 
The value of 2 for which the equation (2) vanishes, lies therefore 
between 2.884 ... and 2.933, and the shape of this equation 
shows that it must le nearer to 2.933 than to 2.884. We find in 
fact, Ant 29252. 
With the aid of this value of 2, we may calculate the values of 
AGES ane ee Hot Ue equations of p. 230. But if the degree 
1—x—y Uy 
of approximation with which 2, is determined is not high, the 
coordinates of the point to which À, relates, are only known inac- 
curately. 
These coordinates however may be caleulated directly by means 
of the following equations : 
a,(1-w—y) FG tty a toll) Ha, ef, _5(1-w-y) Ha +a, Ui 
ba U ub at+b,y vb (1-a-y) +3, ab, ef bisll-e-y) dbs Hbey 
We obtain these equations when we determine the centre of the 
ellipse | 
Ary = A Dery 
and when we eliminate the quantity 4 from the equations /’, = 0 
and j’, = 0. So we find: 
_ (a, — U, Ja it sij) de (a,,—«, ) y 2 (4,,— Pigs 
bb) (le) + Ek dy + Uit, HP 
Ak (a, —d,3) (1—«—y) + (4,,— “3 yy + (ais a y 
TIE (1—«—y) En pre a y+ B b) y 
Introducing the condition, that the centre lies on the ellipse itself 
we get the given equations. 
bb, ee b. +0, 
In the case that 6,, = ——, b,,= Bs. and b,, =——— 
equations may be satisfied approximately, then the locus of the centres 
is greatly simplified and may be written as follows: 
(a,—a,,)(l—«—y) + (a, 2a, )u+(a 1s— 4 My ER 
ich 
bk 
(a,—a,,)1 — &—Y) Ha, dp) (413 — 45) ¥ 
oi b,- 6, 
It is therefore a straight line, at least in approximation. With the 
given numeric values we find: 
0, 6(1—a mil 280 +0, 2076 — 1,1(.1—x—y) +0,70762+0,528y 
0,2 0,6 
