STEINElt’s EXTENSION OF MALFATTl’s PROBLEM.
75
£ + £+e ( v + 2&%) {V& (^+o -/(17+2 eg)} = o,
! + C+0(i7 + 2^)-^LtfO/i _
&X
Va
Va -f a,
r=0;
these may be written
¿£ + i¥77 + i\r£=:0,
X'f + M' v + N'£= 0,
where
£= 1 + 2№-^+5(Va-2«/). if=fl + ^V a + a J = I _^Va + a jVgr
V P,7, V/S,7, V/S, 7 ,
X' = 1+2№ _«£Ö±M(' 1 _
Va.
£,X
Va + a.
, Jf = 0
, ^ = 1;
or since £, £ are equal to 1, Y + Z, YZ respectively,
1 : Y+Z : YZ= MN' - M'N: NL' - N'L : LM - L'M
- - i2 ^ )(/+(?VS)
^/7/
Va + a/ V/8/y,
(*+5 - Ä</+■'*>
^x
Va + a/ V/8/y,
Also
whence
F + £
F£
/• + <9Vgt = ^ 7 = —
/+ ^ K fry,’
2 V2 V«T^ V/^xA _ V2 Va + g,^ A _
_ 2^2 Va+a, Vft/y, A, V2 Va +
K V V/3/y, / v
V a / N
Va + a/
Va, \
Va + a/
and by forming the analogous expressions for Z + X and ZX, X 4- 1 and X Y, the
values of X, Y, Z may be determined. But the equations in question simplify them
selves in a remarkable manner by the notation before alluded to.
10—2