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