695] 
407 
695. 
A LINK-WORK FOR a*: EXTRACT FROM A LETTER TO 
MR. SYLVESTER. 
[From the American Journal of Mathematics, t. I. (1878), p. 386.] 
I suppose the following is substantially your link-work for x 2 . I use a slot to 
make B move in the line OA; but this could be replaced by proper link-work. 
Supposing 0 and A fixed; the line OB is movable, and I wanted to have the 
distance OB measured in a fixed direction. This can be done by a hexagon OABQB'A' 
with equal sides, and two other equal links B'R, BR: then of course, if 0, R, Q 
are in linea, the hexagon will be symmetrical as to OQ, and OB' will be equal to OB, 
and B' may be made to move in the fixed line OB'. If 
BOA =\6, OA = AB = a, AC=CD = %a, 
then 
OB = 2a cos 16, OB = a (1 + cos #) = 2a cos 2 \ 0, 
or 
2a. OD = (OB) 2 . 
November 30, 1877.