wide and 3,630
yards long. Find the dimensions of the garden.

_Answer._--60, 60-1/2.

_Solution._--The number of yards and fractions of a yard traversed in
walking along a straight piece of walk, is evidently the same as the
number of square-yards and fractions of a square-yard, contained in that
piece of walk: and the distance, traversed in passing through a
square-yard at a corner, is evidently a yard. Hence the area of the
garden is 3,630 square-yards: _i.e._, if _x_ be the width, _x_ (_x_ +
1/2) = 3,630. Solving this Quadratic, we find _x_ = 60. Hence the
dimensions are 60, 60-1/2.

* * * * *

Twelve answers have been received--seven right and five wrong.

C. G. L., NABOB, OLD CROW, and TYMPANUM assume that the number of yards
in the length of the path is equal to the number of square-yards in the
garden. This is true, but should have been proved. But each is guilty of
darker deeds. C. G. L.'s "working" consists of dividing 3,630 by 60.
Whence came this divisor, oh Segiel? Divination? Or was it a dream? I
fear this solution is worth nothing. OLD CROW'S is shorter, and so (if
possible) worth rather less. He says the answer "is at once seen to be
60 x 60-1/2"! NABOB'S calculation is short, but "as rich as a Nabob" in
error. He says that the square root of 3,630, multiplied by 2, equals
the length plus the breadth. That is 60.25 x 2 = 120-1/2. His first
assertion is only true of a _square_ garden. His second is irrelevant,
since 60.25 is _not_ the square-root of 3,630! Nay, Bob, this will _not_
do! TYMPANUM says that, by extracting the square-root of 3,630, we get
60 yards with a remainder of 30/60, or half-a-yard, which we add so as
to make the oblong 60 x 60-1/2. This is very terrible: but worse remains
behind. TYMPANUM proceeds thus:--"But why should there be the half-yard
at all? Because without it there would be no space at all for flowers.
By means of it, we find reserved in the very centre a small plot of
ground, two yards long by half-a-yard wide, the only space not occupied
by walk." But Balbus expressly said that the walk "used up the whole of
the area." Oh, TYMPANUM! My tympa is exhausted: my brain is num! I can
say no more.

HECLA indulges, again and again, in that most fatal of all habits in
computation--the making _two_ mistakes which cancel each other. She
takes _x_ as the width of the garden, in yards, and _x_ + 1/2 as its
length, and makes her first "coil" the su