APPLES 
the box. over half way between the first 
and second Repeat, placing the apples in 
the same relative position as the first 
three, until the upper head of the box 
isreached This first layer may end with 
two apples and one space, or with one ap- 
ple and two spaces Begin the second 
layer by placing an apple above the space 
left between the first two apples in the 
pottom layer. The apple will fall down 
into the space a trifle Place the next 
two apples on either side of the first. 
The three will be of such a size that the 
outer two will not slip toward the lower 
head over half way on either side of the 
middle one The apples in the second 
and third layers fit directly over the in- 
terstices between two apples in the lay- 
er underneath, except the end apples, 
which fit over a space between an apple 
and the head of the box. Three layers 
of the two-one pack fill the box. 
(1) When the outer rows of a layer 
touch one head of the box, with spaces 
at the other end, the middle row touches 
the other head with a space at the op- 
posite end; and all the rows contain the 
same number of apples. In the box 
with all layers constructed thus, every 
layer contains the same number of ap- 
ples. The number of apples in the box is 
determined by counting the number in 
the top layer and multiplying by three, 
the number of layers. (2) When the 
outer rows of a layer reach from head to 
head of the box, the middle row has a 
space at both ends, and contains one ap- 
ple less. On the other hand, when the 
359 
middle row touches both heads of the box 
and the outer rows each has a space at 
both ends, each contains one apple less. 
The layer constructed after the latter 
contains one apple less than the layer 
constructed atter the former manner Now 
the first and third layers of the box each 
contains the same number of apples; but 
they are constructed after the former 
manner and the second layer after the lat- 
ter Therefore the second layer contains 
one apple less than the first and the third. 
To determine the number of apples in this 
box, count the apples in the top layer, 
multiply by three, and substract one. 
Where the outer rows of the first layer 
each contains four apples and the middle 
row also four, the pack is described as 
being three deep, two-one wide, and four- 
four Jong, with 36 apples to the box. 
When the outer rows of the first layer 
each contains five apples and the middle 
row four, the pack is described as be- 
ing three deep, twoone wide, and five- 
four long, with 41 apples to the box. 
When the outer rows of the first layer 
each contains five apples and the middle 
row also five, the pack is described as 
being three deep, two-one wide, and five- 
five long, with 45 apples to the box. 
The two-one pack, though correct, is 
rarely used. Few apples grow large 
enough to pack into it, and these are 
usually of too poor quality for commercial 
purposes. It is sometimes put up as an 
exhibition pack with which to stun the 
Jand looker. To decide whether a certain 
size of apple should be packed in the two- 
one or in the two-two pack, try to place 
three of the apples cheek to cheek in a 
row crosswise of the box. If the apples 
are so large transversely that there is not 
room for three of them in the row, they 
are to be packed two-one. If three of 
them fit across snugly, or if they are so 
small that three do not reach across, they 
are to be packed two-two. 
Two-Two Pack 
To begin the two-two pack, place an 
apple in the lower left hand corner of the 
box, then one in the middle of the space 
between the first apple and the right hand 
