MAG 
First place the 1 next below the centre 
cell, and thence descend to the right till the 
4 runs off at the bottom, which therefore 
carry to the top corner on the same column 
as it would have fallen in; but as that runs 
off at the side,' bring it to the beginning of 
the second line, and thence descend to the 
light till they arrive at the cell occupied 
by 1; cany the, 8 therefore to the next 
diagonal cell to the left, and so proceed 
till 10 runs off at the bottom, which carry 
therefore to ttie top of its column, and so 
proceed till 13 runs off at the side, which 
therefore bring to the beginning of the 
same line, and thence proceed till 15 ar- 
rives at the cell occupied by 8 ; from 
this therefore descend diagonally to the 
left ; but as 16 runs off at the bottom, 
carry it to the top of its proper column, 
and thence descend till 21 runs off’ at the 
side, which is therefore brought to the be- 
ginning of its proper line ; but as 22 arrives 
at the ceil occupied by 15, descend diago- 
nally to the left, which brings it into the 
first column, but off at the bottom, and 
therefore it is carried to tlie top of that co- 
lumn ; thence descending till S9 runs off 
both at bottom and side, which therefore 
carry to the highest unoccupied cell in the 
last column ; and here, as 30 runs off at the 
side, bring it to the beginning of its proper 
column, and thence descend till 35 runs off 
at the bottom, which therefore, carry to 
the beginning or top of its own column ; 
and here, as 36 meets with the cell occu- 
pied by 29, it is brought from thence dia- 
gonally to the left ; thence descending, 38 
runs off at the side, and therefore it is 
brought to the beginning of its proper line ; 
thence descending 41 runs off at the bot- 
tom, which therefore is carried to the be- 
ginning or top of its column ; from whence 
descendinff, 43 arrives at the cell occupied 
by 36, and therefore it is brought down 
from thence to the left ; thence descending, 
46 runs off at the side, which therefore is 
brought to the beginning of its line ; but 
here, as 47 runs off at the bottom, it is car- 
ried to the beginning or top of its column, 
from whence descending with 48 and 49, 
the square is completed, the sum of every 
row and column and diagonal making just 
175. Dr. Franklin carried this curious spe- 
culation further than any of his predecessors 
in the same w'ay. He constructed both a 
magic square of squares, and a magic circle 
of circles, the description of which is as fol- 
lows. The magic square of squares is 
formed by dividing the great square into 
MAG 
256 little squares, in which all the numbers 
from 1 to 256, or the square of 16, are 
placed, in 16 columns, which may be taken 
either horizontally or vertically. Their chief 
properties are as follow. 1. The sum of 
the 16 numbers in each column or row, ver- 
tical or horizontal, is 2056. 2. Every half 
column, vertical and horizontal, makes 
1028, or just one half of the same sum 2056. 
3. Half a diagonal ascending, added to half 
a diagonal descending, makes also the same 
sum 2056 ; taking these half diagonals from 
the ends of any side of the square to the 
middle of it ; and so reckoning them either 
upward or downward, or sideways from 
right to left, or from left to right. 4. The 
same.with all the parallels to the half diago- 
nals, as many as can be drawn in the great 
square : for any two of tliem being directed 
upward and downward, from the place 
where they begin, to that where tliey end, 
their sums still make the same 2056. Also 
the same holds true downv/ard and upward ; 
as well as if taken sideways to the middle, 
and back to the same side again. Only one 
set of these half diagonals and their parallels, 
is drawn in the same square upward and 
downward ; but another set may be drawn 
from any of the other three sides. 5. The 
four corner numbers in the great square 
added to the four central numbers in it, 
make 1028, the half sum of any vertical or 
horizontal column, which contains 16 num- 
bers ; and also equal to half a diagonal or 
its parallel. 6. If a square hole, equal in 
breadth to four of the little squares or cells, 
be cut in a paper, through which any of the 
16 little cells in the great square may be 
seen, and the paper be laid upon the great 
square ; the sum of all the 16 numbers, 
seen through the hole, is always equal to 
2056, the sum of the 16 numbers in any ho- 
rizontal or vertical column. 
MAGISTERY, an old chemical term, 
very nearly synonymous with preeijiitate, 
but is now rarely used except in the follow- 
ing combinations : magistery of bismuth, 
which is the white oxide of this metal preci- 
pitated from tlie nitrous solution by the ad- 
dition of water; magistery of sulphur, which 
is sulphur precipitated from its alkaline solu- 
tion by an acid. 
MAGNA charta. See Liberty. 
MAGNESIA, in chemistry, an earth, 
the properties of which were not fully 
known till Dr. Black, about the middle of 
the last centuiy, investigated its nature. 
In the pursuit, the Doctor was led to the 
important discovery of the carbopic acid 
