thing to set down except the
degree mark from the first column. With the twelve we go up the
adjoining loop column, and the sum must be even, as this place is
vacant in the answer; the _r_-curve column next, downward, and then
another row of degree marks. The succession must be obvious by this
time. When the last column, the one in loops to the extreme left, is
added, the sum has to be reduced to unity by successive halvings. Here
we seem to have eleven; hence we enter one loop, and carry five to the
next place, which, it must be remembered, is of _r_-curves. Halving
five we express the remainder by entering one of these curves, and
carry the quotient, two, to the degree mark place. Halving again gives
one in the next place, that of _l_-curves; and the work is complete.

It is recommended that this work be gone over several times for
practice, until the appearance and order of the characters and the
details of the method become familiar; that, when the work can be done
mechanically and without hesitation, the time occupied in a complete
addition of the example, and the mistakes made in it, be carefully
noted; that this be done several times, with an interval of some days
between the trials, and the result of each trial kept separate; that
the time and mistakes by the ordinary figures in the same example, in
several trials, be observed for comparison. Please pay particular
attention to the difference in the kind of work required by the two
methods in its bearing on two questions--which of them would be easier
to work by for hours together, supposing both equally well learned?
and in which of them could a reasonable degree of skill be more
readily acquired by a beginner? The answer to these questions, if the
comparison be a fair one, is as little to be doubted as is their high
importance.

_Example in addition by two notations_

77,823,876
14,348,907
8,654,912
5,764,801
4,635,857
1,594,323
6,417,728
4,782,969
83,886,075
34,012,224
2,903,111
48,828,125
1,724,826
7,529,536
43,344,817
10,000,000
8,334,712
1,953,125
11,308,417
759,375
21,180,840
9,765,625
18,643,788
1,000,000
44,739,243
1,889,568
2,517,471
40,353,607
4,438,414
1,679,616
23,708,715
11,890,625
945,754
823,543
15,308,805
60,466,176
30,685,377
10,077,696
19,416,381
43,046,721
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