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Page 35
We stop at this point because 24 was a previous modified dividend,
written under the form 240 above. Our two infinite numbers (which need
not in practice be written down) are, with their difference:
. .
10,958,904,058 . .
10,958,904,109.5890410958904
----------------------------
. .
51.5890410958904
. .
Hence the quotient sought is 5.158904109.
_Example 2._ Find the reciprocal of 333667.
The whole work is here given:
3 3 3 6 6|7 |7
2 3 3 5 6 7 - 1 6 3 4 9 6|9
2 1 0 2 1 0 3 -
-------------
2 2 6 5 5 9|9
2 1 0 2 1 0 3 -
-------------
2 3 2 8 6 6|2
4 6 7 1 3 4 -
-----------
7 0 0 0 0 0
. .
_Answer_, 0.000002997.
_Example 3._ Find the reciprocal of 41.
_Solution._--
4|1 |9
----- -----
3 7|9 3 3|3
- 1 1 1 -
-----
1 4|4
1 4 8 -
-----
1 6|2
7 4 -
---
9 0
. .
_Answer_, 0.02439.
C.S. PEIRCE.
* * * * *
[SCIENCE.]
EXPERIMENTS IN BINARY ARITHMETIC.
Those who can perform in that most necessary of all mathematical
operations, simple addition, any great number of successive examples
or any single extensive example without consciousness of a severe
mental strain, followed by corresponding mental fatigue, are
exceptions to a general rule. These troubles are due to the quantity
and complexity of the matter with which the mind has to be occupied at
the same time that the figures are recognized. The sums of pairs of
numbers from zero up to nine form fifty-five distinct propositions
that must be borne in memory, and the "carrying" is a further
complication. The strain and consequent weariness are not only felt,
but seen, in the mistakes in addition that they cause. They are, in
great part, the tax exacted of us by our decimal system of arithmetic.
Were only quantities of the same value, in any one column, to be
added, our memory would be burdened with nothing more than the
succession of numbers in simple counting, or that of multiples of two,
three, or four, if the counting is by groups.
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