e that half.
3. To take the half of the last triple.
4. To take the half of that half.

Thus, it will be seen, there are four cases where the half is to be
taken; the three first are denoted by one of the eight following Latin
words, each word being composed of three syllables; and those that
contain the letter i refer to those cases where the half cannot be
taken without a fraction; therefore, in those cases, the person who
makes the deduction is to add 1 to the number divided. The fourth case
shows which of the two numbers annexed to every word has been chosen;
for if the fourth half can be taken without adding 1, the number
chosen is in the first column; but if not, it is in the second.

_The words._ _The numbers they denote._

Mi-se-ris 8 0
Ob-tin-git 1 9
Ni-mi-um 2 19
No-ta-ri 3 11
In-fer-nos 4 12
Or-di-nes 13 5
Ti-mi-di 6 14
Te-ne-ant 15 7

For example:

Suppose the number chosen is 9
To which is to be added 1
----
10
The triple of that number is 30
The half of which is 15
The triple of that half must be 45
And the half of that[A] 23
The triple half of that half 69
The half of that[A] 35
And the half of that half[A] 18

[A] At all these stages, 1 must be added, to take the half
without a fraction.

While the person is performing the operation, you remark, that at the
second and third stages he is obliged to add 1; and, consequently,
that the word _ob-tin-git_, in the second and third syllables of which
is an i, denotes that the number must be either 1 or 9; and, by
observing that he cannot take the last half without adding 1, you know
that it must be the number in the second column. If he makes no
addition at any one of the four stages, the number he chose must be
15, as that is the only number that has not a fraction at either of
the divisions.

_The Lamp Chronometer._

Figure 4 represents a chamber lamp, A, consisting of a cylindrical
vessel made of tin, in the shape of a candle, and is to be filled with
oil. This vessel should be about three inches high and one inch
diameter, placed in a stand, B. The whole apparatus, of lamp and
stand, can be purchased, ready-made, at any tin-shop in London. To the
stand, B, is