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 fixed the handle C, which supports the frame D, about 12 inches high, and four inches wide. This frame is to be covered with oiled paper, and divided into 12 equal parts by horizontal lines, at the end of which are written the numbers for the hours, from 1 to 12, and between the horizontal lines, and diagonals, divided into halves, quarters, &c. On the handle C, and close to the glass, is fixed the style or hand E. [Illustration: Fig. 4.]