[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.
Fig. 4.
Now, as the distance of the style from the flame of the lamp is only half an inch, then, if the distance of the frame from the style be six inches, while the float that contains the light descends by the decrease on the oil, one inch, the shadow of the style of the frame will ascend 12 inches, being its whole length, and show by its progression, the regular increase of the hours, with their several divisions.
You must be careful always to burn the same oil, which must be the best; and the wick must never vary in size; if these precautions are not attended to, the dial never can be accurate.
The Phial of the Four Elements.
Take a phial, six or seven inches long, and about three quarters of an inch in diameter. In this phial put, first, glass coarsely powdered; secondly, oil of tartar per deliquum; thirdly, tincture of salt of tartar; and lastly, distilled rock oil.