The Astronomical Hour-Lines, and the Equinoctial Line being drawn, as also a diurnal Arc or Parallel of the Sun’s rising for any Hour, at pleasure, as, for the Hour of 4 at Paris, which Arc will be the same as the Summer Tropick, you may find two Points (as we shall shew here) in each of the aforesaid Lines, viz. one in the Equinoctial Line, and the other in the diurnal Arc drawn, by means of which it will not be difficult to prick down the Italian and Babylonian Hour-Lines; because they being the common Sections of great Circles of the Sphere and a Dial-Plane, will be represented in right Lines thereon.
Now suppose it be required to draw the first Babylonian Hour-Line upon the horizontal Dial of Figure 7, first consider that when the Sun is in the Equinoctial he rises at 6, and at 7 he has been up just an Hour; whence it follows, that the first Babylonian Hour-Line must pass thro’ the Point wherein the Astronomical Hour-Line of 7 cuts the Equinoctial Line; the second thro’ the Intersection of the Hour-Line of 8; the third thro’ that of the Hour-Line of 9; and so of others.
But when the Sun rises at 4 in the Morning, the Point in the Tropick of ♋︎, wherein the Hour Line of 5 cuts it, is that thro’ which the first Babylonian Hour-Line must pass; the Intersection of the Hour-Line of 6 in the said Tropick, that thro’ which the second Babylonian Hour-Line must pass; the Intersection of the Hour-Line of 7 with the said Tropick, that Point thro’ which the third Babylonian Hour-Line must pass; and so of others. Then if a Ruler be laid to the Point wherein the Hour-Line of 5 cuts the Tropick of Cancer, and or the Point in the Equinoctial Line cut by the Hour-Line of 7, and you draw a right Line thro’ them; this Line will represent the first Babylonian Hour-Line. Proceeding in this manner for the other Babylonian Hour-Lines, you will find that the 8th Babylonian Hour-Line will pass thro’ the Point the Tropick of Cancer is cut by the Astronomical Hour-Line of 12, and the Point in the Equinoctial cut by the Hour-Line of 12; and the 5th Babylonian Hour-Line thro’ the Point in the said Tropick cut by the Hour-Line of 7 in the Evening, and the Point in the Equinoctial Line cut by the Hour-Line of 5.
One of the Babylonian Hour-Lines being drawn, it is afterwards easy to draw all the’ others; because they proceed orderly from one Astronomical Hour-Line to the other, on the Parallel and the Equinoctial Line, as appears per Figure. Finally, The Sun lets at the 16th Babylonian Hour, when the Day is 16 Hours long: he sets at the 12th when he is in the Equinoctial; and at the 8th when the Night is 16 Hours long, because he always rises at the 24th Babylonian Hour.
You must reason nearly in the same manner for pricking down the Italian Hour-Lines. Here we always reckon the Sun to set at the 24th Flour; and consequently in Summer, when the Nights are but 8 Hours long, he rises at the 8th Italian Hour; at the Time of the Equinox he rises at the 12th Italian Hour; and in Winter, when the Nights are 16 Hours long, he rises at the 16th Italian Hour: and therefore the Hour-Line of the 23d Italian Hour must pass thro’ the Intersection of the Astronomical Hour-Line of 7, and the Summer Tropick the Intersection of the Hour-Line of 5, and the Equinoctial Line, and the Intersection of the Hour-Line of 3, and the Winter Tropick. But two of the said Points are sufficient for drawing the said Italian Hour-Line. The 22d Italian Hour-Line passes thro’ the Intersection of the Hour-Line of 6 in the Evening, and Summer Tropick, the Intersection of the Hour-Line of 4, and the Equinoctial Line, and the Intersection of the Hour-Line of 2, and the Winter Tropick. Proceeding on thus, you will find that the 18th Italian Hour-Line passes thro’ the Points of the 12th Equinoctial Hour, that is, at the Time of the Equinox, it is Noon at the 18th Italian Hour; whereas at the Time of the Summer Solstice it is Noon at the 16th Italian Hour, and at the Winter Solstice it is Noon at the 20th Italian Hour, in all Places where the Pole is elevated 49 Degrees, as may be seen in the following Table.
A Table for drawing the Babylonian Hour-Lines upon Dials.
Babylonian Hours |
Passing in the Parallel of |
♋︎ |
♈︎ |
♑︎ |
thro’ |
1 | 5 | 7 | 9 |
2 | 6 | 8 | 10 |
3 | 7 | 9 | 11 |
4 | 8 | 10 | 12 |
5 | 9 | 11 | 1 |
6 | 10 | 12 | 2 |
7 | 11 | 1 | 3 |
8 | 12 | 2 | 4 |
9 | 1 | 3 | 5 |
10 | 2 | 4 | 6 |
11 | 3 | 5 | 7 |
12 | 4 | 6 | 8 |
13 | 5 | 7 | 9 |
14 | 6 | 8 | 10 |
15 | 7 | 9 | 11 |
16 | 8 | 10 | 12 |
A Table for drawing the Italian Hour-Lines upon Dials.
Italian Hours |
Passing in the Parallel of |
♋︎ |
♈︎ |
♑︎ |
thro’ |
23 | 7 | 5 | 3 |
22 | 6 | 4 | 2 |
21 | 5 | 3 | 1 |
20 | 4 | 2 | 12 |
19 | 3 | 1 | 11 |
18 | 2 | 12 | 10 |
17 | 1 | 11 | 9 |
16 | 12 | 10 | 8 |
15 | 11 | 9 | 7 |
14 | 10 | 8 | 6 |
13 | 9 | 7 | 5 |
12 | 8 | 6 | 4 |
11 | 7 | 5 | 3 |
10 | 6 | 4 | 2 |
9 | 5 | 3 | 1 |
8 | 4 | 2 | 12 |
The Use of the Italian Hour-Lines upon a Dial may be to find the Time of the Sun’s setting, in substracting the Italian Hour present from 24; and by the Babylonian Hours may be known the Time of the Sun’s rising.