第一部·星位数字的读法　第二至四则　上升差、半弧与时量

CANON II.

第二则。

The Ascensional Difference.

上升差。

In the first part of the ascensional difference, look for the Pole's elevation of the country, and in the first colume the declination of the place; which, if it be with the integral degrees, the ascensional difference required is placed in the common angle; but if the declination be with the degrees and minutes, then take the proportional part, as in Canon I.

在上升差表的第一部分，找本地的极高，在第一栏找该处的赤纬；赤纬若是整度，所求的上升差就在共同的格中；但若赤纬带度和分，就取比例部分，如第一则。

If the given declination be 12, at the Pole's elevation 42°, the ascensional difference is placed in the common angle, 11° 2'; but if the declination be given 12° 25', the ascensional difference at declination 13, is 12; wherefore the difference between the former is 58', from which 24' is due, i. e. to be taken; in their room, 25' to be added, and the ascensional difference becomes 11° 26'.—Another way.—If you have already by you the tables of oblique ascension of the given place, and the right ascension, substract the less from the greater, and the remainder is the ascensional difference.

若给定的赤纬是十二度，极高四十二度，上升差在共同的格中，为十一度二分；但若给定的赤纬是十二度二十五分，赤纬十三度的上升差是十二度；因此两者之差是五十八分，其中应得二十四分，即要取的数；对着那二十五分，要加上去，上升差成为十一度二十六分。——另一法。——若手边已有给定地方的斜升表与赤经表，以大减小，余数就是上升差。

In like manner, if you have already the semi-diurnal or nocturnal arc, substract from the 90°, if it be less; if greater, substract therefrom the 90°, and the remainder is the ascensional difference.

同样，若手边已有半昼弧或半夜弧，它若小于九十度，就从九十度中减去它；若大于九十度，就从它减去九十度，余数就是上升差。

CANON III.

第三则。

The semi-diurnal or nocturnal arcs are thus obtained; the semi-diurnal in degrees and minutes, by adding the ascensional difference to 90; when a star in the six northern signs: by substracting 90, when in the southern, the contrary. The semi-nocturnal, is found by substracting the ascensional difference from 90°, when a star declines to the north; by adding to 90, when to the south; for either the remainder sums will be the semi-nocturnal or diurnal arc in degrees and minutes.

半昼弧或半夜弧这样求得：星在北方六个星座时，以度和分表示的半昼弧，由九十度加上升差得到；在南方星座时则相反，由九十度减去上升差。半夜弧，在星向北偏离时，由九十度减去上升差求得；向南时，由九十度加上升差求得；所得的余数或和数，就是以度和分表示的半夜弧或半昼弧。

If the declination above given, viz. 12° 25' be northern, the semi-diurnal arc will become 101° 26', by adding the ascensional difference 11° 26' to 90: if the declination be south, the semi-nocturnal will be the same; if the declination be north, and substract from 90, there will remain the semi-nocturnal arc 78 34; but if it be southern, the semi-diurnal will be the same.

若上面给的赤纬十二度二十五分是北赤纬，九十度加上上升差十一度二十六分，半昼弧就是一百零一度二十六分：若赤纬是南的，半夜弧也是这个数；若赤纬是北的而从九十度中减去，剩下半夜弧七十八度三十四分；但若是南的，半昼弧也是这个数。

If you would reduce the semi-diurnal or semi-nocturnal arc into hours and minutes, (see Canon XI.) you will likewise have the semi-diurnal and semi-nocturnal arc of the places in the ecliptic from the tables of semi-diurnal and nocturnal arcs at your Pole's elevation.

若你要把半昼弧或半夜弧化为时和分（见第十一则），你也可以从你的极高下的半昼弧与半夜弧表中，得到黄道上各点的半昼弧与半夜弧。

If the sign of the given degree be in the first part, look for its degree in the descendant degree placed to the left; but if it be at the latter part, in the ascendant degree, which is to the right, and in the common angle of meeting, you will have the arc required, whose denomination you will perceive under the very sign, whether diurnal or nocturnal.

若给定度数的星座在表的前半部分，就在左边下行的度数中找它的度数；若在后半部分，就在右边上行的度数中找；在相交的共同格中，你就得到所求的弧，它的名目是昼还是夜，你在那个星座的下面就能看出。

And remember, if these are minutes, to take the proportional part; but if it be denominated semi-diurnal, and you want the semi-nocturnal, on the contrary, substract the arc found from 12 hours, and the remainder is the other arc required.

还要记住，若有分数，要取比例部分；若所得的名为半昼弧，而你要的是半夜弧，就反过来，从十二小时中减去所得之弧，余数就是所求的另一弧。

In the nativity of Charles V. the Sun is in 14° 30' of ♓: at the Pole's elevation 52°, I find the sign ♓ in the latter part; wherefore, to the 14 ascendant degrees, I take in the common angle the semi-nocturnal arc, 6h 33'; but because the Sun has above 30', I substract one minute, and there remains of the semi-nocturnal arc, 6h 32': whereas, if I want the semi-diurnal arc, I take 6h 32', from 12h, and there remains 5h 28' of the latitudinal planets, provided their declination does not exceed 23° 32'.

在查理五世的本命中，太阳在双鱼十四度三十分：在极高五十二度下，我发现双鱼在表的后半部分；因此，对着上行的十四度，我在共同的格中取得半夜弧六时三十三分；但因为太阳多出三十分，我减去一分，剩下半夜弧六时三十二分：若我要半昼弧，就从十二时中减去六时三十二分，剩下五时二十八分；有纬度的行星〔亦可如此求〕，只要它们的赤纬不超过二十三度三十二分。

The said semi-diurnal or nocturnal arc, in the hours and minutes, may be had thus: After reducing their declination to the longitude of the ecliptic, in the manner explained in Canon I. with this degree of the ecliptic, I enter the table of the semi-diurnal arc, and take out the hours and minutes corresponding thereto, in the manner we have mentioned, &c. as in the nativity of Sebastian. Saturn hath declination, 7° 47' and is reduced, to 19° 50' of ♎, or 10° 10' of ♓, whose semi-diurnal arc at the Pole's elevation 40°, is 6° 27'.

上述以时和分表示的半昼弧或半夜弧，可以这样求得：先按第一则所讲的方法把它们的赤纬还原为黄道上的黄经，再以这个黄道度数查半昼弧表，按我们所说的方法取出相应的时和分，等等，如在塞巴斯蒂安的本命中。土星赤纬七度四十七分，还原为天秤十九度五十分，或双鱼十度十分，它在极高四十度下的半昼弧是六度二十七分。

CANON IV.

第四则。

The Horary Times.

时量。

These may be taken several ways; first, the diurnal from the partition of the semi-diurnal arc in degrees and minutes taken by six; the nocturnal from the position of the semi-nocturnal; likewise by six, from the six temporal hours; the cardinal signs of the world are mutually distant: let the semi-diurnal arc be 104° 45', the 104° divided by 6 make 17, and there remains 2; which, reduced to minutes, and these added to the other 45, makes 165; which, when divided by 6, the remainder is 27', and the horary times 17° 27' diurnal.

时量可用几种方法求得；第一，昼时量由以度和分表示的半昼弧除以六得出；夜时量由半夜弧同样除以六得出，因为世界的四角彼此相隔六个季节时：设半昼弧为一百零四度四十五分，一百零四度除以六得十七，余二；化为分，加上另外的四十五分，得一百六十五分；除以六，得二十七分，于是昼时量为十七度二十七分。

Secondly, the horary times of the parts of the ecliptic are judged of in the proper tables; as at the pole's elevation 45, the 15° of the ecliptic of ♉, the horary times are diurnal 17° 51'. Thirdly, the semi-diurnal arc taken in the hours and minutes, if produced by two with the half, is transmuted into the diurnal horary times; and in like manner the semi-nocturnal arc into the nocturnal horary times; as the semi-diurnal arc is 15 of ♉, at the Pole 45°, is 7h. 9', which, deducted by 2, with the half, becomes 17° 52'.

第二，黄道各部分的时量可在专门的表中查得；如在极高四十五度下，黄道上金牛十五度的昼时量是十七度五十一分。第三，以时和分表示的半昼弧，乘以二又二分之一，就变成昼时量；半夜弧同样变成夜时量；如在极高四十五度下，金牛十五度的半昼弧是七时九分，乘以二又二分之一，成为十七度五十二分。

Fourthly, of the planets having latitude, let their received declination be brought back to the ecliptic in the manner as explained in Canon I. and with that degree of the ecliptic in the table of horary times, they may be taken as above-mentioned; but if the planet has a greater declination, these 23° 32', the horary times cannot be taken any other way, except by the help of the ascensional difference.

第四，有纬度的行星，按第一则所讲的方法把所得的赤纬还原到黄道上，以那个黄道度数查时量表，就可如上所说取得；但若行星的赤纬大于二十三度三十二分，时量就只能借上升差求得，别无他法。

But if you have the diurnal horary times, and want the nocturnal, or the contrary, substract your sum from 30, and the rest will be the horary times required; as in the given example, I substract 17° 51' from 30, and there remains the horary times nocturnal 12° 9'.

若你有昼时量而要夜时量，或者相反，就从三十度中减去你所得之数，余数就是所求的时量；如在所给的例子中，我从三十度减去十七度五十一分，剩下夜时量十二度九分。