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Exemplarious translation:
３．〈辯證〉一：〈漢人釀酒〉
漢人有飲酒一石不亂，予以製酒法較之，每粗米二斛，釀成酒六斛六斗．今酒之至醨者，每秫一斛，不過成酒一斛五斗，若如漢法，則粗有酒氣而已．能飲者飲多不亂，宜無足怪．然漢之一斛，亦是今之二斗七升，人之腹中，亦何容置二斗七升水邪？或謂：「石乃鈞石之石，百二十斤．」以今秤計之，當三十二斤，亦今之三斗酒也．于定國飲酒數石不亂，疑無此理．
3. Analyses 1: How the people of Han Dynasty brewed wine
During the Han Dynasty, people drinking a whole dan of wine (approx. 34 litre/9 US-gallons) did not have a touch of being drunk, because they had a recipe to make wine lighter during the brewing process. Using two hu of course grain, they obtained six hu and six dou of wine (36 l/9 gall for 118 l/30 gall wine). Nowadays, using one hu of millet, we obtain only one hu and five dou of wine (66 l/17gall for 100 l/27 gall wine). Using the recipe of the Han time, our wine would contain only a small touch of alcohol. There is no wonder if people of the Han Dynasty drank lots of wine without getting drunk. But one hu of Han measure is only two dou and seven sheng of modern (Song time) measure. What can this amount of almost pure water (18 l/5 gall) in your stomach do to you? A commentator says, "one dan" means a dan of four jun, or 120 jin. Comparing it with modern measures, it corresponds to 32 jin that are only three dou of wine (20 l/5 gall). There is nothing to wonder about if Yu Dingguo of the Han Dynasty drank one dan of wine without getting drunk!
７．〈象數〉一：〈日月食〉
又問：「日月之行，月一合一對，而有食不食，何也？」
予對曰：黃道與月道，如二環相疊而小差．凡日月同在一度相遇，則日為之食；在一度相對，則月為之夸．雖同一度，而月道與黃道不相近，自不相侵．同度而又近黃道、月道之交，日月相值，乃相陵掩．正當其交處，則食而既，不全當交道，則隨其相犯淺深而食．
凡日食，當月道自外而交入於內，則食起於西南，復於東北．自內而交出於外，則食起於西北，而復於東南．日在交東，則食其內．日在交西，則食其外．食既，則起於正西，復於正東．〈凡月食…〉
交道每月退一度餘，凡二百四十九交而一期．故西天法羅〈目+侯〉，計度皆逆步之，乃今之交道也．交初謂之「羅〈目+侯〉」，交中謂之「計度」．
7. Astronomy and mathematics 1: Eclipse of sun and moon
Another question: When sun and moon are on the same side or on the opposite side of the earth ball, why is there sometimes an eclipse, and sometimes not? I give you an answer: The "yellow path", the ecliptic of the sun, and the "white path", the moon's path, have the shape of two rings that go around the earth; they are almost lying in one plain, with only a small difference. If sun and moon meet each other one the same side of the earth in the same longitude degree of their paths, there will be a solar eclipse, and if they are on opposite sided of the earth in the same longitude degree of their paths, there will be a lunar eclipse. But if sun and moon run in the same longitude degree of their paths, there will be no eclipse if the yellow path and the white path do not overlap. If they are running in the same longitudinal angle, and the yellow path and the white path come near, sun and moon will touch directly and one of them will cover the other. If they cross the same point at the same time, there will be a total eclipse; otherwise, there will be a partial eclipse and the one covers one part of the other more or less deep.
During a solar eclipse, the moon crosses the yellow path from south to north, and the eclipse begins in the southwest and proceeds to northeast. If the moon crosses the yellow path from north to south, the eclipse starts in the northwest and proceeds to southeast. If the sun is slightly to the east of the crossing point of the yellow and white paths, the upper part of the sun will be eclipsed; if the sun is slightly to the west of the crossing point, the lower part of it will be eclipsed. A total eclipse begins in the west and proceeds to the east. [Then follows the same description for the lunar eclipse.] The crossing point of yellow path and white path proceed each month one degree (1°5' to the west), describing a total circle of 249 crossing points (in 18.6 years). The old Indian astronomers called descending node (crossing point from where the yellow path descends under the white path in western direction) "luohou", and the ascending node (crossing point where the yellow path ascends over the white path in western direction), "jidu".
１１．〈官政〉一：〈鹽〉
鹽之品至多，前史所載，夷狄間自有十餘種．中國所出亦不減數十種．今公私通行者四種：一者，末鹽，海鹽也．河北、京東、淮南、兩浙、江南東西、荊湖南北、福建、廣南東西十一路食之．其次顆鹽，解州鹽澤及晉、絳、潞、澤所出．京畿、南京、京西、陜西、河東、褒、劍等處食之．又次井鹽，井取之．益、梓、利、夔四路食之．又次崖鹽，生於土崖之間．階、成、鳳等州食之．
唯陜西路，顆鹽有定課，歲為錢二百三十萬緡．自餘盈虛不常，大約歲入二千餘萬緡．唯末鹽歲自抄三百萬，供河北邊〈入+米〉；其他皆給本處經費而已．緣邊買仰給於度支者，河北則海、末鹽，河東、陜西則顆鹽及蜀茶為多．運鹽之法，凡行百里，陸運斤四錢，船運斤一錢，以此為率．
11. Offices and government 1: Salt
There exist very many different kinds of salt; from the historical records we can learn that the southern barbarians Yi and Di knew more than ten kinds. Even in the central plain of China, there existed not less than ten different types of salt. Today, there are four types officially accepted:
First, the "end salt" (moyan) that is made from sea salt. It is produced and consumed in the ten circuits of Hebei, Jingdong (east of Kaifeng), Huainan, Liangzhe (modern Zhejiang), Jiangnan East and West (modern Jiangsu and Jiangxi), Jinghu South and North (modern Hunan and Hubei), Fujian, and Guangxi East and West.
Second, the "grain salt" (keyan), produced in the salt lakes of Xiezhou, Jinzhou, Jiangzhou, Luzhou, and Zezhou (all Shanxi), and consumed in the capital Kaifeng, Nanjing (south of Kaifeng), Jingxi (Henan), Shaanxi, Hedong (Shanxi), Baocheng (Shaanxi), and Jiange (Sichuan).
Third, the "well salt" (jingyan), prospected from mines in the earth, and consumed in the four circuits of Yizhou, Zizhou (both Sichuan), Lizhou (Shaanxi) and Kuizhou (Sichuan).
Fourth, the "cliff salt" (yanyan), produced from earthen cliffs, and consumed in Jiezhou, Chengzhou (both Gansu) and Fengzhou (Shaanxi).
In the circuit of Shaanxi, there is a fixed tax on "grain salt", (with a state income of) 2.300.000.000 qian (or 2.3 mio min or guan) p.a., but except this, the taxes are everywhere different, with an income of more than 20.000.000 min p.a. The state income by the tax for "end salt" is 3 mio., including the trade for foods in Hebei. The other taxes are provided to the local government. The salt types sold to the financial ministry and its offices, are mainly sea salt or "end salt" in the circuit of Hebei, and "grain salt" and tea from Shu (Sichuan) in the circuits of Hedong and Shaanxi. The standard price for salt shipment are: 4 qian per jin of salt for land transport, and 1 qian per jin for water transport, both amounts for one hundred miles (li).
Translated by Ulrich Theobald.
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