Chapter 261: Estimating Work

By the time the north wind arrives it is already early winter, the landscape bleak and all things bare. On this day in the first ten days of the tenth month, in the eastern outskirts of Shangcai, a few extra chariots and riders appeared. Zhang Han and the Qin Mohist Cheng Shang rode in a chariot, while Heifu rode on horseback. Under the protection of over a hundred soldiers, they left the encampment and headed east.

The charioteer drove at a very slow pace so that the Army Director of Works Zhang Han could carefully observe the surrounding terrain. When they reached a certain stretch of land, Zhang Han shouted, "Halt!"

Setting up camp requires careful site selection, and constructing ramparts is no different. Heifu observed that this place had grassy marshes to the left, a flowing spring to the right, the protection of a small hill at the back, yet a very flat field of vision facing east. A road passed through, and several li away there were woods and grasslands suitable for firewood and grazing — it could be called a site with all four provisions.

Heifu looked it over and said, "Isn't this the eastern outskirts wildland that Commandant Li mentioned? I heard that back in the day, the Commandant of Justice and his sons often led yellow hounds to chase crafty hares here. It is indeed suitable for setting up camp and building ramparts."

The rampart construction work to be done now was also part of Zhang Han's duty of "quartering the troops and settling them."

The "settling" in "quartering the troops and settling them" means to pacify and stabilize — it means that once the ramparts are built, there is no fear of enemy raids or frontal assaults, and the army can be quartered in peace. When construction tasks are allocated fairly and reasonably, chaos and conflict will not arise from it.

As they spoke, Zhang Han and the others also dismounted and began taking up instruments such as the level, compass, set square, and marking cord. On the boundless Shangcai plain, they began carrying out construction surveys.

Zhang Han raised the "level," which hung with a weight, got off the chariot, tested for flatness and straightness, and compared the differences in elevation between the terrain. Meanwhile, Cheng Shang pulled the pacing cord, measuring carefully step by step on the ground, while a clerical assistant beside him recorded the distances.

As for the "compass," it is a tool for correcting circles; the "set square" is a tool for drawing squares, also known as a carpenter's square. Zhang Han and the Qin Mohists had already worked wonders with these simple tools. They could determine the horizontal, measure heights, depths, and distances, and also draw circles and squares. By placing them in different positions when in use, they could also determine the height, distance, and size of objects. As for the margin of error, that depended entirely on the operator's experience.

Seeing Heifu's curious expression, Zhang Han further explained, "It is said that when Yu the Great tamed the waters, he rode a chariot on land, a boat on water, a sledge through mud, and a litter in the mountains. With level and marking cord on the left, compass and set square on the right, he carried these four means of travel to open up the Nine Provinces and connect the Nine Roads."

Though this was legend, it was most likely people attributing the inventions of skilled craftsmen to sage kings. Just like that, they spent half a day surveying the sections for building the ramparts. Every hundred paces, they also drove dyed-black wooden poles deep into the earth as markers.

When they returned to the encampment in the evening, Zhang Han, armed with the day's survey data, had several Senior Accounting Clerks skilled in arithmetic calculate the quantity of work so it could be assigned to the laborer battalions for construction.

Heifu had the good fortune to witness the era's dazzlingly complex engineering quantity calculations.

On the open ground of the camp, a great many counting rods were laid out on the ground. Heifu was no stranger to these, for Qin regulations required local officials to keep counting rods on hand for unforeseen needs. Mathematics was one of the Six Arts of the gentleman in the Spring and Autumn period and an essential skill for Qin officials. In local governance — field measurement, grain taxation, equitable transport, and levies — all required extensive numerical calculation. If a person was innumerate, they did not even qualify to be a petty clerk drawing a dou of grain in salary!

In Xianyang and the commandery seats, there were also specialized "Accounting Clerks" who calculated the annual household registrations, taxes, reclaimed fields, coin and grain stores, banditry, and legal cases of each commandery and county, using these to assess performance — this was called the "Annual Accounting." These men were equivalent to later-day accountants, their daily work dealing with numbers. Accountants were also conscripted in wartime as specialized personnel, serving as assistant officers to the Army Director of Works or the Army Logistics Officer, helping to measure hillside heights, gauge river depths, coordinate supplies and grain, and allocate troop numbers.

At this moment, the Accounting Clerks were sitting inside the tent, sweating profusely as they manipulated the counting rods. Heifu went over to look and found that they were all calculating problems like: "Now there is a moat, with a top width of 1 zhang 6 chi 3 cun, a bottom width of 1 zhang, a depth of 6 chi 3 cun, and a length of 13 zhang 2 chi 1 cun. What is its volume?" and "The work is 766 chi, and adding one-fifth for earth removal, the fixed work is 612 and four-fifths chi. How many laborers are needed?"

Although the Accounting Clerks were swiftly manipulating the counting rods to perform rod calculus, to Heifu it still seemed extremely complicated and troublesome.

Zhang Han, however, did not feel this way. Instead, he said with a smile, "In the past, calculating earthwork and manpower was even more complicated. Fortunately, in the Censorate there was an official in charge of charts, books, and records who, based on actual projects like constructing city walls, digging canals, and building granaries, wrote a treatise called 'Estimating Work' and submitted it to the Privy Treasurer. Since then, when it comes to calculating the earth volume for building ramparts and the number of convict laborers needed, one need only plug the numbers into the algorithms he devised..."

"Estimating Work" is the method of measuring volume and calculating labor for engineering projects. Zhang Han also showed Heifu that scroll of "Estimating Work" he carried with him. Each section was divided into problems, solutions, and formulas.

Heifu looked at it and found it very familiar. Isn't this "The Nine Chapters on the Mathematical Art"?

"Shaorong, could that official you mentioned be named Zhang Cang?"

"Oh?" Zhang Han was somewhat surprised. "The Platoon Leader also knows Zhang Cang?"

"A distinguished disciple of Xunzi from Lanling — I have long heard of him."

Heifu smiled. "Moreover, two years ago I served as the Patrolman of Huyou in Yangwu County, Dang Commandery, and became acquainted with Zhang Cang's two uncles, Zhang Fu and Zhang Bo. I also heard from them about this Zihu's deeds. I never expected him to be so multi-talented!"

"That is only natural. Zhang Zihu is one who leaves nothing unlearned and masters all he studies."

Zhang Cang was a junior fellow disciple of Li Si and could be considered a member of the "Li Si faction." As an official of the Privy Treasurer, many matters involved precise calculations, and Zhang Han had dealt with Zhang Cang often. He then recounted an amusing anecdote about Zhang Cang:

"When Zhang Cang first took up his post at the Censorate, the Grand Censor saw that he was born fair-skinned, plump, and so stout that even walking was somewhat difficult, and took a considerable dislike to him. He pointed at Zhang Cang's round, bulging belly and asked, 'What is inside there?' Zhang Zihu, however, took no offense. He merely slapped his belly and laughed heartily, saying, 'What's inside is all learning — a belly full of statecraft and scholarship!'"

"The Grand Censor was also a great talent of vast erudition. He tested Zhang Cang on the spot with some questions, and Zhang Cang answered every one. There were even some obscure texts that the Grand Censor himself had never read. So he had him put in charge of the archive's charts and books. Zhang Cang loves books as if his life depended on it. He often brings a bit of dried provisions and sits among the piles of bamboo slips for days on end. Now, I fear he has nearly finished reading all the books from Han, Zhao, Wei, and Yan that the Censorate collected. Everyone says that as his belly grows ever larger and fatter, he's probably trying to stuff all the knowledge under heaven inside it!"

Thinking of that supremely clever yet ever-fatter fellow, Zhang Han could not help but laugh. "When the Platoon Leader goes to Xianyang in the future, you'll know just what kind of man he is!"

"I certainly will!"

Heifu marveled inwardly. Most people merely study by rote, but Zhang Cang not only had a vast range of interests, he could also transform what he learned into practical application — that was truly remarkable.

He glanced again at the Accounting Clerks swiftly manipulating the counting rods and thought to himself, "If we had the vertical algorithm of Arabic numerals and the abacus, these engineering quantity calculations could probably be done much faster."

However, Heifu did not rashly offer up this treasure. That knowledge — he actually only had the math level of a middle school student left. Teaching it to ordinary people would be of little great use. He thought that when he went to Xianyang in the future, he would find a chance to reveal it to Zhang Cang. He wondered if it might bring a mathematical revolution to this era?

After the quantity of work was calculated, Zhang Han assigned tasks to the ten thousand Southern Commandery laborers allocated to him. They were responsible for building three li of ramparts. Thus, throughout the first ten days of the tenth month, the far outskirts of Shangcai became a huge construction site, with yellow dust filling the sky as thousands of laborers carried earth on their backs...

The method used to build the walls was still the rammed-earth method Heifu had participated in back in Anlu County. Another several thousand laborers skillfully used tools to fell the forest trees near Shangcai. After stripping the branches and sawing them into planks, they finally nailed them together into wooden panels. Once the panels were filled with earth, the laborers swung heavy tamping pestles and pounded the loose, worked earth with a mighty crash! The fiery, bustling work chants shook the countryside, and basically one layer of rammed earth was added each day.

Platoon leaders like Heifu also led their soldiers, fully armed, waiting quietly outside the construction site, ready to respond to any Chu army harassment that might come at any time.

"Is this not also a way of luring the enemy?"

On the border between Qin and Chu, tens of thousands of Qin soldiers protected tens of thousands of laborers at work. They fed their horses and sharpened their weapons, constantly prepared for battle, fearing only that the Chu army would not come.

Chu chariot and cavalry scouts also watched this scene from afar, but their main army never dared to rashly attack, for Xiang Yan knew that this could also be a trap Wang Jian had laid for him.

Several days later, a thick earthen wall over a zhang high appeared out of nowhere in the eastern outskirts of Shangcai, rising from the ground. At the positions where marker poles had been driven every hundred paces earlier, Zhang Han was also urging the laborers to build even taller and sturdier corner towers.

It was at this moment that an accident occurred...

A corner tower that had just been tamped was tested for its sturdiness by Zhang Han and his men. Yet after a dozen men shouldered a wooden ram and struck it heavily a few times, cracks appeared! And large chunks of earth broke off and fell!

"If the Chu army attacks, how can this corner tower defend against the enemy? It will surely become a breach for the enemy to break through. A thousand-li dike is destroyed by an ant nest!"

"All those who built this corner tower shall be flogged ten strokes, then tear it down and rebuild it!"

Zhang Han glared fiercely at the petty Director of Works clerk responsible for this section, saying that if it happened a second time, the man in charge would be beheaded, and the rest would follow him in death!

The petty Director of Works clerk was obsequiously compliant. Zhang Han said to Heifu with some vexation, "The Supervising Censor demands that the corner towers must reach the hardness of the walls in Guanzhong — impregnable. But that requires a very long time of tamping to achieve. Right now, the construction period is only a bit over ten days. In such haste, I fear it will be difficult to tamp them to that standard. Moreover, the quality of the soil directly affects the sturdiness of the ramparts and corner towers. The best soil is fine but not loose, oily and moist but not dry, bright and clear but not dull. But the soil here in Shangcai is truly mediocre, far inferior to the yellow earth of Guanzhong..."

In this era, Shangcai had a relatively high forest coverage rate, and the soil contained a fair amount of humus. Using such nearby soil to tamp ramparts and corner towers indeed made quality hard to guarantee.

Zhang Han decided to have men bypass the near for the far, digging dry, loose, and fine yellow earth from a distance to build the corner towers — only thus could quality be assured. Heifu's eyes rolled, and he offered Zhang Han an idea.

"Shaorong, in the village lanes of Anlu in Southern Commandery, there is a local method for building houses. After drying, it becomes exceptionally hard. Not only does it remain unchanged when soaked in water, even iron nails are difficult to drive into it! It remains intact and undamaged after centuries of wind and rain!"

After saying this, fearing Zhang Han might not believe him, he brought out his brother-in-law as a scapegoat: "My brother-in-law Chuan is not only proficient in woodworking but has also used this method to build houses for people."

"There is such a method?" Zhang Han was immediately very interested and asked Heifu to explain in detail.

Heifu smiled. This was a common method for building houses in his rural hometown in his past life, not yet popular in this era. He pointed at the gurgling branch of the Ru River not far away and said, "It's very simple, and the materials are not hard to come by. Mix common yellow earth with fired clam-lime and river sand, then tamp it together — it's called tabby!"

PS: Second chapter in the evening.

(End of chapter)