Chapter 97: Footprint Studies

"That was during the spring plowing season. I was on leave, home to help with the fields, working barefoot alongside my eldest brother and my brother-in-law, the three of us. Back home, we were still barefoot as we washed the mud off together. That was when I noticed, standing side by side, the length of our feet — my brother-in-law's the longest, mine next, and my eldest brother's the shortest. The same went for height: my brother-in-law was the tallest, a full eight chi; I am seven chi six cun; my eldest brother, seven chi three cun."

"A sudden whim struck me then. I fetched a Qin ruler and measured the foot length of the three of us, noting the figures on a wooden board. After returning to my post at the ting, I mulled it over repeatedly but could make no sense of it. Not until last month, when the ting had little official business and I had leisure time, did I fetch some counting rods and try dividing each man's height by his foot length. The result astonished me — the numbers I got were startlingly consistent!"

"Six and three-quarters! Gentlemen, this is the ratio I calculated between a man's height and the length of his foot!"

Heifu slowly recounted the "experience" of how he had discovered this, speaking with such conviction it sounded entirely true.

In truth, it was simply something taught to him in a past-life elective called "Footprint Studies" during his three-year police academy degree. At least he had attended every class and hadn't returned all that knowledge to the teacher...

As he explained the matter, Xi, Nu, Yue, and Anpu all listened, utterly absorbed, and Heifu had no need to worry that they wouldn't understand what "division" or "fractions" were. To assume that would be to gravely underestimate the ancients.

The Qin state's meticulously detailed system of laws and administration required a large cohort of mathematically proficient officials, so the study halls had specialized instruction in the *Book of Numbers*. The minor clerks in the Anlu County government offices, especially those in the Granary Section and the Household Section, could all basically recite the Qin-era version of the "nine-nine multiplication table" — only they recited it backwards, from "nine nines are eighty-one" down to "two-halves make one," which already falls within the scope of division. It couldn't be helped; their daily work was calculating all manner of grain and household registers, and the rations provided to officials were often precise down to fractions.

Moreover, in this era, operational rules for fractions already existed: combining fractions (fraction addition), subtracting fractions (fraction subtraction), multiplying fractions (fraction multiplication), reducing fractions (fraction division), and even comparing fractions (comparing fraction sizes) and averaging fractions (finding the mean of fractions). Apart from not using Arabic numerals, it was virtually no different from later ages.

After all, Li Si's fellow disciple, the great mathematician named Zhang Cang, was currently working in the Censorate offices in Xianyang, the Qin capital. And though *The Nine Chapters on the Mathematical Art* was compiled as a book in the Han dynasty, it was in fact born from over a century of accumulated practical mathematics in the Qin state...

Since everyone present had some grounding in mathematics, explaining it was far less taxing for Heifu. He concisely presented the figure six and three-quarters, and the next step was to verify whether this ratio was reliable.

The others still looked hesitant. After all, although Qin statute clerks recorded footprint sizes when handling cases, they mostly did so to compare them *after* a suspect was caught; they rarely worked in reverse, using footprints to apprehend a criminal.

So Heifu smiled and said, "These past few days, I've had several men at Huyang Ting try it. Their heights and foot lengths, without exception, all yielded this number when divided. If you gentlemen have doubts, why not give it a try yourselves?"

"Fine! Ting Chief Heifu, use the length of my footprint to calculate my height!"

The Clerk Aide Anpu was the first to step forward. He took a Qin ruler, removed his boot, measured his foot, and announced his foot size: "Neither more nor less, exactly one chi and one cun!"

Yue, who was the best at arithmetic among them, took up the counting rods to calculate. The rods were little sticks, and using them was quite complicated.

Seeing him struggle with the calculation, Heifu nevertheless refrained from rashly introducing "Arabic numerals" and "vertical-form calculation." He knew the time was still far from ripe to present such things.

The Qin state's system was too unique, unlike any other dynasty before or after. Things from later ages were only worth presenting when they could yield the maximum benefit...

After a short while, Yue arrived at the result. "Would the Clerk Aide's height be seven chi and four cun?"

Anpu, who had been somewhat skeptical, was momentarily stunned by the result. "Almost exactly!"

"Try mine!"

Nu, as a Statute Clerk who had dealt with footprints for so many years, had never known that a footprint could be used to deduce a murderer's height. He was instantly fascinated.

Soon, the heights of both Nu and Yue were also deduced from their foot lengths, and indeed, they closely matched their actual statures.

"Though not yet accurate to the last hair's breadth, it is remarkably close. Ting Chief Heifu, you have discovered yet another remarkable method for solving cases..."

Xi, who had been watching from the side for some time, affirmed Heifu's discovery, but also couldn't help sighing with regret. "Had this technique existed earlier, many of the cases that have passed through my hands over the years could have been solved faster. A number of utterly vicious bandits might not have escaped by luck, only to kill again."

Now that Heifu's "footprint method" had been proven reliable, the next step was to bring out the *Fengzhen Shi* records that Nu had taken that day and examine the footprints left by the culprit.

At that moment, Anpu raised another point: although height could indeed be deduced from foot length, could wearing shoes cause a deviation?

Heifu glanced at the deerskin riding boots on Anpu's feet and smiled. "Clerk Aide, those murderers and bandits are hardly comparable to officials. They can't afford good shoes, let alone xi or boots — they can only wear hemp shoes."

It turned out that in this era, footwear mainly came in forms like xi, boots, and lü. Xi were wooden-soled shoes sewn with brocade and patterned silk, worn only by nobles who did no manual labor. Boots were made of leather and only became common after the adoption of Hu-style mounted archery in the Warring States period, typically seen on officials and riders.

The vast majority of commoners and rank-and-file soldiers still wore straw or cloth shoes, generally called lü. Since lü were shoes that merely wrapped the foot, the discrepancy between the shoe print and the actual foot length was relatively small.

The *Fengzhen Shi* was quickly fetched. According to that day's record, the footprint was one chi and two cun long...

"Calculating by the Qin standard of one chi equaling 23.1 centimeters, the bandit is someone who could wear a size 44 shoe. What a pair of big feet..." Heifu grumbled inwardly.

Meanwhile, Yue had also calculated the bandit's height. He announced in surprise and delight, "It's worked out! Multiplied by six and three-quarters, the bandit's height is roughly eight chi and one cun!"

"1.87 meters. Even in a later era with better nutrition, that would still count as a burly, towering man..."

The truth was out. Heifu couldn't help but whistle. This made the search much easier. In all of Anlu County, there couldn't be more than fifty men of that height!

The height of Qin people wasn't as the terracotta warriors suggest, with every figure nearly 1.8 meters tall. Perhaps that was the standard build for men from the Guanzhong region?

In any case, in Anlu County, Heifu had found that his own height of 1.75 meters already made him stand head and shoulders above the crowd. Most men in the county seat were under 1.7 meters, and in the rural areas where nutrition was poorer, many were as short as 1.6 meters.

That was hardly surprising, since the Qin standard for adulthood was "six chi seven cun," roughly 155 centimeters...

Once the "murderer's" height was calculated, Yue was elated. The long-stalled mystery case had finally seen a breakthrough.

Clerk Aide Anpu was also itching for action, ready to lead the county soldiers in a search for a man of towering height and bulk who carried a sword. Even if the man had now discarded the scabbard and the blade inside, it would be useless; with their methods, they were bound to find a flaw.

The look Nu directed at Heifu grew increasingly full of admiration, even tinged with shame that he had served as a Statute Clerk for so many years, only to have Heifu repeatedly propose novel methods. He instinctively felt that both the preservation of the crime scene and the footprint method should be recorded and reported to the commandery office and the Commandant of Justice, to become standard practice, even law, and spread throughout the land!

Only Xi remained extremely cautious. He took Yue's counting rods and performed the calculation again himself. After confirming that the figure "eight chi and two cun" was correct, he did not rejoice but instead grew more worried, his brow furrowing even tighter.

"In that case, a new problem arises."

He stared at the group and said:

"How could a burly man eight chi and two cun tall be so nimble as to leap through a window a mere three chi wide to commit murder?"

Heifu also recognized this flaw at that moment. Cold sweat instantly covered his forehead as he realized with a start that he had overlooked a critical issue.

That footprint was very fresh, indeed left on that very day. But was it truly left by the murderer?

If not, then when the murderer climbed up from the muddy ground to the window, exerting force with his steps, why did he leave no footprints of his own?

It was as if a bucket of cold water had been dumped over them. The excitement from moments ago vanished, and they all fell into frowning, intense thought.

"There is another possibility."

Heifu's mind raced, and he blurted out, "We were thinking of this case too simply before."

"The murderer is very likely not just one person!"

(End of chapter)