Chapter 27: Navigation

The quadrant had been in existence in this time for less than half a century. Now, someone was telling Li Huamei that this new device was even better, and of course, she was skeptical—though it was indeed more compact.

“You’re bragging,” she said, dismissing it with a curt phrase. Unlike her master who often operated in the East Asian seas, Li Huamei’s ship mainly sailed to Goa, and sometimes to Manila. Through the windows of these two colonial cities, she had seen most of Europe’s new gadgets, but she had never heard of a navigational instrument better than the quadrant.

“Hehe, there are many things you haven’t seen. A sextant is nothing,” Lin Chuanqing said with an air of indifference.

Li Huamei noticed a place that seemed to be inlaid with a lens and was about to touch it when someone shouted, “Don’t touch it! You’ll scratch the glass.”

Turning around, she saw a man she didn’t recognize. He was in his late thirties, tall and large. The short-hairs were generally tall, but this one was exceptionally so, at least six feet seven or eight inches (1.9 meters), a head taller than those around him, with a robust build, a round face, and large eyes. He wore a blue, front-opening short jacket, a common attire for the Australians—they called it a training uniform. Someone had told her that blue was for the navy, gray for the army, and the colorful ones were worn by everyone. His skin was dark and rough, clearly weathered by the sea and wind, and his expression was resolute and serious.

Behind him stood six boys in matching black, stand-up collar student uniforms, all looking to be between thirteen and fourteen. Their faces were tanned, and they stood steadily on the swaying deck. Each carried a green canvas schoolbag and stood neatly in a row.

“Commissar Chen, giving the kids another lesson?” From the way Lin Chuanqing greeted him first, this man must be a high-ranking short-hair.

“Yes, these boys from the navigation class have only ever rowed boats in Bopu. This trip is a good opportunity for an internship.”

He walked over and took the sextant from Li Huamei’s hand, saying in a deep voice, “The most important part of this thing is the glass lens. If you scratch it, it’s useless.”

Li Huamei said, “I’ve never seen one before. What a rare thing, treating it like a treasure.”

The burly man ignored her completely. Seeing Meng De stumble back from the ship’s rail, he reprimanded him without expression, “A sailor’s instrument is his life! You just throw it aside like that and you still want to be in the navy?!”

“Yes, yes, I—” Meng De could barely stand, but it was clear he held this man in great awe. He tried to stand at attention.

“Go back to your cabin. Dismissed!”

“Yes!” Meng De tried to come to attention and salute, but a wave of nausea washed over him, and he rushed back to the rail.

“You know how to use a quadrant?” Chen Haiyang turned to look at the woman before him. It was the first time he had observed her up close. By modern standards, she was not short, at least 165cm, which was even taller for the time. She had a slender figure, and her hair was thinned and tied back in a ponytail, giving her a somewhat modern look at first glance—no wonder the otaku in the navy were so smitten.

“Of course, I do. It’s how I make a living,” Li Huamei said seriously, seeing that he was a tough character.

“Show me how to use it first,” Chen Haiyang was currently very interested in ancient navigation techniques. Many of the navigation devices on modern ships could not be manufactured in this time, so how to apply mature ancient and early modern techniques had become a major topic in training the new generation of sailors.

“Alright, I’ll go get my box,” she said, flicking her ponytail that had fallen to her ear. “But you have to teach me how to use this sextant later!”

“Deal,” he replied crisply.

“Commissar Lin, is it okay to let her use the sextant?” Lin Chuanqing asked his namesake after Li Huamei had gone below deck.

“It’s no big deal. We were going to teach these kids anyway,” Chen Haiyang said. “Besides, she’s teaching us things too.”

“Well, to be honest, I’d like her to give me some pointers on steering too.”

“You’ve got to be kidding. You’re an old sea dog who dared to cross the Pacific in a small motor-sailer. You need someone to teach you this?”

“A motor-sailer has an engine, at least,” Lin Chuanqing said, gripping the wheel tightly. “This pure sailboat… the feel is just not right.”

As they were talking, Li Huamei climbed back up to the quarterdeck, carrying a box. It was quite large and bulky.

“This is my full set of instruments,” she said, opening it.

Inside the box were several instruments, books, and rolled-up sea charts.

“There are a few more things on the Hangzhou. They’re fixed, so there’s no need to bring them.”

Chen Haiyang watched with interest as she took out the first item. It was quite large, made of bronze, with a radius of about 0.6 meters. It was cast in bronze with a hollow center. The outer edge of the quadrant was engraved with angles, the smallest division being 0.25 degrees. Two bronze rings were attached to the center for suspension, and a thin silk thread with a lead weight at the end hung from the center. On one straight edge of the quadrant were two bronze blocks with two small holes, about 5mm in diameter, which could be used to sight the stars.

“This is the quadrant,” Li Huamei explained. “Some people call it a mariner’s astrolabe.”

“Wait, I remember the quadrant looking different,” Chen Haiyang said. The more he looked at it, the more he felt it was different from the pictures of quadrants he had seen in his naval academy textbooks.

“This is the quadrant,” Li Huamei said, then she understood. “You must be talking about the English quadrant.” She then took out another instrument from the box. It was much smaller, also made of bronze, and somewhat resembled a sextant.

“This is clearly a backstaff!” Chen Haiyang slapped his thigh, remembering the standard name from his textbooks.

“Backstaff? I don’t know that name. Everyone calls it the English quadrant. But it’s very useful and accurate.”

The English quadrant. Chen Haiyang thought that was a very direct name—it was invented by the English navigator John Davis.

“We can’t look at the astrolabe now. I’ll demonstrate it for you tonight. Let’s look at the quadrant first.”

Chen Haiyang instructed the students, “All of you, watch Instructor Li’s operation carefully!”

“So you’re making me an instructor,” Li Huamei chuckled. “Well, I’ll make a fool of myself then.” She raised the backstaff.

The backstaff was so named to distinguish it from the cross-staff that was used before it. Their methods of use were similar, but one required direct observation of the sun, while the other required the user to have their back to the sun.

When operating it, the observer stood with their back to the sun and aimed at the horizon through the sight on the large arc and the slit on the small arc. The shadow vane was set by estimation, and adjusted until the shadow of the upper vane fell on the upper edge of the slit. The horizon could be seen at the same time. The readings from the two arcs were added together to get the zenith distance. Then, the latitude could be calculated using a formula. Because the large arc was diagonally divided, even small angles could be read accurately, greatly improving the accuracy of latitude calculation.

Li Huamei demonstrated the operation once, then had the naval cadets do it one by one and calculate the latitude. Although most of these children came from seafaring families, almost all of them were illiterate, let alone knew mathematics. They had to rely on cramming at the National School to catch up on their knowledge, so their calculations were naturally very slow. After much measuring and calculating, the answers they came up with were quite different from the number Li Huamei had measured.

Chen Haiyang reviewed the calculations of several students. Some had made clear calculation errors, but their observation numbers and calculation processes were correct. It seemed the students had a decent aptitude. After all, in the shore-based teaching prior to this, they had already been taught basic geographical and astronomical knowledge, such as the shape of the Earth, latitude and longitude, and time zones. Otherwise, just explaining the concept of latitude would have been enough to drive a person mad.

“They know about latitude and longitude?” Li Huamei was a little surprised. In the Ming Dynasty, almost no one understood this concept, not even the people who made their living at sea every day. They weren’t interested in knowing—ancient Chinese navigation had its own system.

Chen Haiyang found it strange. Weren’t latitude and longitude the most basic concepts in navigation? “We’ve taught them all. How else can you navigate?”

Li Huamei was a bit emotional. “In the Ming Dynasty, I doubt there are more than ten people who know what latitude and longitude are.” A doubt arose in her mind. These Australians claimed to be descendants of Song dynasty immigrants who had been lost in Australia. If they were isolated overseas, how did they know about European science? And these instruments. It was as if they had always been in contact with Europe. But the Europeans had never heard of this place. It was very strange.

Next, she took out a small bronze disc with scales, small holes, and a pointer. The edge was serrated, looking a bit like a circular saw blade at first glance.

“A nocturnal. But we can’t use it now. We have to wait until midnight.”

“To determine the time of midnight by the transit of a star across the meridian?” Chen Haiyang speculated.

“You’re good, you knew just by looking! Have you used one before?”

“No, I never even knew such a thing existed in the world until you took it out.”

“This is a nautical almanac,” she said, taking out a book with a rough, heavily worn hardcover.

“This is—”

“The Seaman’s Kalender.” Chen Haiyang had been a naval officer and his English was decent. He could naturally read the title.

“You know English?”

“A little,” Chen Haiyang said humbly.

“Hehe, that’s impressive,” Li Huamei said casually, wondering why all these Australians knew a few words of English. If the Australians were a trading nation, Dutch or Spanish would seem more useful.

She didn’t know that thanks to the universal education and the college entrance examination system of another time, almost everyone in China under the age of thirty knew a few words of English.

The book was full of astronomical charts that sailors needed, mainly meridian charts, tables of distance and departure for every quarter-point of the compass and every degree, as well as tables of logarithms of natural numbers, trigonometric functions, and tide tables. It was a very convenient handbook for sailors.

“This book is only sold in England now. It’s hard to find. I got this one from an English ship last time.” It was clearly a prize of war.

The other book was printed in Portuguese, which Chen Haiyang couldn’t read, so he had to rely on Li Huamei’s explanation.

The book was called “Regimento do estrolabio e do quadrante” (Rules for the Astrolabe and Quadrant). Its purpose was to provide a reference table for determining latitude and longitude. Whether using the sun or the stars to determine position, it was necessary to relate the change in latitude to the distance traveled. Sailors had a distance table, usually posted at each point of the compass, for adding or subtracting latitude. The book included a distance table, a latitude table from Cape of Good Hope to the equator, and a table of the sun’s declination for a four-year cycle. This book was published as a guide for navigators and had a very long history. It was officially published in 1509, but earlier versions may have existed even earlier. At least Columbus used it on his voyage in 1492. It was subsequently revised and reprinted many times.

Chen Haiyang flipped through these manuals, looking at the numerous rules and tables. The efforts made by humanity to break through their geographical limitations and explore new worlds were truly great. Although these manuals looked rough, and some of the rules and numbers were even wrong, they were the accumulation of the wisdom and experience of countless sailors. Standing before them, he couldn’t help but feel a sense of reverence.

Wasn’t this Li Huamei before him also one of those pioneering navigators? Chen Haiyang, who had always been suspicious and hostile towards her, now felt a subtle new emotion in his heart.

The naval cadets were all half-grown boys. Although bound by strict military discipline, they couldn’t help but peek at the many strange and unseen gadgets coming out of the box when Chen Haiyang wasn’t looking.

The last thing Li Huamei took out was a roll of paper. “These are sea charts. Very expensive,” she said jokingly.

These charts were Mercator charts, drawn according to the latest scientific achievements of the time. Medieval charts were plane charts. This type of chart was originally a pattern of compass rhumb lines developed for medieval Mediterranean charts. It gave all north-south lines as parallel, and as the distance from the equator increased, the east-west distances became more distorted. As a result, the bearings on the chart often had large errors. Mercator invented a new projection chart. The most basic feature of this projection chart, and what distinguished it from plane charts, was that it gave the true bearing or rhumb line between any two points. The accuracy was greatly improved.

Most of these charts were of the East Asian and Southeast Asian seas, and there were also charts of the Indian Ocean. Chen Haiyang, of course, knew the value of these charts. In the past, they were a huge fortune.

“Can you go to Goa?”

“I run the Goa-Macau route. I’ve been to Madras too.”

“You really are a navigator,” he said sincerely. At heart, Chen Haiyang was an explorer and an outdoor enthusiast. After leaving the army, he had once crossed the Siguniang Mountains alone and had also sailed a sailboat in the Qiongzhou Strait. He felt a great sense of kinship with this kindred spirit.