Global colonization began with Ming Dynasty pirates.

"Begin measuring speed!"

After more than an hour of torment, the boys were finally able to steer the boat in one direction. Then, urged by Lin Hao, they immediately began practicing the second skill.

"Begin!" With Lin Yi's command, he flipped the hourglass in his hand to start timing, while another boy began to release the rope in his hand.

One end of the hemp rope was tied to a bamboo board, and the other end was wound around a spindle. As the sailboat moved forward, the hemp rope on the spindle was continuously...

He rolled over and started timing. Another sailor held a rope, one end of which was tied to a triangular wooden board that floated on the sea, while the other end was wrapped around a spindle. As the sailboat moved forward, the rope would loosen from the spindle and pass through the boy's hand.

"Stop!" Lin Yi shouted as the sand in the hourglass ran out.

Then the boy who was setting out the bamboo clappers announced a number, which was the number of knots in the rope that had passed through his palm during that time.

Lin Yi quickly did a mental calculation, then said to Lin Hao, "Reporting to Young Master, speed measurement complete, current speed 5 knots."

"Hmm, your measurement is quite good. The next group will continue measuring the speed and keep monitoring. Tonight, we'll practice measuring the latitude and then calculate the ship's position."

Lin Hao nodded. Once the complicated operations were no longer required, the teenagers' performance met Lin Hao's expectations. Of course, it might be because measuring the speed was too simple.

In this era, the direction and speed of navigation had to be measured and recorded at all times. In the Ming Dynasty, this was compiled into a navigation map, while in the West it was called a nautical log.

Knowing the direction and speed, and the latitude of the two points, you can determine the position of the current point relative to the previous point simply by combining trigonometric functions. Connecting all the points forms the navigation route map, and theoretically, you can know your exact location.

Yes, theoretically. In reality, the error is quite large, and it becomes increasingly outrageous as time and weather conditions change.

To truly know a location, one still needs to measure latitude and longitude, but unfortunately, before the invention of the nautical horn, measuring longitude was too difficult.

Although everyone knows that longitude can be calculated if the local time is known, this is simply impossible, as current pendulum clocks cannot keep accurate time in the turbulent conditions of the sea. It was not until the invention of the marine chronometer in the 18th century that this problem was truly solved.

Latitude, on the other hand, is something that both the East and the West have mastered.

The Ming Dynasty used a star-gazing board for measurement. The star-gazing board is composed of 12 square ebony boards, with the largest side length being 24 centimeters (twelve-finger board) and the smallest being 2 centimeters (one-finger board), supplemented by notched ivory blocks for fine adjustment.

When using a star chart to measure latitude, the observer needs to extend their arm, keep the chart perpendicular to the sea surface, and then adjust the chart so that its upper edge is tangent to the star and its lower edge is parallel to the sea surface. The star altitude (latitude) can be obtained from the index (1 index ≈ 1.9°) of the chart.

According to the records in "Zheng He's Nautical Charts", when Zheng He sailed to the Western Ocean, the latitude data measured when he passed through the Strait of Malacca was "the North Star seven fingers triangle level water".

The corresponding latitude is 14 degrees 2, which is only 20 kilometers away from the actual latitude.

At this time, the West used an astrolabe or a cross, both of which were based on the same principle. What really led to the difference later was the sextant, which was proposed by the famous Newton and Hooke based on the principles of geometric optics and subsequently became a standard tool for navigation in the 18th century.

Lin Hao had his students use a sextant to measure latitude. Once they understood the principle, and with a blacksmith who was competent, a sextant could be easily made. However, it took Lin Hao a lot of effort to get the scale on it accurate.

As night fell, at Lin Hao's instruction, the group did not turn back but continued sailing.

After a simple meal, the group began measuring the latitude.

Latitude measurement is much more convenient at night than during the day. During the day, you can only measure the midday sun, but at night, there are too many celestial bodies that can be measured.

However, the most popular method is measuring Polaris, because Polaris is on the Earth's axis of rotation and is infinitely far away from Earth. This means that the line connecting Polaris to the current location is parallel to the Earth's axis, and the measured altitude angle is the latitude, without needing to convert it based on the position of celestial bodies.

Lin Yi was the first to take measurements. He took out a metal instrument and began operating it on the sea surface.

This instrument is equivalent to one-sixth of a circle, hence the name sextant.

The key to the entire sextant is the two mirrors. The first mirror is an index mirror fixed on the top selectable scale. As the arm rotates, the direction changes, and the bottom of the scale points to the graduation mark.

The second side is a horizontal mirror that is fixed to the sextant frame and cannot be moved.

The key feature is the second mirror, which is half a reflecting mirror and the other half a glass lens, allowing the observer to simultaneously observe the sea horizon and celestial bodies.

According to the law of reflection, the angle of incidence equals the angle of reflection. When a second mirror is introduced and forms an angle with the first mirror, the angle of refraction of the light will be twice that angle. This principle forms the mathematical basis for the sextant's magnified angle measurement, and the instrument's scale is calibrated accordingly.

When the scale arm is rotated 20 degrees, the angle between the two mirrors is 20 degrees, but the light deflection angle is 40 degrees, so the scale is directly marked 40 degrees.

Lin Yi first spent more than ten seconds determining the position of Polaris, and then began to measure by placing his eyes on the frontmost cylinder.

He kept rotating the measuring rod, and after about half a minute, Lin Yi finally completed the measurement. He then fixed the measuring rod and carefully checked the scale.

"Reporting to Young Master, the measured angle of North Star is 26.5 degrees." Lin Yi's report caused Lin Hao to fall silent for a moment.

It's not that the measurement is wrong. Since the other party has measured it, the result is roughly the same. Lin Hao remained silent because they officially set sail at noon. At that time, the latitude of Dongluo Island was 26.4 degrees, obtained by measuring the sun at noon on Dongluo Island.

This means that the teenagers drove with all their might for a whole day and only traveled 10 kilometers north. That's quite a speed.

However, considering everyone's poor performance in handling the boat today, Lin Hao expressed his understanding.

"Understood. You take turns measuring, and at the same time measure Vega and other stars to correct their positions." Sextants are easy to make, but the mirrors and glass on them are not. At first, Lin Hao used bronze mirrors to make do. He only recently purchased mirrors from Macau, which were very expensive. Therefore, there are only two sextants equipped with glass mirrors.

Although rubbing a glass mirror by hand is a basic skill for a time traveler, since anyone who has studied junior high school chemistry is familiar with the principle, it's not that they can't, but that they dare not.

Before having a stable base and sufficient military strength, Lin Hao dared not bring out anything too advanced, otherwise he wouldn't even know how he died.

"I really want a permanent base; Dongluo Island is just too small."