In the past, ships often carried small cannons that wer used when approaching shore in a dense fog to estimate the distance to the hidden land. How would this work?

The use of cannons to estimate distance in dense fog was a common practice in the past. Here's how it would work:

1. The ship approaching the shore would fire a small cannon towards the land.

2. Once the cannonball hits the water, it would create a loud boom or splash, which could be heard by the crew on the ship and potentially on land as well.

3. By timing the interval between when the cannon was fired and when the sound of the impact reached the observer, they could estimate the distance to the hidden land.

4. The crew on the ship would measure the time it took for the sound to reach them using a device called a "linstock," which was essentially a long stick with a small flag or piece of cloth at the end. When the boom was heard, the linstock would be dipped into water, and the time it took for the crew to see the splash would be measured using knots tied onto the stick.

5. By knowing the speed of sound in air (approximately 343 meters per second or 1,125 feet per second at sea level), the crew could calculate the distance of the land by multiplying the elapsed time by the speed of sound.

It's important to note that this method was not very accurate and had limitations. Factors such as wind speed, air temperature, and the density of the fog could affect the speed of sound and introduce potential errors. Additionally, variations in crew members' abilities to time the intervals accurately could also impact the results. Nonetheless, in the absence of more precise instruments, this method provided a rough estimation of distance that could be useful when navigating through foggy conditions.