@Lustig Andrei,
Lustig Andrei wrote:What's the big deal about mechanical clocks? Or any clocks for that matter?
As you already noted, things get trickier at sea, and that's where accurate (accurate to at least a matter of a few minutes) clocks become important, crucially important. Human beings have known, literally for thousands of years, how to find latitude (how far north or south they are of an arbitrary point or line). But finding longitude, finding how far east or west one is of a particular point, is extremely difficult. That can be accomplished by celestial observation, but it takes literally hours, and a steady observation platform--and at sea, one often doesn't have hours of clear weather in which to observe celestial bodies, and almost never has a steady platform.
However, if one can observe the sun at "local noon," which requires just minutes of clear weather, and does not require a steady platform, one can find one's longitude,
if one has an accurate clock. Set your clock to the time determined by local noon at an arbitrary point such as, oh, i don't know, Greenwich, east of London?--and as long as your clock keeps accurate time, you can compare the time on your clock to your observation of local noon and determine just how far east or west you are of Greenwich.
This can be very important for avoiding things like running onto a rocky coast at night, or reaching your destination before your crew dies off from scurvy. It has been shown to be crucially important by historical events. Le Sieur de la Salle had reached the mouth of the Mississippi River overland, so he determined to take an expeditino there by sea to establish a colony. He knew the lattitude, but he had no way to determine the longitude. He set sail, and he made landfall on the island which is today the heart of Galveston, Texas. That meant he was far, far to the west of the Mississippi River. To his credit, he realized he needed to find the river to the east, so he set off with a party of his men. By that time, the people of the expedition were becoming despondent, and the men had begun to mistrust La Salle. When he wandered off with his party of men looking to the east for the river, they eventually murdered him, and buried the body. Then they wandered back west, and lied about what had happened. Eventually, a few of them admitted the truth, and the story finally came out.
A good, reliable clock would have saved La Salle's life, and would have dramatically affected the colonization of North America.