In the late 1800's men would still wear pocket watches. And wearing a wrist watch was considered, girly. A popular expression between men, would be that they would rather wear a skirt, than wear a wristwatch. However, this all changed when Britaon and Africa fought against each other at war. The British soldiers became really good at excecuting timely attacks. One of the ways they did this, was by tieing straps to their watches, or what they called, "wristlets." By making these wristlets or by turning pocket watches into wrist watches, this freed up the soldiers hands and they were able to move easier and faster, while at the same time, with precise timing.
This gave the British soldiers a huge advantage over the African soldiers. And ultimately, the wristlets helped the Bristish win the war. Eventually, when World War II broke out, pilots were then requesting wrist watches to help them track time easier and make precise timed attacks on the enemies, while at the same time, freeing up their hands. This made the wristwatches even more popular.
At the time, big watch Brands like Omega or Patek Philippe, quickly began producing and marketing wrist watches and promoting them to the public, which eventually caught on. So, the first wrist watches can be credited to soldiers at war, rather than to some of the big brands, which some take credit for introducing the wrist watch. Whatever the case may be, no pun intended, the wrist watches overthrew the pocket watches popularity forever. Another more modern example, is how the iphone caused the demise of the ipod.
Image credit to TimesTicking
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