Just a comment that it is not a taffrail log as my understanding of that is that the meter is mounted on the taffrail and the rotations travel to that to measure distance travelled. The rotor is very similar but shorter than the one illustrated as there is no mechanism inside it.

With a harpoon log the rotations are transmitted to the 'meter' in the log itself.

I am not sure how one could usefully use it in a well

It is a harpoon ships log for measuring distance when trailed behind the boat. The 'dials' are covered in use by a sliding cover that rotates around the cylindrical shape.

As the log is pulled through the water it rotates on the eye fixed to the cable and rotations measure distance.

I have an identical one. It is made of bronze. (One fin of mine was replaced in use with a copper one)

Mine is a Walker Patent Harpoon Ships Log A2. London. The distance is measured in 'miles' in tens, ones and quarters on the respective dials on a white enamelled backplate.