It was a device used by coastal artillery as a back-up method of range finding. The primary [pre-radar] method used "base end stations" to get a cross-fix on the target. Here is a training film
showing how that worked. The BES method relied on at least two stations having visual on the target AND communications with the Plotting Room.
If, for whatever reason this was not the case, the individual stations and the battery's own observation post usually had a depression rangefinder. Since the elevation of the installed (and leveled) rangefinder could be precisely surveyed, then measuring the angle in degrees from horizontal to the waterline of the target could provide a trigonometric range to the target.
For example: Nagato & Mutsu are bombarding San Francisco. Fort Barry, on the Marin headlands has an observation post at the top of the cliffs, 70 meters above the waves. The depression rangefinder measures the angle from the horizon to Mutsu's waterline as 0.3 degrees. 70m / tan0.3 = ~13,369 meters. This was in-range for Battery Wallace's 12" barbetted guns, but just outside the reach of Battery Mendell's 12" disappearing guns
and Battery Alexander's 12" mortars
Note that, to get an accurate solution, the depression rangefinder had to see the target's waterline, which meant that it was effectively useless at night or in bad weather, or if the target was hull-down or too far away to get a decent angle measurement.
Hope this helps.
Just because it's stupid, futile and doomed to failure, that doesn't mean some officer won't try it.
-- R. Rather