The most likely usage known to me … but there may be more …
It can be very convenient to have a lower power objective for ‘field scanning’ to identify a region of interest: ergo, if the ‘main’ objective is already an oil-immersion one, it makes sense for the low power to also be oil immersion.
Leitz and Nikon both favoured supplementary caps, but there is no reason to suppose that Cooke could not make the feature integral.
What this does not explain, however, is why the Seller has failed to focus it !
… I suspect that it’s just a matter of “must try harder”
MichaelG.
.
Edit: __ this might be the other discussion which Dave had in mind:
https://www.model-engineer.co.uk/forums/topic/unusual-cooke-microscope-objective/
… if nothing else, it gives some indication of Cooke’s position at the leading-edge of microscopy.