Other ranks correspond in their heads (8)
I believe the answer is:
mentally
'in their heads' is the definition.
(I've seen this before)
'other ranks correspond' is the wordplay.
'other ranks' becomes 'men' (I can't justify this - if you can you should give a lot more credence to this answer).
'correspond' becomes 'tally' (synonyms).
'men'+'tally'='MENTALLY'
Can you help me to learn more?
(Other definitions for mentally that I've seen before include "in their heads" , "without pencil and paper" , "how intelligence is developed" , "by way of intellect" , "not physically" .)