what does the following Latin phrase mean in English:  adpellite ad medium

Although I had only high school Latin, I would guess that this phrase
means "reversion to the mean."  I am not even close to having enough
confidence to post an answer, but I look forward to a commentor or
another researcher confirming or rejecting this suggestion.

If this is used in a legal context, it may mean "appeal to the middle ground."

"ADPELL : V - call (upon); address; dun; solicit; appeal (to); bring
to court; accuse; name;

ADPELL : V - drive to, move up, bring along, force towards; put ashore
at, land (a ship);

ADPELLATIO : N - appeal (to higher authority); name, term; noun;
title, rank; pronunciation;

ADPELLATIV : ADJ - appellative, belonging to a species; 

ADPELLATIV : ADJ - of the nature of a noun, nominal; 

ADPELLATOR : N - appellant, one who appeals; 

ADPELLATORI : ADJ - of/used in appeals; 

ADPELLIT : V - call or name (frequently or habitually);"

http://www.incunabulabooks.com/ibrflata.htm

From this page, adpellite is the plural active imperative of 'adpelle'
which means 'bring to land':
http://www.arts.cuhk.edu.hk/~lha/latin_lessons/conjugation/verb_3.pl?prstem=adpell;pfstem=adpul;sustem=adpuls;instem=adpellere;english=bring%20to%20land

Change -e to -ite to get the present plural active imperative:
carpite! capite! ponite! currite!
http://www.slu.edu/colleges/AS/languages/classical/latin/tchmat/grammar/whprax/w1impva.htm

In a political context, I could see that as a call to action phrase
used to mean 'We must bring them to the middle! (adopt a centrist or
moderate stance on an issue or mindset).

Alternatively, it could be a phrase used in a late night TV ad urging
you to call Miss Cleo for all your psychic needs.

Hope that helps,
* V *