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The Collaborative International Dictionary
In this connection

Connection \Con*nec"tion\, n. [Cf. Connexion.]

  1. The act of connecting, or the state of being connected; the act or process of bringing two things into contact; junction; union; as, the connection between church and state is inescapable; the connection of pipes of different diameters requires an adapter.

    Syn: link, connectedness.

  2. That which connects or joins together; bond; tie.

  3. any relationship between things or events; association; alliance; as, a causal connection between interest rates and stock prices.

    Syn: relation.

    He [Algazel] denied the possibility of a known connection between cause and effect.
    --Whewell.

    The eternal and inseparable connection between virtue and happiness.
    --Atterbury.

    Any sort of connection which is perceived or imagined between two or more things.
    --I. Taylor.

  4. A relation; esp. a person connected with another by marriage rather than by blood; -- used in a loose and indefinite, and sometimes a comprehensive, sense.

    4. The persons or things that are connected; as, a business connection; the Methodist connection.

    Men elevated by powerful connection.
    --Motley.

    At the head of a strong parliamentary connection.
    --Macaulay.

    Whose names, forces, connections, and characters were perfectly known to him.
    --Macaulay.

  5. something that connects other objects.

    Syn: connexion, connector, connecter, connective.

  6. (usually plural) an acquaintance or acquaintances who are influential or in a position of power and to whom you are connected in some way (as by family or friendship); as, he has powerful connections.

  7. a communications channel; as, my cell phone had a bad connection.

  8. (Transportation) a vehicle in which one may continue a journey after debarking from another vehicle; the departing vehicle of a connection[9]; as, my connection leaves four hours after my arrival; I missed my connection.

    Note: A connection may be more specifically referred to as a connecting flight, a connecting train, etc.

  9. (Transportation) the scheduled arrival of one vehicle and departure of a second, sufficiently close in time and place to allow the departing vehicle serve as a means of continuing a journey begun or continued in the first vehicle; as, we can get a connection at Newark to continue on to Paris; -- most commonly used of airplanes, trains, and buses arriving and departing at the same terminal.

  10. (Transportation) the transfer of a passenger from one vehicle to another to continue a journey; as, the connection was made in Copenhagen; -- most commonly of scheduled transportation on common carriers.

  11. (Commerce) a vendor who can supply desired materials at a favorable price, or under conditions when other sources are unavailable; as, to get a bargain from one's connection in the jewelry trade; to have connections for the purchase of marijuana; -- often used in the pl..

  12. (Psychol.) the process of bringing ideas or events together in memory or imagination.

    Syn: association, connection, connexion.

    In this connection, in connection with this subject.

    Note: [A phrase objected to by some writers.]

    Note: This word was formerly written, as by Milton, with x instead of t in the termination, connexion, and the same thing is true of the kindred words inflexion, reflexion, and the like. But the general usage at present is to spell them connection, inflection, reflection, etc.

    Syn: Union; coherence; continuity; junction; association; dependence; intercourse; commerce; communication; affinity; relationship.

Wiktionary
in this connection

prep.phr. (context sometimes proscribed English) In connection with this subject.