Regarding this last point, Gerhard points out that since the human nature is anhypostasis, it can only be spoken of as the human nature of the Logos- even in the abstract. Hence, the divine glory is communicated to it hypostatically in that it participates in person of the Logos and therefore also his the eternal reception of himself from the Father. In that the Logos receives within his hypostasis the fullness of the glory of the divine ousia, so the human nature which subsists within the person of the Son also receives it through its unity with the divine person of the Son. Hence, this communication of glory is, as Gerhard notes, "hypostatic" rather than substantial (which would be Docetic) or accidental (which would be Nestorian).
The logic of this position is undeniable if you buy into the catholic-ecumenical theology of the first six ecumenical councils. Calvin, wishing to get around the idea of hypostatic reception of the divine glory while at the same time maintaining the doctrine of the ancient Church developed an unusual Trinitarian theology. Interestingly enough in his recent systematic theology, Michael Horton endorses Calvin's rather strange position.
Calvin makes the argument that the divine nature is incapable of self-communication. Well (you will ask), how can that be? Obvious the Father (the font of divinity) communicates himself in the Son and the Son and the Father do so in the procession of the Spirit. Calvin responses by saying that communication in the form of begetting and procession are a function of the person and not the divine nature. The divine nature is what all three persons share in common. You can see where this goes! For this reason, the later Reformed orthodox could claim that the even though the human nature participated in the hypostasis of the Son, he did not receive the divine glory of God's ousia. This is because the divine person became incarnate and not the divine nature. If the divine nature became incarnate, they claimed, then all three person would be incarnate.
Let's examine what's wrong with this. Most fundamentally it seems to strangely make the divine nature a fourth thing along side the persons. Actually, in terms of classical Trinitarian theology, Thomas Aquinas' description of the relationship between the divine persons and the ousia is probably the best. The divine persons are "subsisting relations." In other words, what makes a person a person within the Godhead is his relationship of begetting and procession to the others. The person "subsist" in these relations. Moreover, since the Father is the font of divinity, the divine nature is not something abstract alongside the persons, but possesses its reality in and through the subsisting relationships. In other words, there is no separating the divine persons and nature the way Calvin wishes to. The divine nature only possesses its actuality through the concrete subsisting relations of the Trinitarian persons. Hence, participation in second person of the Trinity is necessarily participation in the divine nature which is exists in its fullness in the Son as he possesses his reality through his relationship to the Father and Spirit.
Now it gets weird. A small minority modern Reformed Trinitarian thinkers have taken Calvin's odd Trinitarian theology to a next level. These folks would be: Charles Hodge, Robert Reymond, and Loraine Boettner. According to these theologians, there are no relationships of procession or begetting in the Trinity. Reymond in particular makes the rather bizarre claim that "Father" and "Son" language simply refer to unity of substance (what about the Spirit then?). All claim that "begetting" and "procession" language refers to temporal activity and not eternal relationships. Begetting would then be the act of Incarnation, whereas procession would be the sending of the Holy Spirit. Boettner claims that apply such language to the eternal reality of God confuses the immanent with the economic Trinity. Of course, without collapsing the immanent and economic Trinity into one another (as modern theologians after Hegel have tended to do), one may legitimately ask doesn't God's temporal activity reflect his eternal being? If not, then why not? Is he different in himself than he is in his Word and work?
How then are we to conceive the unity of the Trinity apart from subsisting relations? All of these thinkers seem to think of the Trinity as three persons somehow fused together into a single entity without any relations to subsist in. True to the Reformed fixation on the concept of covenant, Reymond talks of a "covenantal" relationship between the persons (this has lead to charges of Tri-theism from other Reformed theologians). This is an especially odd way of thinking insofar as it also calls into question the simplicity of the divine nature. In other words, because of divine aseity, God isn't made of up other stuff compounded together to make God-God (unlike creatures!). If God is "made up" of three persons existing alongside one another in some sort of undefined ontological unity (rather than subsisting through self-communicating fecundity of the single divine nature itself) then God would in a sense seem to be compounded rather than simple.
Although most contemporary Reformed theologians have rejected these views, it is not hard to see how Calvin's odd Trinitarian theology led to these conclusions. Unless we view the divine nature as existing in and through the persons and there subsisting relations to one another, it is hard to conceptualize the unity of the divine substance or the logic of the distinctions of the persons. Moreover, if one accepts the classical Trinitarian theology in this description of the divine being, it is difficult to see how one could reject the Lutheran understanding of the hypostatic union and the communication of glory.