In John 14:26 we see the Father sending the Comforter, the Holy Spirit, in the Son's name. Now we need to ask what or who is in the Son's name. Does this modifier—in the Son's name—modify the Father's sending or does it modify the sent One? It modifies the Sender, not the sent One. The Father in the Son's name sent the Spirit. The Sender is the Father, but the Father sent in the Son's name. This makes the Sender, the Father, one with the Son. Thus, the Father as the Son sent the Spirit. John 14:26 makes the Father and the Son one in sending the Spirit. The Son is the Father because the Father is in the Son's name.
John 15:26 reveals the Son sending from with the Father the Spirit of reality proceeding from with the Father. The Greek preposition para, translated "from" in the Recovery Version, literally means from with. The Son sent the Spirit from the Father and with the Father. Thus, the Son sent both the Father and the Spirit. When the Spirit was sent, the Father was also sent because the Spirit was sent with the Father.
John 14:26 says that the Father is the Sender, whereas 15:26 says that the Son is the Sender. When we compare these two verses, we see the mystery of the Triune God. According to the proper biblical theology, the Three of the Divine Trinity are distinct but not separate. Whereas the Son prays to the Father, He also declares that the Father is in Him and that He is in the Father (John 14:10). The Three of the Godhead coinhere. To coinhere is to indwell mutually. In the Godhead, the Three coinhere, that is, They dwell within one another. They are three, yet They are still one. This is a mystery.
In the Old Testament, in both Exodus and Zechariah, there is the type of the lampstand. There is one lampstand with seven lamps. The stand is one while the lamps are seven. Although it is one lampstand, there are seven lamps. Although our Triune God is one God, He is three in His Godhead. The Father, the Son, and the Spirit are distinct, but They are not separate. There is only distinction in the Godhead but no separation. The Three of the Godhead are not separate because They dwell in one another. They cannot be separated, but They are distinct because They are the Father, the Son, and the Spirit. Our God is three-one. We need a revelation of our mysterious Triune God in His divine trinity.
The divine transmission of the Divine Trinity to the believers is revealed in John 16:13-15. This transmission is just like the transmission of electrical current. When the electricity is switched on, there is a current of electricity, a moving of electricity, and that moving is the transmission. First, all that the Father has is the Son's (v. 15). This means that what the Father has is transmitted into the Son. Second, all that the Son has is received by the Spirit (v. 14b). This is a further step of this transmission. The Father transmits to the Son, and then there is a transmitting from the Son to the Spirit. Third, all that the Spirit has received of the Son is disclosed to the believers (vv. 13, 15b). Eventually, all that the Trinity is and has is ours.
Verse 3 of hymn #501 in Hymns talks about this transmission. This verse says:
All things of the Father are Thine;
All Thou art in Spirit is mine;
The Spirit makes Thee real to me,
That Thou experienced might be.
This verse tells us that whatever the Father has is the Son's, whatever the Son is has been received by the Spirit, and then the Spirit discloses to us whatever He has received of the Son. This transmission is from the Father to the Son, from the Son to the Spirit, and from the Spirit to us. This is the move of the Divine Trinity.