Fox repeats this call over and over: "Keep your testimony...for your worship in the spirit and in the truth, that Christ Jesus hath set up" (Works, 8:34); "keep up your testimony in the light, power, and spirit of God, for the worship that Christ set up above sixteen hundred years since, in spirit and in truth,...which is a worship that cannot be shaken." (8:84) This is a testimony that the Quakers had before the peace testimony was formulated in 1660, and I think in Fox's mind it was the most important of the Quaker testimonies. It is the thing that brings people to Christ, as they see that we are gathering together to feel his living presence in our midst. -- Lewis Benson

In the fourth lecture of the series Rediscovering the Teaching of George Fox given at Moorestown meetinghouse in 1982, Lewis Benson examines the origin and nature of early Quaker worship. His intent is "to get a new perspective on the problems of contemporary Quakerism, and to bring something into the life of the Society of Friends today which is the heritage of all Quakers but has not survived in any living tradition."

There is an assumption among Liberal Quakers that waiting in silence during the hour of worship replicates the early Quaker practice, an assumption which fails to take into account that the intent of early Quakers was entirely different from that of contemporaries, which centers on personal reflection that is sequentially shared. Early Quaker worship was attended by "people who had heard and received this everlasting gospel and who were filled with a fervent desire to gather together in the name of Jesus to wait to feel his presence in their midst as their living teacher, leader, ruler, counsellor, and orderer." Early Friends gathered together and quieted themselves in order to receive and  hear their heavenly prophet, receive intercession from their heavenly priest, be ruled as a people by their heavenly king, and be fed by their heavenly shepherd. Their cohesion was the result of waiting together for guidance, acceptance, and instruction that came from heaven, and not from one another's personal perspectives.  

For Fox, meeting in the name of Jesus has a very definite content, and it has to do with the gospel experience, the experience of Christ as present, and present in a functioning way. I have found 22 references where Fox makes it clear that "meeting in the name" involves such a definite experience (Benson).

That this revolutionary way of worship should have been lost from Quaker communities over the last several hundred years is not surprising; for it had likewise been lost since the apostles' days and not recovered until the early Quakers practiced it 1600 years later. Yet corporate worship in spirit and in truth, meeting "in the name of Jesus," remains forever available to reclaim yet once more by any who come to be "children of the New Covenant."

Benson's essay can be found at the website of New Foundation Fellowship under the Resources tab which features Benson's writings. Here's a link: The New Worship.