Does anyone know what James White might be referring to here?

From a quick Wiki search:

Period of the catacombs

We know with certainty, from the unanimous testimony of the Fathers of the early centuries, that during the persecutions the Christians kept the Eucharist in their homes with worshipful love. When the Eucharistic celebration finished the consecrated bread was distributed and safeguarded in small jars or boxes by the faithful, to be taken when they felt the need of it. The archaeologist G. B. de Rossi, basing himself on a text of Saint Cyprian and on the Acts of the martyrs of Nicomedia, under Diocletian, calls these small jars arca or arcula. Cardinal Bona, in his Rerum liturgicarum, at n. 17, cites the text of the dispositions imparted by a bishop of Corinth, that inform us of the rite of a domestic communion. «If your house is endowed with an oratory, you will set the vase containing the Eucharist on the altar, if there is no oratory, on a decent table. You will spread a small cloth on the table and you will there deposit the sacred fragments; you will burn some grains of incense and you will sing the trisagion [our Sanctus, ed.] and the symbol; then, after having made three genuflexions, in sign of adoration, you will take the Body of Jesus Christ religiously». Saint Eusebius informs us that priests kept the Eucharist in their homes so as to take communion to the sick. From ancient documents we also know that the Eucharist was worn hanging from the neck, both inside the wrappings that Saint Ambrose calls oraria, and in containers of gold, silver, ivory, wood, and even clay, commonly called encolpia. The encolpium was a small box containing relics and also the book of the Gospels that believers wore round their necks out of devotion. We know some examples found in the tombs of the Vatican cemetery, cubed-shaped, with hanger and decorated on the front with the monogram of Christ between the alpha and the omega.

https://web.archive.org/web/20070927014317/http://www.30giorni.it/us/articolo.asp?id=9045 https://en.wikipedia.org/wiki/Church_tabernacle#History

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