The precise nature of the element which eludes must be left to the judgment of my readers, but, personally, I reserve my own, out of fairness to an unfinished deposition.
There is a generic difference between Doctor Bataille and Miss Vaughan.
He is an ordinary human being, and if we may trust the many pictures which represent him in his narrative, exceedingly unpretending at that.
We have also some portraits of Miss Vaughan, who is aggressive and good to look at; but this is not the generic distinction.

Doctor Bataille, poor man, is the scion of an ordinary ancestry within the narrow limits of flesh and blood.

Miss Vaughan, on the contrary--I hope my readers will bear with me--has been taught from her childhood to believe that she was of the blood royal of the descending hierarchy, and I cannot gather from her vague mode of expression whether she has altogether rejected the legend of her descent, which is otherwise sufficiently startling.
The position of authority and influence occupied by Miss Vaughan in what she terms high Masonry is to be explained, as she modestly informs us, not by her personal qualities, but by a traditional secret concerning her family, which is known only to the Elect Magi.

Miss Vaughan and her paternal uncle are the last descendants of the alchemist Thomas Vaughan, whom she terms a Rosicrucian, and identifies with Eirenaeus Philalethes, author of "The Open Entrance to the Closed Palace of the King." On the 25th of March 1645, she tells us, on the authority of her family history, Thomas Vaughan, having previously obtained from Cromwell the privilege of beheading the "noble martyr" Laud, Archbishop of Canterbury--the title to nobility, in her opinion, seems to rest in the probability of his secret connection with Rome--steeped a linen cloth in his blood, burnt the said cloth in sacrifice to Satan, who appeared in response to an evocation, and with whom he concluded a pact, receiving the philosophical stone, and a guaranteed period of life extending over thirty-three years from that date, after which he was to be transported without dying into the eternal kingdom of Lucifer, to live with a glorified body in the pure flames of the heaven of fire.
After this compact, he wrote the "Open Entrance," the original MS.

of which, together with its autograph Luciferian interpretation on the broad margins, is a precious heirloom in the family.