“The most curious developments of piacular sacrifice take place in the worship of deities of the totem type. Here the natural substitute for the death of a criminal of the tribe is an animal of the kind with which the worshippers and their god alike count kindred—an animal, that is, which must not be offered in a sacrificial feast, and which indeed it is impious to kill. Thus, Hecaté was invoked as a dog, and dogs were her piacular sacrifices. And in like manner in Egypt the piacular sacrifice of the cow-goddess Isis-Hathor was a bull, and the sacrifice was accompanied by lamentations as at the funeral of a kinsman.” Under the head of _Mystical or Sacramental Sacrifices_—i. e. sacrifices at initiations and in the _Mysteries_: “According to Julian, the mystical sacrifices of the cities of the Roman empire were... offered once or twice a year, and consisted of such victims as the dog of Hecaté, which might not ordinarily be eaten or used to furnish forth the tables of the gods.... The mystic sacrifices seem always to have had an atoning efficacy; their special feature is that the victim is not simply slain and burned or cast away, but that the worshippers partake of the body and blood of the sacred animal, and that so his life passes, as it were, into their lives and knits them to the deity in living communion. “In the Old Testament the heathen mysteries seem to appear as ceremonies of initiation by which a man was introduced into a new worship.... But originally the initiation must have been introduction into a particular social community.... From this point of view the sacramental rites of mystical sacrifice are a form of blood-covenant.... In all the forms of blood-covenant, whether a sacrifice is offered or the veins of the parties opened and their own blood used, the idea is the same: the bond created is a bond of kindred, because one blood is now in the veins of all who have shared the ceremony.” A learned friend writes me: “I doubt whether a real distinction can be made between _propitiatory and expiatory_ sacrifices. Propitiation is by expiation. The basic idea in all sacrifices of that nature appears to be _substitution_; that is, something taking the place of the offender.... It seems that the basis of all sacrifice is to be found in a relationship, or _kinship_ (through blood), between the deity—who is only the representative of the tribal head regarded as still living in the spirit-world—and the worshipper.