These ignorant and conflicting accounts, and both from the same man, give as good a demonstration, perhaps, of what I have above mentioned, as to the inefficiency of Indian traditions as anything I could at present mention. They might, perhaps, have been in this instance however the creeds of different sects, or of different priests amongst them, who often advance diametrically opposite theories and traditions relative to history and mythology. And however ignorant and ridiculous they may seem, they are yet worthy of a little further consideration, as relating to a number of curious circumstances connected with the unaccountable religious ceremonies which I have just described. The Mandan chiefs and doctors, in all their feasts, where the pipe is lit and about to be passed around, deliberately propitiate the good-will and favour of the Great Spirit, by extending the stem of the pipe _upwards_ before they smoke it themselves; and also as deliberately and as strictly offering the stem to the four _cardinal points_ in succession, and then drawing a whiff through it, passing it around amongst the group. The _annual religious ceremony_ invariably lasts _four_ days, and the other following circumstances attending these strange forms, and seeming to have some allusion to the _four_ cardinal points, or the “four tortoises,” seem to me to be worthy of further notice. _Four_ men are selected by Nu-mohk-muck-a-nah (as I have before said), to cleanse out and prepare the medicine-lodge for the occasion—one he calls from the _north_ part of the village—one from the _east_—one from the _south_, and one from the _west_. The _four_ sacks of water, in form of large tortoises, resting on the floor of the lodge and before described, would seem to be typical of the same thing; and also the _four_ buffalo, and the _four_ human skulls resting on the floor of the same lodge—the _four_ couples of dancers in the “bull-dance,” as before described, and also the _four_ intervening dancers in the same dance, and also described The bull-dance in front of the medicine-lodge, repeated on the _four_ days, is danced _four_ times on the first day, _eight_ times on the second, _twelve_ times on the third, and _sixteen_ times on the _fourth_; (adding _four_ dances on each of the _four_ days,) which added together make _forty_, the exact number of days that it rained upon the earth, according to the Mosaic account, to produce the Deluge. There are _four_ sacrifices of black and blue cloths erected over the door of the medicine-lodge—the visits of O-kee-hee-de (or Evil Spirit) were paid to _four_ of the buffaloes in the buffalo-dance, as above described; and in every instance, the young men who underwent the tortures before explained, had _four_ splints or skewers run through the flesh on their legs—_four_ through the arms and _four_ through the body.