the boars head.
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Jack's denial that they killed the beast reveal about him that beast still exists. His plan that they keep on the "right side of the beast" suggest that people frequent make offerings to satisfy the beast. I think Jack truly believe there's a beast because he had seen it on the mountain top. His continuing to promote the existence of the beast to the others give him advantage over them by making obey him if they want to be safe!
When Jack and his tribe kill the pig they stick the pigs head on a spear and put it in the clearing as an offering to "the beast". They do not know that the beast is actually a part of them and not a physical being.
they went after the beast but jack decide to forget the beast and play rolling rock
Ralph finds and takes the stick on which the pig's head had been mounted, as an offering to the beast. It is only later, when he uses it as a spear to jab one of the hunting boys, than Ralph realises that the stick has a point at each end. He then knows what Jack's intentions for him are (to mount his own head as an offering to the beast).
The gift is the pig's head on a stick which Jack leaves as an offering to the beast. The beast is not an animal it is simply the evil within each and every one of us, something which Golding also refers to as 'the darkess of man's heart' in the last chapter. So essentially Jack and his tribe by paying homage to the beast are really giving themselves over as a gift to the darkness, or the evil, within themselves.