The man .. who is the speaker... shows the conflict between his head and heart which said two different things.. in the poem... his head is telling him to man up and not to show any signs of cowardice and to hit the snake..but his heart tells him to be proud that the snake had come to his pond... for drinking the water.. the conflict happens because both the head and heart cant decide on what is supposed to be done and in the poem..his head wins.. although he later becomes guilty .. 
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Dh Lawrence's head was telling him to kill the snake as the golden snakes in Sicily were poisonous and his heart was telling him to wait for the snake to finish and not harm the snake because he thought of the snake as a king without crown drinking from his trough so felt a pleasure.