E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
I must put on my conjuring capi.e. your question requires deliberate thought, and I must reflect on it. Eric XIV., King of Sweden, was a great admirer of magic, and had an enchanted cap made, either to keep his head warm or for mystification. He pretended to have power over the elements; and when a storm arose, his subjects used to say The king has got on his conjuring cap.