E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A white bow in the clouds during foggy weather is so called. Such a bow was seen in England during January, 1888. A week preceding, the weather had been clear, sunshiny, and genial, then followed several days of thick fog, during which the white bow appeared. The bow was followed by several days of brilliant mild weather.