The words and lyrics of the nursery rhyme consists of the old proverb and how people believe the weather can be predicted. Rainbows remained a mystery until the seventeenth century when the French scientist, Rene Descartes, investigated interactions between light and water and Sir Isaac Newton determined that "white" sunlight is actually a combination of red, orange, yellow, green, blue, indigo, and violet light - exactly the colors that make up the spectrum of a rainbow. The magical apparition of a rainbow still gives great pleasure and excitement - whatever the prediction it always signifies clear and sunny skies ahead.
There are several rhymes of this nature, some of which also have significant historical relevance such as:
If Candlemas day (2 February) be dry and fair
If St Paul's day (29 June) be fair and clear
St. Swithin's day if thou dost rain