The thinner the ice, the more anxious is everyone to see whether it will bear.

The poem is:
I hate to be a kicker
I always long for peace
But the wheel that does the squeaking
Is the one that gets the grease. to wit the wag of a dog's tail" appears at the beginning of the Disney film Lady and the Tramp.

Josh Billings was the pen name of 19th century American humorist Henry Wheeler Shaw (21 April 1818 – 14 October 1885).