An Essay on the Principles of Human Action was written by

The correct option is William Hazlitt.

Detailed Explanation:
An Essay on the Principles of Human Action (fully titled An Essay on the Principles of Human Action: Being an Argument in Defence of the Natural Disinterestedness of the Human Mind) is a philosophical treatise written by the English essayist, literary critic, and philosopher William Hazlitt. Published in 1805, this work was Hazlitt's first major publication and represented his significant contribution to metaphysics and ethics.

In this essay, Hazlitt argues against the prevailing egoistic philosophies of his time (such as those of Thomas Hobbes and Claude Adrien Helvétius), which claimed that all human actions are ultimately motivated by self-interest. Instead, Hazlitt proposes that the human mind is naturally disinterested, meaning that we are naturally capable of feeling sympathy and acting for the welfare of others, particularly when projecting our feelings into the future.

Context of Other Options:
- Charles Lamb: A famous English essayist and poet, best known for his Essays of Elia and the children's book Tales from Shakespeare, which he co-authored with his sister Mary Lamb.
- Jean Jacques Rousseau: A major Genevan philosopher of the Enlightenment whose political philosophy influenced the French Revolution. His famous works include The Social Contract and Emile, or On Education.
- William Godwin: An English journalist, political philosopher, and novelist, considered one of the first exponents of utilitarianism and anarchism. His most famous work is An Enquiry Concerning Political Justice.