Bertrand Russell gave the Lowell Lectures in March and April of 1914; these lectures produced 'Our Knowledge of the External World'. Russell attempts to analyze the relationship of the crude data of our senses to the notions of physics such as space, time, and matter. Russell takes his analysis to illustrate the method of logical analysis used to such wonderful effect by thinkers in the late nineteenth-century to the notions of continuity, infinity, and the infinitesimal. These analyses effected a new epoch of clarity in the philosophy of mathematics; Russell hopes that a similar new age of clarity can be effected in the rest of philosophy through logical analysis; here, he undertakes the first stages of this analysis in the philosophy of physics.