We have come a long way in telling time. The first clocks were the sundials of the Sumerians and Egyptians. For obvious reasons, these could not be relied upon when night fell. The next advancement fell to the Greek clockmakers who created water clocks that worked whatever the hour. Read this article which is a guide to restoring a brass clock.
The case: Cleaning
History In 1500, Peter Henlin invented a spring powered clock; in the 1600s, Galileo and Christian Huygens developed the pendulum clock. The brass clock can be considered an interesting piece of history in the clock's development. Cleaning the case Clean the case of the brass clock carefully, without disturbing the layer of oxide which acts as a protective layer for the brass. Apply a cleaner that is acidic and ammonia-free to a soft cloth and gently rub the brass case. Examples of cleaners to use are tetrachloroethylene or acetone. Only remove any dirt or oil that may be on the clock's case. The only reason to remove the oxide layer beneath would be if you intend on lacquering the case or painting it. Be gentle especially with the brass finials as you do not want to bend them or accidentally snap them off.
The Case: Polishing
If the case needs more than just cleaning and is severely corroded, polishing may be necessary. Polishes that contain fine rottenstone mixed with ethyl alcohol and water (at a 1:1 ratio) and gilders whiting or chalk work well. Rub it onto the brass of the clock with a soft cloth or a cotton ball, then remove any residue left over with alcohol and water. When you are finished polishing the brass case of the clock, make sure that you put on gloves before handling it, so as to not transfer the oils and salt form your hands to the brass.
Test a small portion of the dial before cleaning the dial. If the pattern remains, continue. When cleaning the dial of the clock, do so gently so as not to remove any paint or other markings original to the clock. Use the same kind of polish as you used to polish the case. Use only cotton balls or a soft cloth like a cotton nappy to apply the polish. Lightly brush or wipe away the residue polish with a clean cotton nappy.