The correct answer is D) examine the condition of the flame. The purpose of a 'peep' hole in the boiler casing is to allow the operator to visually inspect the condition of the flame inside the boiler. This is an important safety and operational check, as the flame condition can provide information about the combustion process and any potential issues that may be occurring. Observing the flame through the peep hole allows the operator to ensure the flame is stable, burning cleanly, and not exhibiting any abnormal characteristics. The other answer choices are incorrect because they do not accurately describe the primary purpose of the peep hole. Checking the refractory cones, stack smoke, or soot blower operation, while potentially important boiler checks, are not the main function of the peep hole.