IT will never be possible to furnish mathematical proof of a causal relationship between smoking and lung cancer. This means that, before action against smoking can be taken, in view of the danger of lung cancer, we must be satisfied on the following two points. First there must exist strong indications that smoking is an important causative factor in lung cancer, and, secondly, it must be highly improbable that one or more other factors could be the main cause.As far as the latter point is concerned: all attempts to exculpate smoking have so far been unsuccessful. The longer such success remains unachieved, the smaller the probability that the greatest danger might lie in other still unknown factors.As regards the first point: there is no doubt whatsoever that the indications that there is a danger inherent in smoking are very strong. The results of all retrospective investigations invariably implicate smoking.However, against this retrospective method of investigation a serious objection can be raised: the material for comparison, a group of persons not suffering from lung cancer, is necessarily highly selected. In view of this, investigations by means of the so-called prospective method, against which, it was thought, this objection could not be raised, were set up. The preliminary results of two of these prospective investigations have now become known (Doll and Hill, 1954;Hammond and Horn, 1954). They seem fully to corroborate the conclusions reached previously in the retrospective investigations.However, Berkson (1955) alleges that the prospective method also involves the danger of selection. Berkson attempts to demonstrate that this is the case in Hammond and Horn's material. He bases his opinion mainly on two facts: (1) the death rates found by Hammond and Horn are lower than the rates given by the official American mortality statistics, and (2) the percentage of non-smokers in Hammond and Horn's population exceeds the percentage found in the general American population.* Berkson (1955) goes so far as to infer that the excess of the death rates for smokers, as found by Hammond and Horn (1954) in lung cancer and in coronary disease. might wholly be explained by the action of this selection. It seemed necessary, therefore, to test the correctness of this view thoroughly. This will be done in the present paper.