that it is due to the cause a. This is an à posteriori probability of cause. But I could not calculate it, if a convention more or less justified did not tell me in advance what is the à priori probability for the cause a to come into play—I mean the probability of this event to some one who had not observed the effect. To make my meaning clearer, I go back to the game of écarté mentioned before. My adversary deals for the first time and turns up a king. What is the probability that he is a sharper? The formulæ ordinarily taught give 89, a result which is obviously rather surprising. If we look at it closer, we see that the conclusion is arrived at as if, before sitting down at the table, I had considered that there was one chance in two that my adversary was not honest. An absurd hypothesis, because in that case I should certainly not have played with him; and this explains the absurdity of the conclusion. The function on the à priori probability was unjustified, and that is why the conclusion of the à posteriori probability led me into an inadmissible result. The importance of this preliminary convention is obvious. I shall even add that if none were made, the problem of the à posteriori probability would have no meaning. It must be always made either explicitly or tacitly.
Let us pass on to an example of a more scientific character. I require to determine an experimental law; this law, when discovered, can
