The inductive part of the problem is completed, since we have found that the urn most likely contains three white and one black ball, and have assigned the exact probability of each possible supposition. But we are now in a position to resume deductive reasoning, and infer the probability that the next drawing will yield, say a white ball. For if the box contains three white and one black ball, the probability of drawing a white one is certainly 3/4; and as the probability of the box being so constituted is 27/46, the compound probability that the box will be so filled and will give a white ball at the next trial, is 27/46 × 3/4 or 81/184. Again, the probability is 16/46 that the box contains two white and two black, and under those conditions the probability is 1/2 that a white ball will appear; hence the probability that a white ball will appear in consequence of that condition, is 16/46 × 1/2 or 32/184. From the third supposition we get in like manner the probability 3/46 × 1/4 or 3/184. Since one and not more than one hypothesis can be true, we may add together these separate probabilities, and we find that 81/184 + 32/184 + 3/184 or 116/184 is the complete probability that a white ball will be next drawn under the conditions and data supposed. *General Solution of the Inverse Problem.* In the instance of the inverse method described in the last section, the balls supposed to be in the ballot-box were few, for the purpose of simplifying the calculation. In order that our solution may apply to natural phenomena, we must render our hypotheses as little arbitrary as possible. Having no *à priori* knowledge of the conditions of the phenomena in question, there is no limit to the variety of hypotheses which might be suggested. Mathematicians have therefore had recourse to the most extensive suppositions which can be made, namely, that the ballot-box contains an infinite number of balls; they have then varied the proportion of white to black balls continuously, from the smallest to the greatest possible proportion, and estimated the aggregate probability which results from this comprehensive supposition.