We may put it still more generally in this way:--Let *a*, *b*, *c*, &c. be the probabilities of a conclusion grounded on various arguments. It is only when all the arguments fail that our conclusion proves finally untrue; the probabilities of each failing are respectively, 1 - *a*, 1 - *b*, 1 - *c*, &c.; the probability that they will all fail is (1 - *a*)(1 - *b*)(1 - *c*) ...; therefore the probability that the conclusion will not fail is 1 - (1 - *a*)(1 - *b*)(1 - *c*) ... &c. It follows that every argument in favour of a conclusion, however flimsy and slight, adds probability to it. When it is unknown whether an overdue vessel has foundered or not, every slight indication of a lost vessel will add some probability to the belief of its loss, and the disproof of any particular evidence will not disprove the event. We must apply these principles of evidence with great care, and observe that in a great proportion of cases the adducing of a weak argument does tend to the disproof of its conclusion. The assertion may have in itself great inherent improbability as being opposed to other evidence or to the supposed law of nature, and every reasoner may be assumed to be dealing plainly, and putting forward the whole force of evidence which he possesses in its favour. If he brings but one argument, and its probability *a* is small, then in the formula 1 - (1 - *a*)(1 - *c*) both *a* and *c* are small, and the whole expression has but little value. The whole effect of an argument thus turns upon the question whether other arguments remain, so that we can introduce other factors (1 - *b*), (1 - *d*), &c., into the above expression. In a court of justice, in a publication having an express purpose, and in many other cases, it is doubtless right to assume that the whole evidence considered to have any value as regards the conclusion asserted, is put forward.