part, in regard to the occurrence of high-water-in which case the probability against the occurrence of an anomalous low-water would be as a thousand to one. It may further be conceived that though on all the other thousand occasions, I observed a perfect harmony between the phenomena of high and low-water and the indications of the instrumentyet that on one occasion the instrument deceived me-it having anomalously stood at low-water though there was high-water on the sea as usual. In this case my expectation of a high-water grounded on past experience will prevail over my faith in the information of the tide-index. The truth is that against the actual occurrence of the anomalous low-water, the probability is as a thousand to one -whereas against a wrong deposition on the part of the instrument the probability is only as a thousand to two. There is a double chance for an irregularity on the part of the instrument, rather than an irregularity on the part of the ocean-and I am therefore not yet dislodged from my belief that though the instrument did attest a low-water, the high-water took place as usual.

17. One can imagine a still greater degree of irregularity on the part of the tide-index. The number of failures (including the case in question) may have been five or ten or twenty or fifty-in which case the chances of error in the information given would just be represented by these respective numbers and I would persist in my conviction of there having been a high-water with a strength equal in the first case to that of two to one, in the second of five to one, in the third of ten to one,

in the fourth of twenty to one, and in the fifth with a strength equal to that of fifty to one.

18. But we can imagine an instrument that never misgave or made a false indication in the whole course of our experience. We We may have observed the stated recurrence of a high-water at the usual interval a thousand times, and as many times, we may have without fail observed the rise in the tide-index which corresponds thereunto. That a low-water should occur instead of the next expected high-water is a thing improbable in the ratio of a thousand to one. That the high-water should occur and yet the index point to a low-water is also a thing improbable, and in the same ratio of a thousand to one. The one improbability exactly balances or neutralizes the other. The mind is left in a midway state or in a state of pure scepticism on the question-and it remains to be seen whether it is possible by means of any accession to the testimony of these tide-indices, to arrive at a legitimate belief in the occurrence of an anomalous low-water; or, to express it otherwise, belief in the violation of a wonted order to which we never had witnessed a single exception in the whole of our past experience.

19. It may be conceived in this way. The same instrument which set in a particular way so relates it to the water of the sea as to indicate the variations of its level, may be so set as to relate it similarly to other water of variable level, as to that of a pond or a well or a vessel, the liquid in all which was subject to alternate elevations and depressions. We have already made the supposition of having observed the unfailing punctuality

of its informations in regard to the tides so as to establish the probability of a thousand to one in favour of that information being true. But should it inform us of a low-water at the time when, on the strength of a thousand past instances, we were left to expect a high-water the probability for the truth of this information is exactly countervailed by an equal probability opposed to it. By applying the same instrument however to the measurement of other fluctuations in the level of water beside those of the sea, the samples of its correct indication may be multiplied indefinitely — and instead of a thousand observed instances in which it spoke the truth, we may in virtue of this larger application be able to allege twenty thousand. After this it remains no longer a contest of equal experiences, but of unequal-and the difference is all in favour of the witnessing instrument. If it depone to a matter against which, apart from its own information, there is the probability of a thousand to one, it should now be recollected that in the verity of this information there is a probability of twenty thousand to one. Or in other words we have a probability of twenty to one for the anomalous low-water. So that with the evidence of one instrument alone, the violation of a long observed order may be abundantly established; and it is a possible thing that the experience which stands opposed to the testimony of this solitary witness may, singly in the witness itself, be greatly surpassed by the experience in its favour.*

The accuracy of the tide-gauge may obtain enhanced confirmation by observing the truth of its depositions, not at the

20. Or the accession to the evidence of the tideindex may be obtained in another way. Instead of widening the range of its application, so as to collect twenty thousand instances of its accuracy wherewith to overbear the thousand instances of regular high-water, the very same power and, superiority of evidence could be had by means of another tide-index. We have supposed a number of these instruments which, either from their various mechanisms, or from their being constructed with more or less skill, gave forth their depositions with more or less accuracy. Let us compute the effect then which lies in the concurrence of two testimonies to the fact of an anomalous low-water -one given by a tide-index of yet unfailing correctness, and another which in the thousand instances of regular high-water failed no less than fifty times. Still it has been twenty times right for once being wrong; and the presumption in favour of its testimony for any indifferent thing is just as twenty to one-though in favour of its testimony for an anomalous low-water in the face of a thousand regular high-waters it be only as one to fifty. This however does not prevent the multiple effect of its evidence when united with that of another instrument. This tide-index which has been right

highest and lowest levels of the tide only, but at all intermediate ones so that our experience of this accuracy may greatly overpass our experience of the regularity whether of high or low

water.

This mathematical style of reasoning on a question which respects the truth of Christianity will be excused first by those who feel it to be effective; and secondly because if effective, it is the best fitted to neutralize the mischievous influence superadded to the scepticism of Hume by the great name of La Place.

without exception in a thousand instances, has acquired the probability of a thousand to one for its next deposition-and, should the other instrument which has been right twenty times for one, agree in the same deposition, the united testimony of both has precisely the force of twenty thousand to one for any indifferent thing-and in the present case of twenty to one for an anomalous lowwater. There is no one versant in the doctrine of probabilities who will dispute the soundness or accuracy of these conclusions a doctrine not only of mathematical precision in the abstract-but whose precision is verified on the average in all the practical affairs of experience and human life. The probability arising from the concurrence of the two testimonies which we have now specified is just as we have stated it. And to vary the supposition should the tide-index which has failed ten times in a thousand, agree in its evidence with the tide-index that has failed twenty times-still the former has only been wrong once in a hundred times and the other once in fifty-so that their united testimony has in it the strength of five thousand to one for an indifferent thing and five to one for an anomalous low-water. It were easy to calculate the results in all other instances of agreement. The joint testimony of the tide-gauge that has failed five times with that which has failed fifty times has in it the absolute force of four thousand to one, or the relative force of four to one for an anomalous low-water. The joint effect of the one that has failed five times with the one that has failed ten is equivalent to twenty in favour of