coalescence of the evidence into a proof, which I have compared to the running into a limit, in the case of mathematical ratios. Just as an algebraical series may be of a nature never to terminate or admit of valuation, as being the equivalent of an irrational quantity or surd, so there may be some grave imperfections in a body of reasons, explicit or implicit, which is directed to a proof, sufficient to interfere with its successful issue or resolution, and to balk us with an irrational, that is, an indeterminate, conclusion. So much as to the principle of conclusions made upon evidence in criminal cases; now let us turn to an instance of its application in a particular instance. Some years ago there was a murder committed, which unusually agitated the popular mind, and the evidence against the culprit was necessarily circumstantial. At the trial the Judge, in addressing the Jury, instructed them on the kind of evidence necessary for a verdict of _guilty_. Of course he could not mean to say that they must convict a man, of whose guilt they were not certain, especially in a case in which two foreign countries, Germany and the American States, were attentively looking on. If the Jury had any doubt, that is, reasonable doubt, about the man’s guilt, of course they would give him the benefit of that doubt. Nor could the certitude, which would be necessary for an adverse verdict, be merely that which is sometimes called a “practical certitude,” that is, a certitude indeed, but a certitude that it was a “duty,” “expedient,” “safe,” to bring in a verdict of guilty. Of course the Judge spoke of what is called a “speculative certitude,” that is, a certitude of the fact that the man was guilty; the only question being, what evidence was sufficient for the proof, for the certitude of that fact. This is what the Judge meant; and these are among the remarks which, with this drift, he made upon the occasion:—