"Those who take this view adduce the analogy of Geometry to show that Ethics ought to deal with ideally perfect human relations, just as Geometry treats of ideally perfect lines and circles. But the most irregular line has definite spatial relations with which Geometry does not refuse to deal: though of course they are more complex than those of a straight line. So in Astronomy, it would be more convenient for purposes of study if the stars moved in circles, as was once believed; but the fact that they move not in circles but in ellipses, and even in imperfect and perturbed ellipses, does not take them out of the sphere of scientific investigation: by patience and industry we have learned how to reduce to principles and calculate even these more complicated motions. It is, no doubt, a convenient artifice for purposes of instruction to assume that the planets move in perfect ellipses (or even--at an earlier stage of study--in circles): we thus allow the individual's knowledge to pass through the same gradations in accuracy as that of the race has done. But what we want, as astronomers, to know is the actual motion of the stars and its causes: and similarly as moralists we naturally inquire what ought to be done in the actual world in which we live." (P. 19, Sec. Ed.) Beginning with the first of these two statements, which concerns Geometry, I must confess myself surprised to find my propositions called into question; and after full consideration I remain at a loss to understand Mr. Sidgwick's mode of viewing the matter. When, in a sentence preceding those quoted above, I remarked on the impossibility of solving "mathematically a series of problems respecting crooked lines and broken-backed curves," it never occurred to me that I should be met by the direct assertion that "Geometry does not refuse to deal" with "the most irregular line." Mr. Sidgwick states that an irregular line, say such as a child makes in scribbling, has "definite spatial relations." What meaning does he here give to the word "definite?" If he means that its relations to space at large are definite in the sense that by an infinite intelligence they would be definable, the reply is that to an infinite intelligence all spatial relations would be definable: there could be no indefinite spatial relations--the word "definite" thus ceasing to mark any distinction. If, on the other hand, when saying that an irregular line has "definite spatial relations," he means relations knowable definitely by human intelligence, there still comes the question, how is the word "definite" to be understood? Surely anything distinguished as definite admits of being defined; but how can we define an irregular line? And if we cannot define the irregular line itself, how can we know its "spatial relations" definite? And how, in the absence of definition, can Geometry deal with it? If Mr. Sidgwick means that it can be dealt with by the "method of