Those who take this view[25] adduce the analogy of Geometry to show that Ethics ought to deal with ideally perfect human relations, just as Geometry treats of ideally straight lines and perfect circles. But the irregular lines which we meet with in experience have spatial relations which Geometry does not ignore altogether; it can and does ascertain them with a sufficient degree of accuracy for practical purposes: though of course they are more complex than those of perfectly straight lines. 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 learnt how to reduce to principles and calculate even these more complicated motions. It may be useful for purposes of instruction to assume that the planets move in perfect ellipses: 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. In neither case can we hope to represent in our general reasonings the full complexity of the actual considerations: but we endeavour to approximate to it as closely as possible. It is only so that we really grapple with the question to which mankind generally require an answer: ‘What is a man’s duty in his present condition?’ For it is too paradoxical to say that the whole duty of man is summed up in the effort to attain an ideal state of social relations; and unless we say this, we must determine our duties to existing men in view of existing circumstances: and this is what the student of Ethics seeks to do in a systematic manner.