INTRODUCTION.
'It was a lovely Autumn evening, and the glorious effects of chromatic aberration were beginning to show themselves in the atmosphere as the earth revolved away from the great western luminary, when two lines might have been observed wending their weary way across a plane superficies. The elder of the two had by long practice acquired the art, so painful to young and impulsive loci, of lying evenly between his extreme points; but the younger, in her girlish impetuosity, was ever longing to diverge and become an hyperbola or some such romantic and boundless curve. They had lived and loved: fate and the intervening superficies had hitherto kept them asunder, but this was no longer to be: a line had intersected them, making the two interior angles together less than two right angles. It was a moment never to be forgotten, and, as they journeyed on, a whisper thrilled along the superficies in isochronous waves of sound, "Yes! We shall at length meet if continually produced!"' (Jacobi's Course of Mathematics, Chap. i.)
We have commenced with the above quotation as a striking illustration of the advantage of introducing the human element into the hitherto barren region of
