THE best method of classifying curves is to commence with one which is founded on properties which are unaltered by projection. We thus obtain ten principal species of quartic curves, viz. anautotomic, uninodal, unicuspidal, binodal, nodocuspidal, bicuspidal, trinodal, binodocuspidal, nodobicuspidala and tricuspidal; but each of these species admits of a variety of subsidiary divisions, owing to the fact that all curves of a higher degree than the third may possess compound singularities.