[In particular a curve and its reciprocal have this rational or (I, r) correspond ence, and it has been already seen that a curve and its reciprocal have the same deficiency.] A curve of a given order can in general be rationally transformed into a curve of a lower order; thus a curve of any order for which D=o, that is, a unicursal curve, can be transformed into a line; a curve of any order having the deficiency r or 2 can be rationally transformed into a curve of the order D+2, deficiency D; and a curve of any order deficience = or> 3 can be rationally transformed into a curve of the order D+3, deficiency D.