240 
ON THE RATIONAL TRANSFORMATION BETWEEN TWO SPACES. [447 
Let the r-tuple curve consist of three right lines meeting in a point: this is an 
actual triple point, and the formulse do not apply. But calculating the postulation- 
terms by the formula, we have m r — 3, p r = ^3.2- 0, =3; and the terms are 
[-|r (r + 1) n — (r + 1) (2r — 5)] 3 — -g [0— 1) (?— 2) (?— 3) (r — 4) + 4r (r + 1) (2r + 1)], 
which are 
= \r (r + 1) (3 n — 4?" + 4) — (r — 1) (r — 2) (r — 3) (r — 4), 
or say 
= (r + 1) (3n — 4r 4- 4) +1 (— r 4 + 10r 3 — 35r 2 + 5Or — 24). 
I have found by an independent investigation that this value requires the correction 
+ ^ [r 4 — 8r 3 + 30r 2 — 56r + 24 + \ {1 — (—) r 1}], 
and that the true value of the postulation is 
= \r (r + 1)(3w — 4r + 6) + ^ [ 2r®—5r 2 — 6r + i {1 ~' ( — ) r 1}]j 
viz., that this is the number of the conditions to be satisfied that a surface of the 
order n may have for an r-tuple curve three given right lines meeting in a point.