1. If w (mod 2ω 1 , 2ω 2 ) is an elliptic parameter for points of a normal elliptic curve C = 1 C n [ n − 1], then it is well known that the sets of n points in which C is met by primes have a constant parameter sum k (mod 2ω l , 2ω 2 ), and we may express this for convenience by saying that k is the prime parameter sum for the parametrisation of C by w . If we take the origin of w (the point for which w ≡ 0) to be one of the points of hyperosculation of C , then k ≡ 0, and we may say that w is a normal parameter for C . In the same way, if Γ is the Grassmannian image curve of the generators of a normal elliptic scroll 1 R 2 n [ n − 1], then a normal parametrisation of Γ defines a normal parameter w for the generators of 1 R 2 n , such that n of the generators have parameter sum zero if and only if they belong to a linear line-complex not containing all the generators of 1 R 2 n ; or, in particular, if they all meet a space [ n – 3] that is not met by every generator of the scroll. In this paper we are concerned in the first instance with the type of normal elliptic scroll 1 R 2 2 m +1 [2 m ] whose points can be represented by the unordered pairs ( u 1 ; u 2 ) of values of an elliptic parameter u (mod 2ω 1 , 2ω 2 ); and we establish a significant connection between any normal parametrisation of the generators of 1 R 2 m +1 and an associated parametric representation ( u 1 u 2 ) of its points. We also add a brief note to indicate the lines along which this kind of connection can be extended to apply to a general normal elliptic scrollar variety 1 R k mk +1 [ mk ] whose points can be represented by the unordered sets ( u 1 , …, u k ) of values of an elliptic parameter u .