R. Funalis De Candolle in Prodromus Systematis Naturalis Regni Vegetabilis 3 : 475-476. 1828 (page 476).

3. R. FUNALIS (Salm-Dyck cat. hort. Dyck.) erectiuscula, ramis longis teretibus obtusis
subglabris sparsè punctatis spinulis minutissimis solitariis appressis. ? in Americâ
merid. Cactus funalis Spreng. syst. 2. p. 496. R. grandiflorus Haw. rev. 72. suppl. 83.
Hook. in bot. mag. t; 2740. Setae pallidae arctè appressae regulariter distantes. Flores
numerosi albidi vix unciales. Flores lactei, petalis imbricatis obtusis. Stigm. 4 rotata.

English Translation

Plant mostly erect, branches long tubular, blunt. sub glabrous, few spots, a very small single appressed spine. Growing in South America. Pale bristles closely appressed at regular intervals. Numerous white flowers barely an inch long. Flowers wheel shaped, milky, petals over lapping, blunt. Stigma has 4 lobes.

Treated as a synonym of R. grandiflora by B&T in Bradleya 13

R funalis (cord-like); Fig. 89.
Detail from Cactus Culture –Watson 1889
-Stem straggling, branched. Branches numerous, composed of long, terete joints, rather thicker than a goose-quill, glaucous-green, slightly roughened on the surface, with depressions for the dot-like cushions. Branchlets usually fascicled and spreading. Flowers white, produced in spring, on the sides of the young joints, 1 in. across, large for the genus. Introduced from Central America about 1830. An easily-grown plant, sturdy, rather straggling, but very free-flowering. In old specimens the branches become semi-pendulous. It grows best when kept in a warm house. Syn. R grandiflora.