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Finally, while rotating in the lathe, the paraboloid is perforated through the axis with a steel drill and turpentine.

Paraboloids can be made true enough for most purposes, if finished as above described, but if great accuracy is a desideratum, the figure may be corrected after the rough turning, by means of the following appliance.

It is a property of the paraboloid that the face of every section taken parallel to the axis, is an exact counterpart, and, in form, is the same parabola. This enables us to verify and correct the figure. From the further end of a base-board, clamped to the bed of the lathe, hinge a piece of board about two inches wide. Let this be so adjusted that when the front edge is raised the upper plane of the board falls exactly parallel with the lathe centers. Rough file out a piece of sheet brass, something like the template, to serve as a grinder. Lay this on the face of the hinged piece of wood, and press it up on the revolving glass, smeared with fine emery and water. After a few turns lower the board and shift the brass grinder endways to another position, either in or out. Repeat this continually, occasionally turning the brass over in order to equalize the sides. By this operation the parabolic figure of both the grinder and the glass will soon correct each other; of course, a piece of the swing board must be scooped out sufficiently to admit nearly half the paraboloid.

In accordance with the above mode of procedure, the parabola is originated and its size pre-determined by the given focal distance. The ordinary dry parabolic illuminator is usually made about inch focus; for an immersion will do better; but if this is to be used as an an animalcule holder, will be found sufficient.

NOTES ON THE STRUCTURE OF OPHIOGLOSSUM. BY MARK W. HARRINGTON, M. A., F. L. S.

(Received December 16th, 1878.)

During the winter of 1876-7, I had the opportunity of studying, in the botanical laboratory of Professor Hofrath Schenck, of Leipzig, the structure of O. pedunculosum, Desv., and of comparing it with the structure of several other species of the genus. I compared my results at each stage with those ob

tained by Russow,* as well as those obtained by Holle. In the following notes I mention only the points of structure when I find them differing from Holle's or Russow's account, or when they are mentioned by neither. As Holle carefully analyzed earlier literature, the following notes on points not mentioned by him may fairly be considered new. When the species is not mentioned, O. pendunculosum is always meant. A.-Root.

The outer walls of the epidermal cells are not visibly thickened in O. pedunculosum, or O. vulgatum, L. The parenchyma is uniform and filled with starch and oil. The grumous masses and mycelial threads in the middle parenchymatous cells, described by Russow and Holle, I found in about half of the specimens of O. vulgatum, but in no other species. The xylem of the root is usually on the under side of the bundle, though it is sometimes at the side, and rarely above. The vessels of the xylem were, in nearly every case, reticulated. The protective sheath was not distinctly marked by woodiness, but in longitudinal sections the radial walls were beautifully wavy. The parenchyma of the bundle has little starch, but contains many tears of a brownish-yellow color.

The roots of O. lușitanicum and O. pendulum are like that of O. pedunculosum. In O. pendulum the epidermis is often imperfect; the deterioration is caused by fungi. The external wall, when present, is decidedly thickened. In both species the xylem is proportionately larger than in O. pedunculosum. It is is large as the phloem. The vessels are more frequently scalariform than reticulated.

O. Bergianum, Schldl., a S. African species, has a diarch vascular bundle. The xylem is divided into two opposite parts, with the phloem between and partly embracing them. The protective sheath is decidedly woody.

DESCRIPTION OF PLATE XVI.

Fig. 1.-Transverse section of vascular bundle of O. pedunculosum. The upper side is toward the center; x, xylem, þ, phloem.

Fig. 2.-Transverse section of a vascular bundle in the leaf of 0. pendulum. The xylem (x) inside and the phloem (p) forms a ring around it, separated from it, above and below, by parenchyma (c).

* Histologie der Leit-bündel Cryptogamen. Mem. de l'acad. Imp. de St. Petersbourg, VII. Série, Tome XIX., No. 1., pp. 117-128.

Bau and Entwickelung der Ophioglosseen Bot. Zeit., 1875.

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O. macrorhizum, Kze, has a diarch bundle, like that of O. Bergianum.

B.-Rhizome.

The epidermis is present in limited places. Holle found none in vulgatum. No cork was present in pedunculosum or vulgatum. Russow found it abundant, and Holle found some in vulgatum. There is a vascular net work in the rhizome, and the vascular bundle from leaf or root incorporates itself in this network. I could not demonstrate a direct connection between each leaf and a corresponding root, as Holle was able to do. Indeed, I could find no comparison in number or position between the leaves and roots, and was unable to draw Holle's conclusion from his own drawings from nature. Reticulated vessels were present in the rhizome. The rhizomes of lusitanicum, Bergianum, macrorhizum, and pendulum had the structure of that of pedunculosum.

C.-Leaf.

The structure in pedunculosum, lusitanicum, reticulatum, and macrorhizum, was like that of vulgatum. In Bergianum the external wall of the epidermal cells is much thickened. The edges of the leaf are thick, the structure compact, and the stomata small. The whole structure of the leaf suggests its habitat; viz., the dry climate of S. Africa.

In pendulum the phloem has very thick walls and surrounds the xylem. The latter is in a zone running through the center of the circle formed by the phloem and abutting on it at each end. The space on each of the xylem, between it and the phloem, is filled with parenchyma. This arrangement is replaced by the ordinary one in the lower part of the leaf and in the petiole.

D.-Spike.

In pedunculosum, a special preparation is made in the tissue for the dehiscence of the sporangium. In pedunculosum, lusitanicum, Bergianum, macrorhizum, palmatum, Surinamense, reticulatum, and bulbosum, the sporangia show no trace of a division into two compartments.

In vulgatum there is an incomplete wall extending from the axial side of the sporangium, parallel to the axis of the spike. It presents a bow-shaped edge toward the exterior, being farther extended at the upper and lower ends than in the middle. In pendulum this division wall is usually nearly complete, and

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