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(4.) Each of the companion surfaces contains, among all the possible systems of parallel sections, one system of coaxal hyperbolas. The locus of the asymptotes of these hyperbolas form two hyperbolic paraboloids, intersecting each other in two straight lines.
(5.) These two hyperbolic paraboloids have each a pair of asymptotic surfaces, whose equation is
Features (1), (2), and (3) are represented in Plate VII.
If now we consider a2, b2, and c2 as arbitrary constants, capable of assuming all values from through 0 to ∞ we get seven other surfaces, six of which are real, one imaginary, but all closely related to the principal surface. The remarkable relations existing between corresponding cross-sections of each pair of surfaces is brought out in the following exhibit of results. The following abbreviations are used: E. for ellipses, L. for lines, I. E. for imaginary ellipses, H. for hyperbolas, and C. H. for hyperbolas lying along the z-axis.
The study of the form and curvatures of these surfaces leads to
the following results:
(1.) Surfaces I, II, VII, and VIII have regions of both elliptic
and hyperbolic curvature and these regions are separated by lines of parabolic curvature.
(2.) Surfaces III and V have hyperbolic curvature only. (3.) Surfaces IV and VI have elliptic curvature only.
The paper, of which this is an abstract, is accompanied by ten figures and eight plates, representing the several surfaces in parallel perspective. The paper will be published in full elsewhere.
Hastings College, Hastings, Nebr.,
A FORM OF WEIR NOTCH.
OSCAR VAN PELT STOUT.
(Printed in full in the Transactions of the Nebraska Engineer
ing Society, Vol. I, No. 1, pp. 13-16.)
NOTES ON PHYLLOPOD CRUSTACEA.
H. ANDERSON LAFLER AND A. S. PEARSE.
It is greatly to be regretted that so interesting a sub-order as the Phyllopoda, a group characteristic of the plains region, one
us being peculiar to it, has been so completely neglected by our western naturalists. These creatures possess very singular means of adaptation to changed environment and the greatest vitality of species, although weak and delicate as individuals. Their method of reproduction is so bizarre as to excite the greatest interest in the student. Their broad, leaf-like feet are the characteristics from which the sub-order derives its name, Phyllopoda.
The carapace of the higher genera consists of a broad, thin plate, which covers the anterior portion of the body. In the lower forms it is bent downward, forming two valves similar in appearance to those of some small mollusks. These enclose the entire body.
Our Phyllopods are found in puddles such as are left after rains, in buffalo wallows, in slight hollows made by excavations for railway embankments, in draws which dry up during the summer months, and in places of similar nature. The eggs, after being carried for a time in the egg sacs, are allowed to drop to the bottom of the puddles. The water evaporates during the summer and leaves the eggs in the dry mud exposed to the heat of summer and the cold of winter until the hollows fill again and conditions are favorable to their development. The eggs then hatch out and the cycle of life is again begun.
At De Witt, Nebr., where most of our specimens were taken, Apus lucasanus was one of the most common species. It was first
observed on June 16, 1895, occurring abundantly in pools by the side of railway tracks. It was also abundant in a draw about one mile north of that place. Some specimens were secured and placed in a large jar, but they lived only a few hours. One or two of the more vigorous individuals were observed sucking the blood of their weaker companions. The bodies of the latter were pale and almost devoid of blood, while those of the former were gorged and of a dark red color. The same thing was noted at a later date of two specimens in a pool. This fact is of peculiar interest, as Dr. Merrill, of the Smithsonian Institute, writes us that he finds no mention of such "cannabalistic" tendencies in this species. They decreased steadily in numbers until the 27th of June, when they disappeared. In the latter part of September, however, two specimens believed to be of this species were taken, but we found no others, although the pool was carefully dredged. In May of the present year (1896), the pools being again filled, Apus lucasanus was taken again in the same places. Some specimens not yet identified, but probably of this species, were secured near Hudson, Colo., in the latter part of August. Three specimens of a species of Apus somewhat larger than lucasanus have also been taken, one of them in September, 1895, and the other two in June, 1896.
In September, 1895, we found this species in several pools which were scattered for some distance along the draw mentioned above. So numerous were they that every cow track along the edges of the pools yielded eight or ten specimens. Two pairs were found in copulation. Specimens apparently of this species were taken on May 23 of this year in the same draw. These were probably young forms, for at a subsequent visit they were found to have increased in size. These specimens taken this year were of a bright red color, but faded badly when placed in alcohol. If individuals of this species are touched when swimming they immediately close their shells and drop to the bottom.