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In a paper like this, the influence of the perturbations is of course, not to be considered ;-still less the mutual action of the asteroids upon one another. Be it allowed me here, however, to express my belief that in future calculations this influence cannot always be neglected.

Should, at any future time, as is by no means impossible, two of those coupled in the following table, approach the node at the same time, their mutual action must, in spite of their excessively small mass, be extremely strong.

Such an occurrence is for Ceres and Pallas and for similar pairs, where the periods of revolution are very nearly equal, not so probable as for such pairs as Flora and Astræa, whose periods of revolution differ by 317, days and which revolve, moreover, in planes inclined to another by a small angle.

The following are those nodes at which the asteroid orbits are at a less distance from one another than one-fifth of the mean radius-vector of the earth, and where, as before, the first mentioned orbit is referred to the other.

Distance of the orbits.

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The shortness of the period in which Astræa and Flora complete each an integral number of revolutions (nineteen revolutions of Flora are very nearly equal to fifteen of Astræa), renders such an approach to one another in the vicinity of the above mentioned node, by no means improbable. Indeed if the elements of both planets could at present be considered as sufficiently accurate, it would be very easy to name a not very distant epoch, at which this must happen.

A somewhat similar relation is that of Iris and Hebe to Flora, and of Iris to Vesta, in the descending nodes. The periods of revolution are in the case of Iris and Vesta, very nearly equalon the other hand the mutual inclination of the two orbits is very small.

The periods of Iris and Flora are to one another, nearly as 9 to 8, of Hebe and Flora, nearly as 15 to 13. Here however

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the inclination is in both cases quite considerable, so that these must approach much nearer to their common node in order that such a mutual action may take place, than is necessary for the first mentioned pair.

The table of longitudes in the orbit shows whether at such an approach the planets would be visible, or lost in the solar rays.

Although the planes of the Vesta and Flora orbits are inclined by so small an angle, yet at the point of nearest approach they are 0.222 distant from one another. On the other hand we find that the following orbits,

Iris and Astræa in 8 Pallas and Hebe in 88
Hebe and Astræa in 88 Ceres and Hebe in 8

Juno and Vesta in 8 are at a distance nearly equal to that of the earth from the sun, -but that this is for the different orbits in different nodes. Farther from one another than the astronomical unit are,

Iris and Pallas,

Flora and Pallas, in their descending nodes.

In order to give a still clearer view of the situation of the asteroidal orbits, I have stereographically projected the poles of all these planes of the several planet-orbits and of the sun's equator upon the accompanying chart, on the preceding page.

The observation of Dr. Olbers that the asteroids varied considerably in the intensity of their light, from day to day, seems to hold also for the newly discovered ones. In order to determine this definitely, and if confirmed to find the periods, long series of observations are requisite.

The investigations* of Gauss concerning the Zodiacs of the planets have rendered it comparatively easy to compute for every asteroid, the limits of its geocentric places. Gauss has done this for Ceres and Pallas,t and Prof. Goldschmidt for Iris, I and calculators will not be wanting to do the same for the other five. By this means the search for former observations is facilitated, since it has thus become possible, in the case of every missing star, to decide at the first glance whether any one of the asteroids can ever have been in that place.

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ART. IV.-Continuation of the List of Localities of Algæ in the

United States; by Prof. J. W. Bailey.

(Continued from vol. iii, ii Ser., p. 403.)

DEFERRING for the present, a list of American Desmidiaceæ and select Diatomaceæ or Bacillariæ with which I intended to complete this paper, I proceed to give the following catalogue of genuine Algæ, localities of which have been recently discovered in the United States.

For some of the most interesting species I am indebted to Prof. Lewis R. Gibbes of Charleston College, South Carolina, who, in addition to some fine Algæ, collected by himself in Charleston Harbor, gave me a most valuable collection made at Key West, Florida, by Dr. F. Wurdemann.

The Algæ from Key West are generally so different from those of the Northern Atlantic, which I have hitherto chiefly studied, that I determined to submit them to the examination of the distinguished British Algologist, W. H. Harvey of Trinity College, Dublin, who by means of his extensive Herbarium and great familiarity with the Algæ of all parts of the world, could easily determine the proper position of the species which to me appeared new or doubtful. To this gentleman I am greatly indebted for his liberal communication of information, relating to many of our Algæ which, for want of standard collections in this country, I was unable to determine satisfactorily.

I am also indebted to the eminent French Algologist, Dr. Montagne, for interesting remarks upon some specimens which I sent to him.

A few additional localities are given of plants already included in the preceding portions of this list.

MELANOSPERMEÆ.

Sargassum vulgare, Ag. Key West, Florida. Dr. F. Wurdemann.

Padina Pavonia, Lamour., fine specimens. Key West.
Dictyota ciliata, J. Ag. Key West. Fine specimens.
Dictyota linearis? Key West.

Ectocarpus viridis, Harv. Mss. Charleston, S. C. "Not in fruit and therefore a doubtful species, but its color very remarkable.” Harv.

Ectocarpus fasiculatus, Harv. Rhode Island. Common. Ectocarpus littoralis, Lyngb. New Brighton, Staten Island.

Chordaria divaricata, Harv. Stonington, Conn. Fine specimens near the light-house.

RHODOSPERMEÆ. Rhodymenia cristata, Grev. Massachusetts Bay. Fine specimens of this interesting plant were given me by Miss Saltonstall of Salem, Mass. It has been found also at Newport and Staten Island, while in the Eastern Atlantic, according to Harvey, it is not found south of the Orkney Islands.

Amansia multifida, Lamour. Key West.
Laurencia obtusa, Lamour. Key West.
Laurencia pinnatifida, Lamour. Key West.

Laurencia Baileyanum, Mont. in litt. I had supposed this to be a variety of L. dasyphylla, but Dr. Montagne, to whom I sent some specimens of it, pronounces it new, and gives the following as its specific characters.

L. Baileyanum, Mont. Fronde elongata filiformi subsimplici, ramentis subternis lineari-lanceolatis utrinque attenuatis erectis obsessa. (Individuum tetrasporophorum)." He adds, that “notwithstanding the close affinity of this Alga to Laurencia tenuissima and to L. dasyphylla, it cannot be confounded with either of them. The absence of ramification distinguishes it sufficiently from the first, and the form of the ramenta does not permit it to be referred to the second, from which it is in other respects quite distinct.

It occurs at Newport, R. I., Stonington, Conn., and Fort Hamilton, N. Y.

Hypnea robusta, Harv. MSS. “A fine species quite new to me.” Harv. Key West.

Hypnea musciformis, Lamour. Key West.
Ceramium clavulatum, Ag. Abundant at Key West.

Ceramium fastigiatum, Harv. Common at Newport, R. I., and Fort Hamilton, N. Y.

Callithamnion Baileyi, Harv. mss. "A distinct and beautiful species.” Harv. Abundant at Fort Hamilton and New Brighton, N. Y.

Callithamnion arachnoideum, Ag. Rhode Island.
Alsidium triangulare, J. Ag. Key West.

Polysiphonia (Alsidium ?) Gibbesii, Harv. mss. Key West. “A very remarkable plant.” Harv.

Polysiphonia breviarticulata, Ag. "A Mediterranean species, the Florida specimens very similar to the European but smaller.” Harv.

Polysiphonia variegata, Ag. Very fine specimens near the light-house at Stonington, Conn.

Polysiphonia nigrescens, Grev. I collected beautiful specimens of a slender variety of this plant at New Brighton, N. Y.

Polysiphonia Harveyi, Bailey. A distinct and beautiful species which I found growing in considerable quantity on leaves

F Ceramium clavulatus, Lamour.

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