7. If the particles were perfectly hard and spherical, the specific heat under constant volume would be to that under constant pressure as 3 to 5. If they were hard, but not spherical, this ratio would be that of 3 to 4. The latter result follows from an elegant theorem given by Professor Maxwell in Vol. XX. of the Philosophical Magazine; viz. that if the particles are hard, but not spherical, the sum of their vires vivæ of translation will be equal to that of their vires vivæ of rotation. Unless it can be shown that this ratio will be lessened by supposing that the non-spherical particles are not hard and unyielding, which certainly seems improbable, this result will present the greatest difficulty which the theory has to encounter. Considering the number and variety of the phenomena of gases which are accounted for on this theory, and especially the exactness with which it accounts for the hitherto inexplicable phenomena of diffusion, there seems to be a considerable probability in its favor. The small discrepancy between the observed and computed ratio of the specific heats (1.42 and 1.33) may be found to proceed from some property of the particles not taken account of in the mathematical analysis. The laws of diffusion are obtained on the hypothesis that the gases are separated by an exceedingly thin partition, pierced with extremely small holes. The change of temperature produced by motion proceeds from the changed velocity of impact of the particles against the body, each molecular impact producing a heat-wave. Professor Gray presented the following papers: 1. Characters of some Composite in the Collection of the United States South Pacific Exploring Expedition under Captain Wilkes, with Observations, &c. By ASA GRAY. Vernoniaceæ. MONOSIS INSULARUM (sp. nov.): fruticosa, laxe ramosa; foliis oblongis acuminatis repando-dentatis basis cuneatis in petiolum attenuatis puberulis supra glabratis subtus ad costam venasque cum ramis adpresso-tomentellis; capitulis corymbosis; pappi setis rigidis vix denticulatis, majoribus apice clavellatis. — Tonga and Feejee Islands. A true congener of M. Wightiana, DC., the type of the genus, which stands in nearly the same relation to Gymnanthemum that De Candolle's section Eremosis does to Vernonia. ALBERTINIA BRASILIENSIS, Spreng. To this belongs Gardner's Vernonia platycephala, and Nuttall's Symblomeria Baldwiniana. ties PARANEPHELIUS UNIFLORUS, Poepp. & Endl. Of this three variemay be recognized, viz. a. PINNATIFIDUS, B. BULLATUS (P. bullatus, Gray, Wedd. Chl. And. 1, p. 214), y. OVATUS (P. ovatifolius, Gray, ined. P. ovatus, Wedd. 1. c. t. 37), which Weddell as well as I myself had distinguished as species; but an attentive examination of various specimens leads to the conclusion that they are all forms of one. LIABUM LYRATUM (sp. nov.): herbaceum; foliis supra hirsutiusculis glabratisve subtus arachnoideo-tomentosis, caulinis lyrato-lobatis petiolis basi auriculatis plerumque connatis, summis sessilibus basi dilatata connatis, lobo terminali maximo subinciso et repando-denticulato; pedunculo terminali elongato mono- oligocephalo; involucri squamis oblongis substriatis; pappo e setis paleolisve rigidis inæqualibus, exterioribus dimidio brevioribus. Alibum liaboides, Less.?- Obrajillo, Peru: also collected by Matthews, no. 3057. If this proves to be the Alibum liaboides of Lessing, that genus cannot stand upon the characters indicated. For, as well as can be told from imperfect specimens with the heads injured by insects, the pappus is similar in the disk and ray, the exterior not really coroniform; and the plant nearly accords with Liabum, in the extended sense, or with Andromachia § Pleionactis, DC., except that the bristles of the pappus are more stout and rigid, and also fewer. They are fragile and deciduous, when the summit of the achenium appears somewhat like a short crown. Eupatoriacea. CONOCLINIUM SUBGLUTINOSUM (sp. nov.): glabrum; caulibus basi suffruticosis; foliis longe petiolatis late deltoideo-ovatis acuminatis serratis membranaceis tripli- quintuplinerviis utrinque subglutinosis; corymbo polycephalo; involucri squamis 10-13 dorso subglutinosis bicarinatis, exterioribus ovatis, intimis spathulatis acutis; achenio glaberrimo. - Brazil, at the base of the Organ Mountains, near Rio. This may be somewhere described as an Eupatorium, but I do not identify it with any published species. The receptacle is acutely conical. Asteroidea. VITTADINIA, A. Rich. Char. emend. Capitulum multiflorum, heterogamum; fl. radii uni pluriserialibus fœmineis, disci (pluribus paucisve) tubulosis hermaphroditis. Involucrum obconicum seu hemisphæricum, imbricatum, pauci seriale, squamis inæqualibus angustis appressis. Receptaculum planum, nudum, pl. m. alveolatum. Ligulæ parvæ, tubo suo fere semper breviores, nunc exiguæ stylo ipso breviores. Corolla disci tubulosa, 4-5-dentatæ. Antheræ Euasterinearum. Styli rami fl. herm. superne elongato-subulati hirtelli. Achenia compressa, striata, vel 4 - 6-costata, vel tantum marginato-bicostata lateribus enerviis, apice sæpius contracto, disco epigyno parvo. Pappus simplex, conformis, e setis capillaribus scabris uni - pauciserialibus. Suffrutices vel herbæ Oceanicæ, caulibus ramosis plerumque foliosissimis, foliis alternis. Capitula aut solitaria ramos terminantibus aut corymbosis: ligula abæ vel purpureæ. Vittadinia, A. Rich. Bot. Voy. Astrol. Fl. N. Zel. (1834), p. 250. Vittadinia, Tetramolopium § 1 & Eurybiopsis, DC. Prodr. De Candolle's Eurybiopsis is essentially identical with the older Vittadinia of A. Richard, and has been referred to it by Dr. Hooker. The only observed difference is, that the faces of the achenium of Eurybiopsis macrorhiza, if I rightly identify the plant, are nerveless; those of Vittadinia are striate-nerved. There must, however, now be added to the genus several Hawaian species, one of which is strictly an Eurybiopsis; another, the type in part of Tetramolopium, Nees, differs only in its less copious uniserial pappus, and in the shorter, mostly four-ribbed achenia; while others, with corymbose and still smaller heads, have decidedly pluriserial rays, with their more reduced ligules sometimes even shorter than their styles, and the hermaphrodite flowers fewer,in one instance even reduced to unity, so that these are to Vittadinia proper what the Conyzoid Erigerons are to Stenactis or to true Erigeron. The genus, thus augmented, while by its larger-flowered species nearly related to Eurybia (from which De Candolle and Dr. Hooker remark that it technically differs only in its compressed achenia), and nearly congruous with the group of ambiguous Asters designated under the name of Orthomeris by Torrey and Gray, is now seen, on the other hand, to be the analogue of Erigeron. From the latter already too polymorphous genus, Vittadinia would be well distinguished by its striate or ribbed achenia, and the slender subulate tips of the styles, except that, unfortunately, some of the species show neither facial ribs nor striæ, while a few species of Erigeron, as Weddell regards them, have long, and slender tips to their styles, and some North American ones have four-nerved achenia. The habit generally is not that of Erigeron, and the achenia and the more imbricated involucre will dis tinguish those species which might otherwise be confounded with the Canoti. The short, but always distinct ligules are characteristic of the genus. Most of the Sandwich-Island species are decidedly shrubby plants, those of New Zealand and Australia woody at the base; but there are two Australian species which appear to have annual roots. On the other hand, Erigeron fruticosum of Juan Fernandez, which forms a shrub, is apparently a genuine Erigeron. De Candolle assigns uniserial rays to his Eurybiopsis and to the New Zealand Vittadinia, and bi-triserial rays to the Australian Vittadinia; Dr. Hooker regards them as uniserial throughout. When ligules are numerous and narrow, this character has neither definiteness nor significance, as the genus Erigeron shows. To both Eurybiopsis and Vittadinia De Candolle ascribes a "pappus uniserialis," a term which he seems not always to have employed in one and the same sense. In the species known to De Candolle, the very copious bristles of the pappus certainly occupy two or more ranks, just as in Aster. From these there is a gradual transition to the more scanty and obviously uniserial pappus of V. tenerrima and the smaller-flowered species of the Sandwich Islands. For the genus, as here augmented, the name of Tetramolopium might be assigned in virtue of its priority, as it antedates Vittadinia by a year. But the former name was given to two heterogeneous species, viz. one from the Sandwich Islands, which has long remained obscure, and one from the Quitensian Andes, which is a Diplostephium, and with which De Candolle rightly associated two other of Humboldt and Kunth's Asters. In this case the name Vittadinia may fairly be kept up. The three generic names thus brought together may be retained for as many sections, characterized as follows: § 1. VITTADINIA VERA. Achenia elongata, faciebus pluristriatis. Pappus copiosus pluriserialis. Ligulæ pl. m. conspicuæ. Capitula majuscula, solitaria. V. TRILOBA (DC. non Hortul.): caule erecto e radice annua apice subcorymboso cum foliis spathulatis cuneatisve basi longe attenuatis superne trilobis vel tridentatis (ramealibus angustioribus sæpius integerrimis) scabro-hirtellis vel hirsutis; ligulis purpureis breviter exsertis; acheniis clavato-linearibus pluristriatis immarginatis pubescentibus, maturis involucro etiam pappo pluriseriali fulvo æquilongis. Variat foliis caulinis tripartitis, lobis trifidis seu laciniatis. Eastern Australia. The plant which was generally cultivated in the European gar dens, a few years ago, as Vittadinia triloba, and which Dr. Sonder, mistaking it for the genuine Australian plant of that name, has described as Erigeron trilobum, is manifestly De Candolle's Erigeron mucronatum, of Mexico and Venezuela. V. CUNEATA, DC. (Eurybiopsis gracilis, Hook. f. and probably V. dentata, DC.) is not well named. The perennial root, undivided leaves, and less rough pubescence distinguish it from the preceding species. V. SCABRA, DC. (Eurybiopsis scabrida, Hook. f. E. Hookeri, Sonder). Müller's plant, or at least the var. angustifolia, accords pretty well with the character of De Candolle's V. scabra. It appears to be distinguishable by the less copious and shorter pappus, and by the less attenuated achenia, which are evidently margined by ribs considerably stronger than the facial nerves. § 2. EURYBIOPSIS. Achenia minus elongata, marginato-binervia, faciebus haud striatis. Pappus uni-pluriserialis. Cæt. sect. præcedentis. V. HISPIDULA (F. Müll. ined.): undique scabro-hispida seu hispidula; caule erecto e radice annua stricto oligocephalo; foliis caulinis linearibus sessilibus imisve spathulatis paucidentatis; ligulis e pappo leviter exsertis; acheniis appresse-hirtellis obovatis apice breviter acutatis faciebus enerviis pappo fere uniseriali brevioribus. · Eastern and Tropical Australia. V. MACRORHIZA (Eurybiopsis macrorhiza, DC.) if rightly identified with Dr. Müller's specimens from "Providence Hill," considerably resembles dwarf and narrow-leaved forms of V. scabra, but the faces of the achenia are nerveless, as in V. hispidula. The pappus is more copious than in the latter, and about the length of the (immature) linear achenia. V. HUMILIS (sp. nov.): suffruticosa, e basi crassa multicaulis; caulibus foliosissimis; foliis anguste spathulatis integerrimis undique hispidis seu hirtellis aveniis, costa subtus incrassata; pedunculis brevibus solitariis vel subumbellatis; ligulis uniseriatis flores disci (6-12) vix superantibus stylis duplo longioribus; acheniis lineari-oblongis marginatobinervatis hirtellis estriatis pappo subtriseriali inæquali dimidio brevioribus. Variat foliis hirsutioribus vel subglabratis, nunc fere linearibus basi longe attenuatis. Sandwich Islands, on the mountains of Hawaii and Maui. - This species manifestly connects the original Tetramolopium with Eurybiopsis. A depressed and glabrate variety, from the district of Waimea, Hawaii, makes the nearest approach to the Tetra |