Whereupon it was unanimously voted that the invitation be accepted, the letter placed upon the record of the present meeting, and that the officers of the Academy communicate to President Quincy the expression of the extreme interest of the Fellows of the Academy in the occasion which prompted this invitation, and their most cordial acceptance of it. Four hundred and ninety-first meeting. January 30, 1861.STATUTE MEETING. The PRESIDENT in the chair. The Corresponding Secretary read a letter from the Hon. G. M. Dallas, the American Minister at London, enclosing a copy of correspondence with Lord John Russell, Secretary of State, and announcing the liberal donation by the British Government to the American Academy, of a complete set of the Geological Maps and Sections of the Survey of the United Kingdom of Great Britain. Mr. J. E. Oliver, of Lynn, was elected a Fellow, in Class I. Section 1. Professor Peirce presented the results of an investigation of the phyllotaxic numbers and their relations. President Felton gave an account of the progress that had been made, and the results attained, in unrolling and deciphering the Herculanean manuscripts. Dr. C. T. Jackson exhibited specimens of eocene tertiary coal from the Isthmus of Darien, near Chiriqui, similar in character to cannel coal, although of so much more recent formation. Mr. Newcomb presented the results of an investigation of the dynamical theory of gases. One of the most beautiful hypotheses ever propounded in physics is that which has lately been known as the dynamical theory of gases. This theory supposes a gas to be composed of isolated particles, moving about in every direction with great velocity, and continually striking and rebounding from each other. The expansive force is due to col lisions against the sides of the containing vessel. The temperature depends upon the rapidity of the motion, being represented by the vis viva of the separate molecules. This theory has therefore a very intimate relation with the mechanical theory of heat, and is in part dependent on it. The truth of such a theory must be judged of from the agreement of the results deduced from it with observed phenomena. The following physical laws and properties of gases follow from this theory. 1. Mariotte's law. 2. Equal volumes of all gases set free the same amount of heat when compressed by the same fractional part of their volume, this amount being the exact mechanical equivalent of the force employed in producing the compression. Hence, if the compression is considerable, the amount of heat will vary with the rapidity of the compression, being much greater when the whole amount of heat set free is confined in the gas, than when it is suffered to escape as rapidly as it is formed. 3. Gases expand equally for equal increments of temperature. 4. Equal volumes of all gases, measured at the same temperature and pressure, contain the same number of particles.* 5. Gases will diffuse into each other in accordance with the following laws. a. Gases at the same temperature and pressure will diffuse into each other with a velocity directly as the square root of the specific gravity, when measured by the mass which is diffused, and therefore inversely as the specific gravity when measured by volume. B. The temperature of the gas being increased, while its volume remains constant, the diffusive power will increase as the square root of the elasticity. 7. The temperature varying, while the pressure remains constant, the diffusive power will vary inversely as the volume. Or, in general, gases diffuse into each other according to the laws which regulate their flow into a vacuum. 6. A body moving rapidly through a gas will be subject to an increase of temperature, varying as the square of its velocity. For different gases this increase will be directly as the specific gravity of the gas; but the effect of radiation being eliminated, the increase of temperature will in the case of the same gas be independent both of the temperature and the density of the gas. VOL. V. * Maxwell, Philosophical Magazine, January, 1860. 15 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. vive 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. Vernoniacea. 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. PARANEPHELIUS UNIFLORUS, Poepp. & Endl. Of this three varie ties may be recognized, viz. a. PINNATIFIDUS, B. BULLATUS (P. bullatus, Gray, Wedd. Chl. And. 1, p. 214), 7. 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 |