Havana, Cuba. See C. S. report, 1855, p. 324. 1857, Jan., D= 5° 15' E. Jamaica, W. Indies. Karl Friesach, Imp. Acad. of Sciences, 1732, D= 6° to 6° 05′ E. J. Harris at Black river, in March and DeMayne, Owen, See also C. S. report, 1856, p. 214. San Diego, Monterey, San Francisco and Cape Mendocino, California, and for Cape Disappointment, Washington Territory, see C. S. report, 1856, pp. 228 to 235. Sitka, Russian America. ART. XXX.-Caricography; by PROF. C. DEWEY. (Continued from vol. xxviii, p. 232, Second Series.) No. 260. Carex argyrantha, Tuckerman. Spica composita; spiculis 4-8, ovato-rotundis vel obovatis sub-approximatis alternis albis, inferiore subremota, supernè staminiferis, squamosibracteatis, distigmaticis; fructibus ovatis compressis erectis vel sub-patulis nervosis margine membranaceo-alatis viridibus acuminato-rostratis brevibifidis, squamam membranaceam albam lanceolatam aequantibus. Culm 13 feet high, smooth, lax, reclining, and twice longer than the leaves; spikelets nearer above and white; fruit margined or winged widely for its length and width; light green. Rocky Woods, Amherst and Sunderland, Mass.; Prof. Tuckerman, by whom the plant and his description have been kindly presented. It is related to C. Deweyana, and the white-glumed family, silver-flowered, according to its name, but appears to be new and distinct; discovered the last season. Note. C. Rugeliana, Kunze, suppl. to Schkuhr, No. 56, p. 189, is C. aestivalis, Curtis, according to Boott, Illust., p. 54, No. 133. C. miser, Buckley, in this Journal, vol. xlv, p. 173, and vol. xlviii, p. 140, is considered by Dr. Boott to be C. juncea, Willd. System, Veg., 1826, No. 226. See Boott, Lin. Trans. vol. xx, p. 116, and Illust., p. 55. The descriptions of Willd. & Kunze sustain this conclusion of Dr. Boott. 261. C. paludosa, Goodenough. Schk. fig. 103. Spicis pistilliferis, 2-4, sæpe 3, cylindraceis erectis oblongis, arctèfloriferis sub-approximatis, superioribus sessilibus, inferiore sæpe longopedunculata vix vaginata inferne attenuata et hinc sublaxiflora, alternatis et foliaceo-bracteatis; perigyniis (fructibus) ovatis in breve rostrum bidentatum attenuatis vel ovalibus acuminatis brevi-rostratis distinctè et multinervosis subcompressis subglabris tristigmaticis, squamam angustam lanceolatam aequantibus vel lanceolata cuspidata brevioribus. Culm 1-2 feet high, erect, triquetrous, scabrous above, longer than the rough-edged leaves, with leafy bracts equal to or surpassing the culm. Varies, like the European plant, in the length and thickness of its spikes, and in its glumes or scales. Near Boston-Wm. Boott, Esq., in 1859, probably introduced not many years since. Common in England, Germany, and Sweden. 262. C. monile, Tuckerman. Boott, Illust., No. 71. Spicis staminiferis, 2-4, longis, cylindraceis, gracilibus cum squama longo-lanceolata; pistilliferis 2, rarò 1, oblongo-cylindraceis, subremotis, brevi-pedunculatis, sub-densifloris, infima interdum basin attenuata subnutante, foliaceo-bracteatis vix vaginatis; fructibus globosis vel ellipsoideis inflatis brevi-rostratis bidentatis glabris multi-nervatis stramineis cum ore rostri sub-obliquo, squama angusta oblonga lanceolata sub-duplo longioribus. Culm 15-30 inches high, erect, triquetrous, longer than the leaves; bracts surpassing the culm, bright yellowish green. In marshes, not abundant, N. England-Tuckerman; Rhode IslandOlney; New Jersey, Ohio and westward. Note 1. The Carex, No. 197, vol. xlix, p. 47 of this Journal, accidentally misnamed, is C. Vaseyi, Dew., of which No. 197 contains the accurate description. From the preceding, C. monile, Tuck., the fruit is very different, being ovate, long-conic, subtriquetrous-inflated, glabrous and scabro-rostrate. C. Vaseyi is the plant referred to by Dr. Boott, Illust., No. 71, as different from C. vesicaria and C. monile, but not named by him among those sent him from Penn Yan, N. Y., by Dr. Sartwell. The reference of No. 197 above to No. 71 in the Illust. is, of course, an oversight. The correction on 197 is C. Vaseyi, Dew. Note 2. C. bullata, Schk., Fig. 166, described in this Journal, vol. ix p. 71, 1825, from living specimens, and named from its (ball-shaped) nearly globose fruit, seems to me, as it does to Carey in Gray's Manual, distinct from C. cylindrica, Schw., and from the following number. 263. C. physema, Dew. C. bullata, Boott, Illust., No. 71, and Carey (non Schk). Spicis staminiferis, 2-3, cylindraceis, gracilibus, contiguis, infima bracteata; pistillifera 1, interdum 2, subrotunda vel oblongo-cylindracea perdensiflora et crassa remota et subfulva, infima pedunculata et subnutante vel erecta longi-foliacea bracteata; fructibus turgidi-ovatis longicylindraceis rostratis bifurcatisque, inflatis glabris et scabro-dentatis vel serratis, squama lanceolata acuta albi-marginata longioribus et latioribus. Culm 1-2 foot high or more, firm, slender for the thickness of pistillate spike, stiff, triquetrous and often roughish, shorter than the narrow, flat and prim leaves; bright green. Humid meadows, New England to Pennsylvania. On C. bullata, Schk., Fig. 166, the pistillate spikes are shown as long and loose-flowered, and the fruit globose (ovate-globose), inflated abruptly, contracted into a slender, round, long, scabrous bifurcate beak, with a glume about half as long. On the Carex, Boott, Illust., No. 39, the fruit is very large and inflatedovate, with a conic, tapering, three-sided beak, scabrous-dentate, forming thick, dense and large spikes. If the figure by Dr. Boott shows C. bullata, Schk., then the figure in Schk. is a palpable caricature. Trusting to the correctness of the figure of Schk., I may yet say that Dr. Boott has presented a well known and distinct form. It is obvious that it should have another name, which designates the inflation of the fruit or perigynium, like the other. 264. C. Olneyi, Boott, Illust., No. 40. Spicis stamiferis, 2-4, saepe 3, cylindraceis approximatis gracilibus; pistilliferis saepe 2, vel 1-3, cylindaceis sub-crassis densifloris stramineis approximatis plus minus pedunculatis, infima basin tereti laxiflora saepe subnutante, bracteatis; fructibus inflati-ovatis brevi-conico-rostratis scabrobifurcatis nervosis divergentibus, squama lanceolata acuta vel cuspidata longioribus. Culm 15-22 inches high, strong, obtusely triquetrous, scabrous above, shorter than the long and stiff margined leaves. Rhode Island-Olney; probably associated with this group over the country. Were it not for the very different spikes, the fruit would closely ally this species to C. physema, as being a smaller form of it. Remark. This Vesicaria group is of difficult determination, and there has been much confusion in consequence. Hoping that some light has shined upon it, I can only say with Dr. Boott, that "future observation must determine in America the value to be affixed to the species of this group." The following shows the group as here exhibited: C. monile, Tuckerman. Boott, Illust., No. 39. C. Vaseyi, Dew. C. monile, Sart., Exsic. No. 151, and Sill. Journ., [1] vol. 48, p. 47, putting C. Vaseyi for C. monile. C. bullata, Schk. Dew., Sill. Journ. vol. 9, p. 71 (not Boott or Carey). C. physema, Dew. C. bullata, Boott, and Carey in Manual. C. Tuckermani, Boott. Dew., Sill. Journ., vol. 49, p. 47. C. cylindrica, Carey. C. Olneyi, Boott, Illust., and as above. As Dr. Boott has found C. lenticularis, Mx., among the northern Carices, it is now distinguished and identified. The great difficulty had been in the imperfection of the description of Michaux. This is removed by Dr. Boott, which the younger botanists will be glad to see, and also the more complete description. C. lenticularis, Mx. Boott, Illust., No. 76, Fig. 77. C. concolor, R. Br. in this Journal. Spicis cylindraceis obtusis approximatis et sessilibus; staminifera unica, interdum 2, infima brevi, vel terminali superne sæpe fructifera; pistilliferis 2-5, vel rarò pluribus, foliato-bracteatis, interdum inferne staminiferis, infima vix sessili; fructibus ellipticis convexo-lenticularibus, interdum subovatis,,per-brevi-rostellatis nervosis stramineis glabris, squama oblonga obtusa pallida longioribus; planta matura concolore. Culm 8-14 inches high, triquetrous, erect, leafy towards the base, leaves about the length of the culm, and sheaths longer than the culm; terminal spike staminate, often only staminate below, sometimes a shorter staminate sessile spike near it; pistillate spikes 3-4, or more or less, cylindrical, erect, the lowest sometimes vaginate-bracted; stigmas 2; fruit sub-ovate, longer than the oblong obtuse white-edged scale; whole plant light green, nearly of the same color. Var. Lake of Swans and Arctic America, Michaux and Richardson. Albi-montana, has fruit less oval, or ovate and acutish, tapering above, resembling somewhat C. torta, but taller than the Arctic plants. White Mountains, N. H., about ponds-Tuckerman. In Harrison, Me., about ponds, in 1859-—Rev. J. Blake. ERRATA. On p. 232, vol. xxviii, for C. gynocratis read C. gynocrates. On p. 231, same vol., for vol. xxiv, p. 48, read vol. xxvii, p. 81, Sec. Ser., and for the numbers 254, 255 and 256, read 257, 258 and 259. ART. XXXI.-On Numerical Relations existing between the Equivalent Numbers of Elementary Bodies; by M. CAREY LEA, Philadelphia. Part II. (Concluded from p. 111.) On Geometrical Ratios existing between Equivalent Numbers. THE First Part of this paper was devoted to the examination of relations between the equivalent numbers of certain elementary bodies depending upon the number 44-45, and it was attempted to show: 1st. That such relations extend to nearly all the elements:2d. That the particular groups collected together by this relation consist of bodies whose properties are analogous, and that the classification is in harmony with the distinguishing characteristics of the substances classified. The first portion of this Second Part will present a species of relation wholly distinct, it is believed, from any that has hitherto been pointed out, and which may be not inappropriately termed Geometrical Ratios, to distinguish them from the more familiar arithmetical relations which have been heretofore exclusively studied by chemists. The arithmetical relations are susceptible of at least an hypothetical explanation, on the supposition that the common difference in a series of elements may represent the equivalent number of a substance as yet undetermined, which, by its combinations in varying proportions, gives rise to the bodies constituting the successive terms of the series. The analogies which are now to be considered are more difficult of explanation, even by hypothesis. Their accuracy, sometimes absolute, renders improbable the supposition that they are mere casual coincidences. In science it is not permitted to neglect facts merely because we cannot satisfactorily account for them. The nature of these relations consists in this, that if we take two substances and examine the ratio which subsists between the numbers representing their atomic weights, we may find in certain cases, that it is identical with the ratio subsisting between the atomic weights of two other substances, and so on through a considerable number of elements. The ratio between the atomic weights, for instance, of oxygen and nitrogen, is that of four to seven, so likewise is that between those of zirconium and potassium, potassium and barium, with absolute exactitude. What renders this the more remarkable is, that all three of these last substances are striking exceptions to Prout's law that the equivalents of the elements are exact multiples of that of hydrogen; they all have decimals, zirconium 224, potassium 39-2, barium 68.6. Now the ratio just mentioned gives these num |