ARTICLE IV. On the Ratio of Expansion of Gases. By Mr. Matthew Biggs. SIR, (To the Editor of the Annals of Philosophy.) 63, Great Russell-street, Nov. 3, 1823. HAVING had occasion lately to turn my attention to the nature of gaseous bodies generally, and particularly to their conduct under varying temperature, I referred to the works of Dr. Henry and Mr. Brande for information. We are told by both these gentlemen that all aeriform bodies possess the same mechanical properties; that the rate of expansion and contraction under increased or diminished temperature is common to all, and that, according to the experiments of M. Gay-Lussac, which they consider as the most correct, the expansion on increase of temperature is of the volume for every degree of Fahrenheit's scale, between 32° and 212°. I then proceeded to the rules which are given for reducing any volume at any temperature to such other temperature as may be required, and I found them so defective that I doubt not I shall prove to you, that all calculations made from the data there laid down, must have produced erroneous results. After having informed us as above that the increase is of the volume for every degree of the thermometer, they proceed to say, that in order to reduce any given volume at any known temperature to any other that may be required, we must divide the whole volume by 480, multiply the quotient by the number of degrees between that at which the gas is, and that to which it is to be reduced, and then add this product to the volume, if the reduction be made from a lower to a higher temperature; subtract it if from a higher to a lower; the number now found will be the volume at the temperature required. Thus I have 100 cubic inches of gas at 32°; and my object is to ascertain what space they would occupy at 60°, 100 ÷ 480·208; 208 × 28 = 5.824; 5.824+100=105 824 they will have become 105-824 C. I. by an elevation of 28°; but suppose the reverse to be the state of the inquiry, having 105-824 C. I. at 60°, I wish to know their volume at 32°, 105-824-480=220; 220 x 28-6.16; 105.824-6-16-99-664. This cannot be correct, because we know that although bodies expand by the application of heat, they regain their former dimensions when reduced to their former temperature. If I find that 100 C. I. of any gaseous body become 105.824 by an addition of 28° to their temperature, I know that by abstracting the 28° they are again reduced to 100; but not lower, as this mode of calculation would show. To put the error in another light; it is proved that 480 C. I. at 32° become 508 if elevated to 60°. The volume I set out with increases one cubic inch for every additional degree. Now suppose the temperature raised to 61°, the volume will then be 509 C. I. or it will have increased one inch; but 1 is not theo of 508; therefore gas does not increase of its volume for each degree, at any point of the scale, except 32°, as the works I have referred to inform us: 100 volumes at 50° do not become 102.08 if raised to 60°, neither do 100 at 70° become reduced to 97.92 if lowered to 60°, as the examples there given seem to show. Taking the fact that 480 volumes at 32° increase one volume for every additional degree as a foundation, we may easily form a rule by which to ascertain what space any volume at any temperature will occupy at any other temperature between 32° and 212°. Add the number of degrees which the gas is above 32°, to 480; this will be the first number. Add the number of degrees which the required temperature is above 32°, to 480 for the second number. The volume on which the calculation is made will be the third, and the fourth will be the volume required. For example, I have 100 C. I. of gas at 70°, and I wish to know what their volume would be at 60°, o rsuppose the 100 C. 1. to be at 50°, what will they be at 60°? I will now give an extreme case, worked both ways, to show the great inaccuracy of the old method, and the correctness of mine. Raise 100 C. I. from 32° to 212°. 208333; 208333 x 180 = 37.4999; 37-4999 + Reduce 137.5 C. I. from 212° to 32°. 137-5480286458 x 180 51-5624; 137.5 = = 85.9376 660: 480 :: 137·5: 100. Thus the error, by the old rule, amounts to more than 14 cubic inches. I am, Sir, yours, &c. MATTHEW BIGGS. ARTICLE V. A Description of some Insects which appear to exemplify Mr. William S. Macleay's Doctrine of Affinity and Analogy. By the Rev. William Kirby, MA. FRS. and LS.* No objects are more interesting to the scientific naturalist than those which assume the external appearance of one tribe, while their more essential characters and their habits indicate that they belong to another. These objects a prima facie survey would often induce us to refer to a very different set of beings from that to which a more intimate acquaintance with their peculiar diagnostics and economy would lead us. And we shall find, the further we extend our researches, the traces of that plan of Creative Wisdom by which a symbolical relationship, if I may so call it, connects such of his creatures, as in other respects are placed in opposition to each other, as well as a natural affinity those that really approximate. Writers in every department of natural history, when they have been endeavouring to thread the labyrinth of affinities, have been extremely puzzled by this remarkable circumstance. They were aware that those species which connect two proximate tribes, generally partake of the characters of both; but they were not sufficiently aware of this resemblance between objects that are connected by little or no affinity. Hence it has happened not unfrequently, that objects have been referred not to the tribe to which they are really related, but to that which they resemble in some of their less essential characters. Mr. W. S. Macleay, in his acute and learned Hora Entomologica, has furnished the naturalist with a clue which, if heedfully followed, will enable him to guide himself through all the intricacies with which the circumstance here mentioned has perplexed his path. This gentleman has first stated with clearness and precision the distinctions, so often before confounded, between real affinity and those resemblances which are merely analogical; and has proved satisfactorily, that there exist between numerous objects in every department of nature striking coincidences as to external characters, which do not indicate that they are related to each other, or should be placed together in a natural arrangement. In confirmation of the doctrine here alluded to, I have the honour to present to the Linnean Society a description of three new genera of insects which appear to wear the face of a tribe to which they do not belong. * From the Linnean Transactions for 1823, Part I. New Series, VOL. VI. COLEOPTERA PENTAMERA. (Harpalida.) CATASCOPUS Kirby. - Character Essentialis.-Labium s. Ligula tripartitum: lobo intermedio abbreviato; lateralibus apice latioribus. Labrum emarginatum. Character Artificialis.-Labium tripartitum : lobo intermedio abbreviato. Labrum emarginatum: lobis rotundatis. Palpi maxillares articulo secundo incrassato. Oculi magni, valde prominuli. Tibia antica intus medio emarginatæ. Character Naturalis.-Corpus subdepressum, oblongum, glabrum, alatum. Caput horizontale, subtriangulare: collo distincto. Labrum subquadratum, apice emarginatum: lobis rotundatis. Mandibula subtriquetro-trigona, apice forcipate incurvæ acuta, edentulæ. Maxilla lobo interiori incurvo unguiformi acutissimo, exteriori palpiformi biarticulato: articulis longitudine æqualibus. Palpi maxillares quadriarticulati: articulo primo minutissimo; secundo reliquis longiori crassiori subarcuato; tertio secundo breviori subclavato: extimo teretiusculo. Labium tripartitum: lobis coadunatis; lateralibus longioribus dilatatis semicordatis planis: intermedio lateralibus dimidio breviori convexo apice bisetigero. Palpi labiales triarticulati? Mentum trilobum: lobo intermedio brevissimo rotundato. Antenna undecim-articulatæ subfiliformes: articulo primo incrassato; proximis tribus subclavatis sequentibus tenuioribus ; reliquis oblongis compressis; extimo acuto. Oculi laterales, magni, valde prominuli. Frons apud oculos longitudinaliter bistriatus. Nasus s. Clypeus transversus: apice segmento circuli dempto. Truncus. Thorax quadrato-obcordatus, postice constrictus : angulis prominentibus, in medio canaliculatus, apud angulos posticos foveatus, antice et postice truncatus: lateribus marginatis. Prosternum lineare, apud basin pedum anticorum deflexum, apice rotundatum. Mesosternum brevissimum, apice emarginatum. Metasternum antice et postice mucronatum. Scutellum minutum, triangulare. Elytra apice oblique præmorsotruncata. Epipleura* linearis, apud basin elytri dilatata. Tibie calcaribus 2. 2. 2. anticæ intus ante medium emarginatæ. Tarsi articulo penultimo integro. Abdomen in specimine nostro mutilatum. At first sight the little insect exhibiting these characters might be mistaken for a species of Notiophilus of Duméril, or at least be regarded as belonging to a cognate genus. Its large and very prominent eyes, the shape in some measure of its tho * See this term explained Linn. Trans. xii. 377. rax, the striæ of the disk of its elytra less impressed with puncta than those of the limb, as likewise its frontal furrows, give it no inconsiderable appearance of affinity to it. But a closer inspection proves that this is merely an appearance, and that in fact it belongs to a different tribe connected with the Harpalida. Notiophilus and its genuine affinities are distinguished by a particular character indicating some difference in their mode of taking or retaining their prey. The great majority of the Carabi of Linné are remarkable for a notch on the inner side of their anterior tibiæ, armed at its upper angle by a spur, which appears to be of use to them for the above purpose. In the Harpalida and many others this notch is nearly in the middle of the tibia; but in Notiophilus and its affinities its situation is close to its apex. Catascopus, with respect to this part, falls into the former tribe. Again, in Notiophilus the labium consists only of a single lobe, or at least the lateral ones are much shorter than the central; but in the Harpalida they are as long or longer.* In Catascopus also they are very conspicuous, being twice the length of the central lobe. In Elaphrus, Notiophilus, Blethisus, &c. the fore-breast (antepectus), or the part immediately under the thorax, is more or less covered with impressed puncta. In. the Harpalida and Catascopus it is quite free from them. In the former tribe likewise the legs, especially the thighs, are slenderer and less robust than in the latter. The head moreover in these is narrower behind, so as to form a distinct neck; whereas in those, if any thing, it is widest behind, and the neck is formed by the convexity of that part, and not by any constriction of it. From all these circumstances, I think, it is sufficiently evident, that the relation of Catascopus to the Harpalidæ is that of affinity, while that which it bears to the Elaphrida, insects which at first sight it most resembles, is merely that of analogy. But there is still another tribe of which it exhibits many characters, I mean those which constitute M. Latreille's first section of his Carabici, which have the head and thorax much narrower than the abdomen, and truncated or very obtuse elytra; for instance, Anthia, Brachinus, Lebia, &c.; and with these at one time I felt inclined to arrange the genus I am considering; but the different characters of the Labium convinced me that it ought rather to go with the Harpalide. Should any master in Entomology hereafter undertake a new arrangement of Carabus L., he may perhaps bring the Harpalide and the above section nearer to each other; and in this case Catascopus would very well connect the two tribes. The exact place of the genus I have not been able satisfactorily to ascertain. Of all the known genera of the Harpalida it seems to approach nearest to Pterostichus Bon., or Sphodrus Clairv., principally on account of the shape of the thorax; but there must be several intermediate links between them. * Clairville, Ent. Helvet. ii. t. x, xi, xii, &c. c. |