Jan. 24, 1878] 



NATURE 



255 



opinion that the matter had not yet been satisfactorily settled.) 

 — Prof, Lloyd Tanner, on partial differential equations with 

 several dependent variables. — Lord Rayleigh, on the relation 

 between the functions of Laplace and Bessel (in § 783 of Thom- 

 son and Tail's "Natural Philosophy," a suggestion is made to 

 examine the transition from formulae dealing with Laplace's spheri- 

 cal functions to the corresponding formulae proper to a plane). 

 It is evident at once, from this point of view, that Bessel's 

 functions are merely particular cases of Laplace's more general 

 functions, but the fact seems to be very little known. — Mr. Ferrers, 

 in his elementary treatise on Spherical Harmonics, makes no 

 mention of Bessel's functions, and Mr. Todhunter, in his work 

 on these functions, states expressly that Bessel's functions are 

 not connected with the main subject of the book. The object 

 of the present paper was to point out briefly the correspondence 

 of some of the formulae. The author showed that the Bessel's 

 function of zero order {J^ is the limiting form of Legendre's 

 function, P^ (;u), when n is indefinitely great and /u (= cos 0) 

 such that n sin is finite, equal (say) to Z. This was proved by 

 takinglMurphy's series for P^ (Todhunter, § 23). In like manner 

 Bessel's functions of higher order are limits of those Laplace's 

 functions to which Todhunter gives the name of associated func- 

 tions. A theorem was found for the general functions coiTe- 

 spondng to the relation subsisting between three consecutive 

 Bessel's functions W\z.,\Z[J (s)+/ , (3)1= w / (2)!' 



Prof. Cayley stated that the results obtained were very interest- 

 ing)- — Mr. S. Roberts gave some results bearing upon his 

 paper read at the December meeting. — Prof. Cayley gave an 

 expression for the surface of an ellipsoid communicated to him 

 by Prof. Tait. — The Chairman, Professors Cayley, Tanner, and 

 Mr. Webb spoke upon the subject. 



Chemical Society, January 17.— Dr. Gilbert in the chair. 

 —It was announced that a ballot for the election of Fellows 

 would take place at the next meeting of the Society (February 

 7).— The following papers were read : — On the luminosity of 

 benzol when burnt with non-luminous combustible gases, by E. 

 Franklr.nd and L. T. Thorne. After many unsuccessful attempts 

 to burn benzol with a smokeless flame, the authors determined 

 the luminosity of benzol vapour after dilution with hydrogen, 

 carbonic oxide, and marsh-gas. These gases were passed through 

 a benzoliser kept at a constant temperature and burnt in a fish- 

 tail burner. The following results were obtained : — I lb. avoir- 

 dupois of benzol gives, when burnt with hydrogen, the light 

 yielded by 5792 lbs. of spermaceti with carbonic oxide, that of 

 6'ioo lbs. of spermaceti with marsh-gas, that of 77 lbs. of 

 spermaceti. The authors point out that this difference is 

 probably due in part to the different pyrometric thermal effects 

 of the gaseous mixtures. — On the action of reducing agents on 

 potassium permanganate, by F. Jones. Hydrogen reduces per- 

 manganate, sesquioxide of manganese being formed ; ammonia pro- 

 duces in addition a nitrate, a nitrite, and free nitrogen ; phosphme, 

 arsine, and stibire give somewhat similar reactions ; oxalic acid 

 forms manganese sesquioxide, carbonic acid, and oxygen ; strong 

 solutions of permanganate and manganese chloride, when mixed, 

 form sesquioxide of manganese, chlorine and oxygen being 

 evolved. — On the action of sulphuric acid on copper, by Spencer 

 Pickering. According to the author there are only two primary 

 reactions, in one of which copper-sulphate, sulphurous acid, and 

 water are the products, in the other subsulphide of copper, 

 copper sulphate, and water are formed. The author has 

 studied the action at various temperatures and has investi- 

 gated the quantity of sulphuric acid actually used, the effect 

 of an electric current, the action of impurities in the copper, 

 the variations produced by diluting the acid, &c. — On the 

 analysis of sugar, by G. Jones. The author proposes to 

 estimate sucrose volumetrically by adding a oi per cent, 

 solution to a boiling decinormal solution of permanganate, 

 acidulated with sulphuric acid, until the dirty-brown hydrafed 

 peroxide of manganese, which is at first formed, is reduced and 

 dissolved. — On the decomposition products of quinine, by W. 

 Ramsay and J. Dobbie. The authors oxidised quinine with 

 permanganate and obtained a new acid, which they have identi- 

 fied with Dewar's dicarbopyridenic acid, and a red amorphous 

 substance. The same acid was obtained by oxidising Marchand's 

 quinetin. 



* Geological Society, December ^19, 1877.— Prof. P. Martin 

 Duncan, F.R.S., president, in the chair. — Messrs. William 

 Fream, J. G. Hochstatter Godfrey, Herbert Goss, and John 

 Fowke Lancelot Rblleston were elected Fellows of the Society. 



—The following comiuunicalions were read : — On Arpllornis 

 longipennis, Owen, a large bird of flight, from the eocene clay of 

 Sheppey, by Prof. Owen, C.B., F.R.S. In this paper the 

 author described some remains of a large bird obtained by Mr. 

 W. H. Shrubsole from the London clay of Sheppey (already 

 referred to in Natitrb), consisting of parts of fractured humeri 

 belonging to tjie right and left sides of the same species or 

 perhaps individual, and including the head of the bone, with 

 portions of the upper and lower parts of the shaft. The texture 

 of the shaft, the thinness of its bony wall, and the large size of 

 the cavity recall the characters of the wing-bones of the large 

 cretaceous pterodactyles. The author concluded that the bones 

 obtained by Mr. Shrubsole furnished indications of a new genus 

 and species of flying birds, for which he proposed the name of 

 Argillornis longipennis. He regarded It as probably a long- 

 winged natatorial bird, most nearly related to DiomeJea, but 

 considerably exceeding the Albatross {D. exulans) in size. — 

 Contributions to the history of the deer of the European miocene 

 and pliocene strata, by Prof. W. Boyd Dawkins, F.R. S. The 

 author commenced by referring to the difficulties attending the 

 study of the European miocene and pliocene deer, and indicated 

 that the majority of the known antlers may be referred to two 

 categories — an earlier or capreoline, and a later or axidine type. 

 To the Capreoli he referred the following species : — Dicroceros 

 e/egans, h^Lit. (= Prox /urcalus, Hemel), Cervus dicranoceros, 

 Kaup (including C. anoceros and trigonoceros, Kaup), and Cervus 

 Matheronis, Gerv. (= C. bravardi), from; the miocene, and 

 Cervus australis, Gerv., and C. cusanus, Croizet and Jobert, 

 from the pliocene. To the Axeides belong Cervus Perrieri, Cr. 

 and Job. (including C. issiodorensis and pardinensis, of the same 

 authors), C. elneriartim, Cr. and Job. (= C. rusoides. Pom., and 

 C. peroUensis and slylodus, Brav. ), C, suttonensis, sp. n. , and C. 

 cylindroceros, Brav. (including C. gracilis, Brav.), all from 

 pliocene deposits. Besides these, the author noticed a species 

 insertce sedis under the name of Cervus tetraceros, Dawkins, 

 which he regards as coming nearest to the Virginian deer, or 

 cariacou (Cariacus virginianus). From the examination of the 

 antlers of these species he indicates that in the middle miocene 

 age the cervine antler consisted of a simply forked crown, whilst 

 in the upper miocene it becomes more complex, although still 

 small and erect, like that of the roc deer. In the pliocene it 

 becomes larger and more complex, some forms, such as the 

 Cervus dicranios, Nesti, being the most complicated of known 

 antlers. The successive changes are analogous to those observed 

 in the development of the antlers of the living deer with increase 

 of age. In the miocene we have the zero of antler-development, 

 and the capreoline type is older than any other. The nearest 

 living analogue of the miocene deer is, according to the antler, 

 the muntjak (Styloceros), now found only in the oriental region of 

 Asia, along with the tapir, which also co-existed with Cennts 

 dicranoceros in the miocene forests of Germany. The pliocene 

 deer, again, are generally most nearly allied to the oriental axis 

 and rusa deer, the only exception being Cervus cusanus, the 

 antlers of which resemble those of the roe, an animal widely 

 spread over Europe and Northern and Central Asia. The 

 alliance of these pliocene deer with those now living in the Indian 

 region is regarded by the author as a further proof of the warm 

 climate of Europe in miocene times, confirmatory of the con- 

 clusions arrived at by Saportafrom the study of the vegetation. — 

 On the occurrence of Branchipus (or Chirocephalus) in a fossil 

 state, associated with Archcconiscus, and with numerous insect- 

 remains in the eocene freshwater limestone of Gurnet Bay, Isle 

 of Wight, by Henry Woodward, F.R.S. The remains of Crus- 

 tacea and insects noticed in this paper were obtained by Mr. E. 

 J. A'Court Smith from a thin bed of limestone belonging to the 

 Osborne or St. Helen's series at Thorness and Gurnet Bay in the 

 Isle of Wight. The collection is the result of about twenty years* 

 work. The insect-remains comprise about fifty specimens of 

 diptera, including wings of tipulidas and culicidae, and the pupa 

 apparently of a gnat, one wing of a hemipterous insect, and a 

 flattened homopterous insect identified by Mr. F. Smith with 

 Triecphora sanguinolmta ; two specimens referred to the lepi- 

 dopterous genus Liihesia ; only three orthoptera, one a Gryllo- 

 talpa, the other two belonging to a grasshopper ; thirty-five 

 hymenopterous wings, thirty-three of which are referred to ants 

 of the genera Myrmica, Formica, and Camponoius ; twenty-three 

 examples of neuroptera referred to Ternies, Perla, Libelhda, 

 Agrion, Phryganea, and Hemerobius ; and twelve of coleoptera, 

 including species of Hydrophilus, Dyticus, Curculio, Anobium, 

 Dorcus, and Staphylinus. There were also two spiders. Several 

 species of bivalved entomostraca have also been obtained from 



