Feb. 17, 1 881] 



NA TURE 



379 



grapliic formulae by two carbon atoms linked by double bonds. 

 The value assigned by Biiihl in such cases is however 6"i. 

 This somewhat higher figure is deduced from the aggregate 

 value of the six carbon atoms in the nucleus of the aromatic 

 series, which (except in benzol and its simpler substitution pro- 

 ducts) would appear to be nearer 37 than 36. The fact however 

 is susceptible of another interpretation. The replacement of 

 hydrogen by some nomad radicle is an important change ; and if 

 that radicle be CH3 it is evident that according to present views 

 the carbon atom must have all four of its units of atomicity 

 satisfied with carbon, and by analogy we should expect it to have 

 its refraction increased. 



When a carbon atom has all four of its units of atomicity 

 satisfied by other carbon atoms, each of which has the higher 

 value of 6'0 or 6'i, its equivalent of refraction is greatly raised. 

 There are compounds in which the atom^ of carbon actually 

 out-number the atoms of hydrogen or its substitute, such as 

 naphthalene, Ci„Hs (ref- «q- 75'l)i naphthol, CuUaO (79'5), 

 phenanthrene, C'liHn, (loS'3), and pyrene, Cj^H,, (l26'l). 

 That the refraction is greatly raised is evident from the fact that, 

 if we were to reckon all the carbon atoms .at 6t, the refraction 

 equivalent of the body would not be fully accounted for. It is 

 evident that in pyrene only ten of the atoms of carbon can be in 

 the same condition as they are in benzol or styrol, the other six 

 must have all their units of atomicity satisfied by carbon alone. 

 Provisionally I venture to assign S'S as the refraction equivalent 

 of this highest carbon. 



There are several other bodies, such as anthracene, anethol, 

 furfurol, and hydride of cinnamyl, which from their abnormally 

 high refraction appear to contain carbon in this last condition. 



Hydrogen. — The general evidence with regard to hydrogen in 

 organic compounds tends to show that it has only one refraction 

 equivalent, that originally assigned to it by Landolt, I '3. 



O.xygcii. — Briihl has been the first to point out that oxygen in 

 organic compounds has tvvo values, and he comes to the conclu- 

 sion that it has the value 3*4 where the oxygen is attached to a 

 carbon atom by a double linking, but 2 '8 in hydroxyl and where 

 the oxygen is united to two other atoms. This is deduced from 

 experimental data. But there are other results which present 

 difficulties, such as the various alcohols. 



Aitrogcn. — Nitrogen has two values, 4'i and 5T, or there- 

 abouts. 



The lower value, 4 'I, is that originally deduced from cyanogen 

 and metallic cyanides, and it seems to be generally confirmed by 

 the observations on organic cyanides and nitriles. The higher 

 value, 5 "I, is deduced from observations on organic bases and 

 amides. 



Ijhope shortly to submit to the public the whole of the data 

 for these conclusions. 



February 3. — "On the Influence of Temperature on the 

 Musical Pitch of Harmonium Reeds." By Alex. T. Ellis, 



r.R.s. 



The writer gave a tabular account of the experiments on the 

 harmonium reeds of Appunn's treble tonometer at -South Ken- 

 sington Museum, at temperatures differing by from 20° to 26° F., 

 which rendered it jirobable that the pitch of such reeds was 

 affected by temperature to twice the extent of tuning-forks and 

 in the same direction, that is, that they flattened by heat and 

 sharpened by cold about I in 10,000 vibrations in a second for 

 each degree Fahrenheit. 



" On an Improved Bimodular Method of computing Natural 

 and Tabular Logarithms and Anti-Logarithms to Twelve or 

 Sixteen Places, with very brief Tables." By Alex. T. Ellis. 

 F.R.S. / J . 



A bimodular method is one founded on the familiar propo- 

 sition, that if the bimodulus (that is, twice the modulus of any 

 system of logarithms) be multiplied by the difl^erence and divided 

 by the sum of two numbers, the result would be approximatively 

 the difference of their logarithms. The improvement consisted 

 in a simple preparation of a given number to make it lie between 

 two numbers in a given table of interpolation, consisting of 100 

 entries, and in then determining how many places might be 

 trusted without correction, and in correcting the result by a short 

 table so as to give twelve places at sight and sixteen places 

 by means of ordinary table of seven figure logarithms. The 

 antflogarithms were found by first depriving a logarithm of its 

 coiTection, and then dividing the result added to the bimodulus 

 by the result subtracted from the bimodulu^— an entirely new 



rule. Complete tables and worked-out exauples fully explained 

 were added. 



" On the Potential Radix as a Means of Calculating Logarithms 

 to any Required Number of Decimal Places, with a Summary of 

 all Preceding Methods Chronologically Arranged," by Alexander 

 J. Ellis, F.R.S. 



A positive numerical radix consists of the numbers r, 

 I + 'Om r, aird their logarithms, where r varies from i to 9 ; 

 Oin means a series of m successive zeros, and fn varies from i 

 to any required number. The term "radix" is due to Robert 

 Flower (1771) and is preserved in memoriam. It wa^ shown 

 that such a table woula enable any logarithm to be calculated 

 by the improved bimodular method and other methods. A 

 negative numerical radix consists of the numbers I - 'Om r, and 

 their negative logarithms, and it was shown that such a table 

 would serve the same purpose somewhat more easily. Hence 

 the whole process is reduced to the construction of such radixes. 

 A chronological summary was then given of all preceding 

 method^, showing that most of them depended on having such 

 radixes. The construction of a numerical radix is however a 

 very long and troublesome process by the methods ordinarily 

 used. For this purpose the potential radix for natural logarithms 

 was first constructed, consisting of 10% 2'', (I 'I)'', and (i'o„, i)', 

 negative ( I ~ 'Owi i)'', from)- = ito?-= 10 (the latter terms being 

 calculated by simple addition), and then* natural lo;^arithms, first 

 to any number of places from the very simple series for nat. log. 

 (I ± 'Omr], and secondly, by simple addition. This gives a 

 radix from which natural logarithms of all numbers can be 

 calculated to any number of places by the improved bimodular 

 method. But the main use of the potential radix is to calculate 

 the nat. logs, of the numbers of the numerical radix. The radix 

 for tabular logarithms is then found by multiplying by the 

 modulus, already calculated from the potential radius. All this 

 was fully explained by tables and examples. 



Matnematical Society, February 10. — Mr. S. Roberts, 

 F.R.S., president, in the chair. — Mr. W. WoodrulT Benson, 

 University of Michigan, was elected a member, and Prof. Rowe 

 and Mr. J. Parker Smith were admitted into the Society. — The 

 following communications were made ; — On seme integrals ex- 

 pressible in terms of the first complete elliptic integral and of 

 gamma functions, by Mr. J. W. L. Glaisher, F.R.S. — Some 

 theorems of kinematics on a sphere, by Mr. E. B. Elliott, M.A. 

 — Supplement on binomial biordinates, by Sir J. Cockle, F.R.S. 

 — An application of conjugate functions (to the case of mem- 

 branes), by Mr. E. J. Kouth, F.R.S. — Note on Abel's theorem, 

 by Mr. T. Craig. 



Linnean Society, February 3. — Robt. McLachlan, F.R.S., 

 in the chair. — Lieut. -Col. A. A. Davidson was elected a Fellow. 

 — Examples of Prof. C. Semper's method of preserving the soft 

 tissues of animals as teaching-specimens were exhibited on behalf 

 of Herr L. Wiirth of Wiirzburg. — Mr. G. Murray exhibited 

 and made remarks on a Japanese book containing wood sections. 

 — Mr. C, Craig-Christie exhibited, and a note was read on, the 

 presence of what appeared to be deciduous stipules in Ilex aqid- 

 folium, thus contrary to the usually-accepted assertion that the 

 order Ilicinece is exstipulate.— The foUouing paper by Mr. G. 

 Bentham was read: "Notes on Cyperacea; ; with --pecial refer- 

 ence to Lestiljoudois' Essay on Beauvois' Genra." The essay 

 in question was founded on Palisot and Beauvois' MS., which 

 was originally intended to follow his " Agrostographia," and 

 has been almost entirely lost sight of, and random guesses have 

 been made at the species intended by the short characters given 

 in Roemer and- Schultze's " Systema." — Nees von Esenbeck, in 

 the 7th, 8th, and loth vols, of the " Linnjea," and Supplement 

 123, or Kunth in vol. ii. of his excelleni " Enumeratio," appear 

 to have correctly identified many of these. Eighteen so-called 

 genera are now referred to various established genera. Steudel's 

 Synopsis is marred by the author's hazy ideas of species. 

 Boekeler has a thorough knowledge of species, but his diagnoses 

 are often excessively long. Mr. Bentham proposes few changes 

 in the order of genera as set forth by Kunth, and he considers 

 that Boekeler's primary division of the order as to whether the 

 fertile flower is hermaphrodite or female only, bears the test of 

 detailed examination. — Hermaphrodite flowers : — (i) Scirpese, 

 (2) Hypolytere, (3) Rhyncasporea:. Unisexual flowers : — (l) 

 Cryptangea;, (2) Scheri^e, (3) Caricere — A paper w.as read by 

 Mr. A. D. Michael, observations on the life history of Garaasinse. 

 In this the author endeavours to decide some of the disputed 

 and knotty points in reference to these humble parasites ; M. 



