May 3, 1888] 



NATURE 



21 



fifteen sulphides studied by him (those of mercury, zinc, tung- 

 sten, inolybdene, indium, platinum, gold, palladium, silver, 

 thallium, lead, bismuth, iron, nickel, and cobalt) have been 

 obtained in the colloidal state. They bring up to thirty-one the 

 number of colloids now known to science. Some have been pre- 

 pared by Graham's method, others directly by treating the oxides 

 suspended in the water with hydrosulphuric acid. — On the pre- 

 tended pro-atlas of mammals and Hatteria punctata, by Jules 

 Cornet. The bony process between the occipital and the atlas 

 known as the pro-atlas or proto-vertebra, and found in crocodiles 

 and some other reptiles, is here shown not to exist in the 

 mammals as supposed by some naturalists. The view of Smets 

 regarding its absence from Hatteria is also confirmed. — On the 

 process employed by the fresh-waterGasteropods for crawling over 

 the liquid surface, by Victor Willem. This process is shown to 

 be somewhat analogous to that of snails moving on dry land, 

 being effected by secreting a mucus which enables the mollusk to 

 adhere to the surface. — Researches on the volatility of the carbon 

 compounds ; chloro -oxygenated compounds, by Louis Henry. 

 The object of these researches is to examine, in reference to 

 their volatility, the compounds in which chlorine and oxygen are 

 simultaneously combined with carbon. The subject is discussed 

 under three heads : (i) the compounds comprising the system 

 >C-0; (2) the system ->C-OX; (3) the mixed derivatives 

 simultaneously including both these systems. 



Rendiconti del Reale Istituto Lotnbardo, March 22. — Obser- 

 vations made in the Brera Observatory, Milan, during the total 

 lunar eclipse of January 28, 1888, by G. V. Schiaparelli. These 

 observations were made under favourable conditions in accord- 

 ance with the instructions issued by the Pulkova astronomers, 

 with the ultimate view of determining more accurately than has 

 yet been possible the exact length of the diameter of the moon. In 

 the accompanying tables are given the results of the observations, 

 comprising the c comparison-stars with their magnitudes and 

 numbers as in the catalogue distributed by the Pulkova 

 astronomers. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, March 22. — "The Chemical Composition of 

 Pearls." By George Harley, M.D., F.R.S., and Harald S. 

 Harley. 



(1) As regards oyster pearls. Of these, three varieties were 

 examined — British, Australian, and Ceylonese. 



The qualitative analyses showed that they all had an identical 

 composition, and that they consisted solely of water, organic 

 matter, and calcium carbonate. There was a total absence of 

 magnesia and of all the other mineral ingredients of sea-water — 

 from which the inorganic part of pearls must of course be ob- 

 tained. Seeing that ordinary sea-water contains close upon ten 

 and a half times more calcium sulphate than calcium carbonate, 

 one might have expected that at least some sulphates would have 

 been found along with the carbonates, more especially if they 

 are the mere fortuitous concretions some persons imagine them 

 to be ; a view the] authors cannot indorse, from the fact that by 

 steeping pearls in a weak aqueous solution of nitric acid, they are 

 able to completely remove from them all their mineral constituents 

 without in any way altering their shape, and but very slightly 

 changing their naked eye appearances, so long as they are per- 

 mitted to remain in the solution. When taken out they rapidly dry 

 and shrivel up. Dr. George Harley will take occasion to point out 

 in his next communication, which will be on the microscopic 

 structure of pearls, that a decalcified crystalline pearl bears an 

 intimate resemblance to a decalcified bone, in so far as it 

 possesses a perfectly organized matrix of animal matter. No 

 phosphates whatever were found in any of the three before-named 

 varieties of pearls. 



The next point being to ascertain the exact proportions of the 

 substances composing the pearls, and pure white pearls being ex- 

 pensive, from having ascertained that all the three kinds they 

 were operating upon had exactly the same chemical composition, 

 instead of making separate quantitative analyses of them, they 

 simply selected two pearls from each variety, of as nearly the 

 same size and weight — giving a total of 16 grains — and analyzed 

 them collectively, the result obtained being : carbonate of lime 

 9172 per cent ; organic matter (animal), 5 - 94"per cent ; water 

 2 23 per cent. 



(2) Composition of cocoa-nut pearls. 



A portion of a garden pea sized cocoa-nut pearl, weighing 14 

 grains, was subjected to analysis, and found that, like shell-fish 

 pearls it consisted of carbonate of lime, organic matter (animal), 

 and water. 



It had all the external appearances of the pearls found in the 

 large clams (Tridacna gigas) of the Southern Ocean, being per- 

 fectly globular, with a smooth, glistening, dull white surface, and 

 resembling them exactly in microscopic structure. Besides which 

 in chemical composition it bore no similarity to cocoa-nut milk, 

 to which it is supposed to be related ; for cocoa-nut milk is said 

 to contain both the phosphate and the malate, but not the 

 carbonate of lime. That there are pearls found in cocoa-nuts 

 the authors do not presume to deny ; all they mean to say is that 

 they are doubtful if the specimen examined had such an origin. 



(3) As regards mammalian pearls. 



These so-called pearls have been met with in human beings 

 and in oxen. 



In so far as naked-eye appearances are concerned, a good 

 specimen of the variety of pearl now spoken of is quite undis- 

 tinguishable from a fine specimen of Oriental oyster pearl, from 

 its not only being globular in shape, and of a pure white colour, 

 but from its also possessing the iridescent sheen so characteristic 

 of Oriental oyster pearls of fine quality. 



In chemical composition, however, mammalian pearls bear no 

 similarity whatever to pearls found in shell-fish, for they are com • 

 posed of an organic instead of an inorganic material — namely, 

 cholesterin. In microscopic structure again, they bear a marked 

 resemblance to the crystalline variety of shell-fish pearls. 



April 19. — "On Hamilton's Numbers. Part II." By 

 J. J. Sylvester, D.C.L., F.R.S., Savilian Professor of Geo- 

 metry in the University of Oxford, and James Hammond, 

 M.A. Cantab. 



§ 4. Continuation, to an infinite Number of Terms, of the 

 Asymptotic Development for Hypothenusal Numbers. 



In the third section of this paper (Phil. Trans. A., vol. clxxviii. 

 p. 311) it was stated, on what is now seen to be insufficient evi- 

 dence, that the asymptotic development of/ - q, the half of any 

 hypothenusal number, could be expressed as a series of powers 

 of q - r, the half of its antecedent, in which the indices followed 

 the sequence 2, \, 1, f, f, \, . . . 



It was there shown that, when quantities of an order of mag- 

 nitude inferior to that of (q - r)i are neglected, 



p-q=(q- rf + \(g - r)\ + H(? -/} + i?(? - r)l ; 

 but, on attempting to carry this development further, it was 

 found that, though the next term came out T lfp(? ~ . r )*» there 

 was an infinite series of terms interposed between this one and 

 (q - r)h. 



In the present section it will be proved that between (q- r)i and 

 (q - r)i there lies an infinite series of terms whose indices are — 



8 » "17 S3 «5 



¥» lf» 3 21 tit TJB') • • • 



and whose coefficients form a geometrical series of which the 

 first term is T^ffj- and the common ratio $. 



We shall assume the law of the indices (which, it may be re 

 marked, is identical with that given in the introduction to this 

 paper as originally printed in the Proceedings but subsequently 

 altered in the Transactions), and write — 

 p - q = (q - r) 2 + |(? ~ & + WS -r) + Hi? T r ) 1 



+ * A(q - r)i + g- B(q - r)A + £c(* - r)\\ 

 3 3 J 



+ t.D(q - r)tt + *E(j- r)fh + 8cc.,ad inf. . . (l) 



3 6 y 



+ e* 



The law of the coefficients will then be established by proving 

 that— 



A = B = C = D = E= = tt. 



If there were any terms of an order superior to that of 

 (q - r)h, whose indices did not obey the assumed law, any such 

 term would make its presence felt in the course of the work ; for, 

 in the process we shall employ, the coefficient of each term has 

 to be determined before that of any subsequent term can be 

 found. It was in this way that the existence of terms between 



• In the text above, 9 represents some unknown function, the asymptotic 

 value of whose ratio to (?-r)* is not infinite. 



