Nov. 23, 1871] 



NATURE 



75 



mation given by Mr. Stow, and stated that the source of the 

 Vaal was in sandstone, and that it was not until it had traversed 

 some distance that agates, peridot, and spinel were met with. 

 The large diamonds, in his view, occurred principally in old high- 

 level gravels, at a considerable elevation above the river, wliich 

 had much deepened its valley since tlie time of their deposit. 

 At Du Toit's Pan, however, none of tlie diamonds, nor indeed 

 any of the other stones, showed any signs of wear ; and he con- 

 sidered that at that spot was one of the centres at which 

 diamonds had been found in their original niatri.x. Mr.Daintree 

 stated that in Australia there were agate-bearing beds of 

 amygdaloid greenstone similar to those in South Africa, and 

 that he had called attention to their existence in the neighbour- 

 hood of the Burnett River, where since then a diamond of tlie 

 value of So/, had been discovered. Mr. Maskelyne commented 

 on the dissimilarity of the minerals found in the diamond- 

 bearing beds of Brazil from those of Du Toit's Pan or of South 

 Africa generally. He thought that possibly the minerals described 

 as peridot and spinel might be bronzite and garnet, which, how- 

 ever, came from igneous rocks ; and the remarkable fact was 

 that with them occurred unrolled natrolite and diamonds in an 

 equally unrolled condition, which was suggestive of their having 

 been due to a common origin. Mr. Ward gave an account of an 

 examination of some of the rock from Du Toit's Pan, with a 

 view of discovering microscopic diamonds, none of which, how- 

 ever, had been found. Prof Rupert Jones had been equally 

 unsuccessful in the search for minute diamonds, both in sand 

 from Du Toit's and in the ochreous gravel from Klip drift. He 

 pointed out the waterworn condition of the agates from Du Toit's 

 Pan, which showed aqueous action, though there were also 

 several other minerals present in a perfectly fresh and unrolled 

 condition. He thought a careful examination of the constituent 

 parts of the gravel might ultimately throw light on their origin. 

 That iluviatile action was sufiicient to account for their presence 

 had already been shown by Dr. Rubidge and others, who had 

 treated of the grand plateaux and denudations of the district 

 under notice. 



Royal Geographical Society, November 13. — Major- 

 General Sir H. C. Rawlinson, K.C.B., president, in the chair. 

 The president, on opening the session, delivered an address, in 

 which, after paying an eloquent tribute to the worth of the late 

 president. Sir Roderick Murchison, and expressing his sense of 

 the loss which the Society had sustained in his death, he re\iewed 

 the progress of geography since the last meeting of the previous 

 Session. He congratulated the Fellows on being again per- 

 mitted to meet in the handsome and commodious hall of the 

 London University ; and stated that the Council felt that the 

 Senate of that body, in granting the use of the hall, conferred an 

 obhgation not only on the Society but on the public at large, 

 whose instruction and education in geography formed the especial 

 objects of their study. He also announced that the Society had, 

 during the recess, taken up its permanent quarters in Savile Row, 

 wheie it was now located on its own freehold estate. In Physi- 

 cal Geography the important subject of Oceanic Circulation, and 

 Dr. Carpenter's researches thereupon, was prominently noticed ; 

 and he stated that Dr. Carpenter, during his Mediterranean 

 voyage of the past summer, had met the objections of his critics 

 in so far as related to the under-current outwards at the Straits 

 of Gibraltar by experimentally proving that such a current really 

 does exist. In Arctic exploration the recent German expeditions 

 were noticed, particularly the voyage of Messrs. Payer and 

 Wcyprecht, who, last summer, had found an open sea, in lat. 

 70°, between Spitzber^en and Nova Zembla. In Central Asia 

 and Eastern Persia much accurate information had recently been 

 obtained by English travellers and surveyors ; and in Syria their 

 medallist, Captain Burton, had recently, in company with Mr. 

 Drake, examined the Anti-Libanus and the little-known district 

 east of Damascus, — subjects on which this indefatigable traveller 

 would read papers at a subsequent meeting. An excellent de- 

 scriptive paper had been received from the weU-known and able 

 traveller Captain Blakiston, on the subject of the island of Yezo, 

 the circuit of which he had recently explored in the capacity of 

 an official of the Japanese Government. No direct news had 

 been recently received either Irom Dr. Livingstone or Sir Samuel 

 Baker; but authentic intelligence of Livingstone could not be 

 much further delayed, as an able and adventurous American 

 gentleman, Mr. Stanley, left Zanzibar for the shores of Lake 

 Tanganyika in February last, taking with him "Bombay," one 

 of Speke and Grant's "faithfuls," as guide. He (the president) 

 added that if Mr. Stanley succeeded in restoring Livingstone to 



us, or in assisting him to solve the great problem of the upper 

 drainage into the Nile or Congo, he would be welcomed by the 

 Society as heartily and warmly as if he were acting under their 

 own immediate auspices. — A paper was then read "On the 

 Exploration of the Limpopo River," by Captain Frederic Elton. 

 This remarkable journey was performed between July 6 and 

 August 8, 1870, the author starting from the Tati gold-fields and 

 proceeding by an easterly route to the junction of the Tuli River 

 with the Limpopo, and thence descending the great stream or 

 marching along its banks to beyond the junction of the Lipalule, 

 whence he struck across to Lorenco Maiques, in Delagoa Bay. 

 The middle part of the Limpopo, between the Tuli and Lipalule, 

 was found to be encumbered with rapids and waterfalls, some of 

 which, especially the cataracts called Tolo-Azime, were truly 

 magnificent, the river, after a series of rapids five mUes in length, 

 here plunging over a ledge into a deep chasm. These falls mark 

 the spot where the Limpopo leaves the great interior plateau of 

 Africa and descends abruptly into the plains which extend hence- 

 forth to the sea. The paper described the country traversed as 

 rich and abundant in game of all descriptions. 



Mathematical Society, November 9. — Dr. Spottiswoodc, 

 president, in the chair. The following gentlemen were elected 

 to form the council for the ensuing session: — President: Dr. 

 Spottiswoode. Vice-Presidents : Profs. Cayley, Henrici, H. J. S. 

 Smith, and Mr. S. Roberts. Treasurer: Dr. Hirst. Honorary 

 Secretaries : Messrs. M. Jenkins and R. Tucker. Other mem- 

 bers : Profs. Clifford and Crofton, Dr. Sylvester, Hon. J. W. 

 Strutt, Messrs. T. Cotterill, Merrifield, Stirling, and Walker. 

 Mr. A. Freeman was proposed for election. It being unani- 

 mously agreed upon that the number of honorary foreign mem- 

 bers should be increased to six, the president read out the names 

 which the council recommended for nomination, viz. : Dr. 

 Clebsch, M. Hermite, Prof Cremona, Dr. Hesse, and Prof. 

 Betti. The only foreign member at present is M. Chasles. 

 Dr. Sylvester then gave an account of his communication 

 "On the partition of an even number into two primes." 

 In one of his minor papers Euler has enunciated as a theorem, 

 resting entirely on intuition from a comparatively small number 

 of instances, that every even number may be decomposed into a 

 sum of two primes. The object of Dr. .Sylvester's communi- 

 cation was to obtain some measure of the probable number of 

 ways in which such decomposition can be effecied lor any given 

 number ; if it can be shown to be probably greater than the 

 square root of the number itself, it will follow from generally 

 admitted principles of the theory of chances, that the proba- 

 bility of the theorem being universally true above any assigned 

 limit, if proved to be true up to that limit, may be represented 

 by an infinite product of terms, which will approach as near as 

 we please to unity the higher the limit in question is taken. The 

 mere fact of the theorem, as Euler gave it, being proved up to 

 100,000,000, or any other number however great, would leave 

 the probability of its being universally true, absolutely zero, just 

 as the (act of the sun having risen 100,000,000 times would not 

 contribute an atom of probability to the supposition that it would 

 continue to rise lor all time to come. In the case before us, on 

 the contrary, the probability of the theorem being universally 

 true by a sufficiently copious induction, may be made to approach 

 as near as we please to absolute certitude. The author considers 

 that he has established beyond the reach of reasonable doubt that 

 the magnitude which represents the mean probable value of the 

 number of modes of effecting the resolution of a very large even 

 number into two prime numbers is that of the square of the 

 number of primes inferior to the given number divided by the 

 number itself, or which (thanks to the discoveries of Legendre 

 and Tchebichefi) we know to be the same thing, the nunii er of 

 the decompositions in question bears a finite ratio (assignable 

 within limits) to the number tobedecomposed,divided by the square 

 of its Napierian logarithm. If we agree provisionally to call preter- 

 primes in respect to 11, those numbers which are prime themselves, 

 and al?o when subtracted from 11 leave prime remainders, the 

 author shows that the probable number of such preter-primes 

 (/.(•, the most probable value attainable under our present con- 

 ditions of knowledge) may be found approximately by multiply- 

 ing the number of ordinary primes inferior to « by the product 

 of a set of fractions, depending in part on the magnitude and in 

 part on the constitution of the number «. If n is the double of 

 a prime, the product in question is got by multiplying together 



all the quantities -^^ where/ is every odd prime between unity 

 and the square root of 11 ; but if n itself contains any such 



